Finite Group Databasebeta

← #29690015

Subgroups — #29690015

Order 15616.

1242 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446761C212yesmaximal, complemented
5#21446736C212yesmaximal, complemented
6#21446261C212yesmaximal, complemented
7#21446259C212yesmaximal, complemented
8#21445840C211yesmaximal, characteristic, complemented
9#21445839C211yesmaximal, characteristic, complemented
10#21445836C211yesmaximal, characteristic, complemented
11C61×#1806C211yesmaximal, characteristic, complemented
12#16840316C411yescharacteristic, complemented
13#16840316C411yescharacteristic, complemented
14#16840315C2211yescharacteristic
15#16840309C411yescharacteristic, complemented
16#16840309C411yescharacteristic, complemented
17#16840308C2211yescharacteristic
18#16840299C411yescharacteristic, complemented
19#16840299C411yescharacteristic, complemented
20#16840294C411yescharacteristic, complemented
21#16840294C411yescharacteristic, complemented
22#16840292—21no—
23#16840292—21no—
24#16840290—21no—
25#16840290—21no—
26#16840274C2211yescharacteristic
27#16840271—21no—
28#16840271—21no—
29#16840269C2211yescharacteristic
30C4×#11758222—21no—
31C4×#11758222—21no—
32C4×#11758222C2211yescharacteristic
33C2×C4⋊C4×D61—21no—
34C2×C42×D61C2212yes—
35C2×C42×D61C2211yescharacteristic
36#16839818—21no—
37#16839818—21no—
38#16839814—21no—
39#16839814—21no—
40#16839786C2211yescharacteristic
41C2×#14519705C2212yes—
42C2×#14519704C2212yes—
43C2×#14519703C2212yes—
44#16839725C2212yes—
45M16×Dic61C2212yes—
46C4⋊C4×Dic61—21no—
47C4×#11758196C2212yes—
48C4×C4⋊Dic61C2211yescharacteristic
49#16839613—21no—
50#95×D61—21no—
51#16839523C2212yes—
52#16839522C2212yes—
53#16839521C2212yes—
54C4×#41×C61C2211yescharacteristic
55C61×#423C2211yescharacteristic
56C2×#104×C61C2212yes—
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#339C2212yes—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2311yescharacteristic
62C22×C4×D61—22no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194C2312yes—
67#14519776C2×C411yescharacteristic, complemented
68#14519776C2×C411yescharacteristic, complemented
69#14519775C2×C411yescharacteristic, complemented
70#14519773C2×C411yescharacteristic, complemented
71#14519772—21no—
72#14519772—21no—
73#14519770—21no—
74#14519770—21no—
75#14519768C2×C411yescharacteristic, complemented
76#14519768C2×C411yescharacteristic, complemented
77#14519767—21no—
78#14519767—21no—
79#14519766C2×C411yescharacteristic, complemented
80#14519764C2×C411yescharacteristic, complemented
81#14519763—21no—
82#14519763—21no—
83#14519762—21no—
84#14519762—21no—
85#14519761—21no—
86#14519759—21no—
87#14519759—21no—
88#14519758—21no—
89#14519757C2×C411yescharacteristic
90#14519757C2×C411yescharacteristic
91#14519755—21no—
92#14519755—21no—
93#14519754—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519753C2×C411yescharacteristic
97#14519752C2×C411yescharacteristic
98#14519752C2×C411yescharacteristic
99#14519750—21no—
100#14519750—21no—
101#14519749—21no—
102#14519749—21no—
103#14519748C2×C411yescharacteristic
104#14519748C2×C411yescharacteristic
105#14519747—21no—
106#14519745—21no—
107C4×Dic122—21no—
108C4×Dic122—21no—
109C4×Dic122—21no—
110C4×Dic122—21no—
111C4×Dic122C2×C411yescharacteristic, complemented
112C4×Dic122C2×C411yescharacteristic, complemented
113C4×D244—21no—
114C4×D244—21no—
115C4×D244—21no—
116C4×D244—21no—
117C4×D244C2×C411yescharacteristic, complemented
118C4×D244C2×C411yescharacteristic, complemented
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129#14519736—21no—
130#14519736—21no—
131#14519736C2311yescharacteristic
132#14519734—21no—
133#14519734—21no—
134#14519734—21no—
135#14519734—21no—
136#14519734—21no—
137C2×C4⋊Dic61—21no—
138C2×#11758196—22no—
139C4⋊C4×D61—28no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61C2312yes—
144C2×C4×Dic61C2311yescharacteristic
145C42×D61—21no—
146C42×D61—42no—
147C42×D61—42no—
148C42×D61C2×C411yescharacteristic
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61C2×C411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C4⋊#92418—21no—
157C4⋊#92418—21no—
