Finite Group Databasebeta

← #30610993

Subgroups — #30610993

Order 15616.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic, complemented
3#21461222C211yesmaximal, characteristic, complemented
4#21461216C211yesmaximal, characteristic, complemented
5#21461214C211yesmaximal, characteristic, complemented
6#21461209C211yesmaximal, characteristic, complemented
7#21461207C211yesmaximal, characteristic, complemented
8#21461204C211yesmaximal, characteristic, complemented
9#21461198C211yesmaximal, characteristic, complemented
10#21461196C211yesmaximal, characteristic, complemented
11#21461195C211yesmaximal, characteristic, complemented
12#21461193C211yesmaximal, characteristic, complemented
13C2×#16840614C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459844C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17#16840795—21no—
18#16840793—21no—
19#16840792—21no—
20#16840789—21no—
21#16840785C2211yescharacteristic, complemented
22#16840780C2211yescharacteristic, complemented
23#16840734C2211yescharacteristic, complemented
24#16840733C2211yescharacteristic, complemented
25C2×#14519834C2211yescharacteristic, complemented
26D61⋊(C22⋊C8)C2211yescharacteristic, complemented
27C4⋊C4×#6923—21no—
28C4×C4⋊#6923C2211yescharacteristic, complemented
29C22⋊C4×#6923—21no—
30C22⋊C4×#6923—21no—
31C4×C22⋊#6923C2211yescharacteristic, complemented
32C4×C22⋊#6923C2211yescharacteristic, complemented
33#16840698C2211yescharacteristic, complemented
34C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic
41#16840614C2211yescharacteristic
42#16840614C2211yescharacteristic
43#16840614C2211yescharacteristic
44#16840614C2211yescharacteristic, complemented
45#16840614C2211yescharacteristic, complemented
46#16840614C2211yescharacteristic, complemented
47#16840614C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840475C411yescharacteristic, complemented
53#16840467C411yescharacteristic, complemented
54#16840465C411yescharacteristic, complemented
55#16840463—21no—
56#16840430C411yescharacteristic, complemented
57#16840408—21no—
58#16840408C411yescharacteristic, complemented
59#16840407C411yescharacteristic, complemented
60#16840404—21no—
61#16840396—21no—
62#16840396C411yescharacteristic, complemented
63#16840364—21no—
64#16840351—21no—
65#16840349—21no—
66#16840309C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840272C2211yescharacteristic
70C2×#14519752C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81D4×#6923—28no—
82C2×C4⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89#14519844—21no—
90#14519844—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99#14519832—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108C2×#11758222—21no—
109C2×#11758222C2×C411yescharacteristic, complemented
110C2×#11758224C2×C411yescharacteristic, complemented
111C22×D244—21no—
112C22×D244C2×C411yescharacteristic, complemented
113C2×D4×D61—21no—
114C2×D4×D61—21no—
115C2×D4×D61C2×C411yescharacteristic, complemented
116C2×D4×D61D411yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119#14519776C2×C411yescharacteristic, complemented
120#14519773—21no—
121#14519773C2×C411yescharacteristic, complemented
122#14519772—21no—
123#14519772—21no—
124#14519767—21no—
125#14519765—21no—
126#14519765C2×C411yescharacteristic, complemented
127#14519763—21no—
128#14519763—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519761—21no—
133#14519761—21no—
134#14519759—21no—
135#14519757C2×C411yescharacteristic, complemented
136#14519757C2311yescharacteristic
137#14519756—21no—
138#14519756C2×C411yescharacteristic, complemented
139#14519755—21no—
140#14519752—21no—
141#14519752—21no—
142#14519752—21no—
143#14519752C2×C411yescharacteristic, complemented
144#14519752C2×C411yescharacteristic, complemented
145#14519752C2×C411yescharacteristic, complemented
146#14519752C2311yescharacteristic
147#14519752C2311yescharacteristic
148#14519751—21no—
149#14519751C2×C411yescharacteristic, complemented
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519750—21no—
154#14519750—21no—
