Finite Group Databasebeta

← #30609347

Subgroups — #30609347

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840714C211yesmaximal, characteristic
2C2×#16840710C211yesmaximal, characteristic
3C2×#16840709C211yesmaximal, characteristic, complemented
4C2×#16840704C211yesmaximal, characteristic, complemented
5#21461007C211yesmaximal, characteristic, complemented
6#21461005C211yesmaximal, characteristic, complemented
7#21461002C211yesmaximal, characteristic, complemented
8#21461002C211yesmaximal, characteristic, complemented
9#21461002C211yesmaximal, characteristic, complemented
10#21461002C211yesmaximal, characteristic, complemented
11#21460999C211yesmaximal, characteristic, complemented
12#21460999C211yesmaximal, characteristic, complemented
13#21460993C211yesmaximal, characteristic, complemented
14#21460992C211yesmaximal, characteristic, complemented
15#386×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C22⋊#6923C2211yescharacteristic
24C22×C22⋊#6923C2211yescharacteristic
25C22×C22⋊#6923C2211yescharacteristic
26C22×C22⋊#6923C2211yescharacteristic
27C22×C22⋊#6923C2211yescharacteristic
28C22×C22⋊#6923C2211yescharacteristic
29C22×C4×#6923C2211yescharacteristic
30#16840714—24no—
31#16840710—24no—
32#16840709—24no—
33#16840704—24no—
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C22×D4×D61C2211yescharacteristic
49C23×C4×D61C2211yescharacteristic
50C2×C22⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C22⋊C4×D61C2211yescharacteristic
53#16839642C411yescharacteristic, complemented
54#16839641C411yescharacteristic, complemented
55#16839640C411yescharacteristic, complemented
56#16839640C411yescharacteristic, complemented
57#16839639C411yescharacteristic, complemented
58#16839638C411yescharacteristic, complemented
59#16839638C411yescharacteristic, complemented
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#386C411yescharacteristic, complemented
63C23×#6923—22no—
64C23×#6923—22no—
65C23×#6923—22no—
66C23×#6923—41no—
67C23×#6923—41no—
68C23×#6923—41no—
69C23×#6923—41no—
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C23×#6923C2311yescharacteristic
77C23×#6923C2311yescharacteristic
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—22no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923—41no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923—41no—
87C2×C4⋊#6923—41no—
88C2×C4⋊#6923—41no—
89C2×C4⋊#6923—41no—
90C2×C4⋊#6923—41no—
91C2×C4⋊#6923—41no—
92C2×C4⋊#6923D414yescomplemented
93C2×C22⋊#6923—22no—
94C2×C22⋊#6923—22no—
95C2×C22⋊#6923—22no—
96C2×C22⋊#6923—22no—
97C2×C22⋊#6923—22no—
98C2×C22⋊#6923—22no—
99C2×C22⋊#6923—22no—
100C2×C22⋊#6923—22no—
101C2×C22⋊#6923—22no—
102C2×C22⋊#6923—22no—
103C2×C22⋊#6923—22no—
104C2×C22⋊#6923—22no—
105C2×C22⋊#6923—22no—
106C2×C22⋊#6923—41no—
107C2×C22⋊#6923—41no—
108C2×C22⋊#6923—41no—
109C2×C22⋊#6923—41no—
110C2×C22⋊#6923—41no—
111C2×C22⋊#6923—41no—
112C2×C22⋊#6923—41no—
113C2×C22⋊#6923—41no—
114C2×C4×#6923—22no—
115C2×C4×#6923—41no—
116C2×C4×#6923—41no—
117(C2×#6923)⋊C4—22no—
118(C2×#6923)⋊C4—22no—
119(C2×#6923)⋊C4—22no—
120(C2×#6923)⋊C4—22no—
121(C2×#6923)⋊C4—22no—
122(C2×#6923)⋊C4—22no—
123(C2×#6923)⋊C4—22no—
124(C2×#6923)⋊C4—22no—
125(C2×#6923)⋊C4—41no—
126(C2×#6923)⋊C4—41no—
127(C2×#6923)⋊C4—41no—
128(C2×#6923)⋊C4—41no—
129(C2×#6923)⋊C4—41no—
130(C2×#6923)⋊C4—41no—
131C24×D61C2311yescharacteristic
