Finite Group Databasebeta

← #29689262

Subgroups — #29689262

Order 15616.

1442 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840271C211yesmaximal, characteristic
2C2×#16839824C211yesmaximal, characteristic, complemented
3C2×#16839822C211yesmaximal, characteristic, complemented
4#21446617C211yesmaximal, characteristic, complemented
5#21446615C211yesmaximal, characteristic, complemented
6#21446615C211yesmaximal, characteristic, complemented
7#21446614C211yesmaximal, characteristic, complemented
8#21446612C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic, complemented
10#21446611C211yesmaximal, characteristic, complemented
11#21445730C211yesmaximal, characteristic, complemented
12#21445730C211yesmaximal, characteristic, complemented
13#21445728C211yesmaximal, characteristic, complemented
14#21445728C211yesmaximal, characteristic, complemented
15C61×#1955C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18#16840271—24no—
19#16840271—24no—
20C2×#14519762C411yescharacteristic
21C2×#14519759C411yescharacteristic
22C2×#14519755C411yescharacteristic
23C2×#14519754C411yescharacteristic
24C2×#14519750C411yescharacteristic
25C2×#14519749C411yescharacteristic
26C2×#14519747C411yescharacteristic
27C2×#14519745C411yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519734C2211yescharacteristic
32#16839824—24no—
33#16839822—24no—
34C2×C4⋊#92418C2211yescharacteristic, complemented
35C2×#14519706C2211yescharacteristic, complemented
36C2×#14519706C2211yescharacteristic, complemented
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic, complemented
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49C2×#14519689C2211yescharacteristic, complemented
50C2×#14519689C2211yescharacteristic, complemented
51C2×#14519689C2211yescharacteristic, complemented
52C2×#14519689C2211yescharacteristic, complemented
53C2×#14519687C2211yescharacteristic, complemented
54C2×C4×#92418C2211yescharacteristic, complemented
55C2×C8×Dic61C2211yescharacteristic, complemented
56C2×C4×D4×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic, complemented
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic, complemented
61C2×C22⋊C8×C61C2211yescharacteristic, complemented
62C2×#97×C61C2211yescharacteristic, complemented
63C24×D61C2×C411yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—41no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C22×Dic122C2×C411yescharacteristic
71C22×D244C2×C411yescharacteristic
72C22×D244C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C22×C22⋊D61C2×C411yescharacteristic
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C23×Dic61C2×C411yescharacteristic
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519762—24no—
94#14519759—24no—
95#14519755—24no—
96#14519754—24no—
97#14519750—24no—
98#14519749—24no—
99#14519747—24no—
100#14519745—24no—
101C4×D244—22no—
102C4×D244—22no—
103C4×C22⋊D61—22no—
104C4×C22⋊D61—22no—
105C4×C22⋊D61—22no—
106C4×C22⋊D61—22no—
107#14519734D414yes—
108#14519734D414yes—
109C2×C4⋊Dic61C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C4⋊#92418—22no—
124#14519706—22no—
125#14519706—22no—
126C22⋊#92418—41no—
127C22⋊#92418—41no—
128C22⋊#92418—41no—
129C22⋊#92418—41no—
130#14519689—22no—
131#14519689—22no—
132#14519689—22no—
133#14519689—22no—
134#14519689—41no—
135#14519689—41no—
136#14519689—41no—
137#14519689—41no—
138#14519689—41no—
139#14519689—41no—
140#14519689—41no—
141#14519689—41no—
142#14519687—22no—
143C4×#92418—22no—
144C8×Dic61—22no—
145C22×D4×C61C2×C411yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C22⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C42×C61C2311yescharacteristic
158C4⋊C8×C61—22no—
159C22⋊C8×C61—41no—
160C22⋊C8×C61—41no—
161C22⋊C8×C61—41no—
162C22⋊C8×C61—41no—
163#97×C61—22no—
164C24×C61C22×C411yescharacteristic
165C24×C61C22×C411yescharacteristic
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—41no—
