Finite Group Databasebeta

← #72240547

Subgroups — #72240547

Order 2048.

At least 16762 conjugacy classes of subgroups; only the 1376 normal subgroups are shown.

The subgroup lattice has 970 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72240527C211yesmaximal, characteristic, complemented
2#72240527C211yesmaximal, characteristic, complemented
3C2×#417896C211yesmaximal, characteristic, complemented
4C2×#417969C211yesmaximal, characteristic, complemented
5C2×#417969C211yesmaximal, characteristic, complemented
6C2×#432839C211yesmaximal, characteristic, complemented
7#72240512C211yesmaximal, characteristic, complemented
8#72240512C211yesmaximal, characteristic, complemented
9#72240512C211yesmaximal, characteristic, complemented
10#72240512C211yesmaximal, characteristic, complemented
11#72240511C211yesmaximal, characteristic, complemented
12#72240510C211yesmaximal, characteristic, complemented
13#72240510C211yesmaximal, characteristic, complemented
14#72240509C211yesmaximal, characteristic, complemented
15#72240508C211yesmaximal, characteristic, complemented
16#72240508C211yesmaximal, characteristic, complemented
17C2×#392135C211yesmaximal, characteristic, complemented
18C2×#392135C211yesmaximal, characteristic, complemented
19#72240407C211yesmaximal, characteristic, complemented
20#72240406C211yesmaximal, characteristic, complemented
21#72240404C211yesmaximal, characteristic, complemented
22#72240404C211yesmaximal, characteristic, complemented
23#72240400C211yesmaximal, characteristic, complemented
24#72240398C211yesmaximal, characteristic, complemented
25#72240398C211yesmaximal, characteristic, complemented
26#72240193C211yesmaximal, characteristic, complemented
27#72240193C211yesmaximal, characteristic, complemented
28#72240192C211yesmaximal, characteristic, complemented
29#72240192C211yesmaximal, characteristic, complemented
30#72239046C211yesmaximal, characteristic, complemented
31C2×#6628896C211yesmaximal, characteristic
32C22×H(7,𝔽2)C2211yescharacteristic
33C23×B(4,𝔽2)C2211yescharacteristic
34C23×B(4,𝔽2)C2211yescharacteristic
35C23×B(4,𝔽2)C2211yescharacteristic
36C23×B(4,𝔽2)C2211yescharacteristic
37C2×#35367C2211yescharacteristic, complemented
38C2×#35346C2211yescharacteristic
39C2×#35346C2211yescharacteristic
40C2×#35346C2211yescharacteristic
41C22×#2032C2211yescharacteristic, complemented
42C22×#2032C2211yescharacteristic, complemented
43C22×#2032C2211yescharacteristic, complemented
44C22×#2032C2211yescharacteristic, complemented
45C2×#23468C2211yescharacteristic, complemented
46C2×#23468C2211yescharacteristic, complemented
47C2×#20609C2211yescharacteristic
48C2×#20609C2211yescharacteristic
49C2×#20609C2211yescharacteristic
50C2×#20609C2211yescharacteristic
51C2×#20609C2211yescharacteristic
52C2×#20609C2211yescharacteristic
53C2×#20609C2211yescharacteristic
54C2×#20609C2211yescharacteristic
55C2×#20609C2211yescharacteristic
56C2×#20609C2211yescharacteristic
57C2×#20609C2211yescharacteristic
58C2×#20609C2211yescharacteristic
59C2×#20609C2211yescharacteristic
60C2×#20609C2211yescharacteristic
61C2×#20609C2211yescharacteristic
62C2×#20609C2211yescharacteristic
63C2×#20609C2211yescharacteristic
64C2×#20609C2211yescharacteristic
65C2×#20609C2211yescharacteristic
66C2×#20609C2211yescharacteristic
67C2×#20585C2211yescharacteristic
68C2×#20585C2211yescharacteristic
69C2×#20585C2211yescharacteristic
70C2×#20585C2211yescharacteristic
71C2×#20585C2211yescharacteristic
72C2×#20585C2211yescharacteristic
73C2×#20585C2211yescharacteristic
74C2×#20585C2211yescharacteristic
75C2×#20585C2211yescharacteristic
76C2×#20585C2211yescharacteristic
77C2×#20585C2211yescharacteristic
78C2×#20585C2211yescharacteristic
79C2×#20585C2211yescharacteristic
80C2×#20585C2211yescharacteristic
81C2×#20585C2211yescharacteristic
82#5955309C2211yescharacteristic, complemented
83#5955309C2211yescharacteristic, complemented
84#515326C2211yescharacteristic, complemented
85C2×#11172C2211yescharacteristic, complemented
86C2×#11172C2211yescharacteristic, complemented
87C2×#11172C2211yescharacteristic, complemented
88C2×#11172C2211yescharacteristic, complemented
89C2×#11172C2211yescharacteristic, complemented
90C2×#11172C2211yescharacteristic, complemented
91C2×#11172C2211yescharacteristic, complemented
92C2×#11172C2211yescharacteristic, complemented
93C2×#11172C2211yescharacteristic, complemented
94C2×#11172C2211yescharacteristic, complemented
95C2×#11169C2211yescharacteristic, complemented
96C2×#11169C2211yescharacteristic, complemented
97C2×#11169C2211yescharacteristic, complemented
98C2×#11169C2211yescharacteristic, complemented
99C2×#11169C2211yescharacteristic, complemented
100C2×#11169C2211yescharacteristic, complemented
101C2×#11089C2211yescharacteristic, complemented
102C2×#11089C2211yescharacteristic, complemented
103C2×#11089C2211yescharacteristic, complemented
104C2×#11089C2211yescharacteristic, complemented
105C2×#11089C2211yescharacteristic, complemented
