Finite Group Databasebeta

← #30611297

Subgroups — #30611297

Order 15616.

1366 conjugacy classes of subgroups.

The subgroup lattice has 1128 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#21461254C211yesmaximal, characteristic, complemented
4#21461246C211yesmaximal, characteristic, complemented
5#21461245C211yesmaximal, characteristic, complemented
6#21461237C211yesmaximal, characteristic, complemented
7#21461226C211yesmaximal, characteristic, complemented
8#21461225C211yesmaximal, characteristic, complemented
9#21461214C211yesmaximal, characteristic, complemented
10#21461206C211yesmaximal, characteristic, complemented
11#21461205C211yesmaximal, characteristic, complemented
12#21461197C211yesmaximal, characteristic, complemented
13C2×#16840614C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459483C211yesmaximal, characteristic
16C2×#14519864—21no—
17C2×D4×#6923—21no—
18#16840737—21no—
19#16840735—21no—
20#16840735—21no—
21#16840734C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic, complemented
23#16840733C2211yescharacteristic, complemented
24C2×#14519834C2211yescharacteristic, complemented
25C2×#14519834C2211yescharacteristic, complemented
26D61⋊(C22⋊C8)C2211yescharacteristic, complemented
27(C2×#6923)⋊Q8—21no—
28#16840710—21no—
29#16840710—21no—
30#16840705C2211yescharacteristic, complemented
31#16840705C2211yescharacteristic, complemented
32#16840704C2211yescharacteristic, complemented
33C4×C22⋊#6923C2211yescharacteristic, complemented
34C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, 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×#14519823C411yescharacteristic, complemented
53C2×#41×D61C2211yescharacteristic
54#16840430—21no—
55#16840422—21no—
56#16840403—21no—
57#16840401—21no—
58#16840401—21no—
59#16840396—21no—
60#16840396—21no—
61#16840396—21no—
62#16840342C411yescharacteristic, complemented
63#16840342C411yescharacteristic, complemented
64#16840328C411yescharacteristic, complemented
65#16840328C411yescharacteristic, complemented
66#16840326C411yescharacteristic, complemented
67#16840275C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519752C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#121×D61C2211yescharacteristic
73#16840243C411yescharacteristic, complemented
74C61×#537C411yescharacteristic, 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#14519823—44no—
110C2×#11758226C2×C411yescharacteristic, complemented
111C2×#11758226C2×C411yescharacteristic, complemented
112C2×#11758226D411yescharacteristic
113C2×#11758222—21no—
114C2×#11758222C2×C411yescharacteristic
115C2×#11758222C2×C411yescharacteristic
116C2×#11758222C2×C411yescharacteristic
117C2×#11758224D411yescharacteristic
118C2×#11758224D411yescharacteristic
119C2×#11758224D411yescharacteristic
120#41×D61—44no—
121C2×Q8×D61D411yescharacteristic
122C22×D244—21no—
123C22×D244—21no—
124C22×D244C2×C411yescharacteristic, complemented
125C2×D4×D61—21no—
126C2×D4×D61—21no—
127C2×D4×D61—21no—
