Finite Group Databasebeta

← #30611374

Subgroups — #30611374

Order 15616.

1270 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461256C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461240C211yesmaximal, characteristic, complemented
6#21461238C211yesmaximal, characteristic, complemented
7#21461226C211yesmaximal, characteristic, complemented
8#21461225C211yesmaximal, characteristic, complemented
9#21461216C211yesmaximal, characteristic, complemented
10#21461214C211yesmaximal, characteristic, complemented
11#21461210C211yesmaximal, characteristic, complemented
12#21461209C211yesmaximal, characteristic, complemented
13C2×#16840614C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459577C211yesmaximal, characteristic
16#16840794—21no—
17#16840793—21no—
18#16840792—21no—
19#16840791—21no—
20#16840785C2211yescharacteristic, complemented
21#16840784C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic, complemented
23#16840733C2211yescharacteristic, complemented
24C2×#14519834C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic, complemented
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic, complemented
34#16840698C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840614C2211yescharacteristic, complemented
37#16840614C2211yescharacteristic, complemented
38#16840614C2211yescharacteristic, complemented
39#16840614C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic, complemented
41#16840614C2211yescharacteristic, complemented
42#16840614C2211yescharacteristic, complemented
43#16840614C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic, complemented
45#16840614C2211yescharacteristic, complemented
46#16840614C2211yescharacteristic, complemented
47#16840614C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52C2×#14519823—21no—
53#16840415C411yescharacteristic, complemented
54#16840413C411yescharacteristic, complemented
55#16840413C411yescharacteristic, complemented
56#16840404—21no—
57#16840404—21no—
58#16840403—21no—
59#16840400—21no—
60D4×D244C411yescharacteristic, complemented
61D4×D244C411yescharacteristic, complemented
62#16840396C411yescharacteristic, complemented
63#16840396C411yescharacteristic, complemented
64#16840342—21no—
65#16840323—21no—
66#16840323—21no—
67#16840313C2211yescharacteristic
68#16840309C2211yescharacteristic
69C2×#14519752C2211yescharacteristic
70C2×#14519752C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#121×D61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74C61×#547C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107#14519823—44no—
108#14519823—44no—
109C2×#11758226—21no—
110C2×#11758226—21no—
111C2×#11758222—21no—
112C2×#11758222—21no—
113C2×#11758222—21no—
114C22×D244—21no—
115C22×D244—21no—
116C22×D244—21no—
117C22×D244C2×C411yescharacteristic
118C22×D244C2×C411yescharacteristic, complemented
119C2×D4×D61—21no—
120C2×D4×D61—21no—
121C2×D4×D61—21no—
122C2×D4×D61—21no—
123C2×D4×D61—21no—
124C2×D4×D61C2×C411yescharacteristic
125C2×D4×D61C2×C411yescharacteristic, complemented
126C2×D4×D61D411yescharacteristic
127C22×C4×D61C2311yescharacteristic
128C22×C4×D61C2311yescharacteristic
129#14519776C2×C411yescharacteristic, complemented
130#14519774C2×C411yescharacteristic, complemented
131#14519773C2×C411yescharacteristic, complemented
132#14519766—21no—
133#14519763—21no—
134#14519762—21no—
135#14519762—21no—
136#14519762—21no—
137#14519762—21no—
138#14519760—21no—
139#14519760—21no—
140#14519755—21no—
141#14519755—21no—
142#14519753—21no—
143#14519752—21no—