132C24×D61C2311yescharacteristic
133C22×D244C2×C411yescharacteristic
134C22×C22⋊D61C2×C411yescharacteristic
135C22×C22⋊D61C2×C411yescharacteristic
136C2×D4×D61—41no—
137C2×D4×D61—41no—
138C2×D4×D61—41no—
139C2×D4×D61—41no—
140C2×D4×D61D414yes—
141C2×D4×D61Q814yes—
142C23×Dic61C2×C411yescharacteristic, complemented
143C22×C4×D61—22no—
144C22×C4×D61—22no—
145C22×C4×D61—41no—
146C22×C4×D61—41no—
147C22×C4×D61—41no—
148C22×C4×D61—41no—
149C22×C4×D61C2×C411yescharacteristic, complemented
150C22×C4×D61C2×C411yescharacteristic, complemented
151C22×C4×D61C2311yescharacteristic
152C22×C4×D61C2311yescharacteristic
153C22×C4×D61C2311yescharacteristic
154C22×C4×D61C2311yescharacteristic
155C22×C4×D61C2311yescharacteristic
156C2×C22⋊Dic61C2×C411yescharacteristic
157C2×C22⋊Dic61C2×C411yescharacteristic
158C2×C22⋊Dic61C2×C411yescharacteristic, complemented
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic, complemented
164C2×#11758198C2×C411yescharacteristic, complemented
165C22⋊C4×D61—22no—
166C22⋊C4×D61—22no—
167C22⋊C4×D61—41no—
168C22⋊C4×D61—41no—
169C22⋊C4×D61—41no—
170C22⋊C4×D61—41no—
171#14519684C2×C411yescharacteristic, complemented
172#14519684C2×C411yescharacteristic, complemented
173#14519684C2×C411yescharacteristic, complemented
174#14519684C2×C411yescharacteristic, complemented
175#14519684C2×C411yescharacteristic, complemented
176#14519684C2×C411yescharacteristic, complemented
177C22×D4×C61C2×C411yescharacteristic
178C23×C4×C61C2×C411yescharacteristic, complemented
179C2×C22⋊C4×C61C2×C411yescharacteristic
180C2×C22⋊C4×C61C2×C411yescharacteristic
181C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
182#95×C61C2×C411yescharacteristic, complemented
183#95×C61C2×C411yescharacteristic, complemented
184C24×C61C22×C411yescharacteristic
185C24×C61C22×C411yescharacteristic
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61C22×C411yescharacteristic
211C23×D61C22×C411yescharacteristic
212C23×D61C2×D412yes—
213C23×D61C2×D412yes—
214C23×D61C2×Q812yes—
215C23×D61C2×Q812yes—
216C23×D61C2411yescharacteristic
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923—21no—
232C22×#6923—21no—
233C22×#6923—21no—
234C22×#6923—21no—
235C22×#6923—21no—
236C22×#6923—21no—
237C22×#6923—21no—
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—21no—
245C22×#6923—21no—
246C22×#6923—21no—
247C22×#6923—21no—
248C22×#6923—21no—
249C22×#6923—21no—
250C22×#6923—21no—
251C22×#6923—21no—
252C22×#6923—21no—
253C22×#6923—21no—
254C22×#6923—21no—
255C22×#6923—21no—
256C22×#6923—21no—
257C22×#6923—21no—
258C22×#6923—21no—
259C22×#6923—21no—
260C22×#6923—21no—
261C22×#6923—21no—
262C22×#6923—21no—
263C22×#6923—21no—
264C22×#6923—21no—
265C22×#6923—21no—
266C22×#6923—21no—
267C22×#6923—21no—
268C22×#6923—21no—
269C22×#6923—44no—
270C22×#6923—44no—
271C22×#6923—44no—
272C22×#6923—44no—
273C22×#6923—44no—
274C22×#6923—44no—
275C22×#6923—44no—
276C22×#6923C2×D412yes—
277C22×#6923C2×D412yes—
278C22×#6923#4112yes—
279C22×#6923#4112yes—
280C2×D4×C61—41no—
281C2×D4×C61—41no—
282C2×D4×C61C4⋊C414yescomplemented
283C22×C4×C61—22no—
284C22×C4×C61—41no—
285C22×C4×C61—41no—
286C22×C4×C61C22×C411yescharacteristic
287C22×C4×C61C22×C411yescharacteristic
288C22×C4×C61C22×C411yescharacteristic
289C22×C4×C61C22×C411yescharacteristic
290C22×C4×C61C22×C411yescharacteristic
291C2×C22⋊D61—41no—
292C2×C22⋊D61—41no—
293C2×C22⋊D61—41no—