128C2×D4×D61—21no—
129C2×D4×D61C2×C411yescharacteristic, complemented
130C2×D4×D61C2×C411yescharacteristic, complemented
131C2×D4×D61D411yescharacteristic
132C2×D4×D61D411yescharacteristic
133C2×D4×D61D411yescharacteristic
134C22×C4×D61C2311yescharacteristic
135C22×C4×D61C2311yescharacteristic
136C22×C4×D61C2311yescharacteristic
137#14519773—21no—
138#14519773—21no—
139#14519773—21no—
140#14519766—21no—
141#14519763—21no—
142#14519763—21no—
143#14519762—21no—
144#14519762—21no—
145#14519758—21no—
146#14519755—21no—
147#14519755—21no—
148#14519753C2×C411yescharacteristic, complemented
149#14519753C2311yescharacteristic
150#14519752—21no—
151#14519752—21no—
152#14519752—21no—
153#14519752—21no—
154#14519752C2×C411yescharacteristic, complemented
155#14519752C2×C411yescharacteristic, complemented
156#14519752C2311yescharacteristic
157#14519752C2311yescharacteristic
158#14519751C2×C411yescharacteristic, complemented
159#14519751C2×C411yescharacteristic, complemented
160#14519751C2×C411yescharacteristic, complemented
161#14519751C2×C411yescharacteristic, complemented
162#14519750—21no—
163#14519750—21no—
164#14519750—21no—
165#14519750—21no—
166#14519750—21no—
167#14519750—21no—
168#14519749—21no—
169#14519749—21no—
170#14519748C2×C411yescharacteristic, complemented
171#14519748C2311yescharacteristic
172#14519747—21no—
173#14519747—21no—
174#14519747—21no—
175#14519747—21no—
176#14519745—21no—
177#14519745—21no—
178#14519745—21no—
179#14519745—21no—
180#14519745—21no—
181#14519742—21no—
182#14519739—21no—
183#14519739—21no—
184#14519739—21no—
185C4×C22⋊D61—21no—
186C4×C22⋊D61—21no—
187C4×C22⋊D61—21no—
188C4×C22⋊D61—21no—
189#14519737—21no—
190#14519737—21no—
191#14519736C2×C411yescharacteristic, complemented
192#14519735C2×C411yescharacteristic, complemented
193#14519735C2×C411yescharacteristic, complemented
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
200C2×#41×C61C2×C411yescharacteristic, complemented
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61C2×C411yescharacteristic, complemented
203C22⋊Q8×C61C2×C411yescharacteristic, complemented
204#121×C61—21no—
205#121×C61—21no—
206#121×C61—21no—
207#121×C61C2×C411yescharacteristic, complemented
208#121×C61C2×C411yescharacteristic, complemented
209C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61C2×D411yescharacteristic
214C23×D61C2×D411yescharacteristic
215C23×D61C2×D411yescharacteristic
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—42no—
221C22×#6923—42no—
222C22×#6923—42no—
223C22×#6923—42no—
224C22×#6923—81no—
225C22×#6923—81no—
226#41×C61—42no—
227#41×C61—42no—
228C2×Q8×C61C22⋊C411yescharacteristic
229C2×Q8×C61C22×C411yescharacteristic
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61C22⋊C411yescharacteristic
234C2×D4×C61C22⋊C411yescharacteristic
235C2×D4×C61C22⋊C411yescharacteristic
236C2×D4×C61C22×C411yescharacteristic
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61C22×C411yescharacteristic
