Finite Group Databasebeta

← #29717675

Subgroups — #29717675

Order 15616.

1464 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840419C211yesmaximal, characteristic
2C2×#16839988C211yesmaximal, characteristic, complemented
3C2×#16839916C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21449266C211yesmaximal, characteristic, complemented
6#21447059C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21446911C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446108C211yesmaximal, characteristic, complemented
13#21446089C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#452C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840419—24no—
20#16840419—24no—
21C2×#14519764—21no—
22C2×#14519764C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519753C2211yescharacteristic
26C2×#14519748—21no—
27C2×#14519748C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×C22⋊D61—21no—
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839988—24no—
33#16839916—24no—
34C2×#14519709C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41#103×D61—24no—
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46#16839693—21no—
47#16839685—21no—
48#16839669C2211yescharacteristic
49#16839661C2211yescharacteristic
50#16839638—21no—
51#16839622C2211yescharacteristic
52#16839619—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C22×Q16×C61C2211yescharacteristic
59C22×SD16×C61C2211yescharacteristic
60C2×C22⋊Q8×C61C2211yescharacteristic
61C61×#452—24no—
62C2×#103×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×C22⋊C8×C61C2211yescharacteristic
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—41no—
71C2×Q8×D61—41no—
72C2×Q8×D61D414yes—
73C22×C22⋊D61—21no—
74C22×C22⋊D61D411yescharacteristic
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758202—22no—
79C2×#11758202—41no—
80C2×#11758202—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—41no—
86#14519764—28no—
87#14519764—22no—
88#14519764—22no—
89#14519756—28no—
90#14519756—22no—
91#14519756—22no—
92#14519753—22no—
93#14519753—22no—
94#14519748—28no—
95#14519748—22no—
96#14519748D414yes—
97Q8×Dic61—22no—
98Q8×Dic61—22no—
99C4×C22⋊D61—28no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196D411yescharacteristic
111C4⋊C4×D61—22no—
112C4⋊C4×D61—41no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61D411yescharacteristic
119C2×#11758198—21no—
120C2×#11758198D411yescharacteristic
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519709—22no—
124#14519702—22no—
125#14519702—22no—
126#14519701—22no—
127#14519701—22no—
128#14519701—22no—
129#14519700—22no—
130#14519698—22no—
131#14519698—41no—
132C22⋊#92418—41no—
133#14519689—22no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—22no—
141C2×#41×C61—22no—
142C2×#41×C61—41no—
143C2×#41×C61—41no—
144C22×Q8×C61C2311yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C22×D4×C61—21no—
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61—21no—
149C23×C4×C61C2311yescharacteristic
150C2×Q16×C61—22no—
151C2×Q16×C61—22no—
152C2×Q16×C61—22no—
153C2×SD16×C61—22no—
154C2×SD16×C61—22no—
155C2×SD16×C61—41no—
156C22×C8×C61C2311yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C22⋊Q8×C61—22no—
159C22⋊Q8×C61—41no—
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C22⋊C4×C61—21no—
163#103×C61D414yescomplemented
164#102×C61—22no—
165C22⋊C8×C61—22no—
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168C23×D61C2×D411yescharacteristic
169#41×C61—44no—
170#41×C61—44no—
171#41×C61—44no—
172#41×C61—44no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61C2×D412yes—
183C2×Q8×C61C2×D412yes—
184C2×Q8×C61#4112yes—
185C2×D4×C61—24no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61C2×D412yes—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—42no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221Q8×D61—28no—
222Q8×D61—44no—
223Q8×D61—44no—
224Q8×D61—44no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—24no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—81no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2×D412yes—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—24no—
243C2×Dic122—42no—
244C2×Dic122—42no—
245C2×Dic122C2×D412yes—
246Q16×C61—44no—
247SD16×C61—44no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61C2×D412yes—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—42no—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—42no—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262C22⋊Dic61—22no—