106C2×#11089C2211yescharacteristic, complemented
107C2×#11089C2211yescharacteristic, complemented
108C2×#11089C2211yescharacteristic, complemented
109C2×#11089C2211yescharacteristic, complemented
110C2×#11089C2211yescharacteristic, complemented
111C2×#11089C2211yescharacteristic, complemented
112C2×#11089C2211yescharacteristic, complemented
113#357642C2211yescharacteristic, complemented
114#357642C2211yescharacteristic, complemented
115#357642C2211yescharacteristic, complemented
116#357642C2211yescharacteristic, complemented
117#357642C2211yescharacteristic, complemented
118#357642C2211yescharacteristic, complemented
119C2×#10991C2211yescharacteristic, complemented
120C2×#10991C2211yescharacteristic, complemented
121C2×#10991C2211yescharacteristic, complemented
122C2×#10991C2211yescharacteristic, complemented
123C2×#10991C2211yescharacteristic, complemented
124C2×#10991C2211yescharacteristic, complemented
125C2×#10991C2211yescharacteristic, complemented
126C2×#10991C2211yescharacteristic, complemented
127C2×#10991C2211yescharacteristic, complemented
128C2×#10991C2211yescharacteristic, complemented
129C2×#10991C2211yescharacteristic, complemented
130C2×#10991C2211yescharacteristic, complemented
131C2×#10991C2211yescharacteristic, complemented
132C2×#10991C2211yescharacteristic, complemented
133C2×#10991C2211yescharacteristic, complemented
134C2×#10991C2211yescharacteristic, complemented
135C2×#10965C2211yescharacteristic, complemented
136C2×#10965C2211yescharacteristic, complemented
137C2×#10965C2211yescharacteristic, complemented
138C2×#10965C2211yescharacteristic, complemented
139C2×#10965C2211yescharacteristic, complemented
140C2×#10965C2211yescharacteristic, complemented
141C2×#10965C2211yescharacteristic, complemented
142C2×#10965C2211yescharacteristic, complemented
143C2×#10938C2211yescharacteristic, complemented
144C2×#10938C2211yescharacteristic, complemented
145C2×#10938C2211yescharacteristic, complemented
146C2×#10938C2211yescharacteristic, complemented
147C2×#10938C2211yescharacteristic, complemented
148C2×#10938C2211yescharacteristic, complemented
149C2×#10938C2211yescharacteristic, complemented
150C2×#10938C2211yescharacteristic, complemented
151C2×#10938C2211yescharacteristic, complemented
152C2×#10938C2211yescharacteristic, complemented
153C2×#10938C2211yescharacteristic, complemented
154C2×#10938C2211yescharacteristic, complemented
155#123581C2211yescharacteristic, complemented
156#123581C2211yescharacteristic, complemented
157#123581C2211yescharacteristic, complemented
158#123581C2211yescharacteristic, complemented
159#123581C2211yescharacteristic, complemented
160#123581C2211yescharacteristic, complemented
161#123581C2211yescharacteristic, complemented
162#123581C2211yescharacteristic, complemented
163#123581C2211yescharacteristic, complemented
164#123581C2211yescharacteristic, complemented
165#123581C2211yescharacteristic, complemented
166#123581C2211yescharacteristic, complemented
167#123581C2211yescharacteristic, complemented
168#123581C2211yescharacteristic, complemented
169#123539C2211yescharacteristic, complemented
170#123539C2211yescharacteristic, complemented
171#123539C2211yescharacteristic, complemented
172#123539C2211yescharacteristic, complemented
173#123539C2211yescharacteristic, complemented
174#123539C2211yescharacteristic, complemented
175#123539C2211yescharacteristic, complemented
176#123539C2211yescharacteristic, complemented
177#123539C2211yescharacteristic, complemented
178#123539C2211yescharacteristic, complemented
179#123539C2211yescharacteristic, complemented
180#123539C2211yescharacteristic, complemented
181#123527C2211yescharacteristic, complemented
182#123527C2211yescharacteristic, complemented
183#123527C2211yescharacteristic, complemented
184#123527C2211yescharacteristic, complemented
185#123527C2211yescharacteristic, complemented
186#123527C2211yescharacteristic, complemented
187C23×H(5,𝔽2)C2311yescharacteristic
188C23×H(5,𝔽2)C2311yescharacteristic
189C23×H(5,𝔽2)C2311yescharacteristic
190C23×H(5,𝔽2)C2311yescharacteristic
191C23×H(5,𝔽2)C2311yescharacteristic
192C23×H(5,𝔽2)C2311yescharacteristic
193C23×H(5,𝔽2)C2311yescharacteristic
194C22×#543C2311yescharacteristic, complemented
195C23×#120C2311yescharacteristic
196C23×#120C2311yescharacteristic
197C23×#120C2311yescharacteristic
198C23×#120C2311yescharacteristic
199C23×#120C2311yescharacteristic
200C23×#120C2311yescharacteristic
201C23×#120C2311yescharacteristic
202C22×B(4,𝔽2)D418yes—
203C23×#99C2311yescharacteristic
204C23×#99C2311yescharacteristic
205C23×#99C2311yescharacteristic
206C23×#99C2311yescharacteristic
207C23×#99C2311yescharacteristic
208C23×#99C2311yescharacteristic
209C23×#99C2311yescharacteristic
210C23×#99C2311yescharacteristic
211C23×#99C2311yescharacteristic
212C23×#99C2311yescharacteristic
213C23×#99C2311yescharacteristic
214C23×#99C2311yescharacteristic
215C23×#99C2311yescharacteristic
216C23×#99C2311yescharacteristic
