Finite Group Databasebeta

← C2×C3×#2471 #10653333

Subgroups — C2×C3×#2471 #10653333

Order 768.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×C3×#117C211yesmaximal, characteristic, complemented
3C3×#2471C2116yesmaximal, direct product factor
4C2×C3×#399C211yesmaximal, characteristic, complemented
5C2×C3×#397C211yesmaximal, characteristic, complemented
6C2×C3×#396C211yesmaximal, characteristic, complemented
7C2×C3×#392C211yesmaximal, characteristic
8C2×C3×#390C211yesmaximal, characteristic, complemented
9C2×C3×#390C211yesmaximal, characteristic, complemented
10C2×C3×#388C211yesmaximal, characteristic, complemented
11C2×C3×#387C211yesmaximal, characteristic, complemented
12C2×C3×#387C211yesmaximal, characteristic, complemented
13C2×C3×#386C211yesmaximal, characteristic, complemented
14C2×C3×#386C211yesmaximal, characteristic, complemented
15C2×C3×#386C211yesmaximal, characteristic, complemented
16C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
17C2×#2471C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C24×C3×C4C2211yescharacteristic
23C2×C3×#123—28no—
24C2×C3×#123C2218yescomplemented
25C2×C3×#117—28no—
26C2×C3×#117C2218yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C22⋊C4C2211yescharacteristic
46C22×C3×C42C2211yescharacteristic
47C22×C3×C42C2211yescharacteristic
48C22×C3×C42C2211yescharacteristic
49C3×#399C2218yescomplemented
50C3×#397C2218yescomplemented
51C3×#396C2218yescomplemented
52C3×#392C2218yes—
53C3×#390C2218yescomplemented
54C3×#390C2218yescomplemented
55C3×#388C2218yescomplemented
56C3×#387C2218yescomplemented
57C3×#387C2218yescomplemented
58C3×#386C2218yescomplemented
59C3×#386C2218yescomplemented
60C3×#386C2218yescomplemented
61C3×C4×C22⋊C4C2218yescomplemented
62C2×C3×#95C2211yescharacteristic
63C2×C3×#95C2211yescharacteristic
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×#123C2×C311yescharacteristic, complemented
71C22×#117C2×C311yescharacteristic, complemented
72#2471C2×C3116yesdirect product factor
73C2×#399C2×C311yescharacteristic, complemented
74C2×#397C2×C311yescharacteristic, complemented
75C2×#396C2×C311yescharacteristic, complemented
76C2×#392C2×C311yescharacteristic
77C2×#390C2×C311yescharacteristic, complemented
78C2×#390C2×C311yescharacteristic, complemented
79C2×#388C2×C311yescharacteristic, complemented
80C2×#387C2×C311yescharacteristic, complemented
81C2×#387C2×C311yescharacteristic, complemented
82C2×#386C2×C311yescharacteristic, complemented
83C2×#386C2×C311yescharacteristic, complemented
84C2×#386C2×C311yescharacteristic, complemented
85C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4C2314yes—
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C23×C3×C4—24no—
102C23×C3×C4—24no—
103C23×C3×C4—24no—
104C23×C3×C4—24no—
105C23×C3×C4—24no—
106C23×C3×C4—42no—
107C23×C3×C4C2314yes—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2314yes—
116C23×C3×C4C2311yescharacteristic
117C23×C3×C4C2311yescharacteristic
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2311yescharacteristic
120C23×C3×C4C2311yescharacteristic
121C3×#123—232no—
122C3×#117—232no—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4—24no—
125C2×C3×C4⋊C4—24no—
126C2×C3×C4⋊C4—42no—
127C2×C3×C4⋊C4—42no—
128C2×C3×C4⋊C4D418yescomplemented
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—24no—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—42no—
144C2×C3×C22⋊C4—42no—
145C2×C3×C22⋊C4—42no—
146C2×C3×C22⋊C4—42no—
147C2×C3×C22⋊C4—42no—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C22⋊C4C2314yes—
154C2×C3×C22⋊C4C2314yes—
155C2×C3×C22⋊C4C2314yes—
156C2×C3×C22⋊C4C2314yes—
157C2×C3×C22⋊C4C2314yes—
158C2×C3×C22⋊C4C2314yes—
159C2×C3×C22⋊C4C2314yes—
160C2×C3×C22⋊C4C2314yes—
161C2×C3×C42—24no—
162C2×C3×C42—24no—