158#14519705—42no—
159#14519704—42no—
160#14519703—42no—
161#14519689—22no—
162#14519689—22no—
163#14519687—22no—
164C8×Dic61—22no—
165#14519684—21no—
166#14519684—22no—
167C2×#41×C61C2311yescharacteristic
168C2×M16×C61C2312yes—
169C4×Q8×C61C2×C411yescharacteristic, complemented
170C4×Q8×C61C2×C411yescharacteristic, complemented
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C4×D4×C61C2×C411yescharacteristic, complemented
174C4×D4×C61C2×C411yescharacteristic, complemented
175#117×C61—21no—
176#117×C61C2311yescharacteristic
177C2×C4⋊C4×C61—21no—
178C2×C42×C61—21no—
179C2×C42×C61C2312yes—
180C2×C42×C61C2311yescharacteristic
181C4⋊C8×C61—21no—
182C4⋊C8×C61—21no—
183#104×C61—42no—
184#95×C61—21no—
185C23×D61C2×D411yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61C22×C411yescharacteristic
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C22×Dic61—22no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209#11758222—21no—
210#11758222—21no—
211#11758222—21no—
212#11758222—21no—
213#11758222—44no—
214#11758222—44no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244C22×C411yescharacteristic
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—24no—
223C2×C4×D61—28no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—42no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61C22⋊C411yescharacteristic
231C2×C4×D61C22⋊C411yescharacteristic
232C2×C4×D61C22⋊C411yescharacteristic
233C2×C4×D61C22⋊C411yescharacteristic
234C2×C4×D61C22⋊C411yescharacteristic
235C2×C4×D61C22⋊C411yescharacteristic
236C2×C4×D61C22⋊C411yescharacteristic
237C2×C4×D61C22⋊C411yescharacteristic
238C2×C4×D61C22×C411yescharacteristic
239C2×C4×D61C22×C411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122C22×C411yescharacteristic
245M16×C61—22no—
246M16×C61—22no—
247C2×C8×C61—22no—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C411yescharacteristic
252C4⋊C4×C61C22×C411yescharacteristic
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61—22no—
260C42×C61—22no—
261C42×C61C22×C411yescharacteristic
262C42×C61C22×C411yescharacteristic
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280C4⋊Dic61—24no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61C22×C411yescharacteristic
286C4⋊Dic61C22×C411yescharacteristic
287#11758196—28no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298C4×Dic61—21no—
299C4×Dic61—21no—
300C4×Dic61—21no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—44no—
304C4×Dic61C22⋊C411yescharacteristic
305C4×Dic61C22⋊C411yescharacteristic
306C4×Dic61C22⋊C411yescharacteristic
307C4×Dic61C22⋊C411yescharacteristic
308C4×Dic61C22⋊C411yescharacteristic
309C4×Dic61C22⋊C411yescharacteristic
310C4×Dic61C22⋊C411yescharacteristic
311C4×Dic61C22⋊C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316#11758194—22no—
317#11758194—22no—
318C2×#92418—22no—
319C23×C61—21no—
320C23×C61C22×D411yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—21no—
326C22×D61C2×C22⋊C411yescharacteristic
327C22×D61C2×C22⋊C411yescharacteristic
328Q8×C61—21no—
329Q8×C61—21no—
330D4×C61—21no—
331D4×C61—21no—
332D4×C61—41no—
333D4×C61—41no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—42no—
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C23×C411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C612−1+411yescharacteristic
355C2×C4×C612−1+411yescharacteristic
356C22⋊D61—42no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—42no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—24no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378D244—21no—
379D244—21no—
380D244—42no—
381D244—42no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61—42no—
398C4×D61—416no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—42no—
402C4×D61#10414yescomplemented
403Dic122—21no—
404Dic122—21no—
405Dic122—42no—
406Dic122—42no—
407C8×C61—42no—
408#92418—42no—
409#21899—611nomaximal, Sylow
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61C22×C22⋊C411yescharacteristic
416C22×C61#53511yescharacteristic
417C22×C61#53611yescharacteristic
418C2×D61—24no—
419C2×D61—24no—
420C2×D61—21no—
421C2×D61—21no—
