Finite Group Databasebeta

← #30611327

Subgroups — #30611327

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462409C211yesmaximal, characteristic, complemented
2#21462322C211yesmaximal, characteristic, complemented
3#21461257C211yesmaximal, characteristic, complemented
4#21461247C211yesmaximal, characteristic, complemented
5#21461246C211yesmaximal, characteristic, complemented
6#21461237C211yesmaximal, characteristic, complemented
7#21461229C211yesmaximal, characteristic, complemented
8#21461228C211yesmaximal, characteristic, complemented
9#21461217C211yesmaximal, characteristic, complemented
10#21461207C211yesmaximal, characteristic, complemented
11#21461206C211yesmaximal, characteristic, complemented
12#21461197C211yesmaximal, characteristic, complemented
13C2×#16840616C211yesmaximal, characteristic, complemented
14D61⋊#328C211yesmaximal, characteristic, complemented
15#21459497C211yesmaximal, characteristic
16C2×#14519864—21no—
17C2×D4×#6923—21no—
18#16840737—21no—
19#16840735—21no—
20#16840735—21no—
21#16840734C2211yescharacteristic
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26D61⋊(C22⋊C8)C2211yescharacteristic
27(C2×#6923)⋊Q8—21no—
28#16840710—21no—
29#16840710—21no—
30#16840705C2211yescharacteristic
31#16840705C2211yescharacteristic
32#16840704C2211yescharacteristic
33C4×C22⋊#6923C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840616C2211yescharacteristic
41#16840616C2211yescharacteristic
42#16840616C2211yescharacteristic
43#16840616C2211yescharacteristic
44#16840615C2211yescharacteristic
45#16840615C2211yescharacteristic
46#16840615C2211yescharacteristic
47#16840615C2211yescharacteristic
48#16840614C2211yescharacteristic
49#16840614C2211yescharacteristic
50#16840614C2211yescharacteristic
51#16840614C2211yescharacteristic
52C2×#14519825C411yescharacteristic, complemented
53C2×#41×D61C2211yescharacteristic
54#16840427—21no—
55#16840420—21no—
56#16840415—21no—
57#16840410—21no—
58#16840410—21no—
59#16840405—21no—
60#16840404—21no—
61#16840404—21no—
62#16840342C411yescharacteristic, complemented
63#16840342C411yescharacteristic, complemented
64#16840340C411yescharacteristic, complemented
65#16840335C411yescharacteristic, complemented
66#16840335C411yescharacteristic, complemented
67#16840275C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840274C2211yescharacteristic
70C2×#14519753C2211yescharacteristic
71C22⋊Q8×D61C2211yescharacteristic
72C22⋊Q8×D61C2211yescharacteristic
73#16840242C411yescharacteristic, complemented
74C61×#536C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77#14519864—44no—
78C2×#11758213—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84D4×#6923—44no—
85C2×C4⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C4×#6923—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97#14519834C2311yescharacteristic
98#14519834C2311yescharacteristic
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108(C2×#6923)⋊C4C2311yescharacteristic
109#14519825—44no—
110C2×#11758226—21no—
111C2×#11758226C2×C411yescharacteristic, complemented
112C2×#11758226C2×C411yescharacteristic, complemented
113C2×#11758226D411yescharacteristic
114C2×#11758222—21no—
115C2×#11758222—21no—
116C2×#11758222C2×C411yescharacteristic
117C2×#11758222C2×C411yescharacteristic
118C2×#11758222C2×C411yescharacteristic
119C2×#11758222C2×C411yescharacteristic, complemented
120C2×#11758224D411yescharacteristic
121C2×#11758224D411yescharacteristic
122C2×#11758224D411yescharacteristic
123#41×D61—44no—