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61—21no—
247C2×C22⋊D61—21no—
248C2×C22⋊D61—21no—
249C2×C22⋊D61—21no—
250C2×C22⋊D61C22⋊C411yescharacteristic
251C2×C22⋊D61C22⋊C411yescharacteristic
252C2×C22⋊D61C22⋊C411yescharacteristic
253C2×C22⋊D61C22⋊C411yescharacteristic
254C2×C22⋊D61C22⋊C411yescharacteristic
255C2×C22⋊D61C22⋊C411yescharacteristic
256C22×Dic61C2×D411yescharacteristic
257C22×Dic61C2×D411yescharacteristic
258C22×Dic61C2×D411yescharacteristic
259#11758226—42no—
260#11758226—42no—
261#11758226—42no—
262Q8×D61—42no—
263#11758224—24no—
264#11758224—42no—
265#11758224—42no—
266D4×D61—24no—
267D4×D61—42no—
268D4×D61—42no—
269D4×D61—42no—
270D4×D61—42no—
271D4×D61—44no—
272D4×D61—44no—
273D4×D61—81no—
274D4×D61—81no—
275D4×D61—81no—
276D4×D61—81no—
277#11758222—24no—
278#11758222—42no—
279#11758222—44no—
280#11758222—42no—
281C2×D244—21no—
282C2×D244—21no—
283C2×D244—21no—
284C2×D244—21no—
285C2×D244—21no—
286C2×D244—21no—
287C2×D244—21no—
288C2×D244—44no—
289C2×D244—42no—
290C2×D244—81no—
291C2×D244—81no—
292C2×D244C22⋊C411yescharacteristic
293C2×D244C22⋊C411yescharacteristic
294C2×D244C22⋊C411yescharacteristic
295C2×D244C22×C411yescharacteristic
296C2×D244C22×C411yescharacteristic
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—21no—
300C2×C4×D61—21no—
301C2×C4×D61—42no—
302C2×C4×D61—42no—
303C2×C4×D61—42no—
304C2×C4×D61C22×C411yescharacteristic
305C2×C4×D61C22×C411yescharacteristic
306C2×C4×D61C22×C411yescharacteristic
307C2×C4×D61C2×D411yescharacteristic
308C2×C4×D61C2×D411yescharacteristic
309C2×C4×D61C2×D411yescharacteristic
310C2×C4×D61C2×D411yescharacteristic
311C2×C4×D61C2×D411yescharacteristic
312C2×C4×D61C2×D411yescharacteristic
313C2×C4×D61C2411yescharacteristic
314C2×Dic122C22⋊C411yescharacteristic
315C2×Dic122C22⋊C411yescharacteristic
316C2×Dic122C22⋊C411yescharacteristic
317C22⋊#6923—42no—
318C22⋊#6923—42no—
319C22⋊#6923—42no—
320C22⋊#6923—81no—
321#11758217—42no—
322#11758217—42no—
323C2×#92420—21no—
324C2×#92420—21no—
325C2×#92420—21no—
326C2×#92420—21no—
327C2×#92420—42no—
328C2×#92420—42no—
329C4⋊#6923—42no—
330C4×#6923—42no—
331#11758213—42no—
332D61⋊C8—42no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—21no—
336C4⋊C4×C61C22×C411yescharacteristic
337C4⋊C4×C61C22×C411yescharacteristic
338C22⋊C4×C61—21no—
339C22⋊C4×C61—21no—
340C22⋊C4×C61—21no—
341C22⋊C4×C61—21no—
342C22⋊Dic61—21no—
343C22⋊Dic61—21no—
344C22⋊Dic61—21no—
345#11758198—21no—
346#11758198—21no—
347#11758198—21no—
348#11758198—21no—
349#11758198—21no—
350#11758198—21no—
351#11758198—21no—
352#11758198—21no—
353#11758198—21no—
354#11758198—21no—
355#11758198—21no—
356#11758198—21no—
357C4⋊Dic61C22×C411yescharacteristic
358C4⋊Dic61C22×C411yescharacteristic
359#11758196—21no—
360#11758196—21no—
361#11758196—21no—
362#11758196—21no—
363C4×Dic61—21no—
364C4×Dic61—21no—
365C4×Dic61—21no—
366C23×C61—21no—
367C23×C61C2×C22⋊C411yescharacteristic
368C23×C61C2×C22⋊C411yescharacteristic
369C23×C61C2×C22⋊C411yescharacteristic