217C23×#99C2311yescharacteristic
218C23×#99C2311yescharacteristic
219C23×#99C2311yescharacteristic
220C23×#99C2311yescharacteristic
221C23×#99C2311yescharacteristic
222C23×#99C2311yescharacteristic
223C23×#99C2311yescharacteristic
224C23×#99C2311yescharacteristic
225C23×#99C2311yescharacteristic
226C23×#99C2311yescharacteristic
227C23×#99C2311yescharacteristic
228C23×#99C2311yescharacteristic
229C23×#99C2311yescharacteristic
230C23×#99C2311yescharacteristic
231C23×#99C2311yescharacteristic
232C23×#99C2311yescharacteristic
233C23×#99C2311yescharacteristic
234C23×#99C2311yescharacteristic
235C23×#99C2311yescharacteristic
236C23×#99C2311yescharacteristic
237C23×#99C2311yescharacteristic
238C23×#99C2311yescharacteristic
239C23×#99C2311yescharacteristic
240C23×#99C2311yescharacteristic
241C23×#99C2311yescharacteristic
242C23×#99C2311yescharacteristic
243C23×#99C2311yescharacteristic
244C23×#99C2311yescharacteristic
245C23×#99C2311yescharacteristic
246C23×#99C2311yescharacteristic
247C2×#2315C2311yescharacteristic, complemented
248C2×#2315C2311yescharacteristic, complemented
249C2×#2315C2311yescharacteristic, complemented
250C2×#2308C2311yescharacteristic
251C2×#2308C2311yescharacteristic
252C2×#2308C2311yescharacteristic
253C2×#2308C2311yescharacteristic
254C2×#2308C2311yescharacteristic
255C2×#2308C2311yescharacteristic
256C2×#2308C2311yescharacteristic
257C2×#2308C2311yescharacteristic
258C2×#2308C2311yescharacteristic
259C2×#2308C2311yescharacteristic
260C2×#2308C2311yescharacteristic
261C2×#2308C2311yescharacteristic
262C2×#2308C2311yescharacteristic
263C2×#2308C2311yescharacteristic
264C2×#2308C2311yescharacteristic
265C2×#2308C2311yescharacteristic
266C2×#2308C2311yescharacteristic
267C2×#2308C2311yescharacteristic
268C2×#2308C2311yescharacteristic
269C2×#2308C2311yescharacteristic
270C2×#2308C2311yescharacteristic
271C2×#2308C2311yescharacteristic
272C2×#2308C2311yescharacteristic
273C2×#2308C2311yescharacteristic
274C2×#2308C2311yescharacteristic
275C2×#2308C2311yescharacteristic
276C2×#2308C2311yescharacteristic
277C2×#2308C2311yescharacteristic
278C2×#2308C2311yescharacteristic
279C2×#2308C2311yescharacteristic
280C2×#2308C2311yescharacteristic
281C2×#2308C2311yescharacteristic
282C2×#2308C2311yescharacteristic
283C22×#379C2311yescharacteristic, complemented
284C22×#379C2311yescharacteristic, complemented
285C22×#379C2311yescharacteristic, complemented
286C22×#379C2311yescharacteristic, complemented
287C22×#379C2311yescharacteristic, complemented
288C22×#379C2311yescharacteristic, complemented
289C22×#379C2311yescharacteristic, complemented
290C22×#379C2311yescharacteristic, complemented
291C2×#2273C2311yescharacteristic, complemented
292C2×#2273C2311yescharacteristic, complemented
293#20609D418yes—
294#20609D418yescomplemented
295#20585D418yescomplemented
296C2×#1782D414yes—
297C2×#1781D414yes—
298C22×#342C2311yescharacteristic, complemented
299C22×#342C2311yescharacteristic, complemented
300C22×#342C2311yescharacteristic, complemented
301C22×#342C2311yescharacteristic, complemented
302C22×#342C2311yescharacteristic, complemented
303C22×#342C2311yescharacteristic, complemented
304C22×#342C2311yescharacteristic, complemented
305C22×#342C2311yescharacteristic, complemented
306C22×#342C2311yescharacteristic, complemented
307C22×#342C2311yescharacteristic, complemented
308C22×#342C2311yescharacteristic, complemented
309C22×#342C2311yescharacteristic, complemented
310C22×#342C2311yescharacteristic, complemented
311C22×#342C2311yescharacteristic, complemented
312C22×#342C2311yescharacteristic, complemented
313C22×#342C2311yescharacteristic, complemented
314C22×#342C2311yescharacteristic, complemented
315C22×#342C2311yescharacteristic, complemented
316C22×#342C2311yescharacteristic, complemented
317C22×#342C2311yescharacteristic, complemented
318C22×#342C2311yescharacteristic, complemented
319C22×#342C2311yescharacteristic, complemented
320C22×#342C2311yescharacteristic, complemented
321C22×#342C2311yescharacteristic, complemented
322C22×#342C2311yescharacteristic, complemented
323C22×#342C2311yescharacteristic, complemented
324C22×#342C2311yescharacteristic, complemented
325C22×#342C2311yescharacteristic, complemented
326C22×#342C2311yescharacteristic, complemented
327C22×#342C2311yescharacteristic, complemented
328C22×#342C2311yescharacteristic, complemented
329C22×#342C2311yescharacteristic, complemented
330C22×#342C2311yescharacteristic, complemented
331C22×#342C2311yescharacteristic, complemented
332C22×#342C2311yescharacteristic, complemented
333C22×#342C2311yescharacteristic, complemented
334C22×#342C2311yescharacteristic, complemented
335C22×#342C2311yescharacteristic, complemented
336C22×#342C2311yescharacteristic, complemented
337C22×#342C2311yescharacteristic, complemented
338C22×#342C2311yescharacteristic, complemented
339C22×#342C2311yescharacteristic, complemented
340C22×#342C2311yescharacteristic, complemented