124C2×Q8×D61—21no—
125C2×Q8×D61C2×C411yescharacteristic, complemented
126C2×Q8×D61C2×C411yescharacteristic, complemented
127C2×Q8×D61D411yescharacteristic
128C2×D4×D61D411yescharacteristic
129C2×D4×D61D411yescharacteristic
130C2×D4×D61D411yescharacteristic
131C22×C4×D61C2311yescharacteristic
132C22×C4×D61C2311yescharacteristic
133C22×C4×D61C2311yescharacteristic
134#14519776—21no—
135#14519776—21no—
136#14519763—21no—
137#14519763—21no—
138#14519762—21no—
139#14519762—21no—
140#14519762—21no—
141#14519762—21no—
142#14519761—21no—
143#14519759—21no—
144#14519759—21no—
145#14519757C2×C411yescharacteristic, complemented
146#14519757C2311yescharacteristic
147#14519756C2×C411yescharacteristic, complemented
148#14519756C2×C411yescharacteristic, complemented
149#14519755—21no—
150#14519755—21no—
151#14519755—21no—
152#14519755—21no—
153#14519754—21no—
154#14519754—21no—
155#14519753—21no—
156#14519753—21no—
157#14519753—21no—
158#14519753C2×C411yescharacteristic, complemented
159#14519753C2×C411yescharacteristic, complemented
160#14519753C2311yescharacteristic
161#14519753C2311yescharacteristic
162#14519752—21no—
163#14519752—21no—
164#14519752C2×C411yescharacteristic, complemented
165#14519752C2311yescharacteristic
166#14519751C2×C411yescharacteristic, complemented
167#14519751C2×C411yescharacteristic, complemented
168#14519750—21no—
169#14519750—21no—
170#14519750—21no—
171#14519750—21no—
172#14519749—21no—
173#14519749—21no—
174#14519748—21no—
175#14519747—21no—
176#14519747—21no—
177#14519747—21no—
178C4×Dic122—21no—
179C4×D244—21no—
180C4×D244—21no—
181C4×D244—21no—
182#14519739—21no—
183#14519739—21no—
184#14519737—21no—
185#14519737—21no—
186#14519737—21no—
187#14519737—21no—
188#14519735C2×C411yescharacteristic, complemented
189#14519735C2×C411yescharacteristic, complemented
190C2×C4⋊Dic61C2×C411yescharacteristic, complemented
191C2×#11758196—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2×C411yescharacteristic, complemented
195C4⋊C4×D61C2×C411yescharacteristic, complemented
196C2×#11758198—21no—
197C22⋊C4×D61—21no—
198C22⋊C4×D61—21no—
199C2×#41×C61C2×C411yescharacteristic
200C22×Q8×C61C2×C411yescharacteristic, complemented
201C4⋊Q8×C61—21no—
202#124×C61—21no—
203#123×C61—21no—
204#123×C61—21no—
205C22⋊Q8×C61C2×C411yescharacteristic, complemented
206C22⋊Q8×C61C2×C411yescharacteristic, complemented
207C22⋊Q8×C61C2×C411yescharacteristic, complemented
208C22⋊Q8×C61C2×C411yescharacteristic, complemented
209#117×C61C2×C411yescharacteristic, complemented
210C23×D61C2×D411yescharacteristic
211C23×D61C2×D411yescharacteristic
212C23×D61C2×D411yescharacteristic
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—42no—
218C22×#6923—42no—
219C22×#6923—42no—
220C22×#6923—42no—
221C22×#6923—81no—
222C22×#6923—81no—
223#41×C61—42no—
224C2×Q8×C61—21no—
225C2×Q8×C61—42no—
226C2×Q8×C61C22⋊C411yescharacteristic
227C2×Q8×C61C22×C411yescharacteristic
228C2×Q8×C61C22×C411yescharacteristic
229C2×D4×C61C22⋊C411yescharacteristic
230C2×D4×C61C22⋊C411yescharacteristic
231C2×D4×C61C22⋊C411yescharacteristic
232C22×C4×C61—21no—
233C22×C4×C61C22×C411yescharacteristic
234C22×C4×C61C22×C411yescharacteristic
235C22×C4×C61C22×C411yescharacteristic
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C22×Dic61—21no—
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249#11758226—42no—
250#11758226—42no—
251#11758226—42no—
252#11758226—44no—
253Q8×D61—42no—
254Q8×D61—44no—
255Q8×D61—42no—
256Q8×D61—42no—
257#11758224—24no—