144#14519752—21no—
145#14519752—21no—
146#14519752—21no—
147#14519752—21no—
148#14519752—21no—
149#14519752C2×C411yescharacteristic
150#14519752C2×C411yescharacteristic
151#14519752C2×C411yescharacteristic, complemented
152#14519752C2×C411yescharacteristic, complemented
153#14519752C2311yescharacteristic
154#14519752C2311yescharacteristic
155#14519752C2311yescharacteristic
156#14519751—21no—
157#14519751C2×C411yescharacteristic
158#14519751C2×C411yescharacteristic, complemented
159#14519750—21no—
160#14519750—21no—
161#14519750—21no—
162#14519750—21no—
163#14519750—21no—
164#14519749—21no—
165#14519749—21no—
166#14519748C2311yescharacteristic
167#14519747—21no—
168#14519747—21no—
169#14519747—21no—
170#14519747—21no—
171#14519747—21no—
172#14519747—21no—
173#14519745—21no—
174#14519745—21no—
175C4×D244C2×C411yescharacteristic
176C4×D244C2×C411yescharacteristic, complemented
177D4×Dic61D411yescharacteristic
178#14519739—21no—
179#14519739C2×C411yescharacteristic, complemented
180#14519739C2×C411yescharacteristic, complemented
181#14519739D411yescharacteristic
182C4×C22⋊D61—21no—
183C4×C22⋊D61C2×C411yescharacteristic
184C4×C22⋊D61C2×C411yescharacteristic
185#14519737D411yescharacteristic
186#14519737D411yescharacteristic
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61C2×C411yescharacteristic, complemented
189C4⋊C4×D61D411yescharacteristic
190C2×#11758198—21no—
191C2×#11758198—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61—21no—
194C22⋊C4×D61D411yescharacteristic
195C22⋊C4×D61D411yescharacteristic
196C42×D61C2311yescharacteristic
197C2×#41×C61—21no—
198C4⋊Q8×C61C2×C411yescharacteristic, complemented
199#123×C61—21no—
200#123×C61—21no—
201C22⋊Q8×C61—21no—
202#121×C61C2×C411yescharacteristic
203#121×C61C2×C411yescharacteristic, complemented
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic, complemented
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61C2×D411yescharacteristic
213C23×D61C2×D411yescharacteristic
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—42no—
219C22×#6923—42no—
220C22×#6923—81no—
221#41×C61—44no—
222C2×Q8×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61C22⋊C411yescharacteristic
226C2×D4×C61C22×C411yescharacteristic
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C22×C411yescharacteristic
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758226—42no—
244#11758226—42no—
245#11758226—44no—
246D4×D61—22no—
247D4×D61—22no—
248D4×D61—44no—
249D4×D61—44no—
250D4×D61—44no—
251D4×D61—42no—
252D4×D61—42no—
253D4×D61—42no—
254D4×D61—42no—
255D4×D61—81no—
256D4×D61—81no—
257#11758222—42no—
258#11758222—42no—
259#11758222—44no—
260#11758222—44no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244—21no—
264C2×D244—21no—
265C2×D244—21no—
266C2×D244—21no—
267C2×D244—21no—
268C2×D244—21no—
269C2×D244—21no—
270C2×D244—21no—
271C2×D244—21no—
272C2×D244—44no—
273C2×D244—42no—
274C2×D244—42no—
275C2×D244—42no—
276C2×D244—42no—
277C2×D244—81no—
278C2×D244—81no—
279C2×D244C22⋊C411yescharacteristic
280C2×D244C22×C411yescharacteristic
281C2×D244C22×C411yescharacteristic
282C2×D244C22×C411yescharacteristic
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—81no—
289C2×C4×D61—81no—
290C2×C4×D61C22×C411yescharacteristic
291C2×C4×D61C22×C411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×C4×D61C2411yescharacteristic
299C2×Dic122—21no—
300C22⋊#6923—42no—
301C22⋊#6923—42no—
302C22⋊#6923—81no—
303#11758217—81no—
304C2×#92420—21no—
305C2×#92420—21no—
306C2×#92420—21no—
307C2×#92420—21no—
308C2×#92420—81no—