341C22×#342C2311yescharacteristic, complemented
342C22×#342C2311yescharacteristic, complemented
343C22×#342C2311yescharacteristic, complemented
344C22×#342C2311yescharacteristic, complemented
345C22×#342C2311yescharacteristic, complemented
346#13794C2311yescharacteristic, complemented
347#13794C2311yescharacteristic, complemented
348C27C2411yescharacteristic
349C22×H(5,𝔽2)C2×D414yes—
350C22×H(5,𝔽2)C2×D414yes—
351C22×H(5,𝔽2)C2×D414yes—
352C22×H(5,𝔽2)C2×D414yes—
353C22×H(5,𝔽2)#4114yes—
354C22×H(5,𝔽2)#4114yes—
355C23×#41C2×D412yes—
356C23×#41#4112yes—
357C23×#41#4112yes—
358C24×D4C2×D412yes—
359C24×D4#4112yes—
360C24×D4#4112yes—
361C24×D4C2411yescharacteristic
362C24×D4C2411yescharacteristic
363C24×D4C2411yescharacteristic
364C24×D4C2411yescharacteristic
365C24×D4C2411yescharacteristic
366C24×D4C2411yescharacteristic
367C24×D4C2411yescharacteristic
368C22×#120C2×D414yes—
369C22×#120C2×D414yes—
370C22×#120C2×D414yes—
371C23×C22⋊C4C2411yescharacteristic
372C23×C22⋊C4C2411yescharacteristic
373C23×C22⋊C4C2411yescharacteristic
374C23×C22⋊C4C2411yescharacteristic
375C23×C22⋊C4C2411yescharacteristic
376C23×C22⋊C4C2411yescharacteristic
377C23×C22⋊C4C2411yescharacteristic
378C23×C22⋊C4C2411yescharacteristic
379C23×C22⋊C4C2411yescharacteristic
380C23×C22⋊C4C2411yescharacteristic
381C23×C22⋊C4C2411yescharacteristic
382C23×C22⋊C4C2411yescharacteristic
383C23×C22⋊C4C2411yescharacteristic
384C23×C22⋊C4C2411yescharacteristic
385C23×C22⋊C4C2411yescharacteristic
386C23×C22⋊C4C2411yescharacteristic
387C23×C22⋊C4C2411yescharacteristic
388C23×C22⋊C4C2411yescharacteristic
389C23×C22⋊C4C2411yescharacteristic
390C23×C22⋊C4C2411yescharacteristic
391C23×C22⋊C4C2411yescharacteristic
392C23×C22⋊C4C2411yescharacteristic
393C23×C22⋊C4C2411yescharacteristic
394C22×#99C2×D414yes—
395C22×#99C2×D414yes—
396C22×#99C2×D414yes—
397C22×#99C2×D414yes—
398C22×#99C2×D414yes—
399C22×#99C2×D414yes—
400C22×#99C2×D414yes—
401C22×#99C2×D414yes—
402C22×#99C2×D414yes—
403C22×#99C2×D414yes—
404C22×#99C2×D414yes—
405C22×#99C2×D414yes—
406C22×#99C2×D414yes—
407C22×#99C2×D414yes—
408C22×#99C2×D414yes—
409C22×#99C2×D414yes—
410C22×#99C2×D414yes—
411#2308C2×D414yes—
412#2308C2×D414yes—
413#2308C2×D414yes—
414#2308C2×D414yes—
415#2308C2×D414yes—
416#2308C2×D414yes—
417#2308C2×D414yes—
418#2308C2×D414yes—
419C2×#381C2×D412yes—
420C2×#381C2×D412yes—
421C2×#379C2×D412yes—
422C2×#379C2×D412yes—
423C26#12412yescomplemented
424C26C22×D412yes—
425C26C22×D411yescharacteristic
426C26C2×#4111yescharacteristic
427C26C2×#4111yescharacteristic
428C26H(5,𝔽2)11yescharacteristic
429C26H(5,𝔽2)11yescharacteristic
430C26H(5,𝔽2)11yescharacteristic
431C26H(5,𝔽2)11yescharacteristic
432C26C2511yescharacteristic
433C23×Q8#12412yescomplemented
434C23×D4#12412yescomplemented
435C23×D4#12412yescomplemented
436C23×D4#12412yescomplemented
437C23×D4C22×D412yes—
438C23×D4C22×D412yes—
439C23×D4C22×D412yes—
440C23×D4C22×D412yes—
441C23×D4C22×D412yes—
442C23×D4C22×D412yes—
443C23×D4C22×D412yes—
444C23×D4C22×D412yes—
445C23×D4C22×D412yes—
446C23×D4C22×D412yes—
447C23×D4C22×D412yes—
448C23×D4C22×D412yes—
449C23×D4C22×D412yes—
450C23×D4C22×D412yes—
451C23×D4C2×#4112yes—
452C23×D4C2×#4112yes—
453C23×D4C2×#4112yes—
454C23×D4C2×#4112yes—
455C23×D4C2×#4112yes—
456C23×D4C2×#4112yes—
457C23×D4C2×#4112yes—
458C23×D4C2×#4112yes—
459C23×D4C2×#4112yes—
460C23×D4C2×#4112yes—
461C23×D4H(5,𝔽2)12yes—
462C23×D4H(5,𝔽2)12yes—
463C23×D4H(5,𝔽2)12yes—
464C23×D4H(5,𝔽2)12yes—
465C23×D4H(5,𝔽2)12yes—
466C23×D4H(5,𝔽2)12yes—
467C23×D4H(5,𝔽2)12yes—
468C23×D4H(5,𝔽2)12yes—
469C23×D4H(5,𝔽2)12yes—
470C23×D4H(5,𝔽2)12yes—
471C23×D4H(5,𝔽2)12yes—
472C23×D4H(5,𝔽2)12yes—
473C23×D4H(5,𝔽2)12yes—
474C23×D4H(5,𝔽2)12yes—
475C23×D4H(5,𝔽2)12yes—
476C23×D4H(5,𝔽2)12yes—
477C23×D4H(5,𝔽2)12yes—
478C23×D4H(5,𝔽2)12yes—
479C24×C4#12412yescomplemented
480C24×C4#12412yescomplemented
481C24×C4#12412yescomplemented
482C24×C4C22×D411yescharacteristic
483C24×C4C2×#4111yescharacteristic
484C24×C4C2×#4111yescharacteristic
485C24×C4H(5,𝔽2)11yescharacteristic
486C24×C4H(5,𝔽2)11yescharacteristic
487C24×C4H(5,𝔽2)11yescharacteristic
488C24×C4H(5,𝔽2)11yescharacteristic
489C22×C22⋊C4C22×D412yes—
490C22×C22⋊C4C22×D412yes—
491C22×C22⋊C4C22×D412yes—
492C22×C22⋊C4C22×D412yes—
493C22×C22⋊C4C22×D412yes—
494C22×C22⋊C4C22×D412yes—
495C22×C22⋊C4C22×D412yes—
496C22×C22⋊C4C22×D412yes—
497C22×C22⋊C4C22×D412yes—
498C22×C22⋊C4C22×D412yes—
499C22×C22⋊C4C22×D412yes—
500C22×C22⋊C4C22×D412yes—
501C22×C22⋊C4C22×D412yes—
502C22×C22⋊C4C22×D412yes—
503C22×C22⋊C4C22×D412yes—
504C22×C22⋊C4C22×D412yes—
505C22×C22⋊C4C22×D412yes—
506C22×C22⋊C4C22×D412yes—
507C22×C22⋊C4C22×D412yes—
508C2×#99#120116yes—
509C25#52512yes—
510C25C2×#12412yes—
511C25C2×#12412yes—
512C25C2×#12412yes—
513C25#53412yes—
514C25#53512yes—
515C25#53812yes—
516C25#53812yes—
517C25#53812yes—
518C25D4212yes—
519C25D4212yes—
520C25D4212yes—
521C25#54612yes—
522C25#54612yes—
523C25#54612yes—
524C25#54612yes—
525C25#54612yes—
526C25H(3,𝔽4)12yes—
527C25H(3,𝔽4)12yes—