263C22⋊Dic61—81no—
264#11758202—44no—
265#11758198—22no—
266#11758198—42no—
267C4⋊Dic61—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—81no—
274C4⋊Dic61C2×D412yes—
275#11758196—24no—
276#11758196—22no—
277#11758196—42no—
278#11758196—42no—
279C4×Dic61—24no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C8×D61—44no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61C22×D411yescharacteristic
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61#12012yes—
309C22×D61#13512yes—
310C22×D61#13712yes—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—41no—
315Q8×C61—41no—
316Q8×C61—41no—
317Q8×C61—41no—
318Q8×C61#12114yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—48no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—48no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C22⋊D61—44no—
348C22⋊D61—48no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61#12012yes—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—48no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—48no—
379Dic122—41no—
380Dic122—41no—
381C8×C61—22no—
382C8×C61—41no—
383#92418—41no—
384#92418—41no—
385#24431—611nomaximal, Sylow
386C22×C61—42no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—42no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61C2×#12011yescharacteristic
401C22×C61D4211yescharacteristic
402C22×C61#54611yescharacteristic
403C22×C61C2×#13511yescharacteristic
404C22×C61C2×#13711yescharacteristic
405C22×C61#57711yescharacteristic
406C22×C61#57811yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61#45214yescomplemented
414C4×C61—24no—
415C4×C61—41no—
416C4×C61—42no—
417C4×C61—81no—
418C4×C61C2×#12111yescharacteristic
419C4×C61#53411yescharacteristic
420C4×C61D4211yescharacteristic
421C4×C61#54611yescharacteristic
422Dic61—22no—
423Dic61—42no—
424Dic61—41no—
425Dic61—42no—
426Dic61—41no—
427Dic61—81no—
428Dic61—81no—
429C2×#548—611no—
430C2×#465—611no—
431C2×#452D6111yescharacteristic, complemented
432C2×#451—611no—
433C22×#103—611no—
434#2417—611no—
435#2042—611no—
436#2035—611no—
437#2015—611no—
438#2001—611no—
439#1878—611no—
440#1874—611no—
441#1869—611no—
442#1865—611no—
443#1788—611no—
444C2×C61—81no—
445C2×C61—82no—
446C2×C61#241011yescharacteristic
447C2×C61C2×#45211yescharacteristic
448C2×C61#301311yescharacteristic
449C2×C61#327011yescharacteristic
450C2×C61#328211yescharacteristic
451C2×C61#330011yescharacteristic
452C2×C61#331611yescharacteristic
453D61—24no—
454C22×#41C2×D6111yescharacteristic
455C23×Q8—611no—
456C22×Q16—611no—
457C22×Q16C2×D6111yescharacteristic
458C22×SD16C2×D6111yescharacteristic
459C23×C8—611no—
460#548—1224no—
461#548—1224no—
462C2×#124—611no—
463C2×#124—1221no—
464C2×C22⋊Q8—611no—
465C2×C22⋊Q8—611no—
466C2×C22⋊Q8—1221no—
467C2×C22⋊Q8C2×D6111yescharacteristic
468C2×#121—611no—
469C2×#121—1221no—
470C2×C4×Q8—611no—
471C2×C4×D4—611no—
472C2×C4×D4—1221no—
473C22×C4⋊C4—611no—
474#465—1224no—
475#452—24no—
476#451—1224no—
477C2×#106—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—1224no—
485C2×#103C2×D6111yescharacteristic
486C2×#102—611no—
487C2×#102—611no—
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8C2×D6111yescharacteristic
492#398—1221no—
493#396—1221no—
494#391—611no—
495#389—611no—
496#386—1221no—
497#380—611no—
498#380—1221no—
499#340—611no—
500#340—611no—
501#336—611no—
502#336—611no—
503C61#2443111yescharacteristic, complemented, Sylow
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8—614no—
511C22×Q8—611no—
512C22×Q8—1221no—
513C22×Q8—1222no—
514C22×Q8—1222no—
515C22×Q8—1222no—
516C22×Q8—2441no—
517C22×Q8—2441no—
518C22×Q8C22×D6111yescharacteristic
519C22×Q8C22×D6111yescharacteristic
520C22×D4—21no—
521C22×D4—611no—
522C22×D4—1221no—
523C22×D4C22×D6111yescharacteristic
524C23×C4—21no—
525C23×C4—611no—
526C23×C4—1221no—
527C23×C4—1221no—
528C23×C4C22×D6111yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—1222no—
533C2×Q16—2441no—
534C2×Q16—2441no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—1222no—
541C22×C8—1222no—
542C22×C8—2441no—
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—1222no—
546#124—1228no—
547#124—1222no—
548C22⋊Q8—22no—
549C22⋊Q8—41no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C22⋊Q8—1228no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555#121—614no—
556#121—1222no—
557#121—1228no—
558C4×Q8—1222no—
559C4×Q8—1222no—
560C4×D4—1222no—
561C4×D4—1222no—