309C4⋊#6923—81no—
310C4×#6923—42no—
311C4×#6923—81no—
312#11758213—81no—
313D61⋊C8—81no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61C22⋊C411yescharacteristic
318C4⋊C4×C61C22×C411yescharacteristic
319C4⋊C4×C61C22×C411yescharacteristic
320C4⋊C4×C61C22×C411yescharacteristic
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61C22⋊C411yescharacteristic
325C22⋊C4×C61C22⋊C411yescharacteristic
326C42×C61C22×C411yescharacteristic
327C22⋊Dic61—21no—
328C22⋊Dic61C22⋊C411yescharacteristic
329C22⋊Dic61C22⋊C411yescharacteristic
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—21no—
339#11758198—21no—
340#11758198—21no—
341#11758198—21no—
342#11758198C22⋊C411yescharacteristic
343#11758198C22⋊C411yescharacteristic
344#11758198C22⋊C411yescharacteristic
345#11758198C22⋊C411yescharacteristic
346C4⋊Dic61C22⋊C411yescharacteristic
347C4⋊Dic61C22×C411yescharacteristic
348#11758196—21no—
349#11758196—21no—
350#11758196—21no—
351#11758196C22⋊C411yescharacteristic
352#11758196C22⋊C411yescharacteristic
353C4×Dic61C22×C411yescharacteristic
354C4×Dic61C2×D411yescharacteristic
355C4×Dic61C2×D411yescharacteristic
356C23×C61—21no—
357C23×C61C2×C22⋊C411yescharacteristic
358C23×C61C2×C22⋊C411yescharacteristic
359C22×D61—21no—
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—42no—
369C22×D61—42no—
370C22×D61—42no—
371C22×D61—42no—
372C22×D61—81no—
373C22×D61—81no—
374C22×D61—81no—
375C22×D61—81no—
376C22×D61—81no—
377C22×D61—81no—
378C22×D61—81no—
379C22×D61—81no—
380C22×D61C2×C22⋊C411yescharacteristic
381C22×D61C2×C22⋊C411yescharacteristic
382C22×D61AGL(1,ℤ/8)12yes—
383C22×D61AGL(1,ℤ/8)12yes—
384C22×D61C22×D411yescharacteristic
385C2×#6923—22no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—84no—
398Q8×C61—42no—
399D4×C61—22no—
400D4×C61—41no—
401D4×C61—42no—
402D4×C61—42no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C23×C411yescharacteristic
416C22⋊D61—22no—
417C22⋊D61—22no—
418C22⋊D61—42no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C22⋊D61—41no—
422C22⋊D61—41no—
423C22⋊D61—81no—
424C22⋊D61—81no—
425C22⋊D61—81no—
426C2×Dic61—21no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C2×C22⋊C411yescharacteristic
433C2×Dic61C22×D411yescharacteristic
434D244—22no—
435D244—41no—
436D244—41no—
437D244—41no—
438D244—42no—
439D244—42no—
440D244—42no—
441D244—41no—
442D244—41no—
443D244—41no—
444D244—41no—
445D244—41no—
446D244—41no—
447D244—42no—
448D244—42no—
449D244—81no—
450D244—81no—
451D244—81no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—42no—
463C4×D61—42no—
464C4×D61—42no—
465C4×D61—42no—
466C4×D61—42no—
467Dic122—42no—
468#92420—41no—
469#92420—41no—
470#92420—41no—
471#92420—41no—
472#17620—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61#41812yes—
482C22×C61C22×C22⋊C411yescharacteristic
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—41no—
493C2×D61—41no—
494C2×D61—41no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61—41no—
499C2×D61—41no—
500C2×D61—41no—
501C2×D61—81no—
502C2×D61—81no—
503C2×D61—162no—
504C2×D61—162no—
505C2×D61—162no—
506C2×D61—162no—
507C2×D61#41812yes—
508C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
509C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
510#6923—42no—
511#6923—81no—
512#6923—81no—
513#6923—81no—
514C4×C61—21no—
515C4×C61—21no—
516C4×C61—21no—
517C4×C61—21no—
518C4×C61—21no—
519C4×C61—41no—
520C4×C61—41no—
521C4×C61—41no—
522Dic61—21no—
523Dic61—21no—
524Dic61—21no—
525Dic61—21no—
526Dic61—21no—
527Dic61—41no—
528#3496—611no—
529#2973—611no—