528C25H(3,𝔽4)12yes—
529C25H(3,𝔽4)12yes—
530C25C23×D411yescharacteristic
531C25C23×D411yescharacteristic
532C25C23×D411yescharacteristic
533C25C23×D411yescharacteristic
534C25C23×D411yescharacteristic
535C25C22×#4111yescharacteristic
536C25C22×#4111yescharacteristic
537C25C22×#4111yescharacteristic
538C25C22×#4111yescharacteristic
539C25C2×H(5,𝔽2)11yescharacteristic
540C25C2×H(5,𝔽2)11yescharacteristic
541C25C2×H(5,𝔽2)11yescharacteristic
542C25C2×H(5,𝔽2)11yescharacteristic
543C25C2×H(5,𝔽2)11yescharacteristic
544C25C2×H(5,𝔽2)11yescharacteristic
545C25C2×H(5,𝔽2)11yescharacteristic
546C25C2×H(5,𝔽2)11yescharacteristic
547C25C2×H(5,𝔽2)11yescharacteristic
548C25C2×H(5,𝔽2)11yescharacteristic
549C25C2×H(5,𝔽2)11yescharacteristic
550C25C2×H(5,𝔽2)11yescharacteristic
551C25C2×H(5,𝔽2)11yescharacteristic
552C25C2×H(5,𝔽2)11yescharacteristic
553C25C2×H(5,𝔽2)11yescharacteristic
554C25C2×H(5,𝔽2)11yescharacteristic
555C25C2×H(5,𝔽2)11yescharacteristic
556C25C2×H(5,𝔽2)11yescharacteristic
557C25C2×H(5,𝔽2)11yescharacteristic
558C25C2×H(5,𝔽2)11yescharacteristic
559C25C2×H(5,𝔽2)11yescharacteristic
560C25C2×H(5,𝔽2)11yescharacteristic
561C22×D4C2×#12014yes—
562C22×D4#52514yes—
563C22×D4#53414yes—
564C22×D4#53414yes—
565C22×D4#53414yes—
566C22×D4#53514yes—
567C22×D4#53514yes—
568C22×D4#53514yes—
569C22×D4#53514yes—
570C22×D4#53814yes—
571C22×D4#53814yes—
572C22×D4#53814yes—
573C22×D4D4214yes—
574C22×D4D4214yes—
575C22×D4D4214yes—
576C22×D4D4214yes—
577C22×D4#54614yes—
578C22×D4#54614yes—
579C22×D4#54614yes—
580C22×D4#54614yes—
581C22×D4#54614yes—
582C22×D4#54614yes—
583C22×D4#54614yes—
584C22×D4#54614yes—
585C22×D4#54614yes—
586C22×D4#55114yes—
587C22×D4#55114yes—
588C22×D4#55114yes—
589C23×C4#52512yes—
590C23×C4C2×#12412yes—
591C23×C4C2×#12412yes—
592C23×C4C2×#12412yes—
593C23×C4#53412yes—
594C23×C4#53512yes—
595C23×C4#53812yes—
596C23×C4#53812yes—
597C23×C4#53812yes—
598C23×C4D4212yes—
599C23×C4D4212yes—
600C23×C4D4212yes—
601C23×C4#54612yes—
602C23×C4#54612yes—
603C23×C4#54612yes—
604C23×C4#54612yes—
605C23×C4#54612yes—
606C23×C4H(3,𝔽4)12yes—
607C23×C4H(3,𝔽4)12yes—
608C23×C4H(3,𝔽4)12yes—
609C23×C4H(3,𝔽4)12yes—
610C2×C22⋊C4C2×#12014yes—
611C2×C22⋊C4C2×#12014yes—
612C24#243514yes—
613C24#247214yes—
614C24#247214yes—
615C24#267014yes—
616C24#267014yes—
617C24#267914yes—
618C24#268414yes—
619C24C22×#12011yescharacteristic
620C24C2×#52511yescharacteristic
621C24C2×#52511yescharacteristic
622C24C22×#12411yescharacteristic
623C24C2×#53411yescharacteristic
624C24C2×#53411yescharacteristic
625C24C2×#53411yescharacteristic
626C24C2×#53411yescharacteristic
627C24C2×#53511yescharacteristic
628C24C2×#53511yescharacteristic
629C24C2×#53511yescharacteristic
630C24C2×#53511yescharacteristic
631C24C2×#53511yescharacteristic
632C24C2×#53811yescharacteristic
633C24C2×#53811yescharacteristic
634C24C2×#53811yescharacteristic
635C24C2×#53811yescharacteristic
636C24C2×#53811yescharacteristic
637C24C2×#53811yescharacteristic
638C24C2×D4211yescharacteristic
639C24C2×D4211yescharacteristic
640C24C2×D4211yescharacteristic
641C24C2×D4211yescharacteristic
642C24C2×D4211yescharacteristic
643C24C2×D4211yescharacteristic
644C24C2×D4211yescharacteristic
645C24C2×#54611yescharacteristic
646C24C2×#54611yescharacteristic
647C24C2×#54611yescharacteristic
648C24C2×#54611yescharacteristic
649C24C2×#54611yescharacteristic
650C24C2×#54611yescharacteristic
651C24C2×#54611yescharacteristic
652C24C2×#54611yescharacteristic
653C24C2×#54611yescharacteristic
654C24C2×#54611yescharacteristic
655C24C2×#54611yescharacteristic
656C24C2×#54611yescharacteristic
657C24C2×#54611yescharacteristic
658C24C2×#54611yescharacteristic
659C24C2×#55111yescharacteristic
660C24C2×#55111yescharacteristic
661C24C2×#55111yescharacteristic
662C24#348411yescharacteristic
663C24#348411yescharacteristic
664C24#348411yescharacteristic
665C24#348411yescharacteristic
666C24#348411yescharacteristic
667C24#348411yescharacteristic
668C24#348411yescharacteristic
669C24#348411yescharacteristic
670C24#348411yescharacteristic
671C24#348411yescharacteristic
672C24#348411yescharacteristic
673C24#348411yescharacteristic
674C24#348411yescharacteristic
675C24#348411yescharacteristic
676C24#348411yescharacteristic
677C24#348411yescharacteristic
678C24#348411yescharacteristic
679C24#348411yescharacteristic
680C24#348411yescharacteristic
681C24#348411yescharacteristic
682C24#348411yescharacteristic
683C24#348411yescharacteristic
684C24#348411yescharacteristic
685C24#348411yescharacteristic
686C24#348411yescharacteristic
687C24#348411yescharacteristic
688C24#348411yescharacteristic
689C24#348411yescharacteristic
690C24#348411yescharacteristic
691C24#348411yescharacteristic
692C24#348411yescharacteristic
693C24#348411yescharacteristic
694C24#349011yescharacteristic
695C24#349011yescharacteristic
696C24#349011yescharacteristic
697C24#349011yescharacteristic
698C24#349011yescharacteristic
699C24#349011yescharacteristic
700C24#349011yescharacteristic
