Finite Group Databasebeta

← #29695524

Subgroups — #29695524

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840419C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D61C211yesmaximal, characteristic, complemented
5#21446750C211yesmaximal, characteristic, complemented
6#21446634C211yesmaximal, characteristic, complemented
7#21446252C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21445822C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445651C211yesmaximal, characteristic, complemented
15C2×C61×#417C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840419—24no—
19#16840419C418yescomplemented
20C2×#14519764—21no—
21C2×#14519764C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519748C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839831—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39#103×D61—24no—
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45#16839657—21no—
46#16839635—21no—
47#16839633—21no—
48#16839631C2211yescharacteristic
49#16839622C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C22×M16×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C61×#417—24no—
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—41no—
70C2×Q8×D61—41no—
71C2×Q8×D61C2×C414yescomplemented
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82#14519764—28no—
83#14519764—22no—
84#14519764C2×C414yescomplemented
85#14519756—22no—
86#14519756—28no—
87#14519756C2×C414yescomplemented
88#14519748—28no—
89#14519748—22no—
90#14519748C2×C414yescomplemented
91Q8×Dic61—22no—
92Q8×Dic61C2×C414yescomplemented
93C4×C22⋊D61—28no—
94C4×C22⋊D61—44no—
95C4×C22⋊D61C2×C414yes—
96C4×C22⋊D61D414yes—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196D411yescharacteristic
106C4⋊C4×D61—22no—
107C4⋊C4×D61—41no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61D411yescharacteristic
114C2×#11758198—21no—
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61C2311yescharacteristic
119#14519706—22no—
120#14519702—22no—
121#14519702—41no—
122#14519701—22no—
123#14519701—22no—
124#14519700—22no—
125#14519700—41no—
126#14519698—41no—
127#14519698—41no—
128C22⋊#92418—22no—
129#14519689—22no—
130#14519687—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—22no—
137C2×#41×C61—41no—
138C2×#41×C61—41no—
139C2×#41×C61C2×C414yescomplemented
140C22×Q8×C61C2311yescharacteristic
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61—21no—
144C23×C4×C61—21no—
145C23×C4×C61C2311yescharacteristic
146C2×M16×C61—22no—
147C2×M16×C61—22no—
148C2×M16×C61—41no—
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C2×C4⋊C4×C61—22no—
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61—41no—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156#103×C61—22no—
157#103×C61D414yescomplemented
158#102×C61—22no—
159#102×C61—22no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61C2×D411yescharacteristic
163#41×C61—28no—
164#41×C61—44no—
165#41×C61—44no—
166#41×C61—44no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61C22×C412yes—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61#4112yes—
173C2×D4×C61—24no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61C22×C412yes—
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—24no—
189C22×C4×C61—21no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61—42no—
194C22×C4×C61—81no—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61C22⋊C414yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212Q8×D61—28no—
213Q8×D61—44no—
214Q8×D61—44no—
215Q8×D61—44no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—24no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61—81no—
226C2×C4×D61C22×C412yes—
227C2×C4×D61C2×D412yes—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—24no—
234C2×Dic122—42no—
235C2×Dic122—42no—
236C2×Dic122C22×C412yes—
237M16×C61—44no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61C2×D412yes—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61C2×D412yes—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—42no—
254C22⋊Dic61C22⋊C414yes—
255#11758198—42no—
256#11758198C22⋊C414yes—
257C4⋊Dic61—21no—
258C4⋊Dic61—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C412yes—
264#11758196—24no—
265#11758196—42no—
266#11758196—42no—
267#11758196—81no—
268#11758196C22⋊C414yes—
269C4×Dic61—24no—
270C4×Dic61—42no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C8×D61—44no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—22no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61C2×C22⋊C412yes—