294C2×C22⋊D61—41no—
295C2×C22⋊D61C4⋊C414yescomplemented
296C2×C22⋊D61C4⋊C414yescomplemented
297C22×Dic61—22no—
298C22×Dic61—41no—
299C22×Dic61—41no—
300C22×Dic61C22×C411yescharacteristic
301C22×Dic61C22×C411yescharacteristic
302C22×Dic61C22×C411yescharacteristic
303C22×Dic61C22×C411yescharacteristic
304C22×Dic61C22×C411yescharacteristic
305D4×D61—44no—
306D4×D61—44no—
307D4×D61—44no—
308D4×D61—44no—
309C2×D244—41no—
310C2×D244—41no—
311C2×D244C4⋊C414yescomplemented
312C2×C4×D61—21no—
313C2×C4×D61—21no—
314C2×C4×D61—21no—
315C2×C4×D61—21no—
316C2×C4×D61—21no—
317C2×C4×D61—21no—
318C2×C4×D61—21no—
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—22no—
339C2×C4×D61—22no—
340C2×C4×D61—44no—
341C2×C4×D61—44no—
342C2×C4×D61—44no—
343C2×C4×D61—44no—
344C2×C4×D61—41no—
345C2×C4×D61—41no—
346C2×C4×D61—41no—
347C2×C4×D61—41no—
348C2×C4×D61C2×D412yes—
349C2×C4×D61C2×D412yes—
350C2×C4×D61C2×Q812yes—
351C2×C4×D61#4112yes—
352C22⋊#6923—44no—
353C22⋊#6923—44no—
354C22⋊#6923—44no—
355C22⋊#6923—44no—
356C22⋊#6923—44no—
357C22⋊#6923—44no—
358C22⋊#6923—44no—
359C4⋊#6923—44no—
360C4⋊#6923—44no—
361C4⋊#6923—44no—
362C4⋊#6923—44no—
363C4⋊#6923—44no—
364C4×#6923—44no—
365C22⋊C4×C61—22no—
366C22⋊C4×C61—41no—
367C22⋊C4×C61—41no—
368C22⋊Dic61—22no—
369C22⋊Dic61—41no—
370C22⋊Dic61—41no—
371#11758198—22no—
372#11758198—22no—
373#11758198—41no—
374#11758198—41no—
375#11758198—41no—
376#11758198—41no—
377C23×C61—21no—
378C23×C61—21no—
379C23×C61—21no—
380C23×C61—21no—
381C23×C61—21no—
382C23×C61—21no—
383C23×C61—21no—
384C23×C61—21no—
385C23×C61—21no—
386C23×C61—21no—
387C23×C61—21no—
388C23×C61—21no—
389C23×C61C2×C4⋊C412yes—
390C23×C61C2×C4⋊C412yes—
391C23×C61C23×C411yescharacteristic
392C22×D61—21no—
393C22×D61—21no—
394C22×D61—21no—
395C22×D61—21no—
396C22×D61—21no—
397C22×D61—21no—
398C22×D61—21no—
399C22×D61—21no—
400C22×D61—21no—
401C22×D61—21no—
402C22×D61—21no—
403C22×D61—21no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×D61—22no—
428C22×D61—41no—
429C22×D61—41no—
430C22×D61—41no—
431C22×D61—41no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—41no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459C22×D61—41no—
460C22×D61C2×C4⋊C412yes—
461C22×D61C2×C4⋊C412yes—
462C22×D61C22×D411yescharacteristic
463C22×D61C22×D411yescharacteristic
464C22×D61C22×Q811yescharacteristic
465C22×D61C2×#4111yescharacteristic
466C22×D61C2×#4111yescharacteristic
467C22×D61C2×#4111yescharacteristic
468C22×D61H(5,𝔽2)11yescharacteristic
469C22×D61H(5,𝔽2)11yescharacteristic
470C22×D61H(5,𝔽2)11yescharacteristic
471C22×D61H(5,𝔽2)11yescharacteristic
472C22×D61H(5,𝔽2)11yescharacteristic
473C22×D61H(5,𝔽2)11yescharacteristic
474C22×D61H(5,𝔽2)11yescharacteristic
475C22×D612−1+411yescharacteristic
476C2×#6923—22no—
477C2×#6923—22no—
478C2×#6923—22no—
479C2×#6923—22no—
480C2×#6923—22no—
481C2×#6923—22no—
482C2×#6923—22no—
483C2×#6923—22no—
484C2×#6923—22no—
485C2×#6923—22no—
486C2×#6923—22no—
487C2×#6923—22no—
488C2×#6923—416no—
489C2×#6923—41no—
490C2×#6923—41no—
491C2×#6923—41no—
492C2×#6923—41no—
493C2×#6923—41no—
494C2×#6923—41no—
495C2×#6923—41no—
496C2×#6923—41no—
497C2×#6923—41no—
498C2×#6923—41no—
499C2×#6923—41no—
500C2×#6923—41no—
501C2×#6923—41no—
502C2×#6923—41no—
503C2×#6923—41no—
504C2×#6923—41no—
505C2×#6923—41no—
506C2×#6923—41no—
507C2×#6923—41no—
508C2×#6923—41no—
509C2×#6923—41no—
