Finite Group Databasebeta

← #29695489

Subgroups — #29695489

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840406C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D61C211yesmaximal, characteristic, complemented
5#21446750C211yesmaximal, characteristic, complemented
6#21446634C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446242C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C22×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758189C2211yescharacteristic, complemented
18#16840406—24no—
19#16840406C418yescomplemented
20C2×#14519764C2211yescharacteristic
21C2×#14519758—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519746—21no—
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic, complemented
30C22×C22⋊Dic61—21no—
31#16839833—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839760—24no—
34C2×#14519702C2211yescharacteristic, complemented
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic, complemented
44C2×#14519687C2211yescharacteristic, complemented
45#16839657—21no—
46#16839635—21no—
47#16839633—21no—
48#16839631C2211yescharacteristic, complemented
49#16839622C2211yescharacteristic
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C2×#102×C61—24no—
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519764—22no—
84#14519764C2×C414yescomplemented
85#14519758—28no—
86#14519756—22no—
87#14519756C2×C414yescomplemented
88#14519749—28no—
89#14519748—22no—
90#14519748C2×C414yescomplemented
91#14519746—28no—
92D4×Dic61—22no—
93D4×Dic61C2×C414yescomplemented
94C4×C22⋊D61—44no—
95C4×C22⋊D61C2×C414yes—
96C4×C22⋊D61D414yes—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196D411yescharacteristic
105C4⋊C4×D61—22no—
106C4⋊C4×D61—41no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—28no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198D411yescharacteristic
117C2×C4×Dic61—21no—
118C2×C4×Dic61C2311yescharacteristic
119#14519706—22no—
120#14519702—22no—
121#14519702—41no—
122#14519700—22no—
123#14519700—41no—
124#14519698—22no—
125#14519698—22no—
126#14519698—41no—
127#14519698—41no—
128C22⋊#92418—22no—
129#14519689—22no—
130#14519687—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134C25×C61—21no—
135C22×D4×C61—22no—
136C22×D4×C61—22no—
137C22×D4×C61—21no—
138C22×D4×C61—22no—
139C22×D4×C61—41no—
140C22×D4×C61—41no—
141C22×D4×C61C2×C414yescomplemented
142C22×D4×C61C2311yescharacteristic
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C23×C4×C61C2311yescharacteristic
146C22×C8×C61—22no—
147C22×C8×C61—22no—
148C22×C8×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#102×C61—22no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61D414yescomplemented
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—24no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—81no—
168C24×C61—81no—
169C24×C61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C2×D4×C61—28no—
172C2×D4×C61—24no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—44no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C22×C412yes—
188C2×D4×C61C2×D412yes—
189C2×D4×C61#4112yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—42no—
197C22×C4×C61—42no—
198C22×C4×C61—81no—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61C22⋊C414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—24no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—42no—
219C22×Dic61—42no—
220C22×Dic61—81no—
221C22×Dic61—81no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758224—28no—
226#11758224—44no—
227#11758224—44no—
228#11758224—44no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—81no—
236C2×C4×D61C22×C412yes—
237C2×C4×D61C2×D412yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—44no—
250C2×C8×C61C2×D412yes—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61C2×D412yes—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—42no—
262C22⋊Dic61C22⋊C414yes—
263#11758198—42no—
264#11758198C22⋊C414yes—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C412yes—
271#11758196—24no—
272#11758196—42no—
273#11758196—42no—
274#11758196—81no—
275#11758196C22⋊C414yes—
276C4×Dic61—42no—
277C4×Dic61C22×C412yes—
278C4×Dic61C2×D412yes—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285#11758189—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—48no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—48no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61—84no—
309C23×C61—84no—
310C23×C61—84no—
311C23×C61C2×C22⋊C412yes—
312C23×C61AGL(1,ℤ/8)12yes—
313C23×C61#13712yes—
314C23×C61C22×D411yescharacteristic
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61C2×C22⋊C412yes—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—48no—
328D4×C61—41no—
329D4×C61—41no—
330D4×C61C4×D414yescomplemented
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—84no—
344C2×C4×C61C2×C22⋊C412yes—
345C2×C4×C61C23×C411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C22⋊D61—28no—
352C22⋊D61—48no—
353C22⋊D61—84no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—48no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—84no—
374C2×Dic61C2×C22⋊C412yes—
375C2×Dic61C2×C22⋊C412yes—
376C2×Dic61C2×C22⋊C412yes—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386C8×C61—22no—
387C8×C61—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—24no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—816no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61#41714yescomplemented
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61D4211yescharacteristic
415C22×C61#54611yescharacteristic
416C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C61C2×#13711yescharacteristic
418C22×C61#57611yescharacteristic
419C22×C61#57711yescharacteristic
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C4×C61—22no—
428C4×C61—42no—
429C4×C61—81no—
430C4×C61C2×C4×D411yescharacteristic
431C4×C61#51811yescharacteristic
432C4×C61D4211yescharacteristic
433C4×C61#54611yescharacteristic
434Dic61—22no—
435Dic61—22no—
436Dic61—22no—
437Dic61—42no—
438Dic61—42no—
439Dic61—81no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417—611no—
444C22×#102D6111yescharacteristic, complemented
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—24no—
457C2×C61—44no—
458C2×C61—82no—
459C2×C61D4×C22⋊C411yescharacteristic
460C2×C61C2×#41711yescharacteristic
461C2×C61#289711yescharacteristic