258#11758224—42no—
259#11758224—42no—
260D4×D61—24no—
261D4×D61—42no—
262D4×D61—42no—
263#11758222—24no—
264#11758222—42no—
265#11758222—42no—
266#11758222—44no—
267#11758222—44no—
268#11758222—42no—
269C2×D244—21no—
270C2×D244—21no—
271C2×D244—21no—
272C2×D244—21no—
273C2×D244C22⋊C411yescharacteristic
274C2×D244C22⋊C411yescharacteristic
275C2×D244C22⋊C411yescharacteristic
276C2×D244C22×C411yescharacteristic
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—42no—
285C2×C4×D61—42no—
286C2×C4×D61—42no—
287C2×C4×D61C22×C411yescharacteristic
288C2×C4×D61C22×C411yescharacteristic
289C2×C4×D61C22×C411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2411yescharacteristic
297C2×Dic122—21no—
298C2×Dic122—21no—
299C2×Dic122C22⋊C411yescharacteristic
300C2×Dic122C22⋊C411yescharacteristic
301C2×Dic122C22⋊C411yescharacteristic
302C2×Dic122C22×C411yescharacteristic
303C22⋊#6923—42no—
304C22⋊#6923—42no—
305C22⋊#6923—42no—
306C22⋊#6923—81no—
307#11758217—42no—
308#11758217—42no—
309C2×#92420—21no—
310C2×#92420—21no—
311C2×#92420—21no—
312C2×#92420—21no—
313C2×#92420—42no—
314C2×#92420—42no—
315C4⋊#6923—42no—
316C4×#6923—42no—
317#11758213—42no—
318D61⋊C8—42no—
319C4⋊C4×C61—21no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C4⋊C4×C61—21no—
323C4⋊C4×C61C22×C411yescharacteristic
324C4⋊C4×C61C22×C411yescharacteristic
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C42×C61—21no—
331C22⋊Dic61—21no—
332C22⋊Dic61—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#11758198—21no—
343#11758198—21no—
344#11758198—21no—
345C4⋊Dic61—21no—
346C4⋊Dic61—21no—
347C4⋊Dic61—21no—
348C4⋊Dic61C22×C411yescharacteristic
349C4⋊Dic61C22×C411yescharacteristic
350#11758196—21no—
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—21no—
355#11758196—21no—
356#11758196—21no—
357#11758196—21no—
358C4×Dic61—21no—
359C4×Dic61—21no—
360C23×C61C2×C22⋊C411yescharacteristic
361C23×C61C2×C22⋊C411yescharacteristic
362C23×C61C2×C22⋊C411yescharacteristic
363C22×D61—22no—
364C22×D61—21no—
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—22no—
369C22×D61—21no—
370C22×D61—21no—
371C22×D61—21no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61C2×C22⋊C411yescharacteristic
377C22×D61C2×C22⋊C411yescharacteristic
378C22×D61C2×C22⋊C411yescharacteristic
379C22×D61C22×D411yescharacteristic
380C2×#6923—22no—
381C2×#6923—41no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—84no—
393C2×#6923—84no—
394Q8×C61—41no—
395Q8×C61—42no—
396Q8×C61—41no—
397Q8×C61—41no—
398D4×C61—22no—
399D4×C61—22no—
400D4×C61—41no—
401C2×C4×C61—22no—
402C2×C4×C61—21no—
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×C61C2×C22⋊C411yescharacteristic
410C2×C4×C61C2×C22⋊C411yescharacteristic
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C23×C411yescharacteristic
413C22⋊D61—22no—
414C22⋊D61—22no—
415C22⋊D61—22no—
416C22⋊D61—41no—
417C22⋊D61—41no—
418C22⋊D61—42no—
419C22⋊D61—81no—
420C22⋊D61—81no—
421C22⋊D61#9914yes—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—41no—
428C2×Dic61—81no—
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C22×D411yescharacteristic
433D244—22no—
434D244—22no—
435D244—41no—
436D244—41no—
437D244—42no—
438D244—41no—
439D244—41no—
440D244—42no—
441D244—81no—
442C4×D61—22no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—22no—
446C4×D61—41no—
447C4×D61—41no—
448C4×D61—41no—
449C4×D61—41no—
450C4×D61—41no—
451C4×D61—41no—
452C4×D61—42no—
453C4×D61—42no—
454C4×D61—42no—
455C4×D61—42no—
456C4×D61—42no—
457C4×D61—81no—
