Finite Group Databasebeta

← #29695618

Subgroups — #29695618

Order 15616.

1606 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×#16840407C211yesmaximal, characteristic
2C2×#16839841C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5#21448751C211yesmaximal, characteristic, complemented
6#21446751C211yesmaximal, characteristic, complemented
7#21446630C211yesmaximal, characteristic, complemented
8#21446256C211yesmaximal, characteristic, complemented
9#21446251C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21446130C211yesmaximal, characteristic, complemented
12#21445829C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic, complemented
20#16840407—24no—
21#16840407C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519761—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519751—21no—
27C2×#14519747—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic, complemented
31C22×#11758198—21no—
32#16839841—24no—
33C2×C4⋊#92418C2211yescharacteristic, complemented
34#16839765—24no—
35#16839760—24no—
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic, complemented
48#16839653—21no—
49#16839647—21no—
50#16839640—21no—
51#16839628C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic, complemented
54C4×#11758198—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic, complemented
61C4×C4⋊C4×C61C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—41no—
69C2×#11758224—41no—
70C2×#11758224C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244—21no—
73C22×D244D411yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—41no—
81C2×D4×D61—41no—
82C2×D4×D61C2×C414yescomplemented
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—22no—
91C2×#11758189—41no—
92C2×#11758189—41no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519765—22no—
96#14519765C2×C414yescomplemented
97#14519761—28no—
98#14519757—22no—
99#14519757C2×C414yescomplemented
100#14519752—22no—
101#14519752C2×C414yes—
102#14519751—28no—
103#14519747—28no—
104C4×D244C2×C414yes—
105C4×D244D414yes—
106#14519735—22no—
107#14519735—41no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61D411yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—41no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—28no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198D411yescharacteristic
124C2×#11758198D411yescharacteristic
125C2×C4×Dic61—21no—
126C4⋊#92418—22no—
127#14519702—22no—
128#14519702—41no—
129#14519700—22no—
130#14519700—41no—
131#14519699—22no—
132#14519699—41no—
133#14519698—22no—
134#14519698—22no—
135#14519697—22no—
136#14519697—41no—
137#14519689—22no—
138#14519689—22no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C4×D4×C61—22no—
148C4×D4×C61C2×C414yescomplemented
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153C2×C42×C61—21no—
154C2×C42×C61C2311yescharacteristic
155#102×C61—22no—
156#102×C61D414yescomplemented
157C4×C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C23×D61—21no—
161C23×D61—24no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—81no—
167C23×D61—81no—
168C23×D61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61C22×C412yes—
174C2×D4×C61C2×D412yes—
175C2×D4×C61#4112yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—24no—
179C22×C4×C61—21no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—24no—
186C2×C22⋊D61—24no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C22×Dic61—21no—
192C22×Dic61—24no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758224—28no—
200#11758224—44no—
201#11758224—44no—
202#11758224—44no—
203D4×D61—28no—
204D4×D61—44no—
205D4×D61—44no—
206D4×D61—44no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—24no—
213C2×D244—41no—
214C2×D244—41no—
215C2×D244—81no—
216C2×D244—81no—
217C2×D244C22⋊C414yes—
218C2×D244C22×C412yes—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—81no—
230C2×C4×D61C22×C412yes—
231C2×C4×D61C22×C412yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
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×C61C2×D412yes—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C22×C412yes—
251C4⋊C4×C61C2×D412yes—
252C22⋊C4×C61—24no—
253C42×C61—81no—
254C42×C61C22×C412yes—
255C42×C61C2×D412yes—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—42no—
261#11758198—42no—
262#11758198—81no—
263#11758198C22⋊C414yes—
264#11758198C22⋊C414yes—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C22⋊C414yes—
271#11758196—42no—
272C4×Dic61—42no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279#11758189—44no—
280#11758189—44no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61C22×D411yescharacteristic
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—22no—
302C22×D61—48no—
303C22×D61—48no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—84no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61C2×C22⋊C412yes—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61C4×D414yes—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61C2×C22⋊C412yes—
336C2×C4×C61C2×C22⋊C412yes—
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C22⋊D61—48no—
344C22⋊D61—48no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—48no—
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×Dic61C2×C22⋊C412yes—
360C2×Dic61C2×C22⋊C412yes—
361D244—22no—
362D244—22no—
363D244—44no—
364D244—41no—
365D244—41no—
366D244—84no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—22no—
381C8×C61—41no—
382#92418—41no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—24no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61C22×C22⋊C411yescharacteristic
393C22×C61D4211yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#57511yescharacteristic
396C22×C61#57511yescharacteristic
397C22×C61#57611yescharacteristic
398C22×C61#57711yescharacteristic
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
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—42no—
424C4×C61—42no—
425C4×C61—81no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—81no—
434Dic61—81no—
435C2×#546—611no—
436C2×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1895—611no—
443#1894—611no—
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102D6111yescharacteristic, complemented
450C2×C61—44no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61#289611yescharacteristic
453C2×C61#289711yescharacteristic
454C2×C61#327311yescharacteristic
455C2×C61#327511yescharacteristic