170C23×D61—41no—
171C23×D61—41no—
172C23×D61—41no—
173C23×D61C22×C411yescharacteristic
174C23×D61C22×C411yescharacteristic
175C23×D61C22×C411yescharacteristic
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—41no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—41no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61—41no—
206C2×C22⋊D61—41no—
207C2×C22⋊D61—41no—
208C22×Dic61—22no—
209C22×Dic61—41no—
210C22×Dic61—41no—
211C22×Dic61C22×C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219#11758222—44no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—41no—
224C2×D244—41no—
225C2×D244—41no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—22no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—22no—
244C2×C4×D61—44no—
245C2×C4×D61—44no—
246C2×C4×D61—44no—
247C2×C4×D61—44no—
248C2×C4×D61—41no—
249C2×C4×D61—41no—
250C2×C4×D61—41no—
251C2×C4×D61—41no—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D412yes—
254C2×Dic122—22no—
255C2×Dic122—41no—
256C2×Dic122—41no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C4⋊C4×C61—22no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—22no—
272C42×C61C2×D412yes—
273C42×C61C2×D412yes—
274C22⋊Dic61—22no—
275C22⋊Dic61—22no—
276#11758198—22no—
277#11758198—22no—
278#11758198—22no—
279#11758198—22no—
280#11758198C22⋊C414yes—
281#11758198C22⋊C414yes—
282C4⋊Dic61—22no—
283#11758196—22no—
284#11758196—22no—
285#11758196C22⋊C414yes—
286#11758196C22⋊C414yes—
287C4×Dic61C2×D412yes—
288C4×Dic61C2×D412yes—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61#13112yes—
315C23×C61C23×C411yescharacteristic
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—44no—
336C22×D61—44no—
337C22×D61—44no—
338C22×D61—44no—
339C22×D61—44no—
340C22×D61—44no—
341C22×D61—44no—
342C22×D61C2×C22⋊C412yes—
343C22×D61#13112yes—
344D4×C61—44no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61C2×C22⋊C412yes—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C2×C4×C61H(5,𝔽2)11yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C22⋊D61—44no—
372C22⋊D61—44no—
373C22⋊D61—44no—
374C22⋊D61—44no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—44no—
388C2×Dic61C2×C22⋊C412yes—
389C2×Dic61C2×C22⋊C412yes—
390C2×Dic61C2×C22⋊C412yes—
391D244—44no—
392D244—44no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—44no—
398C4×D61—44no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407Dic122—44no—
408C8×C61—41no—
409C8×C61—41no—
410C8×C61—41no—
411C8×C61—41no—
412#92418—41no—
413#92418—41no—
414#92418—41no—
415#92418—41no—
416#21792—611nomaximal, Sylow
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61C22×C22⋊C411yescharacteristic
432C22×C61#51811yescharacteristic
433C22×C61#51811yescharacteristic
434C22×C61C2×#13111yescharacteristic
435C22×C61C2×#13111yescharacteristic
436C22×C61#56811yescharacteristic
437C22×C61#56811yescharacteristic
438C2×D61—22no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—416no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C4×C61—22no—
461C4×C61—22no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61#53511yescharacteristic
465C4×C61#53511yescharacteristic
466C4×C61#53511yescharacteristic
467C4×C61#53511yescharacteristic
468Dic61—22no—
469Dic61—22no—
470Dic61—22no—
471Dic61—41no—
472Dic61—41no—
473C2×#525—611no—
474C2×#433—611no—
475C2×#433—611no—
476#1955—611no—
477#1955—611no—
478#1955—611no—
479#1955D6111yescharacteristic, complemented
480#1954—611no—
481#1954—611no—
482#1954—611no—
483#1954—611no—
484#1780—611no—
485#1780—611no—
486#1779—611no—
487#1779—611no—
488C2×C61—42no—
489C2×C61—81no—
490C2×C61#230911yescharacteristic
491C2×C61#288011yescharacteristic
492C2×C61#288011yescharacteristic
493C2×C61#297611yescharacteristic
494C2×C61#297611yescharacteristic
495C2×C61#297711yescharacteristic
496C2×C61#297811yescharacteristic
497D61—42no—
498D61—42no—
499D61—81no—
500C22×#41—611no—
501C24×C4—611no—