370C22×D61—22no—
371C22×D61—21no—
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—22no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—42no—
385C22×D61—42no—
386C22×D61—42no—
387C22×D61—81no—
388C22×D61—81no—
389C22×D61—81no—
390C22×D61—81no—
391C22×D61—81no—
392C22×D61—81no—
393C22×D61C2×C22⋊C411yescharacteristic
394C22×D61C2×C22⋊C411yescharacteristic
395C22×D61C2×C22⋊C411yescharacteristic
396C22×D61C22×D411yescharacteristic
397C2×#6923—22no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—84no—
410C2×#6923—84no—
411Q8×C61—41no—
412Q8×C61—41no—
413D4×C61—22no—
414D4×C61—22no—
415D4×C61—41no—
416D4×C61—41no—
417D4×C61—42no—
418D4×C61—81no—
419D4×C61—81no—
420C2×C4×C61—22no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—42no—
427C2×C4×C61—81no—
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C2×C22⋊C411yescharacteristic
430C2×C4×C61C2×C22⋊C411yescharacteristic
431C2×C4×C61C23×C411yescharacteristic
432C22⋊D61—22no—
433C22⋊D61—22no—
434C22⋊D61—22no—
435C22⋊D61—41no—
436C22⋊D61—41no—
437C22⋊D61—42no—
438C22⋊D61—41no—
439C22⋊D61—41no—
440C22⋊D61—42no—
441C22⋊D61—81no—
442C22⋊D61—81no—
443C22⋊D61—81no—
444C22⋊D61—81no—
445C22⋊D61—81no—
446C22⋊D61#9914yes—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—41no—
452C2×Dic61C2×C22⋊C411yescharacteristic
453C2×Dic61C2×C22⋊C411yescharacteristic
454C2×Dic61C2×C22⋊C411yescharacteristic
455C2×Dic61C22×D411yescharacteristic
456D244—22no—
457D244—22no—
458D244—41no—
459D244—41no—
460D244—41no—
461D244—42no—
462D244—42no—
463D244—41no—
464D244—41no—
465D244—41no—
466D244—41no—
467D244—42no—
468D244—81no—
469D244—81no—
470C4×D61—22no—
471C4×D61—22no—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—41no—
475C4×D61—41no—
476C4×D61—41no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—42no—
481C4×D61—42no—
482C4×D61—81no—
483C4×D61—81no—
484Dic122—22no—
485Dic122—22no—
486Dic122—41no—
487#92420—41no—
488#92420—41no—
489#92420—41no—
490#92420—41no—
491#17603—611nomaximal, Sylow
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—21no—
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—21no—
498C22×C61—21no—
499C22×C61—21no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61C2×#9912yes—
504C22×C61C22×C22⋊C411yescharacteristic
505C2×D61—21no—
506C2×D61—21no—
507C2×D61—21no—
508C2×D61—21no—
509C2×D61—21no—
510C2×D61—21no—
511C2×D61—21no—
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—21no—
515C2×D61—42no—
516C2×D61—42no—
517C2×D61—42no—
518C2×D61—42no—
519C2×D61—41no—
520C2×D61—41no—
521C2×D61—41no—
522C2×D61—41no—
523C2×D61—41no—
524C2×D61—41no—
525C2×D61—81no—
526C2×D61—81no—
527C2×D61—162no—
528C2×D61—162no—
529C2×D61—162no—
530C2×D61C2×#9912yes—
531C2×D61#57611yescharacteristic
532C2×D61#57711yescharacteristic
533#6923—42no—
534#6923—81no—
535#6923—81no—
536#6923—81no—
537C4×C61—21no—
538C4×C61—21no—
539C4×C61—21no—
540C4×C61—21no—
541C4×C61—41no—
542C4×C61—41no—
543C4×C61—41no—
544Dic61—21no—
545Dic61—21no—