462C2×C61#326411yescharacteristic
463C2×C61#326611yescharacteristic
464C2×C61#330611yescharacteristic
465C2×C61#331411yescharacteristic
466D61—42no—
467C22×#41—611no—
468C23×D4C2×D6111yescharacteristic
469C22×M16—611no—
470C23×C8C2×D6111yescharacteristic
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—611no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×C4×D4—611no—
480C2×C4×D4—611no—
481C2×C4×D4—1221no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4C2×D6111yescharacteristic
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—24no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102C2×D6111yescharacteristic
498C2×#102C2×D6111yescharacteristic
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380—611no—
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—22no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—611no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4C4×D6114yescomplemented
534C22×D4C22×D6111yescharacteristic
535C22×D4C22×D6111yescharacteristic
536C23×C4—21no—
537C23×C4—611no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1228no—
559#121—1222no—
560#120—1228no—
561C4×D4—614no—
562C4×D4—614no—
563C4×D4—614no—
564C4×D4—1222no—
565C4×D4—2444no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—2441no—
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—611no—
582C2×C22⋊C4—611no—
583C2×C22⋊C4—1228no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—611no—
592C2×C42—1221no—
593C4⋊C8—1222no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—1222no—
602#102—1222no—
603#102—2441no—
604#102—2441no—
605#102C22⋊D6114yescomplemented
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24—611no—
622C24D4×D6111yescharacteristic
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×D4—28no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—24no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—614no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—1224no—
652C2×D4—1224no—
653C2×D4—4881no—
654C2×D4—4881no—
655C2×D4—2442no—
656C2×D4—2442no—
657C2×D4C2×C4×D6112yes—
658C2×D4C2×C4×D6112yes—
659C2×D4#1175822212yes—
660C2×D4C2×C22⋊D6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—81no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—1224no—
676C22×C4—1224no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—4881no—
686C22×C4—4881no—
687C22×C4—4881no—
688C22×C4—2442no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4C2×C4×D6112yes—
693C22×C4D4×D6112yes—
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—2444no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—44no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8C2×C22⋊D6112yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—42no—
714C4⋊C4—614no—
715C4⋊C4—612no—
716C4⋊C4—1221no—
717C4⋊C4—1224no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—4881no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4C2×C22⋊D6112yes—
726C22⋊C4—614no—
727C22⋊C4—614no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C42—612no—
736C42—612no—
737C42—2442no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23—612no—
764C23—1221no—
765C23—1221no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23C22⋊C4×D6112yes—
771C23#1451980112yes—
772C23#1451980612yes—
773C23C2×D4×D6111yescharacteristic
774Q8—1222no—
775Q8—1222no—
776Q8—2441no—
777Q8—2441no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—41no—
785D4—41no—
786D4—1228no—
787D4—4884no—
788D4—2448no—
789D4C4×C22⋊D6114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—612no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—4884no—
819C2×C4—4884no—
820C2×C4—2448no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4C2×#1175822211yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982211yescharacteristic
838C8—22no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—1222no—
864C22—1222no—
865C22—1222no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22—2441no—
870C22#1683976014yescomplemented
871C22C2×C22⋊C4×D6111yescharacteristic
872C22D4×C22⋊D6111yescharacteristic
873C22#1684040211yescharacteristic
874C22C2×#1451980111yescharacteristic
875C22C2×#1451980611yescharacteristic
876C22#1684056311yescharacteristic
877C22#1684056811yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—1222no—
882C4—1222no—
883C4—1222no—
884C4—4881no—
885C4—4881no—
886C4—2442no—
887C4—2442no—
888C4C2×C4×C22⋊D6111yescharacteristic
889C4#1684023511yescharacteristic
890C4D4×C22⋊D6111yescharacteristic
891C4#1684040211yescharacteristic
892C2—24no—
893C2—44no—
894C2—82no—
895C2—2442no—
896C2C22⋊C4×C22⋊D6111yescharacteristic
897C2C2×#1683976011yescharacteristic
898C2#2145434011yescharacteristic
899C2#2145729911yescharacteristic
900C2#2145732911yescharacteristic
901C2#2145777611yescharacteristic
902C2#2145789611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840406C2
cosocleC22×C4×C61C24
hypercenterC22×#102D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839760C2semidirect
4. C4⋊C4×C22⋊D61C2semidirect
5. #21446750C2semidirect
6. #21446634C2semidirect
7. #21446254C2semidirect
8. #21446242C2semidirect
9. #21446133C2semidirect
10. #21446126C2semidirect
11. #21445817C2semidirect
12. #21445756C2semidirect
13. #21445750C2semidirect
14. #21445646C2semidirect
15. C22×#102×C61C2semidirect
17. C22×#11758189C22semidirect
19. #16840406C4semidirect
29. C2×C4⋊C4×D61C22semidirect
32. C2×#14519706C22semidirect
34. C2×#14519702C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519700C22semidirect
37. C2×#14519700C22semidirect
43. C2×#14519689C22semidirect
44. C2×#14519687C22semidirect
48. #16839631C22semidirect
50. #16839619C22semidirect
51. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
69. C2×#11758224C2×C4semidirect
84. #14519764C2×C4semidirect
87. #14519756C2×C4semidirect
90. #14519748C2×C4semidirect
93. D4×Dic61C2×C4semidirect
141. C22×D4×C61C2×C4semidirect
159. #102×C61D4semidirect
330. D4×C61C4×D4semidirect
412. C22×C61#417semidirect
444. C22×#102D61semidirect
515. C61#22419semidirect
533. C22×D4C4×D61semidirect
605. #102C22⋊D61semidirect
789. D4C4×C22⋊D61semidirect
870. C22#16839760semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168398332
C2×#168397602
C4⋊C4×C22⋊D612
#214467502
#214466342
#214462542
#214462422
#214461332
#214461262
#214458172
#214457562
#214457502
#214456462
C22×#102×C612
#2241961