155#14519750—21no—
156#14519749—21no—
157#14519749—21no—
158#14519748C2311yescharacteristic
159#14519747—21no—
160#14519747—21no—
161#14519747—21no—
162#14519745—21no—
163#14519745—21no—
164#14519745—21no—
165#14519742C2×C411yescharacteristic, complemented
166C4×D244—21no—
167C4×D244—21no—
168C4×D244C2×C411yescharacteristic
169C4×D244C2×C411yescharacteristic, complemented
170D4×Dic61—21no—
171D4×Dic61D411yescharacteristic
172#14519739—21no—
173#14519739—21no—
174#14519739C2×C411yescharacteristic, complemented
175#14519739D411yescharacteristic
176C4×C22⋊D61—21no—
177C4×C22⋊D61—21no—
178C4×C22⋊D61C2×C411yescharacteristic
179C4×C22⋊D61C2×C411yescharacteristic
180#14519737—21no—
181#14519737—21no—
182#14519737D411yescharacteristic
183#14519737D411yescharacteristic
184#14519735—21no—
185#14519735C2×C411yescharacteristic, complemented
186#14519734—21no—
187C4⋊C4×D61C2×C411yescharacteristic, complemented
188C4⋊C4×D61D411yescharacteristic
189C2×#11758198—21no—
190C2×#11758198—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61D411yescharacteristic
194C22⋊C4×D61D411yescharacteristic
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61C2×C411yescharacteristic, complemented
198#123×C61—21no—
199#121×C61—21no—
200#121×C61C2×C411yescharacteristic, complemented
201#121×C61C2×C411yescharacteristic, complemented
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic, complemented
205#117×C61C2×C411yescharacteristic, complemented
206C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
207C23×D61—21no—
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210C23×D61C2×D411yescharacteristic
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—24no—
216C22×#6923—24no—
217C22×#6923—81no—
218C22×#6923—81no—
219C22×#6923—81no—
220C22×#6923—81no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61C22⋊C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C22×Dic61—21no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758224—81no—
242D4×D61—24no—
243D4×D61—44no—
244D4×D61—81no—
245D4×D61—81no—
246D4×D61—81no—
247#11758222—81no—
248#11758222—81no—
249#11758222—81no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244—81no—
257C2×D244—81no—
258C2×D244—81no—
259C2×D244C22⋊C411yescharacteristic
260C2×D244C22×C411yescharacteristic
261C2×D244C22×C411yescharacteristic
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—81no—
267C2×C4×D61—81no—
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×C4×D61C2411yescharacteristic
277C2×Dic122—21no—
278C2×Dic122C22×C411yescharacteristic
279C22⋊#6923—24no—
280C22⋊#6923—24no—
281#11758217—81no—
282C2×#92420—21no—
283C2×#92420—21no—
284C2×#92420—21no—
285C2×#92420—21no—
286C2×#92420—81no—
287C4⋊#6923—24no—
288C4×#6923—24no—
289C4×#6923—81no—
290C4×#6923—81no—
291C4×#6923—81no—
292#11758213—81no—
293D61⋊C8—81no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61C22⋊C411yescharacteristic
298C4⋊C4×C61C22×C411yescharacteristic
299C4⋊C4×C61C22×C411yescharacteristic
300C4⋊C4×C61C22×C411yescharacteristic
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61C22⋊C411yescharacteristic
306C22⋊C4×C61C22⋊C411yescharacteristic
307C42×C61—21no—
308C42×C61C22×C411yescharacteristic
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61C22⋊C411yescharacteristic
312C22⋊Dic61C22⋊C411yescharacteristic
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198C22⋊C411yescharacteristic
327#11758198C22⋊C411yescharacteristic
328#11758198C22⋊C411yescharacteristic
329#11758198C22⋊C411yescharacteristic
330C4⋊Dic61—21no—
331C4⋊Dic61—21no—
332C4⋊Dic61C22⋊C411yescharacteristic
333C4⋊Dic61C22×C411yescharacteristic
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196C22⋊C411yescharacteristic
339#11758196C22⋊C411yescharacteristic
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61C22×C411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C23×C61—21no—
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C411yescharacteristic
348C22×D61—22no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—22no—
354C22×D61—21no—