458C4×D61—81no—
459Dic122—22no—
460Dic122—22no—
461Dic122—41no—
462Dic122—42no—
463Dic122—42no—
464Dic122—41no—
465#92420—41no—
466#92420—41no—
467#92420—41no—
468#92420—41no—
469#17608—611nomaximal, Sylow
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61C2×#9912yes—
479C22×C61C22×C22⋊C411yescharacteristic
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
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—42no—
493C2×D61—42no—
494C2×D61—41no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—81no—
498C2×D61—81no—
499C2×D61C2×#9912yes—
500C2×D61#57711yescharacteristic
501C2×D61#57811yescharacteristic
502#6923—42no—
503#6923—81no—
504#6923—81no—
505#6923—81no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61—41no—
513C4×C61—41no—
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—41no—
518Dic61—41no—
519Dic61—41no—
520Dic61C2×#9912yes—
521#3489—611no—
522#2880—611no—
523#2339—611no—
524#1520—611no—
525#1516—611no—
526#1516—611no—
527#1513—611no—
528#1511—611no—
529#1511—611no—
530#1508—611no—
531#1504—611no—
532#1504—611no—
533#1501—611no—
534C2×#328—611no—
535C2×#328—611no—
536C2×C61—22no—
537C2×C61—41no—
538C2×C61—41no—
539C2×C61C22×#9911yescharacteristic
540C2×C61#289811yescharacteristic
541C2×C61#290111yescharacteristic
542D61—21no—
543D61—21no—
544D61—22no—
545D61—41no—
546D61—41no—
547D61—81no—
548C2×2−1+4—611no—
549C22×#41—611no—
550C2×#131—1221no—
551D4×Q8—1221no—
552#548—1221no—
553#547—1221no—
554#547—1221no—
555#547—1221no—
556#546—1221no—
557#546—1221no—
558#546—1221no—
559#537—611no—
560#537—611no—
561#537—611no—
562#536—611no—
563#536—611no—
564#536#692311yescharacteristic, complemented
565#525—611no—
566#525—611no—
567#525—611no—
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—611no—
570C2×C22⋊Q8—611no—
571#520—611no—
572C2×C4×D4—1221no—
573#408—1221no—
574#408—1221no—
575#408—1221no—
576#407—611no—
577#407—611no—
578#407—611no—
579C2×C22⋊C8—611no—
580C2×C22⋊C8—611no—
581C2×C22⋊C8—611no—
582#391—1221no—
583#386—1221no—
584#386—1221no—
585#381—611no—
586#381—611no—
587#380—611no—
588C4×C22⋊C4—611no—
589C2×#95—611no—
590C2×#95—611no—
591#328—611no—
592#328—611no—
593#328—611no—
594#328—611no—
595#328—611no—
596#328—611no—
597#328—611no—
598#328—611no—
599#328—611no—
600#328—611no—
601#328—611no—
602#328—611no—
603#327—611no—
604#327—611no—
605#327—611no—
606#327—611no—
607C61#1760811yescharacteristic, complemented, Sylow
6082−1+4—2444no—
609C2×#41—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—611no—
613C2×#41—611no—
614C2×#41—611no—
615C2×#41—611no—
616C2×#41—611no—
617C2×#41—611no—
618C2×#41—611no—
619C2×#41—1221no—
620C2×#41—1221no—
621C2×#41—1221no—
622C2×#41—2444no—
623C2×#41C2×#692311yescharacteristic
624C22×Q8—611no—
625C22×Q8—611no—
626C22×Q8—611no—
627C22×Q8—1221no—
628C22×Q8C2×#692311yescharacteristic, complemented
629C22×D4—611no—
630C22×D4—611no—
631C22×D4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—1221no—
636C23×C4—1221no—
637#131—2444no—
638C2×M16—1221no—
639C2×M16—1221no—
640C2×M16—1221no—
641C22×C8—1221no—
642C22×C8—1221no—
643C22×C8—1221no—
644C4⋊Q8—21no—
645C4⋊Q8—1221no—
646C4⋊Q8—1221no—
647#124—21no—
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—
658#123—1221no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—611no—
665C22⋊Q8—611no—
666C22⋊Q8—611no—
667C22⋊Q8—1221no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8C2×#692311yescharacteristic, complemented
677C22⋊Q8C2×#692311yescharacteristic, complemented
