Finite Group Databasebeta

← #30610157

Subgroups — #30610157

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic
2#21462496C211yesmaximal, characteristic
3#21461093C212yesmaximal, complemented
4#21461092C212yesmaximal, complemented
5#21461091C214yesmaximal, complemented
6#21461068C214yesmaximal
7C2×#125×D61C211yesmaximal, characteristic
8#16840785—21no—
9#16840784—21no—
10#16840783C2212yes—
11#16840782C2212yes—
12#16840781—21no—
13#16840780—21no—
14#16840779C2212yes—
15#16840778C2212yes—
16#16840767—21no—
17#16840766—21no—
18#16840733C2212yes—
19#16840733C2212yes—
20C4×#11758213—21no—
21C4×#11758213—21no—
22#16840608C2218yes—
23#16840607C2218yes—
24C2×#14519769C411yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519768C2211yescharacteristic
27C2×#14519767C412yes—
28C2×#14519767C2212yes—
29#125×D61—21no—
30#125×D61—21no—
31#125×D61—21no—
32#125×D61—21no—
33#125×D61—21no—
34#125×D61—21no—
35#125×D61—21no—
36#125×D61—21no—
37C2×C4⋊C4×D61C411yescharacteristic
38C2×C4⋊C4×D61C411yescharacteristic
39C2×C4⋊C4×D61C412yes—
40C2×C4⋊C4×D61C2212yes—
41C2×C42×D61C2211yescharacteristic
42C2×#125×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×#11758213—22no—
45#14519844—22no—
46#14519844—22no—
47C4⋊#92420—22no—
48C4⋊#92420—22no—
49#14519834—22no—
50#14519834—22no—
51C22⋊#92420C2314yes—
52C22⋊#92420C2314yes—
53#14519832—22no—
54#14519832—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C412yes—
59C22×C4×D61C2×C412yes—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62#14519769—21no—
63#14519769—21no—
64#14519769—21no—
65#14519769—21no—
66#14519768—21no—
67#14519768—21no—
68#14519768—21no—
69#14519768—21no—
70#14519768—21no—
71#14519768—21no—
72#14519768—21no—
73#14519768—21no—
74#14519767—22no—
75#14519767—22no—
76#14519767—22no—
77#14519767—22no—
78#14519767—22no—
79#14519767—22no—
80#14519767—22no—
81#14519767—22no—
82C2×C4⋊Dic61C2×C412yes—
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C4⋊Dic61C2312yes—
86C2×#11758196C2×C412yes—
87C2×#11758196C2×C412yes—
88C2×#11758196C2×C412yes—
89C2×#11758196C2×C412yes—
90C2×#11758196C2×C412yes—
91C2×#11758196C2312yes—
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119#125×C61—21no—
120#125×C61—21no—
121#125×C61—21no—
122#125×C61—21no—
123C2×C4⋊C4×C61C2×C412yes—
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C412yes—
127C2×C42×C61C2×C411yescharacteristic
128C23×D61C22×C411yescharacteristic
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C412yes—
133C22×C4×C61C22×C411yescharacteristic
134C22×Dic61C22×C412yes—
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C412yes—
138C22×Dic61C2411yescharacteristic
139C2×C4×D61—24no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—42no—
145C2×C4×D61—42no—
146C2×C4×D61—44no—
147C2×C4×D61—44no—
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C411yescharacteristic
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×#92420—24no—
161C2×#92420—24no—
162#11758213—44no—
163#11758213—44no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C42×C61C22⋊C411yescharacteristic
173C42×C61C22⋊C411yescharacteristic
174C42×C61C22⋊C411yescharacteristic
175C42×C61C22⋊C411yescharacteristic
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183C4⋊Dic61—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196C4×Dic61C22⋊C411yescharacteristic
197C4×Dic61C22⋊C411yescharacteristic
198C4×Dic61C22⋊C411yescharacteristic
199C4×Dic61C22⋊C411yescharacteristic
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C23×C61C23×C411yescharacteristic
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61C2×C22⋊C411yescharacteristic
213C22×D61C2×C22⋊C411yescharacteristic
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—41no—
220C2×C4×C61—42no—
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—24no—
232C2×Dic61—41no—
233C2×Dic61—42no—