530#2353—611no—
531#1519—611no—
532#1519—611no—
533#1514—611no—
534#1514—611no—
535#1510—611no—
536#1510—611no—
537#1507—611no—
538#1507—611no—
539#1505—611no—
540#1505—611no—
541C2×#327—611no—
542C2×#327—611no—
543C2×C61—22no—
544C2×C61—41no—
545C2×C61—81no—
546C2×C61#288311yescharacteristic
547C2×C61C2×#41811yescharacteristic
548C2×C61#290111yescharacteristic
549D61—21no—
550D61—21no—
551D61—22no—
552D61—41no—
553D61—81no—
554D61—81no—
555D61—81no—
556C2×H(5,𝔽2)—1221no—
557#547—611no—
558#547—611no—
559#547—611no—
560#547#692311yescharacteristic, complemented
561#546—1221no—
562#546—1221no—
563#546—1221no—
564#546—1221no—
565D42—611no—
566D42—611no—
567D42—611no—
568D42—611no—
569#537—1221no—
570#534—1221no—
571#534—1221no—
572#532—611no—
573#532—611no—
574C2×#121—611no—
575C2×#121—611no—
576C2×#121—611no—
577C2×#121—611no—
578C2×C4×D4—611no—
579#435—1221no—
580#435—1221no—
581#435—1221no—
582#435—1221no—
583#432—611no—
584#432—611no—
585#407—611no—
586#407—611no—
587C2×C22⋊C8—611no—
588C2×C22⋊C8—611no—
589#388—1221no—
590#387—1221no—
591#386—1221no—
592#383—611no—
593#381—611no—
594#380—611no—
595C4×C22⋊C4—611no—
596C4×C22⋊C4—1221no—
597#376—611no—
598C2×#95—611no—
599#327—611no—
600#327—611no—
601#327—611no—
602#327—611no—
603#327—611no—
604#327—611no—
605#327—611no—
606#327—611no—
607#327—611no—
608#327—611no—
609#327—611no—
610#327—611no—
611#327—611no—
612#327—611no—
613#327—611no—
614#327—611no—
615C61#1762011yescharacteristic, complemented, Sylow
616H(5,𝔽2)—2444no—
617H(5,𝔽2)—2444no—
618C2×#41—21no—
619C2×#41—1221no—
620C2×#41—1221no—
621C2×#41—1221no—
622C2×#41—1221no—
623C2×#41—1221no—
624C22×D4—611no—
625C22×D4—611no—
626C22×D4—611no—
627C22×D4—611no—
628C22×D4—611no—
629C22×D4—1221no—
630C22×D4—1221no—
631C22×D4—1221no—
632C22×D4—1221no—
633C22×D4—1221no—
634C22×D4—1221no—
635C22×D4—1221no—
636C22×D4—1221no—
637C23×C4—611no—
638C23×C4—611no—
639C23×C4—1221no—
640C2×M16—1221no—
641C2×M16—1221no—
642C22×C8—1221no—
643C22×C8—1221no—
644C4⋊Q8—611no—
645C4⋊Q8C2×#692311yescharacteristic, complemented
646#127—611no—
647#127—611no—
648#124—1221no—
649#124—1221no—
650#123—21no—
651#123—21no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656#123—1221no—
657#123—1221no—
658C22⋊Q8—21no—
659C22⋊Q8—1221no—
660C22⋊Q8—1221no—
661C22⋊Q8—1221no—
662#121—611no—
663#121—611no—
664#121—611no—
665#121—611no—
666#121—611no—
667#121—611no—
668#121—611no—
669#121—611no—
670#121—611no—
671#121—611no—
672#121—1221no—
673#121—1221no—
674#121—1221no—
675#121—1221no—
676#121—1221no—
677#121—1221no—
678#121—1221no—
679#121—1221no—
680#121—1221no—
681#121—1221no—
682#121—1221no—
683#121—1221no—
684#121—1221no—
685#121—1221no—
686#121C2×#692311yescharacteristic
687#121C2×#692311yescharacteristic, complemented
688#120—1221no—
689#120—1221no—
690#120—1221no—
691#120—1221no—
692#120—1221no—
693#120—1221no—
694#120—1221no—
695#120—1221no—
696C4×D4—611no—
697C4×D4—611no—
698C4×D4—611no—
699C4×D4—611no—
700C4×D4—611no—
701C4×D4—611no—
702C4×D4—611no—
703C4×D4—611no—
704C4×D4—611no—
705C4×D4—611no—
706C4×D4—1221no—
707C4×D4—1221no—
708C4×D4C2×#692311yescharacteristic
709C4×D4C2×#692311yescharacteristic, complemented
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4C2×#692311yescharacteristic
715C2×C4⋊C4C2×#692311yescharacteristic, complemented
716C2×C22⋊C4—611no—
717C2×C22⋊C4—611no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C22⋊C4—1221no—
725C2×C42—611no—
726C2×C42—1221no—
727C2×C42—1221no—
728C4⋊C8—1221no—
729C4⋊C8—1221no—
730C22⋊C8—611no—
731C22⋊C8—611no—