163C2×C3×C42—42no—
164C2×C3×C42C2314yes—
165C2×C3×C42C2314yes—
166C2×C3×C42C2314yes—
167C3×#95C2314yes—
168C3×#95C2314yes—
169C3×#95C2314yes—
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3×#95C2314yes—
173C3×#95C2314yes—
174C3×#95C2314yes—
175C23×D4C22×C311yescharacteristic
176C23×D4C22×C311yescharacteristic
177C23×D4C22×C311yescharacteristic
178C24×C4C22×C311yescharacteristic
179C24×C4C22×C311yescharacteristic
180C2×#123—28no—
181C2×#123C22×C318yescomplemented
182C2×#117—28no—
183C2×#117C22×C318yescomplemented
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186C22×C4⋊C4C22×C311yescharacteristic
187C22×C4⋊C4C22×C311yescharacteristic
188C22×C4⋊C4C22×C311yescharacteristic
189C22×C4⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C22⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C22⋊C4C22×C311yescharacteristic
199C22×C22⋊C4C22×C311yescharacteristic
200C22×C22⋊C4C22×C311yescharacteristic
201C22×C22⋊C4C22×C311yescharacteristic
202C22×C22⋊C4C22×C311yescharacteristic
203C22×C42C22×C311yescharacteristic
204C22×C42C22×C311yescharacteristic
205C22×C42C22×C311yescharacteristic
206#399C22×C318yescomplemented
207#397C22×C318yescomplemented
208#396C22×C318yescomplemented
209#392C22×C318yes—
210#390C22×C318yescomplemented
211#390C22×C318yescomplemented
212#388C22×C318yescomplemented
213#387C22×C318yescomplemented
214#387C22×C318yescomplemented
215#386C22×C318yescomplemented
216#386C22×C318yescomplemented
217#386C22×C318yescomplemented
218C4×C22⋊C4C22×C318yescomplemented
219C2×#95C22×C311yescharacteristic
220C2×#95C22×C311yescharacteristic
221C2×#95C22×C311yescharacteristic
222C2×#95C22×C311yescharacteristic
223C2×#95C22×C311yescharacteristic
224C2×#95C22×C311yescharacteristic
225C2×#95C22×C311yescharacteristic
226C2×#95C22×C311yescharacteristic
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3#4114yes—
247C24×C3#4114yes—
248C24×C3C2412yes—
249C24×C3C2412yes—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—28no—
257C2×C3×D4—28no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C2×C3×D4—416no—
262C2×C3×D4—416no—
263C2×C3×D4—416no—
264C22×C3×C4—232no—
265C22×C3×C4—22no—
266C22×C3×C4—28no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—28no—
277C22×C3×C4—28no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—28no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—28no—
301C22×C3×C4—44no—
302C22×C3×C4—416no—
303C22×C3×C4C2×D414yes—
304C22×C3×C4C2×D414yes—
305C22×C3×C4C2×D414yes—
306C22×C3×C4#4114yes—
307C22×C3×C4#4114yes—
308C22×C3×C4C2412yes—
309C22×C3×C4C2412yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2412yes—
312C22×C3×C4C2412yes—
313C22×C3×C4C2412yes—
314C22×C3×C4C2412yes—
315C22×C3×C4C2412yes—
316C22×C3×C4C2412yes—
317C22×C3×C4C2412yes—
318C22×C3×C4C2412yes—
319C22×C3×C4C2412yes—
320C3×C4⋊C4—28no—
321C3×C4⋊C4—28no—
322C3×C4⋊C4—28no—
323C3×C4⋊C4—44no—
324C3×C4⋊C4—44no—
325C3×C4⋊C4C2×D4116yescomplemented
326C3×C22⋊C4—28no—
327C3×C22⋊C4—28no—
328C3×C22⋊C4—28no—
329C3×C22⋊C4—28no—
330C3×C22⋊C4—28no—
331C3×C22⋊C4—28no—
332C3×C22⋊C4—28no—
333C3×C22⋊C4—28no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C42—28no—
340C3×C42—28no—
341C3×C42—44no—
342C25C23×C311yescharacteristic
343C25C23×C311yescharacteristic
344C25C23×C311yescharacteristic
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4C23×C314yes—
355C22×D4C23×C314yes—
356C22×D4C23×C314yes—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—42no—
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369C23×C4C23×C311yescharacteristic
370C23×C4C23×C314yes—
371C23×C4C23×C314yes—
372C23×C4C23×C311yescharacteristic
373C23×C4C23×C311yescharacteristic
374C23×C4C23×C311yescharacteristic
375C23×C4C23×C311yescharacteristic
376C23×C4C23×C311yescharacteristic