510C2×#6923—41no—
511C2×#6923—41no—
512C2×#6923—41no—
513C2×#6923—41no—
514C2×#6923—41no—
515C2×#6923—41no—
516C2×#6923—41no—
517C2×#6923—41no—
518C2×#6923—41no—
519C2×#6923—41no—
520C2×#6923—41no—
521C2×#6923—41no—
522C2×#6923—41no—
523C2×#6923—41no—
524C2×#6923—41no—
525C2×#6923—41no—
526C2×#6923—41no—
527C2×#6923—41no—
528C2×#6923—41no—
529C2×#6923—41no—
530C2×#6923—41no—
531C2×#6923—41no—
532C2×#6923—41no—
533D4×C61—44no—
534C2×C4×C61—21no—
535C2×C4×C61—21no—
536C2×C4×C61—21no—
537C2×C4×C61—21no—
538C2×C4×C61—21no—
539C2×C4×C61—21no—
540C2×C4×C61—21no—
541C2×C4×C61—21no—
542C2×C4×C61—21no—
543C2×C4×C61—21no—
544C2×C4×C61—21no—
545C2×C4×C61—21no—
546C2×C4×C61—21no—
547C2×C4×C61—44no—
548C2×C4×C61C2×C4⋊C412yes—
549C2×C4×C61C4×D412yes—
550C22⋊D61—44no—
551C22⋊D61—44no—
552C2×Dic61—21no—
553C2×Dic61—21no—
554C2×Dic61—21no—
555C2×Dic61—21no—
556C2×Dic61—21no—
557C2×Dic61—21no—
558C2×Dic61—21no—
559C2×Dic61—21no—
560C2×Dic61—21no—
561C2×Dic61—21no—
562C2×Dic61—21no—
563C2×Dic61—21no—
564C2×Dic61—21no—
565C2×Dic61—44no—
566C2×Dic61C2×C4⋊C412yes—
567C2×Dic61C4×D412yes—
568D244—44no—
569C4×D61—22no—
570C4×D61—22no—
571C4×D61—22no—
572C4×D61—22no—
573C4×D61—22no—
574C4×D61—22no—
575C4×D61—22no—
576C4×D61—22no—
577C4×D61—44no—
578C4×D61—44no—
579C4×D61—41no—
580C4×D61—41no—
581C4×D61—41no—
582C4×D61—41no—
583C4×D61—41no—
584C4×D61—41no—
585C4×D61—41no—
586C4×D61—41no—
587C4×D61—41no—
588C4×D61—41no—
589C4×D61—41no—
590C4×D61—41no—
591#14407—611nomaximal, Sylow
592C22×C61—22no—
593C22×C61—22no—
594C22×C61—22no—
595C22×C61—22no—
596C22×C61—22no—
597C22×C61—22no—
598C22×C61—41no—
599C22×C61—41no—
600C22×C61—41no—
601C22×C61—41no—
602C22×C61—41no—
603C22×C61—41no—
604C22×C61—41no—
605C22×C61—41no—
606C22×C61C22×C4⋊C411yescharacteristic
607C22×C61C2×C4×D411yescharacteristic
608C22×C61C4×#4111yescharacteristic
609C22×C61#51811yescharacteristic
610C22×C61#51811yescharacteristic
611C22×C61#51811yescharacteristic
612C22×C61#52011yescharacteristic
613C2×D61—22no—
614C2×D61—22no—
615C2×D61—22no—
616C2×D61—22no—
617C2×D61—22no—
618C2×D61—22no—
619C2×D61—41no—
620C2×D61—41no—
621C2×D61—41no—
622C2×D61—41no—
623C2×D61—41no—
624C2×D61—41no—
625C2×D61—41no—
626C2×D61—41no—
627C2×D61—42no—
628C2×D61—42no—
629C2×D61—42no—
630C2×D61—42no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—42no—
634C2×D61—42no—
635C2×D61—42no—
636C2×D61—42no—
637C2×D61—42no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61#53411yescharacteristic
644C2×D61#53411yescharacteristic
645C2×D61#53411yescharacteristic
646C2×D61#53511yescharacteristic
647C2×D61#53811yescharacteristic
648C2×D61#53811yescharacteristic
649C2×D61#53811yescharacteristic
650C2×D61#53911yescharacteristic
651C2×D61#54011yescharacteristic
652C2×D61#54211yescharacteristic
653C2×D61#54311yescharacteristic
654C2×D61#54311yescharacteristic
655C2×D61D4211yescharacteristic
656C2×D61#54611yescharacteristic
657C2×D61#54611yescharacteristic
658C2×D61#54611yescharacteristic
659C2×D61#54711yescharacteristic
660C2×D61D4×Q811yescharacteristic
661C2×D61#55011yescharacteristic
662C2×D61#55311yescharacteristic
663C2×D61#55411yescharacteristic
664C2×D61#55411yescharacteristic
665C2×D61#55411yescharacteristic
666C2×D61#55511yescharacteristic
667C2×D61#56011yescharacteristic
668C2×D61#56011yescharacteristic
669C2×D61#56211yescharacteristic
670C2×D61#56211yescharacteristic