546Dic61—21no—
547Dic61—41no—
548Dic61—41no—
549Dic61C2×#9912yes—
550#3488—611no—
551#2880—611no—
552#2339—611no—
553#1519—611no—
554#1516—611no—
555#1516—611no—
556#1513—611no—
557#1510—611no—
558#1510—611no—
559#1507—611no—
560#1504—611no—
561#1504—611no—
562#1501—611no—
563C2×#327—611no—
564C2×#327—611no—
565C2×C61—22no—
566C2×C61—41no—
567C2×C61—41no—
568C2×C61—81no—
569C2×C61C22×#9911yescharacteristic
570C2×C61#289711yescharacteristic
571C2×C61#290111yescharacteristic
572D61—21no—
573D61—21no—
574D61—22no—
575D61—41no—
576D61—41no—
577D61—81no—
578D61—81no—
579C2×H(5,𝔽2)—611no—
580C22×#41—611no—
581C2×#131—1221no—
582#550—1221no—
583#548—1221no—
584#546—1221no—
585#546—1221no—
586#546—1221no—
587D42—1221no—
588D42—1221no—
589D42—1221no—
590#537—611no—
591#537—611no—
592#537#692311yescharacteristic, complemented
593#535—611no—
594#535—611no—
595#535—611no—
596#525—611no—
597#525—611no—
598#525—611no—
599C2×#121—611no—
600C2×#121—611no—
601C2×#121—611no—
602#520—611no—
603C2×C4×D4—1221no—
604#408—1221no—
605#408—1221no—
606#408—1221no—
607#407—611no—
608#407—611no—
609#407—611no—
610C2×C22⋊C8—611no—
611C2×C22⋊C8—611no—
612C2×C22⋊C8—611no—
613#391—1221no—
614#386—1221no—
615#386—1221no—
616#381—611no—
617#381—611no—
618#380—611no—
619C4×C22⋊C4—611no—
620C2×#95—611no—
621C2×#95—611no—
622#328—611no—
623#328—611no—
624#328—611no—
625#328—611no—
626#327—611no—
627#327—611no—
628#327—611no—
629#327—611no—
630#327—611no—
631#327—611no—
632#327—611no—
633#327—611no—
634#327—611no—
635#327—611no—
636#327—611no—
637#327—611no—
638C61#1760311yescharacteristic, complemented, Sylow
639H(5,𝔽2)—2444no—
640C2×#41—611no—
641C2×#41—611no—
642C2×#41—611no—
643C2×#41—611no—
644C2×#41—611no—
645C2×#41—611no—
646C2×#41—611no—
647C2×#41—611no—
648C2×#41—611no—
649C2×#41—1221no—
650C2×#41—2444no—
651C2×#41C2×#692311yescharacteristic
652C2×#41C2×#692311yescharacteristic, complemented
653C22×Q8—611no—
654C22×D4—611no—
655C22×D4—611no—
656C22×D4—611no—
657C22×D4—611no—
658C22×D4—611no—
659C22×D4—611no—
660C22×D4—1221no—
661C22×D4—1221no—
662C22×D4—1221no—
663C22×D4—1221no—
664C22×D4—1221no—
665C22×D4—1221no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—1221no—
670C23×C4—1221no—
671#131—2444no—
672C2×M16—1221no—
673C2×M16—1221no—
674C2×M16—1221no—
675C22×C8—1221no—
676C22×C8—1221no—
677C22×C8—1221no—
678#127—1221no—
679#127—1221no—
680#127—1221no—
681#124—1221no—
682#124—1221no—
683#124—1221no—
684#123—1221no—
685#123—1221no—
686#123—1221no—
687C22⋊Q8—21no—
688C22⋊Q8—611no—
689C22⋊Q8—611no—
690C22⋊Q8—1221no—
691C22⋊Q8—1221no—
692C22⋊Q8C2×#692311yescharacteristic, complemented
693C22⋊Q8C2×#692311yescharacteristic, complemented
694#121—21no—
695#121—21no—
696#121—21no—
697#121—611no—
698#121—611no—
699#121—611no—
700#121—611no—
701#121—611no—
702#121—611no—
703#121—611no—
704#121—611no—
705#121—611no—
706#121—611no—
707#121—1221no—
708#121—1221no—
709#121—1221no—
710#121—1221no—
711#121—1221no—
712#121—1221no—