732C22⋊C8—611no—
733C22⋊C8—611no—
734C22⋊C8—1221no—
735C22⋊C8—1221no—
736C22⋊C8—1221no—
737C22⋊C8—1221no—
738#97—1221no—
739#97—1221no—
740#95—611no—
741#95—611no—
742#95—611no—
743#95—611no—
744#95—1221no—
745#95—1221no—
746#95—1221no—
747#95—1221no—
748#95—1221no—
749C24—611no—
750C24—611no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755#41—44no—
756#41—2442no—
757#41—2442no—
758#41—2444no—
759#41—2444no—
760#41—2442no—
761#41—2442no—
762#41—2444no—
763C2×Q8—21no—
764C2×Q8—1221no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—611no—
768C2×D4—611no—
769C2×D4—611no—
770C2×D4—611no—
771C2×D4—611no—
772C2×D4—611no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—1221no—
776C2×D4—1221no—
777C2×D4—1221no—
778C2×D4—1221no—
779C2×D4—1221no—
780C2×D4—1221no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1221no—
784C2×D4—1222no—
785C2×D4—1222no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1221no—
793C2×D4—4881no—
794C2×D4—4881no—
795C2×D4—4881no—
796C2×D4—4881no—
797C2×D4—2444no—
798C2×D4—2442no—
799C2×D4—2442no—
800C2×D4—2442no—
801C2×D4—2442no—
802C2×D4—2444no—
803C2×D4—2444no—
804C2×D4—2444no—
805C2×D4—2442no—
806C2×D4—2442no—
807C2×D4—2442no—
808C2×D4—2442no—
809C2×D4C22⋊#692311yescharacteristic
810C2×D4C22×#692311yescharacteristic
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—4881no—
835C22×C4—4881no—
836C22×C4—4881no—
837C22×C4—2442no—
838C22×C4—2442no—
839C22×C4C22×#692311yescharacteristic
840C22×C4C22×#692311yescharacteristic
841M16—4881no—
842M16—4881no—
843C2×C8—1221no—
844C2×C8—1221no—
845C2×C8—1221no—
846C2×C8—1221no—
847C2×C8—4881no—
848C2×C8—4881no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—611no—
853C4⋊C4—611no—
854C4⋊C4—611no—
855C4⋊C4—611no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—4881no—
860C4⋊C4C22⋊#692311yescharacteristic
861C4⋊C4C22×#692311yescharacteristic
862C4⋊C4C22×#692311yescharacteristic
863C4⋊C4C22×#692311yescharacteristic
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—611no—
868C22⋊C4—611no—
869C22⋊C4—611no—
870C22⋊C4—611no—
871C22⋊C4—611no—
872C22⋊C4—611no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—1221no—
886C22⋊C4—4881no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C22⋊C4C22⋊#692311yescharacteristic
890C22⋊C4C22⋊#692311yescharacteristic
891C42—611no—
892C42—611no—
893C42—611no—
894C42—4881no—
895C42—2442no—
896C42C22×#692311yescharacteristic
897C23—21no—
898C23—611no—
899C23—611no—
900C23—612no—
901C23—612no—
902C23—611no—
903C23—1221no—
904C23—1221no—
905C23—1221no—
906C23—1221no—
907C23—1221no—
908C23—4881no—
909C23—4881no—
910C23—4881no—
911C23—4881no—
912C23—4881no—
913C23—4881no—
914C23—4881no—
915C23—4881no—
916C23—2441no—
917C23—2441no—
918C23—2441no—
919C23—2441no—
920C23—2442no—
921C23—2442no—
922C23—2442no—
923C23—2442no—
924C23C2×C22⋊#692311yescharacteristic
925C23C2×C22⋊#692311yescharacteristic
926Q8—42no—
927Q8—2442no—
928D4—22no—
929D4—41no—
930D4—42no—
931D4—42no—
932D4—1222no—
933D4—1222no—
934D4—1222no—
935D4—4881no—
936D4—4881no—
937D4—4881no—
938D4—4881no—
939D4—4881no—
940D4—4881no—
941D4—2441no—
942D4—2441no—
943D4—2441no—
944D4—2442no—
945D4—2441no—
946D4—2441no—
947D4—2442no—
948D4—2441no—
949D4—2441no—
950D4—2441no—
951D4—2441no—
952D4—2442no—
953D4—2442no—
954D4—2442no—
955D4—2442no—
956D4—2442no—
957D4—2441no—
958D4—2441no—
959D4—2442no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—611no—
969C2×C4—611no—
970C2×C4—611no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—1222no—
976C2×C4—1221no—