377#123—232no—
378#117—232no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4C3×D418yescomplemented
385C2×C4⋊C4C23×C314yes—
386C2×C4⋊C4C23×C314yes—
387C2×C4⋊C4C23×C314yes—
388C2×C4⋊C4C23×C314yes—
389C2×C4⋊C4C23×C314yes—
390C2×C4⋊C4C23×C314yes—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4C23×C314yes—
405C2×C22⋊C4C23×C314yes—
406C2×C22⋊C4C23×C314yes—
407C2×C22⋊C4C23×C314yes—
408C2×C22⋊C4C23×C314yes—
409C2×C22⋊C4C23×C314yes—
410C2×C22⋊C4C23×C314yes—
411C2×C22⋊C4C23×C314yes—
412C2×C22⋊C4C23×C314yes—
413C2×C22⋊C4C23×C314yes—
414C2×C22⋊C4C23×C314yes—
415C2×C22⋊C4C23×C314yes—
416C2×C22⋊C4C23×C314yes—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—42no—
420C2×C42C23×C314yes—
421C2×C42C23×C314yes—
422C2×C42C23×C314yes—
423#95C23×C314yes—
424#95C23×C314yes—
425#95C23×C314yes—
426#95C23×C314yes—
427#95C23×C314yes—
428#95C23×C314yes—
429#95C23×C314yes—
430#95C23×C314yes—
431C23×C3—28no—
432C23×C3—28no—
433C23×C3—28no—
434C23×C3—28no—
435C23×C3—28no—
436C23×C3—28no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—44no—
460C23×C3—44no—
461C23×C3—44no—
462C23×C3—44no—
463C23×C3—44no—
464C23×C3—44no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3—44no—
470C23×C3—44no—
471C23×C3C22×D412yes—
472C23×C3C2×#4114yes—
473C23×C3C2×#4114yes—
474C23×C3C2×#4112yes—
475C23×C3C2×#4112yes—
476C23×C3C2×#4112yes—
477C23×C3C2×#4112yes—
478C23×C3H(5,𝔽2)12yes—
479C23×C3H(5,𝔽2)12yes—
480C23×C3C2511yescharacteristic
481C3×D4—416no—
482C3×D4—416no—
483C3×D4—416no—
484C2×C3×C4—232no—
485C2×C3×C4—28no—
486C2×C3×C4—28no—
487C2×C3×C4—28no—
488C2×C3×C4—28no—
489C2×C3×C4—28no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—416no—
522C2×C3×C4—44no—
523C2×C3×C4—44no—
524C2×C3×C4—44no—
525C2×C3×C4—44no—
526C2×C3×C4—44no—
527C2×C3×C4—44no—
528C2×C3×C4—44no—
529C2×C3×C4C22×D414yes—
530C2×C3×C4C22×D414yes—
531C2×C3×C4C22×D414yes—
532C2×C3×C4C2×#4114yes—
533C2×C3×C4C2×#4114yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24C3×#4114yes—
554C24C3×#4114yes—
555C24C24×C312yes—
556C24C24×C312yes—
557C24C24×C312yes—
558C24C24×C311yescharacteristic
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—416no—
569C2×D4—416no—
570C2×D4—416no—
571C22×C4—232no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—416no—
610C22×C4C2×C3×D414yes—
611C22×C4C2×C3×D414yes—
612C22×C4C2×C3×D414yes—
613C22×C4C3×#4114yes—
614C22×C4C3×#4114yes—
615C22×C4C24×C312yes—
616C22×C4C24×C312yes—
617C22×C4C24×C312yes—
618C22×C4C24×C312yes—
619C22×C4C24×C312yes—
620C22×C4C24×C312yes—
621C22×C4C24×C312yes—
622C22×C4C24×C312yes—
623C22×C4C24×C312yes—
624C22×C4C24×C312yes—
625C22×C4C24×C312yes—
626C22×C4C24×C312yes—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4C2×C3×D4116yescomplemented
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C42—28no—
647C42—28no—
648C42—44no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—24no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—416no—
664C22×C3—416no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—88no—
673C22×C3#52514yes—
674C22×C3#52914yes—
675C22×C3#54014yes—
676C22×C3#54614yes—
677C22×C3#55014yes—
678C22×C3#55114yes—
679C22×C3#55114yes—
680C22×C3C23×D411yescharacteristic
681C22×C3C22×#4111yescharacteristic
682C22×C3C22×#4111yescharacteristic
683C22×C3C22×#4111yescharacteristic
684C22×C3C22×#4111yescharacteristic
685C22×C3C2×H(5,𝔽2)11yescharacteristic
686C22×C3C2×H(5,𝔽2)11yescharacteristic
687C3×C4—24no—
688C3×C4—24no—
689C3×C4—24no—
690C3×C4—24no—
691C3×C4—24no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4—42no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23C22×C3×D412yes—
740C23C2×C3×#4114yes—
741C23C2×C3×#4114yes—
742C23C2×C3×#4112yes—
743C23C2×C3×#4112yes—
744C23C2×C3×#4112yes—
745C23C2×C3×#4112yes—