355C22×D61—21no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—81no—
361C22×D61—81no—
362C22×D61—81no—
363C22×D61—81no—
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61C22×D411yescharacteristic
367C2×#6923—22no—
368C2×#6923—22no—
369C2×#6923—22no—
370C2×#6923—22no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—41no—
376C2×#6923—41no—
377C2×#6923—41no—
378C2×#6923—41no—
379C2×#6923—84no—
380C2×#6923—84no—
381D4×C61—22no—
382D4×C61—41no—
383D4×C61—42no—
384D4×C61—81no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—81no—
391C2×C4×C61—81no—
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C23×C411yescharacteristic
397C22⋊D61—22no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—42no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C22⋊D61—81no—
405C22⋊D61—81no—
406C22⋊D61#10414yes—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—81no—
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C22×D411yescharacteristic
417D244—22no—
418D244—41no—
419D244—41no—
420D244—41no—
421D244—41no—
422D244—41no—
423D244—41no—
424D244—42no—
425D244—81no—
426D244—81no—
427D244—81no—
428C4×D61—21no—
429C4×D61—21no—
430C4×D61—22no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—42no—
439C4×D61—81no—
440C4×D61—81no—
441C4×D61—81no—
442Dic122—41no—
443Dic122—81no—
444#92420—41no—
445#92420—41no—
446#92420—41no—
447#92420—41no—
448#17547—611nomaximal, Sylow
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61C2×#10412yes—
458C22×C61C22×C22⋊C411yescharacteristic
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—42no—
467C2×D61—42no—
468C2×D61—42no—
469C2×D61—42no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—41no—
474C2×D61—41no—
475C2×D61—41no—
476C2×D61—162no—
477C2×D61—162no—
478C2×D61C2×#10412yes—
479C2×D61#57611yescharacteristic
480C2×D61#57711yescharacteristic
481#6923—42no—
482#6923—42no—
483#6923—42no—
484#6923—42no—
485C4×C61—21no—
486C4×C61—21no—
487C4×C61—21no—
488C4×C61—21no—
489C4×C61—21no—
490C4×C61—41no—
491C4×C61—41no—
492C4×C61—41no—
493Dic61—21no—
494Dic61—21no—
495Dic61—21no—
496Dic61—21no—
497Dic61—41no—
498Dic61—41no—
499Dic61C2×#10412yes—
500#3519—611no—
501#2974—611no—
502#2275—611no—
503#1509—611no—
504#1507—611no—
505#1507—611no—
506#1505—611no—
507#1504—611no—
508#1504—611no—
509#1502—611no—
510#1501—611no—
511#1501—611no—
512#1500—611no—
513C2×#327—611no—
514C2×#327—611no—
515C2×C61—22no—
516C2×C61—41no—
517C2×C61—81no—
518C2×C61#288311yescharacteristic
519C2×C61#289711yescharacteristic
520C2×C61C22×#10411yescharacteristic
521D61—21no—
522D61—21no—
523D61—22no—
524D61—41no—
525D61—81no—
526D61—81no—
527#555—611no—
528#554—611no—
529#553—611no—
530#553—1221no—
531#553#692311yescharacteristic, complemented
532#550—611no—
533#546—611no—
534#546—611no—
535#546—1221no—
536#546—1221no—
537D42—611no—
538D42—1221no—
539#540—1221no—
540#538—1221no—
541#538—1221no—
542#532—611no—
543#529—611no—
544#525—611no—
545#525—611no—
546C2×#121—611no—
547C2×#121—611no—
548#518—1221no—
549C2×C4×D4—611no—
550C2×C4×D4—1221no—
551#436—1221no—
552#435—1221no—
553#435—1221no—
554C8×D4—1221no—
555#432—611no—
556#431—611no—
557#407—611no—
558#407—611no—
559C2×C22⋊C8—611no—
560C2×C22⋊C8—611no—
561C4×C4⋊C4—611no—
562C4×C4⋊C4—1221no—
563C4×C22⋊C4—611no—
564C4×C22⋊C4—611no—
565C4×C22⋊C4—1221no—
566C4×C22⋊C4—1221no—
567#376—611no—
568C2×#95—611no—
569C2×#95—611no—
570#328—611no—
571#328—611no—
572#328—611no—
573#328—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580#327—611no—
581#327—611no—
582#327—611no—
583#327—611no—
584#327—611no—
585#327—611no—
586C61#1754711yescharacteristic, complemented, Sylow
587C2×#41—611no—
588C2×#41—611no—
589C2×#41—1221no—
590C22×D4—611no—
591C22×D4—611no—
592C22×D4—611no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4—1221no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—1221no—
599C23×C4—1221no—
600C2×M16—1221no—
601C2×M16—1221no—
602C22×C8—1221no—
603C22×C8—1221no—
604C4⋊Q8—611no—
605#127—611no—
606#127—1221no—
607#126—21no—
608#126—1221no—
609#126—1221no—