562C4×D4—1228no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—2441no—
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C22⋊C4—21no—
577C2×C22⋊C4—611no—
578C2×C22⋊C4—611no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C42—611no—
586C2×C42—1221no—
587#106—1222no—
588#103—1222no—
589#103—1222no—
590#103—1222no—
591#103—1222no—
592#103—1222no—
593#103—1222no—
594#103C22⋊D6114yescomplemented
595#102—22no—
596#102—1222no—
597#102—2441no—
598C22⋊C8—22no—
599C22⋊C8—1222no—
600C22⋊C8—2441no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—611no—
607C24D4×D6111yescharacteristic
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—612no—
622C2×Q8—1224no—
623C2×Q8—1221no—
624C2×Q8—1228no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8—2442no—
630C2×Q8—2442no—
631C2×Q8—2444no—
632C2×Q8—2444no—
633C2×Q8—2444no—
634C2×Q8D4×D6112yes—
635C2×Q8#1175822412yes—
636C2×Q8C2×C22⋊D6112yes—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—1224no—
646C2×D4—1222no—
647C2×D4—1222no—
648C2×D4—1222no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4D4×D6112yes—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—4881no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4D4×D6111yescharacteristic
684C22×C4C23×D6111yescharacteristic
685Q16—44no—
686Q16—2444no—
687SD16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—2444no—
700C2×C8C2×C22⋊D6112yes—
701C4⋊C4—21no—
702C4⋊C4—42no—
703C4⋊C4—612no—
704C4⋊C4—1222no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—4881no—
713C4⋊C4—2442no—
714C4⋊C4—2442no—
715C4⋊C4C2×C22⋊D6112yes—
716C22⋊C4—42no—
717C22⋊C4—1222no—
718C22⋊C4—1222no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—4881no—
724C22⋊C4—2442no—
725C42—1224no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—612no—
743C23—612no—
744C23—612no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23C2×D4×D6111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—1222no—
758Q8—1222no—
759Q8—2448no—
760Q8—2441no—
761Q8—2441no—
762Q8#1451974814yes—
763D4—22no—
764D4—22no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—2444no—
769D4—2448no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—612no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1221no—
795C2×C4—1222no—
796C2×C4—1221no—
797C2×C4—1222no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—4884no—
803C2×C4—2448no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4C2×D4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C22×C22⋊D6111yescharacteristic
817C2×C4C2×#1175822411yescharacteristic
818C2×C4#1451982211yescharacteristic
819C2×C4#1451982211yescharacteristic
820C8—22no—
821C8—41no—
822C8—2441no—
823C8—2441no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—614no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22#120×D6111yescharacteristic
846C22D4×C22⋊D6111yescharacteristic
847C22#1684039911yescharacteristic
848C22#135×D6111yescharacteristic
849C22#137×D6111yescharacteristic
850C22#1684056911yescharacteristic
851C22#1684057811yescharacteristic
852C4—24no—
853C4—42no—
854C4—41no—
855C4—81no—
856C4—1222no—
857C4—4881no—
858C4—4881no—
859C4—2441no—
860C4—2441no—
861C4—2442no—
862C4—2442no—
863C4C2×#1451974811yescharacteristic
864C4#1684032211yescharacteristic
865C4D4×C22⋊D6111yescharacteristic
866C4#1684039911yescharacteristic
867C2—81no—
868C2—82no—
869C2—1224no—
870C2#2144918911yescharacteristic
871C2#452×D6111yescharacteristic
872C2#2145513811yescharacteristic
873C2#2145738311yescharacteristic
874C2#2145752011yescharacteristic
875C2#2145769911yescharacteristic
876C2#2145792311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
hypercenterC2×#452D61
hypocenterC61#24431
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#16839988C2semidirect
3. C2×#16839916C2semidirect
4. C2×#103×D61C2semidirect
5. #21449266C2semidirect
6. #21447059C2semidirect
7. #21447016C2semidirect
8. #21446911C2semidirect
9. #21446827C2semidirect
10. #21446162C2semidirect
11. #21446133C2semidirect
12. #21446108C2semidirect
13. #21446089C2semidirect
14. #21445759C2semidirect
15. C2×C61×#452C2semidirect
163. #103×C61D4semidirect
413. C2×D61#452semidirect
431. C2×#452D61semidirect
503. C61#24431semidirect
594. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404192
C2×#168399882
C2×#168399162
C2×#103×D612
#214492662
#214470592
#214470162
#214469112
#214468272
#214461622
#214461332
#214461082
#214460892
#214457592
C2×C61×#4522
#2443161