678C22⋊Q8C2×#692311yescharacteristic, complemented
679C22⋊Q8C2×#692311yescharacteristic, complemented
680#121—611no—
681#121—611no—
682#121—611no—
683#121—611no—
684#121—1221no—
685#121—1221no—
686#121—1221no—
687#121—1221no—
688#121—1221no—
689#121—1221no—
690#121—1221no—
691#121—1221no—
692#121—1221no—
693#120—1221no—
694#120—1221no—
695#120—1221no—
696C4×Q8—1221no—
697C4×D4—1221no—
698C4×D4—1221no—
699C4×D4—1221no—
700C4×D4—1221no—
701C4×D4—1221no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4—1221no—
706C4×D4—2444no—
707#117—611no—
708#117—611no—
709#117C2×#692311yescharacteristic, complemented
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C22⋊C4—1221no—
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×C42—1221no—
725C22⋊C8—611no—
726C22⋊C8—611no—
727C22⋊C8—611no—
728C22⋊C8—611no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734C22⋊C8—1221no—
735#95—611no—
736#95—611no—
737#95—611no—
738#95—611no—
739#95—1221no—
740#95—1221no—
741#95—1221no—
742#95—1221no—
743C24—611no—
744C24—611no—
745C24—611no—
746#41—42no—
747#41—1224no—
748#41—1224no—
749#41—2442no—
750#41—2442no—
751#41—2442no—
752#41—2444no—
753#41—2444no—
754#41—2442no—
755#41—2442no—
756#41—2442no—
757#41—2442no—
758#41—2442no—
759#41—2444no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—611no—
763C2×Q8—611no—
764C2×Q8—611no—
765C2×Q8—611no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8—2442no—
769C2×Q8—2442no—
770C2×Q8—2442no—
771C2×Q8—2444no—
772C2×Q8C22⋊#692311yescharacteristic
773C2×Q8C22×#692311yescharacteristic
774C2×Q8C22×#692311yescharacteristic
775C2×D4—611no—
776C2×D4—611no—
777C2×D4—611no—
778C2×D4—611no—
779C2×D4—611no—
780C2×D4—611no—
781C2×D4—611no—
782C2×D4—611no—
783C2×D4—611no—
784C2×D4—611no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1224no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1221no—
793C2×D4—2442no—
794C2×D4—2442no—
795C2×D4C22⋊#692311yescharacteristic
796C2×D4C22⋊#692311yescharacteristic
797C2×D4C22⋊#692311yescharacteristic
798C22×C4—21no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—4881no—
825C22×C4—4881no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4—2442no—
831C22×C4—2442no—
832C22×C4—2442no—
833C22×C4C22×#692311yescharacteristic
834C22×C4C22×#692311yescharacteristic
835C22×C4C22×#692311yescharacteristic
836M16—2442no—
837M16—2442no—
838M16—2442no—
839C2×C8—1221no—
840C2×C8—1221no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—2442no—
844C2×C8—2442no—
845C2×C8—2442no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—611no—
851C4⋊C4—611no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—2442no—
864C4⋊C4C22×#692311yescharacteristic
865C4⋊C4C22×#692311yescharacteristic
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
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—4881no—
886C22⋊C4—2442no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C42—21no—
890C42—1221no—
891C42—1221no—
892C42—2442no—
893C23—611no—
894C23—611no—
895C23—611no—
896C23—611no—
897C23—1221no—
898C23—1221no—
899C23—1222no—
900C23—1221no—
901C23—1221no—
902C23—1221no—
903C23—1221no—
904C23—1222no—
905C23—1221no—
906C23—2441no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23C2×C22⋊#692311yescharacteristic
911C23C2×C22⋊#692311yescharacteristic
912C23C2×C22⋊#692311yescharacteristic
913Q8—41no—
914Q8—41no—
915Q8—41no—
916Q8—42no—
917Q8—1222no—
918Q8—1222no—
919Q8—2441no—
920Q8—2441no—
921Q8—2442no—
922Q8—2442no—
923D4—22no—
924D4—22no—
925D4—41no—
926D4—614no—