502#525—1224no—
503#525—1224no—
504C2×#123—611no—
505C2×#123—611no—
506C2×C22⋊Q8—611no—
507C2×C22⋊Q8—611no—
508C2×#121—611no—
509C2×#121—611no—
510C2×#120—611no—
511C2×#120—611no—
512C2×C4×D4—611no—
513C2×C4×D4—611no—
514C2×C4×D4—611no—
515C2×C4×D4C2×D6111yescharacteristic
516C2×#117—611no—
517#433—1224no—
518#433—1224no—
519C2×C4⋊C8—611no—
520C2×C4⋊C8—611no—
521C2×C4⋊C8—611no—
522C2×C4⋊C8C2×D6111yescharacteristic, complemented
523C2×C22⋊C8—611no—
524C2×C22⋊C8—611no—
525C2×C22⋊C8—611no—
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
537C2×C22⋊C8—611no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8C2×D6111yescharacteristic
540C2×C22⋊C8C2×D6111yescharacteristic
541C2×C22⋊C8C2×D6111yescharacteristic, complemented
542C2×C22⋊C8C2×D6111yescharacteristic, complemented
543C2×#97—611no—
544C2×#97C2×D6111yescharacteristic, complemented
545C2×C4×C8—611no—
546C2×C4×C8—611no—
547C61#2179211yescharacteristic, complemented, Sylow
548C25—611no—
549C2×#41—1222no—
550C2×#41—1222no—
551C2×#41—2441no—
552C2×#41—2441no—
553C2×#41—2441no—
554C2×#41—2441no—
555C22×Q8—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4—611no—
560C22×D4—611no—
561C22×D4—611no—
562C22×D4C4×D6111yescharacteristic
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—1222no—
570C23×C4—1222no—
571C23×C4—2441no—
572C23×C4—2441no—
573C23×C4—2441no—
574C23×C4—2441no—
575C23×C4C22×D6111yescharacteristic
576C23×C4C22×D6111yescharacteristic
577C22×C8—611no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6111yescharacteristic
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585#123—1224no—
586#123—1224no—
587C22⋊Q8—1224no—
588C22⋊Q8—1224no—
589#121—1224no—
590#121—1224no—
591#120—1224no—
592#120—1224no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—1222no—
596C4×D4—1222no—
597C4×D4—1222no—
598C4×D4—1222no—
599C4×D4—1222no—
600C4×D4—1222no—
601#117—614no—
602#117—614no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4C4×D6111yescharacteristic
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—611no—
613C2×C22⋊C4—611no—
614C2×C22⋊C4—611no—
615C2×C22⋊C4—611no—
616C2×C22⋊C4—611no—
617C2×C22⋊C4C4×D6111yescharacteristic
618C2×C22⋊C4C4×D6111yescharacteristic
619C2×C42—611no—
620C2×C42C22×D6111yescharacteristic
621C4⋊C8—22no—
622C4⋊C8—1222no—
623C4⋊C8—1222no—
624C4⋊C8—1222no—
625C22⋊C8—41no—
626C22⋊C8—41no—
627C22⋊C8—41no—
628C22⋊C8—41no—
629C22⋊C8—1222no—
630C22⋊C8—1222no—
631C22⋊C8—1222no—
632C22⋊C8—1222no—
633C22⋊C8—2441no—
634C22⋊C8—2441no—
635C22⋊C8—2441no—
636C22⋊C8—2441no—
637C22⋊C8—2441no—
638C22⋊C8—2441no—
639C22⋊C8—2441no—
640C22⋊C8—2441no—
641C22⋊C8—2441no—
642C22⋊C8—2441no—
643C22⋊C8—2441no—
644C22⋊C8—2441no—
645#97—22no—
646#97—1222no—
647C4×C8—1222no—
648C4×C8—1222no—
649C24—611no—
650C24—611no—
651C24—611no—
652C24—1222no—
653C24—1222no—
654C24—1222no—
655C24—2441no—
656C24—2441no—
657C24—2441no—
658C24—2441no—
659C24C2×C4×D6111yescharacteristic
660C24C2×C4×D6111yescharacteristic
661#41—2444no—
662#41—2444no—
663#41—2444no—
664#41—2444no—
665C2×Q8—1222no—
666C2×Q8—2441no—
667C2×Q8—2441no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—41no—
671C2×D4—1222no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—1222no—
680C2×D4—2441no—
681C2×D4—2441no—
682C2×D4—2441no—
683C2×D4—2441no—
684C2×D4—2441no—
685C2×D4—2441no—
686C2×D4—2441no—
687C2×D4—2441no—
688C2×D4—2441no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—2441no—
728C22×C4—2441no—
729C22×C4—2441no—
730C22×C4—2441no—
731C22×C4—2444no—
732C22×C4—2444no—
733C22×C4—2444no—
734C22×C4—2444no—
735C22×C4—2441no—
736C22×C4—2441no—
737C22×C4C2×C4×D6111yescharacteristic
738C22×C4C2×C4×D6111yescharacteristic
739C22×C4C2×C4×D6111yescharacteristic
740C22×C4C2×C4×D6111yescharacteristic
741C22×C4C23×D6111yescharacteristic
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C4⋊C4—22no—
767C4⋊C4—614no—
768C4⋊C4—614no—
769C4⋊C4—1222no—
770C4⋊C4—1222no—
