Finite Group Databasebeta

← #29695432

Subgroups — #29695432

Order 15616.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16839759C211yesmaximal, characteristic, complemented
3C22×#14519699C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446630C211yesmaximal, characteristic, complemented
7#21446247C211yesmaximal, characteristic, complemented
8#21446242C211yesmaximal, characteristic, complemented
9#21446139C211yesmaximal, characteristic, complemented
10#21446124C211yesmaximal, characteristic, complemented
11#21445830C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C2×C8×D4×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18#16840408—24no—
19#16840408C418yescomplemented
20C2×#14519765C2211yescharacteristic
21C2×#14519762—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519745—21no—
26C2×C4×D244C2211yescharacteristic
27C2×#14519736C2211yescharacteristic, complemented
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30#16839759—24no—
31C2×#14519702C2211yescharacteristic, complemented
32C2×#14519702C2211yescharacteristic, complemented
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519702C2211yescharacteristic, complemented
35C2×#14519699—24no—
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44#16839655—21no—
45#16839648—21no—
46#16839642—21no—
47#16839628C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic
49#16839622C2211yescharacteristic, complemented
50C4×C4⋊Dic61C2211yescharacteristic, complemented
51C22⋊C4×Dic61—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839525C2211yescharacteristic, complemented
56C23×C8×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic, complemented
58C2×C4×D4×C61C2211yescharacteristic
59C8×D4×C61—24no—
60C2×C4⋊C8×C61C2211yescharacteristic, complemented
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C2×C4×C8×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yescomplemented
71C22×Dic122C2311yescharacteristic
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244C2×C414yes—
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86#14519765—22no—
87#14519765C2×C414yescomplemented
88#14519762—28no—
89#14519756—22no—
90#14519756C2×C414yes—
91#14519751—22no—
92#14519751C2×C414yescomplemented
93#14519750—28no—
94#14519745—28no—
95C4×D244—22no—
96C4×D244C2×C414yescomplemented
97#14519736—22no—
98#14519736—41no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—41no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C22⋊C4×D61—28no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119#14519702—22no—
120#14519702—22no—
121#14519702—41no—
122#14519702—41no—
123#14519699—22no—
124#14519699—22no—
125#14519699—22no—
126#14519699—22no—
127#14519699—22no—
128#14519699—41no—
129#14519699—41no—
130#14519699D414yescomplemented
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C22×C8×C61—22no—
140C22×C8×C61—22no—
141C22×C8×C61—22no—
142C22×C8×C61—22no—
143C22×C8×C61—41no—
144C22×C8×C61—41no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C4×D4×C61C2×C414yes—
150C4×D4×C61D414yes—
151C2×C4⋊C4×C61D411yescharacteristic
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C42×C61C2311yescharacteristic
155C4⋊C8×C61—22no—
156C22⋊C8×C61—22no—
157C22⋊C8×C61—22no—
158C4×C8×C61—22no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61C22⋊C414yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61C22×C412yes—
182C22×C4×C61C22×C412yes—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61—81no—
205#11758222—28no—
206#11758222—44no—
207#11758222—44no—
208#11758222—44no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—28no—
217C2×D244—24no—
218C2×D244—21no—
219C2×D244—44no—
220C2×D244—44no—
221C2×D244—44no—
222C2×D244—42no—
223C2×D244—42no—
224C2×D244C22×C412yes—
225C2×D244C22×C412yes—
226C2×D244C2×D412yes—
227C2×D244#4112yes—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—81no—
233C2×C4×D61—81no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—44no—
252C2×C8×C61—44no—
253C2×C8×C61C2×D412yes—
254C4⋊C4×C61C22⋊C414yes—
255C22⋊C4×C61C22⋊C414yes—
256C22⋊C4×C61C22⋊C414yes—
257C42×C61C22×C412yes—
258C42×C61C2×D412yes—
259C22⋊Dic61—24no—
260C22⋊Dic61—42no—
261C22⋊Dic61—42no—
262C22⋊Dic61—81no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—42no—
276C4⋊Dic61C22×C412yes—
277C4⋊Dic61C2×D412yes—
278#11758196—24no—
279C4×Dic61—42no—
280C4×Dic61—81no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61C2×C22⋊C412yes—
292C23×C61C2×C22⋊C412yes—
293C23×C61#13512yes—