701C24#349011yescharacteristic
702C24#349011yescharacteristic
703C24#349011yescharacteristic
704C24#349011yescharacteristic
705C24#349011yescharacteristic
706C24#349011yescharacteristic
707C24#349011yescharacteristic
708C24#349011yescharacteristic
709C24#349011yescharacteristic
710C24#349011yescharacteristic
711C24#349011yescharacteristic
712C24#349011yescharacteristic
713C24#349011yescharacteristic
714C24#349011yescharacteristic
715C24#349011yescharacteristic
716C24#349011yescharacteristic
717C24#349011yescharacteristic
718C24#349011yescharacteristic
719C24#349011yescharacteristic
720C24#349011yescharacteristic
721C24#349011yescharacteristic
722C24C2×H(3,𝔽4)11yescharacteristic
723C24C2×H(3,𝔽4)11yescharacteristic
724C24C2×H(3,𝔽4)11yescharacteristic
725C24C2×H(3,𝔽4)11yescharacteristic
726C24#353211yescharacteristic
727C24#353211yescharacteristic
728C24#353211yescharacteristic
729C24#353211yescharacteristic
730C24#353211yescharacteristic
731C24#353211yescharacteristic
732C24#353211yescharacteristic
733C24#353211yescharacteristic
734C24#353211yescharacteristic
735C24#353211yescharacteristic
736C24#353211yescharacteristic
737C24#353211yescharacteristic
738C24#353211yescharacteristic
739C24#353211yescharacteristic
740C24#353211yescharacteristic
741C24#353211yescharacteristic
742C24#353211yescharacteristic
743C24#353211yescharacteristic
744C24#353211yescharacteristic
745C24#353211yescharacteristic
746C24#353211yescharacteristic
747C24#353211yescharacteristic
748C24#353211yescharacteristic
749C24#353211yescharacteristic
750C24#353211yescharacteristic
751C24#353211yescharacteristic
752C24#353211yescharacteristic
753C24#353211yescharacteristic
754C24#353211yescharacteristic
755C24#353211yescharacteristic
756C24#353211yescharacteristic
757C24#353211yescharacteristic
758C24#353211yescharacteristic
759C24#353211yescharacteristic
760C24#353211yescharacteristic
761C24#353211yescharacteristic
762C24#353211yescharacteristic
763C24#353211yescharacteristic
764C24#353211yescharacteristic
765C24#353211yescharacteristic
766C24#353211yescharacteristic
767C24#353211yescharacteristic
768C24#353211yescharacteristic
769C24#353211yescharacteristic
770C24#353211yescharacteristic
771C24#353211yescharacteristic
772C24#353211yescharacteristic
773C24#353211yescharacteristic
774C22×C4#243514yes—
775C22×C4#247214yes—
776C22×C4#247214yes—
777C22×C4#267014yes—
778C22×C4#267014yes—
779C22×C4#267914yes—
780C22×C4#268414yes—
781C23C2×#247211yescharacteristic
782C23C2×#247211yescharacteristic
783C23C2×#243511yescharacteristic
784C23#3498011yescharacteristic
785C23#3498811yescharacteristic
786C23#3498811yescharacteristic
787C23#3505011yescharacteristic
788C23#3505011yescharacteristic
789C23#3522211yescharacteristic
790C23#3536711yescharacteristic
791C23#3536711yescharacteristic
792C23#3536711yescharacteristic
793C23#3536711yescharacteristic
794C23D4×#12011yescharacteristic
795C23D4×#12011yescharacteristic
796C23#3609811yescharacteristic
797C23#3609811yescharacteristic
798C23#3609811yescharacteristic
799C23#3609811yescharacteristic
800C23#3609811yescharacteristic
801C23#3609811yescharacteristic
802C23#3615211yescharacteristic
803C23#3615211yescharacteristic
804C23#3615811yescharacteristic
805C23#3615811yescharacteristic
806C23#3670211yescharacteristic
807C23#3670211yescharacteristic
808C23#3670211yescharacteristic
809C23#3670311yescharacteristic
810C23#3670311yescharacteristic
811C23#3670311yescharacteristic
812C23#3670311yescharacteristic
813C23#3670311yescharacteristic
814C23#3670311yescharacteristic
815C23#3671411yescharacteristic
816C23#3672511yescharacteristic
817C23#3672511yescharacteristic
818C23#3672511yescharacteristic
819C23#3672511yescharacteristic
820C23#3672511yescharacteristic
821C23#3672511yescharacteristic
822C23#3672511yescharacteristic
823C23#3672511yescharacteristic
824C23#3764411yescharacteristic
825C23#3764411yescharacteristic
826C23#3764411yescharacteristic
827C23#3764411yescharacteristic
828C23#3764411yescharacteristic
829C23#3764411yescharacteristic
830C23#3764511yescharacteristic
831C23#3764511yescharacteristic
832C23#3764511yescharacteristic
833C23#3764511yescharacteristic
834C23#3764511yescharacteristic
835C23#3764511yescharacteristic
836C23#3764511yescharacteristic
837C23#3764511yescharacteristic
838C23#3764511yescharacteristic
839C23#3764511yescharacteristic
840C23#3766011yescharacteristic
841C23#3766011yescharacteristic
842C23#3766011yescharacteristic
843C23#3766011yescharacteristic
844C23#3766011yescharacteristic
845C23#3766011yescharacteristic
846C23#3766011yescharacteristic
847C23#3766011yescharacteristic
848C23#3766011yescharacteristic
849C23#3766011yescharacteristic
850C23#3766011yescharacteristic
851C23#3766011yescharacteristic
852C23#3766011yescharacteristic
853C23#3766011yescharacteristic
854C23#3766011yescharacteristic
855C23#3766011yescharacteristic
856C23#3783211yescharacteristic
857C23#3783211yescharacteristic
858C23#3783211yescharacteristic