671#6923—42no—
672#6923—42no—
673#6923—42no—
674#6923—42no—
675#6923—81no—
676#6923—81no—
677#6923—81no—
678#6923—81no—
679C4×C61—22no—
680C4×C61—22no—
681C4×C61—41no—
682C4×C61—41no—
683C4×C61—41no—
684Dic61—22no—
685Dic61—22no—
686Dic61—41no—
687Dic61—41no—
688Dic61—41no—
689C2×#390—611no—
690C2×#386—611no—
691C2×#386—611no—
692C2×#385—611no—
693C2×#380—611no—
694#1444—611no—
695#1442—611no—
696#1439—611no—
697#1439—611no—
698#1439—611no—
699#1439—611no—
700#1436—611no—
701#1436—611no—
702C22⋊#95—611no—
703C22⋊#95—611no—
704C2×C61—42no—
705C2×C61—42no—
706C2×C61#231511yescharacteristic
707C2×C61#232111yescharacteristic
708C2×C61#233511yescharacteristic
709C2×C61D4×C4⋊C411yescharacteristic
710C2×C61#234911yescharacteristic
711C2×C61#236311yescharacteristic
712C2×C61#237711yescharacteristic
713D61—42no—
714D61—42no—
715D61#266811yescharacteristic
716D61#267311yescharacteristic
717D61#268611yescharacteristic
718D61#269211yescharacteristic
719D61#270811yescharacteristic
720D61#273211yescharacteristic
721D61#278011yescharacteristic
722D61#278411yescharacteristic
723C23×D4—611no—
724C24×C4—611no—
725C24×C4—611no—
726C22×C4⋊C4—611no—
727C22×C4⋊C4—611no—
728C22×C4⋊C4—611no—
729C22×C4⋊C4—611no—
730C22×C4⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4—611no—
734C22×C22⋊C4—611no—
735C22×C22⋊C4—611no—
736C22×C22⋊C4—611no—
737C22×C22⋊C4—611no—
738C22×C22⋊C4—611no—
739C22×C22⋊C4—611no—
740C22×C22⋊C4—611no—
741C22×C42—611no—
742#390—1224no—
743#386—611no—
744#386—611no—
745#386—611no—
746#386—611no—
747#386—611no—
748#386—611no—
749#386—611no—
750#386—1224no—
751#386#692311yescharacteristic, complemented
752#385—1224no—
753#380—1224no—
754C2×#95—611no—
755C2×#95—611no—
756C2×#95—611no—
757C2×#95—611no—
758C2×#95—611no—
759C2×#95—611no—
760C2×#95—611no—
761C2×#95—611no—
762C2×#95—611no—
763C2×#95—611no—
764C2×#95—611no—
765C2×#95—611no—
766C2×#95—611no—
767C2×#95—611no—
768C2×#95—611no—
769C2×#95—611no—
770C61#1440711yescharacteristic, complemented, Sylow
771C25—611no—
772C25—611no—
773C22×D4—611no—
774C22×D4—611no—
775C22×D4—614no—
776C22×D4—614no—
777C22×D4—611no—
778C22×D4—2441no—
779C22×D4—2441no—
780C22×D4—2441no—
781C22×D4—2441no—
782C22×D4C2×#692311yescharacteristic
783C23×C4—611no—
784C23×C4—611no—
785C23×C4—611no—
786C23×C4—611no—
787C23×C4—611no—
788C23×C4—611no—
789C23×C4—611no—
790C23×C4—611no—
791C23×C4—611no—
792C23×C4—611no—
793C23×C4—611no—
794C23×C4—611no—
795C23×C4—611no—
796C23×C4—611no—
797C23×C4—611no—
798C23×C4—611no—
799C23×C4—1222no—
800C23×C4—1222no—
801C23×C4—1222no—
802C23×C4—1222no—
803C23×C4—1222no—
804C23×C4—2441no—
805C23×C4—2441no—
806C23×C4—2441no—
807C23×C4—2441no—
808C23×C4—2441no—
809C23×C4—2441no—
810C23×C4—2441no—
811C23×C4—2441no—
812C23×C4C2×#692311yescharacteristic, complemented
813C2×C4⋊C4—614no—
814C2×C4⋊C4—1222no—
815C2×C4⋊C4—1222no—
816C2×C4⋊C4—1222no—
817C2×C4⋊C4—1222no—
818C2×C4⋊C4—2441no—
819C2×C4⋊C4—2441no—
820C2×C4⋊C4—2441no—
821C2×C4⋊C4—2441no—
822C2×C4⋊C4—2441no—
823C2×C4⋊C4—2441no—
824C2×C4⋊C4—2441no—
825C2×C4⋊C4—2441no—
826C2×C4⋊C4—2441no—
827C2×C4⋊C4—2441no—
828C2×C22⋊C4—611no—
829C2×C22⋊C4—611no—
830C2×C22⋊C4—611no—
831C2×C22⋊C4—611no—
832C2×C22⋊C4—611no—
833C2×C22⋊C4—611no—
834C2×C22⋊C4—611no—
835C2×C22⋊C4—611no—
836C2×C22⋊C4—611no—
837C2×C22⋊C4—1222no—
838C2×C22⋊C4—1222no—
839C2×C22⋊C4—1222no—
840C2×C22⋊C4—1222no—
841C2×C22⋊C4—1222no—