927D4—1222no—
928D4—1222no—
929D4—1222no—
930D4—1222no—
931D4—1222no—
932D4—4881no—
933D4—4881no—
934D4—4881no—
935D4—2441no—
936D4—2441no—
937D4—2441no—
938D4—2441no—
939D4—2442no—
940D4—2442no—
941D4—2441no—
942D4—2441no—
943D4—2442no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—4881no—
967C2×C4—4881no—
968C2×C4—4884no—
969C2×C4—4884no—
970C2×C4—4881no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2442no—
978C2×C4—2442no—
979C2×C4—2442no—
980C2×C4—2442no—
981C2×C4—2442no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4C2×C22⋊#692311yescharacteristic
995C2×C4C2×C22⋊#692311yescharacteristic
996C2×C4C2×C22⋊#692311yescharacteristic
997C2×C4C23×#692311yescharacteristic
998C8—2441no—
999C8—2441no—
1000C8—2441no—
1001C8—2441no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—612no—
1011C22—611no—
1012C22—611no—
1013C22—1221no—
1014C22—1221no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—4881no—
1024C22—4881no—
1025C22—2442no—
1026C22—2442no—
1027C22—2442no—
1028C22—2442no—
1029C22—2441no—
1030C22—2441no—
1031C22—2441no—
1032C22D61⋊#9912yes—
1033C22C22×C22⋊#692311yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—612no—
1043C4—1221no—
1044C4—1221no—
1045C4—1221no—
1046C4—4881no—
1047C4—4881no—
1048C4—4881no—
1049C4—2442no—
1050C4—2441no—
1051C4—2441no—
1052C4—2441no—
1053C2—22no—
1054C2—41no—
1055C2—41no—
1056C2—1221no—
1057C2—1221no—
1058C2—1222no—
1059C2—4881no—
1060C2—2441no—
1061C2—2441no—
1062C2C2×D61⋊#9911yescharacteristic
1063C2#2146244111yescharacteristic
1064C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#536C4
socleC22×C61C22×C22⋊C4
prime radical#21459497C2
cosocleC2×C4×D61C24
hypercenter#536#6923
hypocenterC61#17608
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #21462409C2semidirect
2. #21462322C2semidirect
3. #21461257C2semidirect
4. #21461247C2semidirect
5. #21461246C2semidirect
6. #21461237C2semidirect
7. #21461229C2semidirect
8. #21461228C2semidirect
9. #21461217C2semidirect
10. #21461207C2semidirect
11. #21461206C2semidirect
12. #21461197C2semidirect
13. C2×#16840616C2semidirect
14. D61⋊#328C2semidirect
52. C2×#14519825C4semidirect
62. #16840342C4semidirect
63. #16840342C4semidirect
64. #16840340C4semidirect
65. #16840335C4semidirect
66. #16840335C4semidirect
73. #16840242C4semidirect
74. C61×#536C4semidirect
111. C2×#11758226C2×C4semidirect
112. C2×#11758226C2×C4semidirect
119. C2×#11758222C2×C4semidirect
125. C2×Q8×D61C2×C4semidirect
126. C2×Q8×D61C2×C4semidirect
145. #14519757C2×C4semidirect
147. #14519756C2×C4semidirect
148. #14519756C2×C4semidirect
158. #14519753C2×C4semidirect
159. #14519753C2×C4semidirect
164. #14519752C2×C4semidirect
166. #14519751C2×C4semidirect
167. #14519751C2×C4semidirect
188. #14519735C2×C4semidirect
189. #14519735C2×C4semidirect
190. C2×C4⋊Dic61C2×C4semidirect
194. C4⋊C4×D61C2×C4semidirect
195. C4⋊C4×D61C2×C4semidirect
200. C22×Q8×C61C2×C4semidirect
205. C22⋊Q8×C61C2×C4semidirect
206. C22⋊Q8×C61C2×C4semidirect
207. C22⋊Q8×C61C2×C4semidirect
208. C22⋊Q8×C61C2×C4semidirect
209. #117×C61C2×C4semidirect
564. #536#6923semidirect
607. C61#17608semidirect
628. C22×Q8C2×#6923semidirect
676. C22⋊Q8C2×#6923semidirect
677. C22⋊Q8C2×#6923semidirect
678. C22⋊Q8C2×#6923semidirect
679. C22⋊Q8C2×#6923semidirect
709. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624092
#214623222
#214612572
#214612472
#214612462
#214612372
#214612292
#214612282
#214612172
#214612072
#214612062
#214611972
C2×#168406162
D61⋊#3282
#214594972
#1760861