859C23#3783211yescharacteristic
860C23#3783211yescharacteristic
861C23#3783211yescharacteristic
862C23#3783211yescharacteristic
863C23#3783211yescharacteristic
864C23#3783211yescharacteristic
865C23#3783211yescharacteristic
866C23#3783311yescharacteristic
867C23#3783311yescharacteristic
868C23#3783311yescharacteristic
869C23#3783311yescharacteristic
870C23#3783311yescharacteristic
871C23#3783311yescharacteristic
872C23#3783311yescharacteristic
873C23#3783311yescharacteristic
874C23#3783311yescharacteristic
875C23#3783311yescharacteristic
876C23#3784811yescharacteristic
877C23#3784811yescharacteristic
878C23#3784811yescharacteristic
879C23#3784811yescharacteristic
880C23#3784811yescharacteristic
881C23#3784811yescharacteristic
882C23#3784811yescharacteristic
883C23#3784811yescharacteristic
884C23#4543911yescharacteristic
885C23#4543911yescharacteristic
886C23#4543911yescharacteristic
887C23#4543911yescharacteristic
888C23#4543911yescharacteristic
889C23#4543911yescharacteristic
890C23#4543911yescharacteristic
891C23#4543911yescharacteristic
892C23#4543911yescharacteristic
893C23#4543911yescharacteristic
894C23#4543911yescharacteristic
895C23#4543911yescharacteristic
896C23#4545811yescharacteristic
897C23#4545811yescharacteristic
898C23#4545811yescharacteristic
899C23#4545811yescharacteristic
900C23#4545811yescharacteristic
901C23#4545811yescharacteristic
902C23#4545811yescharacteristic
903C23#4545811yescharacteristic
904C23#4545811yescharacteristic
905C23#4545811yescharacteristic
906C23#4545811yescharacteristic
907C23#4545811yescharacteristic
908C23C2×#267011yescharacteristic
909C23C2×#267011yescharacteristic
910C23C2×#267911yescharacteristic
911C23C2×#268411yescharacteristic
912C23#5315811yescharacteristic
913C23#5315811yescharacteristic
914C23#5315811yescharacteristic
915C23#5315811yescharacteristic
916C23#5315811yescharacteristic
917C23#5315811yescharacteristic
918C23#5315811yescharacteristic
919C23#5315811yescharacteristic
920C23#5899011yescharacteristic
921C23#5899011yescharacteristic
922C23#5899111yescharacteristic
923C23#5899111yescharacteristic
924C23#5899111yescharacteristic
925C23#5899111yescharacteristic
926C23#5899111yescharacteristic
927C23#5899111yescharacteristic
928C23#5899111yescharacteristic
929C23#5899111yescharacteristic
930C23#5900611yescharacteristic
931C23#5900611yescharacteristic
932C23#5900611yescharacteristic
933C23#5900611yescharacteristic
934C23#5900611yescharacteristic
935C23#5900611yescharacteristic
936C22#61716911yescharacteristic
937C22#61716911yescharacteristic
938C22#61753411yescharacteristic
939C22#64805311yescharacteristic
940C22#64838711yescharacteristic
941C22#64838711yescharacteristic
942C22#84529711yescharacteristic
943C22#84529811yescharacteristic
944C22#84529811yescharacteristic
945C22#84568911yescharacteristic
946C22#84568911yescharacteristic
947C22#84569011yescharacteristic
948C22#84569011yescharacteristic
949C22#84638911yescharacteristic
950C22#85055711yescharacteristic
951C22#85055711yescharacteristic
952C22#85088311yescharacteristic
953C22#85088311yescharacteristic
954C22#203200011yescharacteristic
955C22#203200011yescharacteristic
956C22#203200011yescharacteristic
957C22#203200011yescharacteristic
958C22#203200011yescharacteristic
959C22#203200011yescharacteristic
960C22#203208811yescharacteristic
961C22#203250511yescharacteristic
962C22#203250511yescharacteristic
963C22#203256511yescharacteristic
964C22#203256511yescharacteristic
965C22#203256511yescharacteristic
966C22#502075111yescharacteristic
967C2#7221002612yes—
968C2#7221004811yescharacteristic
subgroupG/H
center, socleC22#5020751
commutator, Frattini, cosocleC26C25
prime radicalC2×#6628896C2
LCSG ▷ C26 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C26 ◁ G
LECSG ▷ C26 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #72240527C2semidirect
2. #72240527C2semidirect
3. C2×#417896C2semidirect
4. C2×#417969C2semidirect
5. C2×#417969C2semidirect
6. C2×#432839C2semidirect
7. #72240512C2semidirect
8. #72240512C2semidirect
9. #72240512C2semidirect
10. #72240512C2semidirect
11. #72240511C2semidirect
12. #72240510C2semidirect
13. #72240510C2semidirect
14. #72240509C2semidirect
15. #72240508C2semidirect
16. #72240508C2semidirect
17. C2×#392135C2semidirect
18. C2×#392135C2semidirect
19. #72240407C2semidirect
20. #72240406C2semidirect
21. #72240404C2semidirect
22. #72240404C2semidirect
23. #72240400C2semidirect
24. #72240398C2semidirect
25. #72240398C2semidirect
26. #72240193C2semidirect
27. #72240193C2semidirect
28. #72240192C2semidirect
29. #72240192C2semidirect
30. #72239046C2semidirect
37. C2×#35367C22semidirect
41. C22×#2032C22semidirect
42. C22×#2032C22semidirect
43. C22×#2032C22semidirect
44. C22×#2032C22semidirect
45. C2×#23468C22semidirect
46. C2×#23468C22semidirect
82. #5955309C22semidirect
83. #5955309C22semidirect
84. #515326C22semidirect
85. C2×#11172C22semidirect
86. C2×#11172C22semidirect
87. C2×#11172C22semidirect