746C23C3×H(5,𝔽2)12yes—
747C23C3×H(5,𝔽2)12yes—
748C23C25×C311yescharacteristic
749D4—416no—
750D4—416no—
751D4—416no—
752C2×C4—232no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—416no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4C22×C3×D414yes—
798C2×C4C22×C3×D414yes—
799C2×C4C22×C3×D414yes—
800C2×C4C2×C3×#4114yes—
801C2×C4C2×C3×#4114yes—
802C2×C3—44no—
803C2×C3—44no—
804C2×C3—82no—
805C2×C3#247118yesdirect product factor
806C2×C3C2×#52511yescharacteristic
807C2×C3C2×#52911yescharacteristic
808C2×C3C2×#54011yescharacteristic
809C2×C3C2×#54611yescharacteristic
810C2×C3C2×#55011yescharacteristic
811C2×C3C2×#55111yescharacteristic
812C2×C3C2×#55111yescharacteristic
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—416no—
828C22—416no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—88no—
837C22C3×#52514yes—
838C22C3×#52914yes—
839C22C3×#54014yes—
840C22C3×#54614yes—
841C22C3×#55014yes—
842C22C3×#55114yes—
843C22C3×#55114yes—
844C22C23×C3×D411yescharacteristic
845C22C22×C3×#4111yescharacteristic
846C22C22×C3×#4111yescharacteristic
847C22C22×C3×#4111yescharacteristic
848C22C22×C3×#4111yescharacteristic
849C22C2×C3×H(5,𝔽2)11yescharacteristic
850C22C2×C3×H(5,𝔽2)11yescharacteristic
851C4—24no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C3C2×#247111yescharacteristic, direct product factor, Sylow
864C2—44no—
865C2—44no—
866C2—82no—
867C2C3×#247118yesdirect product factor
868C2C2×C3×#52511yescharacteristic
869C2C2×C3×#52911yescharacteristic
870C2C2×C3×#54011yescharacteristic
871C2C2×C3×#54611yescharacteristic
872C2C2×C3×#55011yescharacteristic
873C2C2×C3×#55111yescharacteristic
874C2C2×C3×#55111yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC2×C3×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×C3×#117C2semidirect
3. C3×#2471C2direct (N × H)
4. C2×C3×#399C2semidirect
5. C2×C3×#397C2semidirect
6. C2×C3×#396C2semidirect
8. C2×C3×#390C2semidirect
9. C2×C3×#390C2semidirect
10. C2×C3×#388C2semidirect
11. C2×C3×#387C2semidirect
12. C2×C3×#387C2semidirect
13. C2×C3×#386C2semidirect
14. C2×C3×#386C2semidirect
15. C2×C3×#386C2semidirect
16. C2×C3×C4×C22⋊C4C2semidirect
17. C2×#2471C3direct (N × H)
24. C2×C3×#123C22semidirect
26. C2×C3×#117C22semidirect
49. C3×#399C22semidirect
50. C3×#397C22semidirect
51. C3×#396C22semidirect
53. C3×#390C22semidirect
54. C3×#390C22semidirect
55. C3×#388C22semidirect
56. C3×#387C22semidirect
57. C3×#387C22semidirect
58. C3×#386C22semidirect
59. C3×#386C22semidirect
60. C3×#386C22semidirect
61. C3×C4×C22⋊C4C22semidirect
70. C22×#123C2×C3semidirect
71. C22×#117C2×C3semidirect
72. #2471C2×C3direct (N × H)
73. C2×#399C2×C3semidirect
74. C2×#397C2×C3semidirect
75. C2×#396C2×C3semidirect
77. C2×#390C2×C3semidirect
78. C2×#390C2×C3semidirect
79. C2×#388C2×C3semidirect
80. C2×#387C2×C3semidirect
81. C2×#387C2×C3semidirect
82. C2×#386C2×C3semidirect
83. C2×#386C2×C3semidirect
84. C2×#386C2×C3semidirect
85. C2×C4×C22⋊C4C2×C3semidirect
128. C2×C3×C4⋊C4D4semidirect
181. C2×#123C22×C3semidirect
183. C2×#117C22×C3semidirect
206. #399C22×C3semidirect
207. #397C22×C3semidirect
208. #396C22×C3semidirect
210. #390C22×C3semidirect
211. #390C22×C3semidirect
212. #388C22×C3semidirect
213. #387C22×C3semidirect
214. #387C22×C3semidirect
215. #386C22×C3semidirect
216. #386C22×C3semidirect
217. #386C22×C3semidirect
218. C4×C22⋊C4C22×C3semidirect
325. C3×C4⋊C4C2×D4semidirect
384. C2×C4⋊C4C3×D4semidirect
632. C4⋊C4C2×C3×D4semidirect
805. C2×C3#2471direct (N × H)
863. C3C2×#2471direct (N × H)
867. C2C3×#2471direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C3×#1172
C3×#24712
C2×C3×#3992
C2×C3×#3972
C2×C3×#3962
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3872
C2×C3×#3862
C2×C3×C4×C22⋊C42
C2×#24713