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61C2×#10412yes—
428C2×D61#42112yes—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—44no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61C2×#10412yes—
437C4×C61#52011yescharacteristic
438C4×C61#52011yescharacteristic
439C4×C61#53711yescharacteristic
440C4×C61#53711yescharacteristic
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—21no—
445Dic61—21no—
446Dic61—44no—
447Dic61—41no—
448Dic61—41no—
449Dic61—41no—
450Dic61C2×#10412yes—
451#3444—611no—
452#2920—611no—
453C2×C4×C4⋊C4—611no—
454#1986—612no—
455#1980—612no—
456#1896—612no—
457#1896—612no—
458#1806—611no—
459#1806—611no—
460#1806—611no—
461#1806D6111yescharacteristic, complemented
462C2×C61—21no—
463C2×C61—21no—
464C2×C61—81no—
465C2×C61#231111yescharacteristic
466C2×C61C22×#10411yescharacteristic
467C2×C61C2×#42111yescharacteristic
468D61—22no—
469D61—22no—
470D61—81no—
471#533—611no—
472#533—611no—
473#533—611no—
474#532—611no—
475#532—611no—
476#532—611no—
477#529—611no—
478#529—611no—
479#529—611no—
480#529—611no—
481#529—1221no—
482#529—1221no—
483#529—1221no—
484#529—1221no—
485#525—611no—
486#525—611no—
487#525—1221no—
488#525—1221no—
489C4×#41—611no—
490C4×#41—1221no—
491C4×#41—1221no—
492C4×#41C2×D6111yescharacteristic
493C22×C4⋊C4—1221no—
494C22×C42—611no—
495C22×C42—612no—
496#432—1221no—
497#432—1221no—
498#431—1221no—
499#431—1221no—
500#423—611no—
501#423C2×D6111yescharacteristic
502C2×#104—612no—
503C2×#104—612no—
504C2×#104—612no—
505C2×#104C2×D6112yes—
506#407—612no—
507C4×M16—612no—
508C4×C4⋊C4—612no—
509C4×C4⋊C4—611no—
510C4×C4⋊C4—1221no—
511C4×C4⋊C4—1221no—
512C4×C4⋊C4C2×D6111yescharacteristic
513C2×#95—1221no—
514#339—612no—
515#339—612no—
516#339—612no—
517#339C2×D6112yes—
518C61#2189911yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—1221no—
521C2×#41—1221no—
522C2×#41C22×D6111yescharacteristic
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—1222no—
527C2×M16—612no—
528C2×M16C22×D6112yes—
529C4⋊Q8—611no—
530C4⋊Q8—611no—
531C4⋊Q8—611no—
532#127—611no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#125—611no—
538#125—611no—
539#125—1221no—
540#125—1221no—
541#124—611no—
542#124—611no—
543#124—1221no—
544#124—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551C22⋊Q8—611no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559#121—611no—
560#121—611no—
561#121—611no—
562#121—611no—
563#121—1221no—
564#121—1221no—
565#121—1221no—
566#121—1221no—
567#120—1221no—
568#120—1221no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8C4×D6111yescharacteristic, complemented
576C4×Q8C4×D6111yescharacteristic, complemented
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4C4×D6111yescharacteristic, complemented
596C4×D4C4×D6111yescharacteristic, complemented
597#117—21no—
598#117—611no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117C22×D6111yescharacteristic
607C2×C4⋊C4—21no—
608C2×C4⋊C4—1228no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1221no—
611C2×C42—21no—
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—611no—
623C2×C42—612no—
624C2×C42—1221no—
625C2×C42—1222no—
626C2×C42—2442no—
627C2×C42—2442no—
628C2×C42C22×D6112yes—
629C2×C42C22×D6111yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—1221no—
633C4⋊C8—1221no—
634#104—42no—
635#104—2442no—
636#104—2442no—
637#104—2442no—
638C22⋊C8—1222no—
639C22⋊C8—1222no—
640#97—1222no—
641C4×C8—1222no—
642#95—21no—
643#95—1222no—
644#95—1221no—
645C24—611no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—21no—
650#41—1221no—
651#41—1221no—
652#41—1221no—
653#41—1221no—
654#41—2444no—
655#41—2444no—
656C2×Q8—611no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—611no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4C2×C4×D6111yescharacteristic
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—1224no—
690C22×C4—1228no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1222no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—2442no—
700C22×C4—2444no—
701C22×C4—2444no—
702C22×C4D4×D6111yescharacteristic
703C22×C4D4×D6111yescharacteristic
704C22×C4C23×D6111yescharacteristic