771C4⋊C4—1222no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—614no—
775C22⋊C4—614no—
776C22⋊C4—1222no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C42—612no—
783C42—612no—
784C42D4×D6112yes—
785C42D4×D6112yes—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—612no—
800C23—612no—
801C23—1221no—
802C23—1221no—
803C23—1221no—
804C23—1221no—
805C23—1221no—
806C23—1221no—
807C23—1221no—
808C23—1221no—
809C23—1221no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—2444no—
821C23—2444no—
822C23—2444no—
823C23—2444no—
824C23—2444no—
825C23—2444no—
826C23—2444no—
827C23#1451978512yes—
828C23C22×C4×D6111yescharacteristic
829Q8—2444no—
830D4—44no—
831D4—2444no—
832D4—2444no—
833D4—2444no—
834D4—2444no—
835D4—2444no—
836D4—2444no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—2444no—
875C2×C4—2444no—
876C2×C4—2444no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4C22⋊C4×D6112yes—
886C2×C4C22⋊C4×D6112yes—
887C2×C4C2×D4×D6111yescharacteristic
888C2×C4C2×D4×D6111yescharacteristic
889C2×C4#1451982211yescharacteristic
890C2×C4#1451982211yescharacteristic
891C2×C4#1451982311yescharacteristic
892C2×C4#1451982311yescharacteristic
893C8—41no—
894C8—41no—
895C8—41no—
896C8—41no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C8—2441no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—1222no—
916C22—1222no—
917C22—1222no—
918C22—1222no—
919C22—1222no—
920C22—1222no—
921C22—24416no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22—2441no—
926C22—2441no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22—2441no—
931C22—2441no—
932C22—2441no—
933C22—2441no—
934C22—2441no—
935C22—2441no—
936C22—2441no—
937C22C2×C22⋊C4×D6111yescharacteristic
938C22#1684023411yescharacteristic
939C22#1684023411yescharacteristic
940C22#131×D6111yescharacteristic
941C22C2×#1451978511yescharacteristic
942C22#1684052711yescharacteristic
943C22#1684052811yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—41no—
948C4—1222no—
949C4—1222no—
950C4—1222no—
951C4—2441no—
952C4—2441no—
953C4#1684032511yescharacteristic
954C4#1684032811yescharacteristic
955C4#1684032811yescharacteristic
956C4#1684033011yescharacteristic
957C2—42no—
958C2—81no—
959C2—4881no—
960C2—2442no—
961C2—2442no—
962C2#2144839811yescharacteristic
963C2#2145426711yescharacteristic
964C2#2145426911yescharacteristic
965C2#2145486611yescharacteristic
966C2#2145486811yescharacteristic
967C2#2145487011yescharacteristic
968C2#2145487811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1955C2
prime radicalC2×#16840271C2
cosocleC22×C4×C61C24
hypercenter#1955D61
hypocenterC61#21792
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#16839824C2semidirect
3. C2×#16839822C2semidirect
4. #21446617C2semidirect
5. #21446615C2semidirect
6. #21446615C2semidirect
7. #21446614C2semidirect
8. #21446612C2semidirect
9. #21446611C2semidirect
10. #21446611C2semidirect
11. #21445730C2semidirect
12. #21445730C2semidirect
13. #21445728C2semidirect
14. #21445728C2semidirect
15. C61×#1955C2semidirect
34. C2×C4⋊#92418C22semidirect
35. C2×#14519706C22semidirect
36. C2×#14519706C22semidirect
39. C2×C22⋊#92418C22semidirect
40. C2×C22⋊#92418C22semidirect
49. C2×#14519689C22semidirect
50. C2×#14519689C22semidirect
51. C2×#14519689C22semidirect
52. C2×#14519689C22semidirect
53. C2×#14519687C22semidirect
54. C2×C4×#92418C22semidirect
55. C2×C8×Dic61C22semidirect
57. C2×C4⋊C8×C61C22semidirect
60. C2×C22⋊C8×C61C22semidirect
61. C2×C22⋊C8×C61C22semidirect
62. C2×#97×C61C22semidirect
479. #1955D61semidirect
522. C2×C4⋊C8C2×D61semidirect
541. C2×C22⋊C8C2×D61semidirect
542. C2×C22⋊C8C2×D61semidirect
544. C2×#97C2×D61semidirect
547. C61#21792semidirect

Maximal subgroups

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

subgroupindex
C2×#168402712
C2×#168398242
C2×#168398222
#214466172
#214466152
#214466142
#214466122
#214466112
#214457302
#214457282
C61×#19552
#2179261