842C2×C22⋊C4—1222no—
843C2×C22⋊C4—1222no—
844C2×C22⋊C4—1222no—
845C2×C22⋊C4—1222no—
846C2×C22⋊C4—1222no—
847C2×C22⋊C4—1222no—
848C2×C22⋊C4—1222no—
849C2×C22⋊C4—1222no—
850C2×C22⋊C4—1222no—
851C2×C22⋊C4—1222no—
852C2×C22⋊C4—2441no—
853C2×C22⋊C4—2441no—
854C2×C22⋊C4—2441no—
855C2×C22⋊C4—2441no—
856C2×C22⋊C4—2441no—
857C2×C22⋊C4—2441no—
858C2×C22⋊C4—2441no—
859C2×C22⋊C4—2441no—
860C2×C22⋊C4—2441no—
861C2×C22⋊C4—2441no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4C2×#692311yescharacteristic
865C2×C22⋊C4C2×#692311yescharacteristic
866C2×C22⋊C4C2×#692311yescharacteristic, complemented
867C2×C42—1222no—
868C2×C42—2441no—
869C2×C42—2441no—
870#95—611no—
871#95—611no—
872#95—611no—
873#95—611no—
874#95—611no—
875#95—611no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—1222no—
881#95—1222no—
882#95—1222no—
883#95—1222no—
884#95—2441no—
885#95—2441no—
886#95—2441no—
887#95—2441no—
888#95—2441no—
889#95—2441no—
890#95C2×#692311yescharacteristic, complemented
891#95C2×#692311yescharacteristic, complemented
892C24—611no—
893C24—612no—
894C24—612no—
895C24—612no—
896C24—612no—
897C24—611no—
898C24—611no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24—1221no—
911C24—1221no—
912C24—1221no—
913C24—1221no—
914C24—1221no—
915C24—1221no—
916C24—1221no—
917C24—1221no—
918C24—1221no—
919C24—1221no—
920C24—1221no—
921C24—1221no—
922C24—1221no—
923C24C22×#692311yescharacteristic
924C24C22×#692311yescharacteristic
925C2×D4—41no—
926C2×D4—41no—
927C2×D4—614no—
928C2×D4—614no—
929C2×D4—614no—
930C2×D4—2441no—
931C2×D4—2441no—
932C2×D4—2444no—
933C2×D4—2444no—
934C2×D4—2444no—
935C2×D4—2444no—
936C2×D4—2441no—
937C2×D4—2441no—
938C2×D4—2441no—
939C2×D4—2441no—
940C2×D4C4⋊#692314yescomplemented
941C22×C4—22no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—612no—
947C22×C4—612no—
948C22×C4—612no—
949C22×C4—612no—
950C22×C4—612no—
951C22×C4—612no—
952C22×C4—612no—
953C22×C4—612no—
954C22×C4—611no—
955C22×C4—611no—
956C22×C4—611no—
957C22×C4—1222no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1222no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
995C22×C4—1221no—
996C22×C4—1221no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1222no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—1221no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—1221no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—2441no—
1039C22×C4—2441no—
1040C22×C4—2441no—
1041C22×C4—2441no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4—2444no—
1045C22×C4—2444no—
1046C22×C4—2441no—
1047C22×C4—2441no—
1048C22×C4—2444no—
1049C22×C4—2444no—
1050C22×C4—2444no—
1051C22×C4—2444no—
1052C22×C4—2444no—
1053C22×C4—2444no—
1054C22×C4—2444no—
1055C22×C4C22×#692311yescharacteristic
1056C22×C4C22×#692311yescharacteristic
1057C22×C4C22×#692311yescharacteristic
1058C22×C4C22×#692311yescharacteristic
1059C22×C4C22×#692311yescharacteristic
1060C4⋊C4—2444no—
1061C4⋊C4—2444no—
1062C4⋊C4—2444no—
1063C4⋊C4—2444no—
1064C4⋊C4—2444no—
1065C22⋊C4—22no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—1222no—
1069C22⋊C4—1222no—
1070C22⋊C4—1222no—
1071C22⋊C4—2441no—
1072C22⋊C4—2441no—
1073C22⋊C4—2441no—
1074C22⋊C4—2441no—
1075C22⋊C4—2441no—
1076C22⋊C4—2441no—
1077C22⋊C4—2444no—
1078C22⋊C4—2444no—
1079C22⋊C4—2444no—
1080C22⋊C4—2444no—
1081C22⋊C4—2444no—
1082C22⋊C4—2444no—
1083C22⋊C4—2444no—