977C2×C4—4884no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2442no—
987C2×C4—2442no—
988C2×C4—2442no—
989C2×C4—2442no—
990C2×C4—2442no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4C2×C22⋊#692311yescharacteristic
1005C2×C4C2×C22⋊#692311yescharacteristic
1006C2×C4C2×C22⋊#692311yescharacteristic
1007C2×C4C2×C22⋊#692311yescharacteristic
1008C2×C4C23×#692311yescharacteristic
1009C8—2441no—
1010C8—2441no—
1011C8—2441no—
1012C8—2441no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—611no—
1022C22—611no—
1023C22—612no—
1024C22—1221no—
1025C22—1221no—
1026C22—1221no—
1027C22—1221no—
1028C22—1221no—
1029C22—1221no—
1030C22—1221no—
1031C22—9762no—
1032C22—9762no—
1033C22—9762no—
1034C22—9762no—
1035C22—4881no—
1036C22—4881no—
1037C22—2442no—
1038C22—2442no—
1039C22—2441no—
1040C22—2441no—
1041C22—2441no—
1042C22—2441no—
1043C22—2441no—
1044C22—2441no—
1045C22—2441no—
1046C22—2441no—
1047C22—2441no—
1048C22#1684075412yes—
1049C22C22×C22⋊#692311yescharacteristic
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—41no—
1056C4—41no—
1057C4—41no—
1058C4—1221no—
1059C4—1221no—
1060C4—1221no—
1061C4—1221no—
1062C4—1221no—
1063C4—4881no—
1064C4—4881no—
1065C4—4881no—
1066C4—2442no—
1067C4—2441no—
1068C2—22no—
1069C2—41no—
1070C2—81no—
1071C2—1221no—
1072C2—1221no—
1073C2—1222no—
1074C2—4881no—
1075C2—4881no—
1076C2—4881no—
1077C2—2441no—
1078C2#2146241911yescharacteristic
1079C2C2×#1684075411yescharacteristic
1080C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459577C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#17620
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462336C2semidirect
3. #21461256C2semidirect
4. #21461254C2semidirect
5. #21461240C2semidirect
6. #21461238C2semidirect
7. #21461226C2semidirect
8. #21461225C2semidirect
9. #21461216C2semidirect
10. #21461214C2semidirect
11. #21461210C2semidirect
12. #21461209C2semidirect
13. C2×#16840614C2semidirect
14. D61⋊#327C2semidirect
20. #16840785C22semidirect
21. #16840784C22semidirect
22. #16840734C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840707C22semidirect
30. #16840705C22semidirect
31. #16840704C22semidirect
33. C4×C22⋊#6923C22semidirect
34. #16840698C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840614C22semidirect
37. #16840614C22semidirect
38. #16840614C22semidirect
39. #16840614C22semidirect
40. #16840614C22semidirect
41. #16840614C22semidirect
42. #16840614C22semidirect
43. #16840614C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
53. #16840415C4semidirect
54. #16840413C4semidirect
55. #16840413C4semidirect
60. D4×D244C4semidirect
61. D4×D244C4semidirect
62. #16840396C4semidirect
63. #16840396C4semidirect
74. C61×#547C4semidirect
118. C22×D244C2×C4semidirect
125. C2×D4×D61C2×C4semidirect
129. #14519776C2×C4semidirect
130. #14519774C2×C4semidirect
131. #14519773C2×C4semidirect
151. #14519752C2×C4semidirect
152. #14519752C2×C4semidirect
158. #14519751C2×C4semidirect
176. C4×D244C2×C4semidirect
179. #14519739C2×C4semidirect
180. #14519739C2×C4semidirect
188. C4⋊C4×D61C2×C4semidirect
198. C4⋊Q8×C61C2×C4semidirect
203. #121×C61C2×C4semidirect
205. C4×D4×C61C2×C4semidirect
207. C2×C4⋊C4×C61C2×C4semidirect
560. #547#6923semidirect
615. C61#17620semidirect
645. C4⋊Q8C2×#6923semidirect
687. #121C2×#6923semidirect
709. C4×D4C2×#6923semidirect
715. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612562
#214612542
#214612402
#214612382
#214612262
#214612252
#214612162
#214612142
#214612102
#214612092
C2×#168406142
D61⋊#3272
#214595772
#1762061