456C2×C61#332211yescharacteristic
457C2×C61#332311yescharacteristic
458D61—42no—
459D61—42no—
460D61—82no—
461C22×#41—611no—
462C23×D4—611no—
463C22×M16—611no—
464C22×M16—611no—
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—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102C2×D6111yescharacteristic
493C2×#102C2×D6111yescharacteristic
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
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⋊C4C2×D6111yescharacteristic, complemented
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340C2×D6111yescharacteristic, complemented
508#340C2×D6111yescharacteristic, complemented
509C61#2242711yescharacteristic, 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—1221no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1222no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4C22×D6111yescharacteristic
530C23×C4—21no—
531C23×C4—611no—
532C23×C4—611no—
533C23×C4—1221no—
534C23×C4—1221no—
535C2×M16—1222no—
536C2×M16—1222no—
537C2×M16—1222no—
538C2×M16—1222no—
539C2×M16—2441no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
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—1228no—
552#121—1222no—
553#120—1228no—
554C4×D4—22no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4C4×D6114yescomplemented
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—2441no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—21no—
582C2×C42—1221no—
583C2×C42C22×D6111yescharacteristic
584C4⋊C8—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—22no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—2441no—
595#102—2441no—
596#102D24414yescomplemented
597C22⋊C8—1222no—
598C22⋊C8—1222no—
599C4×C8—22no—
600#95—21no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—611no—
607C24—611no—
608C24—1224no—
609C24—1221no—
610C24—4881no—
611C24—4881no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24—2442no—
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—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—612no—
630C2×D4—614no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1228no—
634C2×D4—1224no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—2441no—
643C2×D4—2441no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4C2×C4×D6112yes—
652C2×D4C2×D24412yes—
653C2×D4#1175822212yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
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×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—2444no—
687M16—2444no—
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×C8C2×D24412yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—614no—
705C4⋊C4—1224no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—2442no—
711C4⋊C4C2×C4×D6112yes—
712C4⋊C4C2×D24412yes—
713C22⋊C4—24no—
714C22⋊C4—614no—
715C22⋊C4—614no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—4881no—
721C22⋊C4—2442no—
722C22⋊C4—2442no—
723C42—81no—
724C42—2442no—
725C42C2×C4×D6112yes—
726C42D4×D6112yes—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—612no—
735C23—612no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1222no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—2448no—
755C23—2448no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23C2×D4×D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—1222no—
771D4—1222no—
772D4—4884no—
773D4—2444no—
774D4—2448no—
775D4—2448no—
776D4—2441no—
777D4—2441no—
778D4C4×D24414yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—84no—
793C2×C4—612no—
794C2×C4—612no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—4884no—
809C2×C4—2448no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4C22⋊C4×D6112yes—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C22×D24411yescharacteristic
823C2×C4C2×#1175822211yescharacteristic
824C2×C4#1451982311yescharacteristic
825C2×C4#1451982311yescharacteristic
826C8—22no—
827C8—41no—
828C8—2441no—
829C8—2441no—
830C22—24no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—1222no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—48816no—
844C22—4881no—
845C22—4881no—
846C22—4881no—
847C22—4881no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2441no—
852C22—2441no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22D4×D24411yescharacteristic
861C22#1684040811yescharacteristic
862C22#1684055911yescharacteristic
863C22#1684055911yescharacteristic
864C22#1684056311yescharacteristic
865C22#1684056811yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—1222no—
872C4—1222no—
873C4—4881no—
874C4—4881no—
875C4—2442no—
876C4C2×C4×D24411yescharacteristic
877C4#1684023611yescharacteristic
878C4D4×D24411yescharacteristic
879C4#1684040811yescharacteristic
880C2—44no—
881C2—4882no—
882C2—2442no—
883C2—2442no—
884C2C22⋊C4×D24411yescharacteristic
885C2#2145433411yescharacteristic
886C2#2145434011yescharacteristic
887C2#2145742911yescharacteristic
888C2#2145745211yescharacteristic
889C2#2145802511yescharacteristic
890C2#2145804011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840407C2
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839841C2semidirect
3. C2×#16839760C2semidirect
4. C2×#16839765C2semidirect
5. #21448751C2semidirect
6. #21446751C2semidirect
7. #21446630C2semidirect
8. #21446256C2semidirect
9. #21446251C2semidirect
10. #21446135C2semidirect
11. #21446130C2semidirect
12. #21445829C2semidirect
13. #21445756C2semidirect
14. #21445748C2semidirect
15. C4×#102×C61C2semidirect
19. C22×#11758189C22semidirect
21. #16840407C4semidirect
30. C2×C4⋊C4×D61C22semidirect
33. C2×C4⋊#92418C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
47. C2×#14519689C22semidirect
51. #16839628C22semidirect
53. #16839619C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
60. C2×C4×C8×C61C22semidirect
61. C4×C4⋊C4×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
82. C2×D4×D61C2×C4semidirect
96. #14519765C2×C4semidirect
99. #14519757C2×C4semidirect
148. C4×D4×C61C2×C4semidirect
156. #102×C61D4semidirect
449. C4×#102D61semidirect
496. C2×C4×C8C2×D61semidirect
503. C4×C4⋊C4C2×D61semidirect
507. #340C2×D61semidirect
508. #340C2×D61semidirect
509. C61#22427semidirect
557. C4×D4C4×D61semidirect
596. #102D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168404072
C2×#168398412
C2×#168397602
C2×#168397652
#214487512
#214467512
#214466302
#214462562
#214462512
#214461352
#214461302
#214458292
#214457562
#214457482
C4×#102×C612
#2242761