705M16—22no—
706M16—22no—
707M16—1222no—
708M16—1222no—
709C2×C8—22no—
710C2×C8—1222no—
711C4⋊C4—24no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—611no—
715C4⋊C4—611no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1228no—
729C4⋊C4—1224no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4C2×C4×D6111yescharacteristic
733C4⋊C4C2×C4×D6111yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—22no—
756C42—22no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—1221no—
770C42—1221no—
771C42—1221no—
772C42—1222no—
773C42—1222no—
774C42—2444no—
775C42C2×C4×D6111yescharacteristic
776C42C2×C4×D6111yescharacteristic
777C42D4×D6111yescharacteristic
778C42D4×D6111yescharacteristic
779C23—21no—
780C23—611no—
781C23—611no—
782C23—1222no—
783C23—1222no—
784C23—1221no—
785C23—1221no—
786C23—1221no—
787C23C2×D4×D6111yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—1221no—
791Q8—1221no—
792Q8—2442no—
793Q8—2442no—
794D4—21no—
795D4—21no—
796D4—41no—
797D4—41no—
798D4—1221no—
799D4—1221no—
800D4—2442no—
801D4—2442no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805D4—2442no—
806D4—2441no—
807D4—2441no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—611no—
821C2×C4—614no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1222no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1224no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2442no—
850C2×C4—24416no—
851C2×C4—2441no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4C22⋊C4×D6111yescharacteristic
858C2×C4C22⋊C4×D6111yescharacteristic
859C2×C4C22⋊C4×D6111yescharacteristic
860C2×C4C22⋊C4×D6111yescharacteristic
861C2×C4C22×C4×D6111yescharacteristic
862C2×C4C2×D4×D6111yescharacteristic
863C2×C4#1451982211yescharacteristic
864C2×C4#1451982311yescharacteristic
865C2×C4#1451982411yescharacteristic
866C2×C4#1451982511yescharacteristic
867C8—42no—
868C8—2442no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—612no—
875C22—612no—
876C22—1224no—
877C22—1224no—
878C22—1221no—
879C22—1221no—
880C22—1221no—
881C22—1221no—
882C22—2441no—
883C22—2441no—
884C22—2441no—
885C22C2×C22⋊C4×D6111yescharacteristic
886C22#1684032811yescharacteristic
887C22#1684033511yescharacteristic
888C4—21no—
889C4—21no—
890C4—21no—
891C4—44no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—612no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—1221no—
901C4—2444no—
902C4—2441no—
903C4—2441no—
904C4—2441no—
905C4#104×D6112yes—
906C4#1684024211yescharacteristic
907C4#1684024311yescharacteristic
908C4#1684034111yescharacteristic
909C4#1684034211yescharacteristic
910C2—21no—
911C2—21no—
912C2—81no—
913C2—1222no—
914C2—1222no—
915C2—4881no—
916C2#2144840811yescharacteristic
917C2C2×#104×D6111yescharacteristic
918C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#21899
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. C4×C4⋊C4×D61C2semidirect
4. #21446761C2semidirect
5. #21446736C2semidirect
6. #21446261C2semidirect
7. #21446259C2semidirect
8. #21445840C2semidirect
9. #21445839C2semidirect
10. #21445836C2semidirect
11. C61×#1806C2semidirect
12. #16840316C4semidirect
13. #16840316C4semidirect
15. #16840309C4semidirect
16. #16840309C4semidirect
18. #16840299C4semidirect
19. #16840299C4semidirect
20. #16840294C4semidirect
21. #16840294C4semidirect
67. #14519776C2×C4semidirect
68. #14519776C2×C4semidirect
69. #14519775C2×C4semidirect
70. #14519773C2×C4semidirect
75. #14519768C2×C4semidirect
76. #14519768C2×C4semidirect
79. #14519766C2×C4semidirect
80. #14519764C2×C4semidirect
111. C4×Dic122C2×C4semidirect
112. C4×Dic122C2×C4semidirect
117. C4×D244C2×C4semidirect
118. C4×D244C2×C4semidirect
169. C4×Q8×C61C2×C4semidirect
170. C4×Q8×C61C2×C4semidirect
173. C4×D4×C61C2×C4semidirect
174. C4×D4×C61C2×C4semidirect
402. C4×D61#104semidirect
461. #1806D61semidirect
518. C61#21899semidirect
575. C4×Q8C4×D61semidirect
576. C4×Q8C4×D61semidirect
595. C4×D4C4×D61semidirect
596. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591122
#214544512
C4×C4⋊C4×D612
#214467612
#214467362
#214462612
#214462592
#214458402
#214458392
#214458362
C61×#18062
#2189961