294C23×C61C22×D411yescharacteristic
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61C2×C22⋊C412yes—
300C22×D61AGL(1,ℤ/8)12yes—
301C22×D61#13712yes—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61C4×D414yescomplemented
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—48no—
309D4×C61—41no—
310D4×C61—41no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—48no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—84no—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C22⋊D61—28no—
336C22⋊D61—48no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61C2×C22⋊C412yes—
356C2×Dic61C2×C22⋊C412yes—
357C2×Dic61C2×C22⋊C412yes—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—48no—
363C4×D61—84no—
364Dic122—22no—
365Dic122—22no—
366Dic122—48no—
367Dic122—41no—
368Dic122—41no—
369C8×C61—22no—
370C8×C61—41no—
371#92418—41no—
372#92418—41no—
373#22421—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61C22×C22⋊C411yescharacteristic
389C22×C61D4211yescharacteristic
390C22×C61#54611yescharacteristic
391C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C61C2×#13711yescharacteristic
393C22×C61#57711yescharacteristic
394C22×C61#57811yescharacteristic
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61#41714yescomplemented
402C4×C61—24no—
403C4×C61—22no—
404C4×C61—42no—
405C4×C61—81no—
406C4×C61C2×C4×D411yescharacteristic
407C4×C61#51811yescharacteristic
408C4×C61D4211yescharacteristic
409C4×C61#54611yescharacteristic
410Dic61—22no—
411Dic61—22no—
412Dic61—22no—
413Dic61—42no—
414Dic61—42no—
415Dic61—81no—
416Dic61—81no—
417C2×#548—611no—
418C2×#435—611no—
419C2×#417D6111yescharacteristic, complemented
420C22×#103—611no—
421D4×C4⋊C4—611no—
422#1983—611no—
423#1959—611no—
424#1894—611no—
425#1893—611no—
426#1874—611no—
427#1872—611no—
428#1803—611no—
429#1788—611no—
430#1787—611no—
431#1763—611no—
432C2×C61—42no—
433C2×C61—82no—
434C2×C61D4×C22⋊C411yescharacteristic
435C2×C61C2×#41711yescharacteristic
436C2×C61#289811yescharacteristic
437C2×C61#326511yescharacteristic
438C2×C61#327011yescharacteristic
439C2×C61#330811yescharacteristic
440C2×C61#331611yescharacteristic
441D61—24no—
442C22×#41C2×D6111yescharacteristic
443C23×Q8—611no—
444C22×M16C2×D6111yescharacteristic
445C23×C8—611no—
446#548—618no—
447#548—1224no—
448C2×#124—611no—
449C2×#124—1221no—
450C2×C22⋊Q8—611no—
451C2×C22⋊Q8—1221no—
452C2×#121—611no—
453C2×#121—1221no—
454C2×C4×Q8—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C22×C4⋊C4—611no—
459C22×C4⋊C4C2×D6111yescharacteristic
460#435—1224no—
461C2×C4⋊C8—611no—
462#417—24no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—1224no—
470C2×#103C2×D6111yescharacteristic
471C2×#103C2×D6111yescharacteristic
472C2×#102—611no—
473C2×#102—611no—
474C2×#102C2×D6111yescharacteristic
475C2×#102C2×D6111yescharacteristic
476C2×C22⋊C8—611no—
477C2×C22⋊C8—611no—
478C2×#97—611no—
479#389—1221no—
480#385—1221no—
481#385—1221no—
482#384—611no—
483#380—611no—
484#380—611no—
485C4×C4⋊C4—611no—
486#340—611no—
487#340—611no—
488#340—611no—
489#340—611no—
490C61#2242111yescharacteristic, complemented, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C4×D6114yescomplemented
497C22×Q8—614no—
498C22×Q8—611no—
499C22×Q8—1221no—
500C22×Q8—1222no—
501C22×Q8—1222no—
502C22×Q8—1222no—
503C22×Q8—2441no—
504C22×Q8—2441no—
505C22×Q8C22×D6111yescharacteristic
506C22×D4—21no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4C22×D6111yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—611no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4C22×D6111yescharacteristic
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—1222no—
522C22×C8—1222no—
523C22×C8—2441no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526#124—614no—
527#124—1222no—
528#124—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—1228no—
531C22⋊Q8—1222no—
532#121—614no—
533#121—1222no—
534#121—1228no—
535C4×Q8—614no—
536C4×Q8—1222no—
537C4×D4—614no—
538C4×D4—614no—
539C4×D4—1228no—
540C4×D4—2444no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1222no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—2441no—
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—611no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42—1221no—
567C2×C42—1221no—
568C4⋊C8—1222no—
569#103—22no—
570#103—1222no—
571#103—1222no—
572#103—1222no—
573#103—1222no—
574#103—2441no—
575#103—2441no—
576#103C22⋊D6114yescomplemented
577#102—22no—
578#102—22no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583#97—1222no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587C24—21no—