88. C2×#11172C22semidirect
89. C2×#11172C22semidirect
90. C2×#11172C22semidirect
91. C2×#11172C22semidirect
92. C2×#11172C22semidirect
93. C2×#11172C22semidirect
94. C2×#11172C22semidirect
95. C2×#11169C22semidirect
96. C2×#11169C22semidirect
97. C2×#11169C22semidirect
98. C2×#11169C22semidirect
99. C2×#11169C22semidirect
100. C2×#11169C22semidirect
101. C2×#11089C22semidirect
102. C2×#11089C22semidirect
103. C2×#11089C22semidirect
104. C2×#11089C22semidirect
105. C2×#11089C22semidirect
106. C2×#11089C22semidirect
107. C2×#11089C22semidirect
108. C2×#11089C22semidirect
109. C2×#11089C22semidirect
110. C2×#11089C22semidirect
111. C2×#11089C22semidirect
112. C2×#11089C22semidirect
113. #357642C22semidirect
114. #357642C22semidirect
115. #357642C22semidirect
116. #357642C22semidirect
117. #357642C22semidirect
118. #357642C22semidirect
119. C2×#10991C22semidirect
120. C2×#10991C22semidirect
121. C2×#10991C22semidirect
122. C2×#10991C22semidirect
123. C2×#10991C22semidirect
124. C2×#10991C22semidirect
125. C2×#10991C22semidirect
126. C2×#10991C22semidirect
127. C2×#10991C22semidirect
128. C2×#10991C22semidirect
129. C2×#10991C22semidirect
130. C2×#10991C22semidirect
131. C2×#10991C22semidirect
132. C2×#10991C22semidirect
133. C2×#10991C22semidirect
134. C2×#10991C22semidirect
135. C2×#10965C22semidirect
136. C2×#10965C22semidirect
137. C2×#10965C22semidirect
138. C2×#10965C22semidirect
139. C2×#10965C22semidirect
140. C2×#10965C22semidirect
141. C2×#10965C22semidirect
142. C2×#10965C22semidirect
143. C2×#10938C22semidirect
144. C2×#10938C22semidirect
145. C2×#10938C22semidirect
146. C2×#10938C22semidirect
147. C2×#10938C22semidirect
148. C2×#10938C22semidirect
149. C2×#10938C22semidirect
150. C2×#10938C22semidirect
151. C2×#10938C22semidirect
152. C2×#10938C22semidirect
153. C2×#10938C22semidirect
154. C2×#10938C22semidirect
155. #123581C22semidirect
156. #123581C22semidirect
157. #123581C22semidirect
158. #123581C22semidirect
159. #123581C22semidirect
160. #123581C22semidirect
161. #123581C22semidirect
162. #123581C22semidirect
163. #123581C22semidirect
164. #123581C22semidirect
165. #123581C22semidirect
166. #123581C22semidirect
167. #123581C22semidirect
168. #123581C22semidirect
169. #123539C22semidirect
170. #123539C22semidirect
171. #123539C22semidirect
172. #123539C22semidirect
173. #123539C22semidirect
174. #123539C22semidirect
175. #123539C22semidirect
176. #123539C22semidirect
177. #123539C22semidirect
178. #123539C22semidirect
179. #123539C22semidirect
180. #123539C22semidirect
181. #123527C22semidirect
182. #123527C22semidirect
183. #123527C22semidirect
184. #123527C22semidirect
185. #123527C22semidirect
186. #123527C22semidirect
194. C22×#543C23semidirect
247. C2×#2315C23semidirect
248. C2×#2315C23semidirect
249. C2×#2315C23semidirect
283. C22×#379C23semidirect
284. C22×#379C23semidirect
285. C22×#379C23semidirect
286. C22×#379C23semidirect
287. C22×#379C23semidirect
288. C22×#379C23semidirect
289. C22×#379C23semidirect
290. C22×#379C23semidirect
291. C2×#2273C23semidirect
292. C2×#2273C23semidirect
294. #20609D4semidirect
295. #20585D4semidirect
298. C22×#342C23semidirect
299. C22×#342C23semidirect
300. C22×#342C23semidirect
301. C22×#342C23semidirect
302. C22×#342C23semidirect
303. C22×#342C23semidirect
304. C22×#342C23semidirect
305. C22×#342C23semidirect
306. C22×#342C23semidirect
307. C22×#342C23semidirect
308. C22×#342C23semidirect
309. C22×#342C23semidirect
310. C22×#342C23semidirect
311. C22×#342C23semidirect
312. C22×#342C23semidirect
313. C22×#342C23semidirect
314. C22×#342C23semidirect
315. C22×#342C23semidirect
316. C22×#342C23semidirect
317. C22×#342C23semidirect
318. C22×#342C23semidirect
319. C22×#342C23semidirect
320. C22×#342C23semidirect
321. C22×#342C23semidirect
322. C22×#342C23semidirect
323. C22×#342C23semidirect
324. C22×#342C23semidirect
325. C22×#342C23semidirect
326. C22×#342C23semidirect
327. C22×#342C23semidirect
328. C22×#342C23semidirect
329. C22×#342C23semidirect
330. C22×#342C23semidirect
331. C22×#342C23semidirect
332. C22×#342C23semidirect
333. C22×#342C23semidirect
334. C22×#342C23semidirect
335. C22×#342C23semidirect
336. C22×#342C23semidirect
337. C22×#342C23semidirect
338. C22×#342C23semidirect
339. C22×#342C23semidirect
340. C22×#342C23semidirect
341. C22×#342C23semidirect
342. C22×#342C23semidirect
343. C22×#342C23semidirect
344. C22×#342C23semidirect
345. C22×#342C23semidirect
346. #13794C23semidirect
347. #13794C23semidirect
423. C26#124semidirect
433. C23×Q8#124semidirect
434. C23×D4#124semidirect
435. C23×D4#124semidirect
436. C23×D4#124semidirect
479. C24×C4#124semidirect
480. C24×C4#124semidirect
481. C24×C4#124semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#722405272
C2×#4178962
C2×#4179692
C2×#4328392
#722405122
#722405112
#722405102
#722405092
#722405082
C2×#3921352
#722404072
#722404062
#722404042
#722404002
#722403982
#722401932
#722401922
#722390462
C2×#66288962