713#121—1221no—
714#121—1221no—
715#121—1221no—
716#121—1221no—
717#121—1221no—
718#121—1221no—
719#121C2×#692311yescharacteristic, complemented
720#121C2×#692311yescharacteristic, complemented
721#120—1221no—
722#120—1221no—
723#120—1221no—
724#120—1221no—
725#120—1221no—
726#120—1221no—
727#120—1221no—
728#120—1221no—
729#120—1221no—
730C4×Q8—1221no—
731C4×D4—1221no—
732C4×D4—1221no—
733C4×D4—1221no—
734C4×D4—1221no—
735C4×D4—1221no—
736C4×D4—1221no—
737C4×D4—1221no—
738C4×D4—1221no—
739C4×D4—1221no—
740C4×D4—2444no—
741#117—611no—
742#117—611no—
743#117—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—611no—
746C2×C4⋊C4—1221no—
747C2×C4⋊C4C2×#692311yescharacteristic, complemented
748C2×C22⋊C4—1221no—
749C2×C22⋊C4—1221no—
750C2×C22⋊C4—1221no—
751C2×C22⋊C4—1221no—
752C2×C22⋊C4—1221no—
753C2×C22⋊C4—1221no—
754C2×C22⋊C4—1221no—
755C2×C42—1221no—
756C22⋊C8—611no—
757C22⋊C8—611no—
758C22⋊C8—611no—
759C22⋊C8—611no—
760C22⋊C8—1221no—
761C22⋊C8—1221no—
762C22⋊C8—1221no—
763C22⋊C8—1221no—
764C22⋊C8—1221no—
765C22⋊C8—1221no—
766#95—611no—
767#95—611no—
768#95—611no—
769#95—611no—
770#95—1221no—
771#95—1221no—
772#95—1221no—
773#95—1221no—
774C24—611no—
775C24—611no—
776C24—611no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780#41—42no—
781#41—42no—
782#41—1224no—
783#41—1224no—
784#41—2442no—
785#41—2442no—
786#41—2444no—
787#41—2442no—
788#41—2442no—
789#41—2442no—
790#41—2442no—
791#41—2442no—
792C2×Q8—611no—
793C2×Q8—611no—
794C2×Q8—611no—
795C2×Q8—2442no—
796C2×Q8C22⋊#692311yescharacteristic
797C2×Q8C22×#692311yescharacteristic
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—611no—
802C2×D4—611no—
803C2×D4—611no—
804C2×D4—611no—
805C2×D4—611no—
806C2×D4—611no—
807C2×D4—611no—
808C2×D4—611no—
809C2×D4—611no—
810C2×D4—611no—
811C2×D4—611no—
812C2×D4—1221no—
813C2×D4—1221no—
814C2×D4—1221no—
815C2×D4—1221no—
816C2×D4—1221no—
817C2×D4—1221no—
818C2×D4—1221no—
819C2×D4—1221no—
820C2×D4—1224no—
821C2×D4—1221no—
822C2×D4—1221no—
823C2×D4—1221no—
824C2×D4—1221no—
825C2×D4—1221no—
826C2×D4—1221no—
827C2×D4—1221no—
828C2×D4—4881no—
829C2×D4—4881no—
830C2×D4—4881no—
831C2×D4—4881no—
832C2×D4—4881no—
833C2×D4—4881no—
834C2×D4—2442no—
835C2×D4—2444no—
836C2×D4—2442no—
837C2×D4—2442no—
838C2×D4—2442no—
839C2×D4—2444no—
840C2×D4—2442no—
841C2×D4—2444no—
842C2×D4C22⋊#692311yescharacteristic
843C2×D4C22⋊#692311yescharacteristic
844C2×D4C22⋊#692311yescharacteristic
845C2×D4C22×#692311yescharacteristic
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—611no—
860C22×C4—611no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—4881no—
870C22×C4—4881no—
871C22×C4—2442no—
872C22×C4—2442no—
873C22×C4—2442no—
874C22×C4—2442no—
875C22×C4—2442no—
876C22×C4—2442no—
877C22×C4—2442no—
878C22×C4C22×#692311yescharacteristic
879C22×C4C22×#692311yescharacteristic
880C22×C4C22×#692311yescharacteristic
881M16—2442no—
882M16—2442no—
883M16—2442no—
884C2×C8—1221no—
885C2×C8—1221no—
886C2×C8—1221no—
887C2×C8—1221no—