1084C42—2444no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—611no—
1098C23—611no—
1099C23—611no—
1100C23—611no—
1101C23—611no—
1102C23—611no—
1103C23—611no—
1104C23—611no—
1105C23—611no—
1106C23—611no—
1107C23—611no—
1108C23—611no—
1109C23—611no—
1110C23—611no—
1111C23—612no—
1112C23—612no—
1113C23—1222no—
1114C23—1222no—
1115C23—1222no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—1222no—
1124C23—1222no—
1125C23—1222no—
1126C23—1222no—
1127C23—1222no—
1128C23—1222no—
1129C23—1222no—
1130C23—1222no—
1131C23—1222no—
1132C23—1222no—
1133C23—1222no—
1134C23—1222no—
1135C23—1222no—
1136C23—1222no—
1137C23—1221no—
1138C23—1221no—
1139C23—1221no—
1140C23—1221no—
1141C23—1221no—
1142C23—1221no—
1143C23—1221no—
1144C23—1221no—
1145C23—1221no—
1146C23—1221no—
1147C23—1221no—
1148C23—1221no—
1149C23—2441no—
1150C23—2441no—
1151C23—2441no—
1152C23—2441no—
1153C23—2441no—
1154C23—2441no—
1155C23—2441no—
1156C23—2441no—
1157C23—2441no—
1158C23—2441no—
1159C23—2441no—
1160C23—2441no—
1161C23—2441no—
1162C23—2441no—
1163C23—2441no—
1164C23—2441no—
1165C23—2441no—
1166C23—2441no—
1167C23—2441no—
1168C23—2441no—
1169C23—2441no—
1170C23—2441no—
1171C23—2441no—
1172C23—2441no—
1173C23—2441no—
1174C23—2441no—
1175C23—2441no—
1176C23—2441no—
1177C23—2441no—
1178C23—2441no—
1179C23—2441no—
1180C23—2441no—
1181C23C2×C4⋊#692312yes—
1182C23C2×C4⋊#692312yes—
1183C23C23×#692311yescharacteristic
1184D4—44no—
1185D4—2444no—
1186D4—2444no—
1187D4—2444no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—44no—
1202C2×C4—612no—
1203C2×C4—612no—
1204C2×C4—1222no—
1205C2×C4—1222no—
1206C2×C4—1222no—
1207C2×C4—1222no—
1208C2×C4—1222no—
1209C2×C4—1222no—
1210C2×C4—1222no—
1211C2×C4—1222no—
1212C2×C4—1221no—
1213C2×C4—1221no—
1214C2×C4—1221no—
1215C2×C4—1221no—
1216C2×C4—1222no—
1217C2×C4—1222no—
1218C2×C4—1222no—
1219C2×C4—1222no—
1220C2×C4—1222no—
1221C2×C4—1222no—
1222C2×C4—1222no—
1223C2×C4—1222no—
1224C2×C4—1222no—
1225C2×C4—1222no—
1226C2×C4—1222no—
1227C2×C4—1222no—
1228C2×C4—1221no—
1229C2×C4—1221no—
1230C2×C4—1221no—
1231C2×C4—1221no—
1232C2×C4—1221no—
1233C2×C4—1221no—
1234C2×C4—1221no—
1235C2×C4—1221no—
1236C2×C4—1221no—
1237C2×C4—2444no—
1238C2×C4—2444no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4—2441no—
1247C2×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2444no—
1252C2×C4—2441no—
1253C2×C4—2441no—
1254C2×C4—2441no—
1255C2×C4—2441no—
1256C2×C4—2441no—
1257C2×C4—2441no—
1258C2×C4—2441no—
1259C2×C4—2441no—
1260C2×C4—2441no—
1261C2×C4—2441no—
1262C2×C4—2441no—
1263C2×C4—2441no—
1264C2×C4—2441no—
1265C2×C4—2441no—
1266C2×C4—2441no—
1267C2×C4—2441no—
1268C2×C4—2441no—
1269C2×C4—2441no—
1270C2×C4—2441no—
1271C2×C4—2441no—
1272C2×C4—2441no—
1273C2×C4—2441no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4—2441no—
1277C2×C4—2441no—
1278C2×C4—2441no—
1279C2×C4—2441no—
1280C2×C4—2441no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4—2441no—
1286C2×C4—2441no—
1287C2×C4—2441no—
1288C2×C4—2441no—
1289C2×C4—2441no—
1290C2×C4—2441no—
1291C2×C4—2441no—
1292C2×C4—2441no—
1293C2×C4—2441no—
1294C2×C4—2441no—
1295C2×C4—2441no—
1296C2×C4—24416no—
1297C2×C4C2×C4⋊#692312yes—
1298C2×C4D4×#692312yes—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—611no—
1314C22—611no—
1315C22—611no—
1316C22—611no—
1317C22—611no—
1318C22—611no—
1319C22—611no—
1320C22—611no—
1321C22—611no—
1322C22—611no—