294C23×C61#13512yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—48no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—48no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317D4×C61—28no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61C2×C22⋊C412yes—
335C2×C4×C61C2×C22⋊C412yes—
336C2×C4×C61C2×C22⋊C412yes—
337C2×C4×C61C2×C22⋊C412yes—
338C2×C4×C61C23×C411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C22⋊D61—48no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—84no—
365D244—22no—
366D244—22no—
367D244—22no—
368D244—22no—
369D244—22no—
370D244—48no—
371D244—41no—
372D244—41no—
373D244C4×D414yes—
374C4×D61—48no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—22no—
381C8×C61—41no—
382C8×C61—41no—
383C8×C61—41no—
384#22414—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61#41614yescomplemented
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61D4211yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61C2×#13511yescharacteristic
403C22×C61C2×#13511yescharacteristic
404C22×C61#57611yescharacteristic
405C22×C61#57711yescharacteristic
406C2×D61—24no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—816no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—22no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61#51811yescharacteristic
427C4×C61D4211yescharacteristic
428C4×C61#54611yescharacteristic
429Dic61—42no—
430Dic61—42no—
431Dic61—42no—
432Dic61—81no—
433Dic61—81no—
434Dic61—81no—
435C2×#546—611no—
436C2×C8×D4D6111yescharacteristic, complemented
437C2×#416—611no—
438C22×#102—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1893—611no—
443#1892—611no—
444#1875—611no—
445#1872—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—24no—
451C2×C61—42no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61C2×#41611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#328011yescharacteristic
456C2×C61#328211yescharacteristic
457C2×C61#329611yescharacteristic
458C2×C61#329711yescharacteristic
459D61—44no—
460D61—82no—
461C22×#41—611no—
462C23×D4—611no—
463C23×C8C2×D6111yescharacteristic
464C23×C8C2×D6111yescharacteristic, complemented
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4C2×D6111yescharacteristic
475C2×#117—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478C8×D4—24no—
479C2×C4⋊C8C2×D6111yescharacteristic, complemented
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—1224no—
494C2×C22⋊C8C2×D6111yescharacteristic
495C2×C22⋊C8C2×D6111yescharacteristic, complemented
496C2×C4×C8C2×D6111yescharacteristic, complemented
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380—611no—
503C4×C4⋊C4—611no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509C61#2241411yescharacteristic, complemented, Sylow
510C25—1221no—
511C2×#41—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—614no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—1222no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1222no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4D24411yescharacteristic
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4C22×D6111yescharacteristic
534C23×C4C22×D6111yescharacteristic
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6111yescharacteristic
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
550#121—614no—
551#121—1222no—
552#121—1228no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—1222no—
556C4×D4C4×D6114yes—
557C4×D4C22⋊D6114yes—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1222no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—2441no—
569C2×C4⋊C4D24411yescharacteristic
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1228no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4D24411yescharacteristic
580C2×C22⋊C4D24411yescharacteristic
581C2×C42—1221no—
582C2×C42—1221no—
583C2×C42C22×D6111yescharacteristic
584C4⋊C8—22no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—614no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—1221no—
606C24—1224no—
607C24—1221no—
608C24—4881no—
609C24—4881no—
610C24—2442no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24C2×D24411yescharacteristic
615C24C2×D24411yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—612no—
631C2×D4—612no—
632C2×D4—1228no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1224no—
644C2×D4—4881no—
645C2×D4—4881no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4—2444no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4#1175819814yes—
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—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—4881no—