888C2×C8—2442no—
889C2×C8—2442no—
890C2×C8—2442no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—611no—
895C4⋊C4—611no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—2442no—
901C4⋊C4C22×#692311yescharacteristic
902C4⋊C4C22×#692311yescharacteristic
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—1221no—
908C22⋊C4—1221no—
909C22⋊C4—1221no—
910C22⋊C4—1221no—
911C22⋊C4—1221no—
912C22⋊C4—1221no—
913C22⋊C4—1221no—
914C22⋊C4—1221no—
915C22⋊C4—1221no—
916C22⋊C4—1221no—
917C22⋊C4—1221no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4—1221no—
921C22⋊C4—1221no—
922C22⋊C4—4881no—
923C22⋊C4—2442no—
924C22⋊C4—2442no—
925C22⋊C4—2442no—
926C42—1221no—
927C42—1221no—
928C42—1221no—
929C42—2442no—
930C23—21no—
931C23—611no—
932C23—611no—
933C23—611no—
934C23—611no—
935C23—1221no—
936C23—1221no—
937C23—1222no—
938C23—1221no—
939C23—1221no—
940C23—1221no—
941C23—1221no—
942C23—1222no—
943C23—1221no—
944C23—1221no—
945C23—4881no—
946C23—4881no—
947C23—4881no—
948C23—4881no—
949C23—4881no—
950C23—4881no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2442no—
956C23—2442no—
957C23—2442no—
958C23C2×C22⋊#692311yescharacteristic
959C23C2×C22⋊#692311yescharacteristic
960C23C2×C22⋊#692311yescharacteristic
961Q8—41no—
962Q8—41no—
963Q8—1222no—
964Q8—1222no—
965Q8—2441no—
966D4—22no—
967D4—22no—
968D4—41no—
969D4—41no—
970D4—42no—
971D4—81no—
972D4—81no—
973D4—614no—
974D4—1222no—
975D4—1222no—
976D4—1222no—
977D4—1222no—
978D4—1222no—
979D4—4881no—
980D4—4881no—
981D4—4881no—
982D4—4881no—
983D4—4881no—
984D4—4881no—
985D4—4881no—
986D4—2441no—
987D4—2441no—
988D4—2441no—
989D4—2442no—
990D4—2441no—
991D4—2441no—
992D4—2441no—
993D4—2441no—
994D4—2442no—
995D4—2442no—
996D4—2442no—
997D4—2441no—
998D4—2441no—
999D4—2442no—
1000D4—2441no—
1001D4—2441no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—42no—
1009C2×C4—81no—
1010C2×C4—611no—
1011C2×C4—611no—
1012C2×C4—611no—
1013C2×C4—611no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—4881no—
1024C2×C4—4881no—
1025C2×C4—4884no—
1026C2×C4—4884no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2442no—
1034C2×C4—2442no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4C2×C22⋊#692311yescharacteristic
1048C2×C4C2×C22⋊#692311yescharacteristic
1049C2×C4C2×C22⋊#692311yescharacteristic
1050C2×C4C23×#692311yescharacteristic
1051C8—2441no—
1052C8—2441no—
1053C8—2441no—
1054C8—2441no—
1055C22—21no—
1056C22—21no—
1057C22—21no—
1058C22—21no—
1059C22—21no—
1060C22—21no—
1061C22—21no—
1062C22—21no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—612no—
1067C22—611no—
1068C22—611no—
1069C22—1221no—
1070C22—1221no—
1071C22—1221no—
1072C22—1221no—
1073C22—1221no—
1074C22—1221no—
1075C22—1221no—
1076C22—1221no—
1077C22—1221no—
1078C22—1221no—
1079C22—9762no—
1080C22—9762no—
1081C22—9762no—
1082C22—4881no—
1083C22—4881no—
1084C22—2442no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2441no—
1089C22—2441no—
1090C22—2441no—
1091C22—2441no—
1092C22—2441no—