610#125—1221no—
611#125C2×#692311yescharacteristic, complemented
612#124—611no—
613#124—1221no—
614#124—1221no—
615#124—1221no—
616#123—21no—
617#123—1221no—
618#123—1221no—
619#123—1221no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623C22⋊Q8—611no—
624C22⋊Q8—611no—
625C22⋊Q8—611no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628#121—21no—
629#121—611no—
630#121—611no—
631#121—611no—
632#121—611no—
633#121—611no—
634#121—611no—
635#121—611no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#121—1221no—
643#121—1221no—
644#121—1221no—
645#121—1221no—
646#121—1221no—
647#121—1221no—
648#121C2×#692311yescharacteristic, complemented
649#121C2×#692311yescharacteristic, complemented
650#120—1221no—
651#120—1221no—
652#120—1221no—
653#120—1221no—
654#120—1221no—
655#120—1221no—
656C4×Q8—611no—
657C4×D4—21no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—611no—
664C4×D4—611no—
665C4×D4—611no—
666C4×D4—611no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4—1221no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4—1221no—
676C4×D4—1228no—
677C4×D4C2×#692311yescharacteristic
678C4×D4C2×#692311yescharacteristic, complemented
679#117—611no—
680#117—1221no—
681#117—1221no—
682#117C2×#692311yescharacteristic, complemented
683C2×C4⋊C4—611no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—1221no—
686C2×C4⋊C4C2×#692311yescharacteristic, complemented
687C2×C22⋊C4—611no—
688C2×C22⋊C4—611no—
689C2×C22⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C42—611no—
696C2×C42—1221no—
697C2×C42—1221no—
698C2×C42—1221no—
699C2×C42—1221no—
700C4⋊C8—1221no—
701C4⋊C8—1221no—
702C22⋊C8—611no—
703C22⋊C8—611no—
704C22⋊C8—611no—
705C22⋊C8—611no—
706C22⋊C8—1221no—
707C22⋊C8—1221no—
708C22⋊C8—1221no—
709C22⋊C8—1221no—
710#97—1221no—
711C4×C8—1221no—
712#95—611no—
713#95—611no—
714#95—611no—
715#95—611no—
716#95—1221no—
717#95—1221no—
718#95—1221no—
719C24—611no—
720C24—611no—
721C24—1221no—
722C24—1221no—
723#41—4881no—
724#41—4881no—
725#41—4881no—
726#41—4881no—
727C2×Q8—611no—
728C2×Q8—1221no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—611no—
732C2×D4—611no—
733C2×D4—611no—
734C2×D4—611no—
735C2×D4—611no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1224no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—4881no—
751C2×D4—4881no—
752C2×D4—4881no—
753C2×D4—4881no—
754C2×D4—4881no—
755C2×D4—4881no—
756C2×D4—2444no—
757C2×D4C22⋊#692311yescharacteristic
758C2×D4C22×#692311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1224no—
776C22×C4—1224no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—4881no—
784C22×C4—4881no—
785C22×C4—4881no—
786C22×C4—4881no—
787C22×C4—4881no—
788C22×C4—4881no—
789C22×C4C22×#692311yescharacteristic
790C22×C4C22×#692311yescharacteristic
791M16—4881no—
792M16—4881no—
793C2×C8—1221no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—4881no—
798C2×C8—4881no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—611no—
803C4⋊C4—611no—
804C4⋊C4—611no—
805C4⋊C4—611no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1224no—
812C4⋊C4—1221no—
813C4⋊C4C22⋊#692311yescharacteristic
814C4⋊C4C22×#692311yescharacteristic
815C4⋊C4C22×#692311yescharacteristic
816C4⋊C4C22×#692311yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—611no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1224no—
838C22⋊C4—1224no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4C22⋊#692311yescharacteristic
845C22⋊C4C22⋊#692311yescharacteristic
846C42—21no—
847C42—611no—
848C42—611no—
849C42—611no—
850C42—1221no—
851C42—1221no—
852C42—1224no—
853C42—4881no—
854C42—4881no—
855C42—4881no—
856C42C22×#692311yescharacteristic
857C23—21no—
858C23—611no—
859C23—611no—
860C23—611no—
861C23—1222no—
862C23—1221no—
863C23—1221no—
864C23—1221no—
865C23—1221no—
866C23—1222no—
867C23—1221no—
868C23—1221no—
869C23—4881no—
870C23—4881no—
871C23—4881no—
872C23—4881no—
873C23—2441no—
874C23—2441no—
875C23—2442no—
876C23—2442no—
877C23C2×C22⋊#692311yescharacteristic
878C23C2×C22⋊#692311yescharacteristic
879Q8—4881no—