671C22×C4—4881no—
672C22×C4—4881no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4C2×C4×D6112yes—
678C22×C4C2×C4×D6112yes—
679C22×C4C2×D24411yescharacteristic
680C22×C4C2×D24411yescharacteristic
681C22×C4C2×D24411yescharacteristic
682C22×C4C2×D24411yescharacteristic
683C22×C4C2×C22⋊D6112yes—
684C22×C4C2×C22⋊D6112yes—
685C22×C4C23×D6111yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—44no—
698C2×C8—44no—
699C2×C8D4×D6112yes—
700C4⋊C4—612no—
701C4⋊C4—612no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1224no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—2442no—
712C4⋊C4#1175819814yes—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C22⋊C4#1175819814yes—
722C22⋊C4#1175819814yes—
723C42—4881no—
724C42—2442no—
725C42C2×C4×D6112yes—
726C42C2×C22⋊D6112yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—1222no—
741C23—4884no—
742C23—4884no—
743C23—4884no—
744C23—4884no—
745C23—4884no—
746C23—2448no—
747C23—2448no—
748C23—2441no—
749C23—2441no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23C2×#1175819812yes—
759C23C2×#1175819812yes—
760C23#1451979912yes—
761C23#1451979912yes—
762C23C22×D24411yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—28no—
768D4—614no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—1222no—
774D4—4884no—
775D4—2448no—
776D4—2448no—
777D4—2441no—
778D4—2441no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—4884no—
799C2×C4—4884no—
800C2×C4—2448no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
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×C4—2441no—
815C2×C4—2441no—
816C2×C4C2×#1175819812yes—
817C2×C4C2×#1175819812yes—
818C2×C4C2×#1175819812yes—
819C2×C4C2×#1175819812yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C22×C22⋊D6111yescharacteristic
823C2×C4#41×D6111yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982311yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—1224no—
844C22—48816no—
845C22—4881no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2442no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22#1683975914yescomplemented
859C22C22×#1175819811yescharacteristic
860C22D4×D24411yescharacteristic
861C22#1684040711yescharacteristic
862C22C2×#1451979911yescharacteristic
863C22C2×#1451979911yescharacteristic
864C22#1684056711yescharacteristic
865C22#1684057411yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—4881no—
871C4—4881no—
872C4—4881no—
873C4—2442no—
874C4—2442no—
875C4—2442no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4D4×C22⋊D6111yescharacteristic
879C4#1684040011yescharacteristic
880C2—24no—
881C2—42no—
882C2—4882no—
883C2—2444no—
884C2D4×#1175819811yescharacteristic
885C2C2×#1683975911yescharacteristic
886C2#2145434611yescharacteristic
887C2#2145750611yescharacteristic
888C2#2145753111yescharacteristic
889C2#2145765611yescharacteristic
890C2#2145767111yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C8×D4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
cosocleC22×C4×C61C24
hypercenterC2×C8×D4D61
hypocenterC61#22414
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16839759C2semidirect
3. C22×#14519699C2semidirect
4. #21448748C2semidirect
5. #21446749C2semidirect
6. #21446630C2semidirect
7. #21446247C2semidirect
8. #21446242C2semidirect
9. #21446139C2semidirect
10. #21446124C2semidirect
11. #21445830C2semidirect
12. #21445760C2semidirect
13. #21445751C2semidirect
14. C4×#14519699C2semidirect
15. C2×C8×D4×C61C2semidirect
19. #16840408C4semidirect
27. C2×#14519736C22semidirect
31. C2×#14519702C22semidirect
32. C2×#14519702C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519702C22semidirect
47. #16839628C22semidirect
49. #16839622C22semidirect
50. C4×C4⋊Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839525C22semidirect
57. C23×C8×C61C22semidirect
60. C2×C4⋊C8×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C2×C4×C8×C61C22semidirect
70. C2×#11758222C2×C4semidirect
87. #14519765C2×C4semidirect
92. #14519751C2×C4semidirect
96. C4×D244C2×C4semidirect
130. #14519699D4semidirect
398. C22×C61#416semidirect
436. C2×C8×D4D61semidirect
464. C23×C8C2×D61semidirect
479. C2×C4⋊C8C2×D61semidirect
495. C2×C22⋊C8C2×D61semidirect
496. C2×C4×C8C2×D61semidirect
509. C61#22414semidirect
858. C22#16839759semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168397592
C22×#145196992
#214487482
#214467492
#214466302
#214462472
#214462422
#214461392
#214461242
#214458302
#214457602
#214457512
C4×#145196992
C2×C8×D4×C612
#2241461