1093C22—2441no—
1094C22D61⋊#9912yes—
1095C22C22×C22⋊#692311yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—612no—
1104C4—1221no—
1105C4—1221no—
1106C4—1221no—
1107C4—4881no—
1108C4—4881no—
1109C4—4881no—
1110C4—2442no—
1111C4—2441no—
1112C4—2441no—
1113C2—22no—
1114C2—41no—
1115C2—41no—
1116C2—81no—
1117C2—1221no—
1118C2—1221no—
1119C2—1222no—
1120C2—4881no—
1121C2—4881no—
1122C2—2441no—
1123C2—2441no—
1124C2C2×D61⋊#9911yescharacteristic
1125C2#2146244011yescharacteristic
1126C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#537C4
socleC22×C61C22×C22⋊C4
prime radical#21459483C2
cosocleC2×C4×D61C24
hypercenter#537#6923
hypocenterC61#17603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #21462409C2semidirect
2. #21462322C2semidirect
3. #21461254C2semidirect
4. #21461246C2semidirect
5. #21461245C2semidirect
6. #21461237C2semidirect
7. #21461226C2semidirect
8. #21461225C2semidirect
9. #21461214C2semidirect
10. #21461206C2semidirect
11. #21461205C2semidirect
12. #21461197C2semidirect
13. C2×#16840614C2semidirect
14. D61⋊#327C2semidirect
21. #16840734C22semidirect
22. #16840734C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. C2×#14519834C22semidirect
26. D61⋊(C22⋊C8)C22semidirect
30. #16840705C22semidirect
31. #16840705C22semidirect
32. #16840704C22semidirect
33. C4×C22⋊#6923C22semidirect
34. C2×(C2×#6923)⋊C4C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840614C22semidirect
41. #16840614C22semidirect
42. #16840614C22semidirect
43. #16840614C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. C2×#14519823C4semidirect
62. #16840342C4semidirect
63. #16840342C4semidirect
64. #16840328C4semidirect
65. #16840328C4semidirect
66. #16840326C4semidirect
73. #16840243C4semidirect
74. C61×#537C4semidirect
110. C2×#11758226C2×C4semidirect
111. C2×#11758226C2×C4semidirect
124. C22×D244C2×C4semidirect
129. C2×D4×D61C2×C4semidirect
130. C2×D4×D61C2×C4semidirect
148. #14519753C2×C4semidirect
154. #14519752C2×C4semidirect
155. #14519752C2×C4semidirect
158. #14519751C2×C4semidirect
159. #14519751C2×C4semidirect
160. #14519751C2×C4semidirect
161. #14519751C2×C4semidirect
170. #14519748C2×C4semidirect
191. #14519736C2×C4semidirect
192. #14519735C2×C4semidirect
193. #14519735C2×C4semidirect
194. C4⋊C4×D61C2×C4semidirect
195. C4⋊C4×D61C2×C4semidirect
200. C2×#41×C61C2×C4semidirect
202. C22⋊Q8×C61C2×C4semidirect
203. C22⋊Q8×C61C2×C4semidirect
207. #121×C61C2×C4semidirect
208. #121×C61C2×C4semidirect
209. C2×C4⋊C4×C61C2×C4semidirect
592. #537#6923semidirect
638. C61#17603semidirect
652. C2×#41C2×#6923semidirect
692. C22⋊Q8C2×#6923semidirect
693. C22⋊Q8C2×#6923semidirect
719. #121C2×#6923semidirect
720. #121C2×#6923semidirect
747. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624092
#214623222
#214612542
#214612462
#214612452
#214612372
#214612262
#214612252
#214612142
#214612062
#214612052
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C2×#168406142
D61⋊#3272
#214594832
#1760361