880Q8—2441no—
881D4—22no—
882D4—41no—
883D4—42no—
884D4—81no—
885D4—614no—
886D4—1222no—
887D4—1222no—
888D4—4881no—
889D4—4881no—
890D4—4881no—
891D4—4881no—
892D4—4881no—
893D4—4881no—
894D4—4881no—
895D4—4881no—
896D4—2441no—
897D4—2441no—
898D4—2441no—
899D4—2441no—
900D4—2441no—
901D4—2441no—
902D4—2442no—
903D4—2442no—
904D4—2441no—
905D4—2441no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—1222no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—4881no—
928C2×C4—4881no—
929C2×C4—4881no—
930C2×C4—4881no—
931C2×C4—4884no—
932C2×C4—4884no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2442no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4C2×C22⋊#692311yescharacteristic
952C2×C4C2×C22⋊#692311yescharacteristic
953C2×C4C2×C22⋊#692311yescharacteristic
954C2×C4C2×C22⋊#692311yescharacteristic
955C2×C4C23×#692311yescharacteristic
956C8—2441no—
957C8—2441no—
958C8—2441no—
959C8—2441no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—611no—
969C22—611no—
970C22—612no—
971C22—1221no—
972C22—1221no—
973C22—1221no—
974C22—1221no—
975C22—1221no—
976C22—1221no—
977C22—1221no—
978C22—9762no—
979C22—9762no—
980C22—2442no—
981C22—2442no—
982C22—2442no—
983C22—2442no—
984C22—2441no—
985C22—2441no—
986C22—2441no—
987C22—2441no—
988C22—2441no—
989C22—2441no—
990C22D61⋊#10412yes—
991C22C22×C22⋊#692311yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—21no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—612no—
1001C4—1221no—
1002C4—1221no—
1003C4—1221no—
1004C4—1221no—
1005C4—2442no—
1006C4—2442no—
1007C4—2442no—
1008C4—2442no—
1009C4—2441no—
1010C4—2441no—
1011C2—22no—
1012C2—41no—
1013C2—81no—
1014C2—1221no—
1015C2—1221no—
1016C2—1222no—
1017C2—4881no—
1018C2—4881no—
1019C2—2441no—
1020C2#2146241911yescharacteristic
1021C2#2146244011yescharacteristic
1022C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459844C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#17547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462258C2semidirect
3. #21461222C2semidirect
4. #21461216C2semidirect
5. #21461214C2semidirect
6. #21461209C2semidirect
7. #21461207C2semidirect
8. #21461204C2semidirect
9. #21461198C2semidirect
10. #21461196C2semidirect
11. #21461195C2semidirect
12. #21461193C2semidirect
13. C2×#16840614C2semidirect
14. D61⋊#327C2semidirect
21. #16840785C22semidirect
22. #16840780C22semidirect
23. #16840734C22semidirect
24. #16840733C22semidirect
25. C2×#14519834C22semidirect
26. D61⋊(C22⋊C8)C22semidirect
28. C4×C4⋊#6923C22semidirect
31. C4×C22⋊#6923C22semidirect
32. C4×C22⋊#6923C22semidirect
33. #16840698C22semidirect
34. C2×(C2×#6923)⋊C4C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. #16840475C4semidirect
53. #16840467C4semidirect
54. #16840465C4semidirect
56. #16840430C4semidirect
58. #16840408C4semidirect
59. #16840407C4semidirect
62. #16840396C4semidirect
74. C61×#553C4semidirect
109. C2×#11758222C2×C4semidirect
110. C2×#11758224C2×C4semidirect
112. C22×D244C2×C4semidirect
115. C2×D4×D61C2×C4semidirect
119. #14519776C2×C4semidirect
121. #14519773C2×C4semidirect
126. #14519765C2×C4semidirect
135. #14519757C2×C4semidirect
138. #14519756C2×C4semidirect
143. #14519752C2×C4semidirect
144. #14519752C2×C4semidirect
145. #14519752C2×C4semidirect
149. #14519751C2×C4semidirect
165. #14519742C2×C4semidirect
169. C4×D244C2×C4semidirect
174. #14519739C2×C4semidirect
185. #14519735C2×C4semidirect
187. C4⋊C4×D61C2×C4semidirect
197. #125×C61C2×C4semidirect
200. #121×C61C2×C4semidirect
201. #121×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
205. #117×C61C2×C4semidirect
206. C2×C4⋊C4×C61C2×C4semidirect
531. #553#6923semidirect
586. C61#17547semidirect
611. #125C2×#6923semidirect
648. #121C2×#6923semidirect
649. #121C2×#6923semidirect
678. C4×D4C2×#6923semidirect
682. #117C2×#6923semidirect
686. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214622582
#214612222
#214612162
#214612142
#214612092
#214612072
#214612042
#214611982
#214611962
#214611952
#214611932
C2×#168406142
D61⋊#3272
#214598442
#1754761