1323C22—611no—
1324C22—611no—
1325C22—611no—
1326C22—611no—
1327C22—611no—
1328C22—611no—
1329C22—611no—
1330C22—611no—
1331C22—611no—
1332C22—611no—
1333C22—611no—
1334C22—611no—
1335C22—611no—
1336C22—611no—
1337C22—611no—
1338C22—611no—
1339C22—611no—
1340C22—611no—
1341C22—1222no—
1342C22—1222no—
1343C22—1222no—
1344C22—1222no—
1345C22—1222no—
1346C22—1222no—
1347C22—2442no—
1348C22—2442no—
1349C22—2442no—
1350C22—2442no—
1351C22—2442no—
1352C22—2442no—
1353C22—2442no—
1354C22—2442no—
1355C22—2442no—
1356C22—2442no—
1357C22—2442no—
1358C22—2442no—
1359C22—2442no—
1360C22—2442no—
1361C22—2442no—
1362C22—2442no—
1363C22—2441no—
1364C22—2441no—
1365C22—2441no—
1366C22—2441no—
1367C22—2441no—
1368C22—2441no—
1369C22—2441no—
1370C22—2441no—
1371C22C22×C4⋊#692311yescharacteristic
1372C22C2×D4×#692311yescharacteristic
1373C22#41×#692311yescharacteristic
1374C22#1684082911yescharacteristic
1375C22#1684082911yescharacteristic
1376C22#1684082911yescharacteristic
1377C22#1684083111yescharacteristic
1378C4—22no—
1379C4—22no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—1222no—
1384C4—1222no—
1385C4—4881no—
1386C4—4881no—
1387C4—4881no—
1388C4—4881no—
1389C4—2442no—
1390C4—2442no—
1391C4—2442no—
1392C4—2442no—
1393C4—2441no—
1394C4—2441no—
1395C4—2441no—
1396C2—42no—
1397C2—42no—
1398C2—611no—
1399C2—611no—
1400C2—611no—
1401C2—611no—
1402C2—611no—
1403C2—611no—
1404C2—611no—
1405C2—611no—
1406C2—2442no—
1407C2—2442no—
1408C2#2146229811yescharacteristic
1409C2#2146230411yescharacteristic
1410C2#2146231811yescharacteristic
1411C2D4×C4⋊#692311yescharacteristic
1412C2#2146233211yescharacteristic
1413C2#2146234611yescharacteristic
1414C2#2146236011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenter#386#6923
hypocenterC61#14407
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
3. C2×#16840709C2semidirect
4. C2×#16840704C2semidirect
5. #21461007C2semidirect
6. #21461005C2semidirect
7. #21461002C2semidirect
8. #21461002C2semidirect
9. #21461002C2semidirect
10. #21461002C2semidirect
11. #21460999C2semidirect
12. #21460999C2semidirect
13. #21460993C2semidirect
14. #21460992C2semidirect
53. #16839642C4semidirect
54. #16839641C4semidirect
55. #16839640C4semidirect
56. #16839640C4semidirect
57. #16839639C4semidirect
58. #16839638C4semidirect
59. #16839638C4semidirect
62. C61×#386C4semidirect
92. C2×C4⋊#6923D4semidirect
142. C23×Dic61C2×C4semidirect
149. C22×C4×D61C2×C4semidirect
150. C22×C4×D61C2×C4semidirect
158. C2×C22⋊Dic61C2×C4semidirect
163. C2×#11758198C2×C4semidirect
164. C2×#11758198C2×C4semidirect
171. #14519684C2×C4semidirect
172. #14519684C2×C4semidirect
173. #14519684C2×C4semidirect
174. #14519684C2×C4semidirect
175. #14519684C2×C4semidirect
176. #14519684C2×C4semidirect
178. C23×C4×C61C2×C4semidirect
181. C2×C22⋊C4×C61C2×C4semidirect
182. #95×C61C2×C4semidirect
183. #95×C61C2×C4semidirect
282. C2×D4×C61C4⋊C4semidirect
295. C2×C22⋊D61C4⋊C4semidirect
296. C2×C22⋊D61C4⋊C4semidirect
311. C2×D244C4⋊C4semidirect
751. #386#6923semidirect
770. C61#14407semidirect
812. C23×C4C2×#6923semidirect
866. C2×C22⋊C4C2×#6923semidirect
890. #95C2×#6923semidirect
891. #95C2×#6923semidirect
940. C2×D4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407142
C2×#168407102
C2×#168407092
C2×#168407042
#214610072
#214610052
#214610022
#214609992
#214609932
#214609922
#386×D612
#1440761