588C24—611no—
589C24D4×D6111yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—612no—
598C2×Q8—1224no—
599C2×Q8—1221no—
600C2×Q8—1228no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—2442no—
606C2×Q8—2442no—
607C2×Q8—2444no—
608C2×Q8—2444no—
609C2×Q8—2444no—
610C2×Q8C2×C4×D6112yes—
611C2×Q8#1175822212yes—
612C2×Q8C2×C22⋊D6112yes—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—614no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1224no—
625C2×D4—2442no—
626C2×D4—2442no—
627C2×D4C2×C4×D6112yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—81no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—1224no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—4881no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4C2×C4×D6112yes—
661C22×C4D4×D6112yes—
662C22×C4D4×D6111yescharacteristic
663C22×C4C23×D6111yescharacteristic
664M16—44no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—2444no—
677C2×C8C2×C22⋊D6112yes—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—42no—
682C4⋊C4—614no—
683C4⋊C4—612no—
684C4⋊C4—1224no—
685C4⋊C4—1221no—
686C4⋊C4—1224no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—4881no—
692C4⋊C4—2442no—
693C4⋊C4—2442no—
694C4⋊C4C2×C22⋊D6112yes—
695C22⋊C4—614no—
696C22⋊C4—614no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—2442no—
702C22⋊C4—2442no—
703C42—612no—
704C42—612no—
705C42—1224no—
706C42—2442no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—612no—
721C23—612no—
722C23—612no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23C22⋊C4×D6112yes—
728C23C2×D4×D6111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—1222no—
733Q8—1222no—
734Q8—2448no—
735Q8—2441no—
736Q8—2441no—
737Q8C4×C22⋊D6114yescomplemented
738D4—22no—
739D4—22no—
740D4—48no—
741D4—41no—
742D4—41no—
743D4—1228no—
744D4—2448no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—84no—
762C2×C4—612no—
763C2×C4—612no—
764C2×C4—612no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—2448no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4C22⋊C4×D6112yes—
790C2×C4C22×C4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4C22×C22⋊D6111yescharacteristic
793C2×C4C2×#1175822211yescharacteristic
794C2×C4#1451982211yescharacteristic
795C2×C4#1451982211yescharacteristic
796C8—22no—
797C8—41no—
798C8—2441no—
799C8—2441no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—614no—
815C22—1222no—
816C22—1222no—
817C22—1222no—
818C22—1222no—
819C22—1222no—
820C22—1222no—
821C22C2×C22⋊C4×D6111yescharacteristic
822C22D4×C22⋊D6111yescharacteristic
823C22#1684040211yescharacteristic
824C22AGL(1,ℤ/8)×D6111yescharacteristic
825C22#137×D6111yescharacteristic
826C22#1684057211yescharacteristic
827C22#1684057811yescharacteristic
828C4—22no—
829C4—24no—
830C4—42no—
831C4—81no—
832C4—1222no—
833C4—1222no—
834C4—1222no—
835C4—4881no—
836C4—4881no—
837C4—2442no—
838C4—2442no—
839C4C2×C4×C22⋊D6111yescharacteristic
840C4#1684023511yescharacteristic
841C4D4×C22⋊D6111yescharacteristic
842C4#1684040211yescharacteristic
843C2—42no—
844C2—82no—
845C2—1224no—
846C2C22⋊C4×C22⋊D6111yescharacteristic
847C2#417×D6111yescharacteristic
848C2#2145435011yescharacteristic
849C2#2145730811yescharacteristic
850C2#2145738311yescharacteristic
851C2#2145781111yescharacteristic
852C2#2145793111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
cosocleC22×C4×C61C24
hypercenterC2×#417D61
hypocenterC61#22421
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839831C2semidirect
3. C2×#103×D61C2semidirect
4. C4⋊C4×C22⋊D61C2semidirect
5. #21446750C2semidirect
6. #21446634C2semidirect
7. #21446252C2semidirect
8. #21446244C2semidirect
9. #21446133C2semidirect
10. #21446126C2semidirect
11. #21445822C2semidirect
12. #21445759C2semidirect
13. #21445752C2semidirect
14. #21445651C2semidirect
15. C2×C61×#417C2semidirect
19. #16840419C4semidirect
71. C2×Q8×D61C2×C4semidirect
84. #14519764C2×C4semidirect
87. #14519756C2×C4semidirect
90. #14519748C2×C4semidirect
92. Q8×Dic61C2×C4semidirect
139. C2×#41×C61C2×C4semidirect
157. #103×C61D4semidirect
305. Q8×C61C4×D4semidirect
401. C2×D61#417semidirect
419. C2×#417D61semidirect
490. C61#22421semidirect
496. C2×#41C4×D61semidirect
576. #103C22⋊D61semidirect
737. Q8C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404192
C2×#168398312
C2×#103×D612
C4⋊C4×C22⋊D612
#214467502
#214466342
#214462522
#214462442
#214461332
#214461262
#214458222
#214457592
#214457522
#214456512
C2×C61×#4172
#2242161