234C2×Dic61C2×C22⋊C411yescharacteristic
235C2×Dic61C2×C22⋊C411yescharacteristic
236C2×Dic61C2×C22⋊C411yescharacteristic
237C2×Dic61C2×C22⋊C411yescharacteristic
238C2×Dic61C22×D411yescharacteristic
239C2×Dic61C22×D411yescharacteristic
240C4×D61—22no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—44no—
252C4×D61—44no—
253C4×D61—44no—
254C4×D61—44no—
255C4×D61#10114yes—
256#92420—44no—
257#92420—44no—
258#17394—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61C22×C22⋊C411yescharacteristic
262C22×C61#56812yes—
263C2×D61—28no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61#41012yes—
269C2×D61C2×#10112yes—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—42no—
276C4×C61—42no—
277C4×C61C2×#10112yes—
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—21no—
282Dic61—21no—
283Dic61—42no—
284Dic61—42no—
285Dic61C2×#10112yes—
286C22×#125—611no—
287#2920—611no—
288#2920—611no—
289#1470—614no—
290#1470—612no—
291#1470—612no—
292#1463—614no—
293C2×C61—22no—
294C2×C61#287911yescharacteristic
295C2×C61C2×#41011yescharacteristic
296C2×C61C22×#10111yescharacteristic
297D61—22no—
298D61—22no—
299C2×#125—612no—
300C2×#125—612no—
301C2×#125—611no—
302C2×#125—611no—
303C2×#125—611no—
304C2×#125—1221no—
305C2×#125—1221no—
306C2×#125—1221no—
307C2×#125—1221no—
308C2×#125—1221no—
309C2×#125—1221no—
310C2×#125—1221no—
311C2×#125—1221no—
312C2×#125#692311yescharacteristic
313C22×C4⋊C4—611no—
314C22×C4⋊C4—611no—
315C22×C4⋊C4—612no—
316C22×C4⋊C4—612no—
317C22×C42—611no—
318#432—612no—
319#432—612no—
320#432—1221no—
321#432—1221no—
322#431—612no—
323#431—612no—
324#431—1221no—
325#431—1221no—
326#423—1221no—
327#423—1221no—
328#407—612no—
329#407—612no—
330C4×M16—1221no—
331C4×M16—1221no—
332#324—618no—
333#324—618no—
334C61#1739411yescharacteristic, complemented, Sylow
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—612no—
339C23×C4—612no—
340C2×M16—1222no—
341C2×M16—1222no—
342#125—21no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—1222no—
347#125—1222no—
348#125—1222no—
349#125—1222no—
350#125—1222no—
351#125—1222no—
352#125—1222no—
353#125—1222no—
354#125—1221no—
355#125—1221no—
356#125—1221no—
357#125—1221no—
358#125—1221no—
359#125—1221no—
360#125—1221no—
361#125—1221no—
362#125—1221no—
363#125—1221no—
364#125—1221no—
365#125—1221no—
366C2×C4⋊C4—612no—
367C2×C4⋊C4—612no—
368C2×C4⋊C4—612no—
369C2×C4⋊C4—612no—
370C2×C4⋊C4—612no—
371C2×C4⋊C4—612no—
372C2×C4⋊C4—612no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4—1222no—
392C2×C4⋊C4C2×#692311yescharacteristic
393C2×C4⋊C4C2×#692312yes—
394C2×C4⋊C4C2×#692312yes—
395C2×C4⋊C4C2×#692311yescharacteristic
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42C2×#692311yescharacteristic
408C4⋊C8—1222no—
409C4⋊C8—1222no—
410C4⋊C8—1222no—
411C4⋊C8—1222no—
412C22⋊C8—614no—
413C22⋊C8—614no—
414C22⋊C8—1222no—
415C22⋊C8—1222no—
416#97—1222no—
417#97—1222no—
418C4×C8—1222no—
419C4×C8—1222no—
420C24—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—1224no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—2442no—
444C22×C4—2444no—
445C22×C4—2442no—
446C22×C4—2444no—
447C22×C4C22×#692312yes—
448C22×C4C22×#692311yescharacteristic
449C22×C4C22×#692311yescharacteristic
450C22×C4C22×#692312yes—
451C22×C4C22×#692311yescharacteristic
452M16—2444no—
453M16—2444no—
454C2×C8—1224no—
455C2×C8—1224no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—1222no—
465C4⋊C4—1222no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—1222no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42C22⋊#692311yescharacteristic
497C42C22⋊#692311yescharacteristic
498C42C22⋊#692311yescharacteristic
499C42C22⋊#692311yescharacteristic
500C23—611no—
501C23—611no—
502C23—1222no—
503C23—1222no—
504C23—1222no—
505C23C23×#692311yescharacteristic
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—611no—
514C2×C4—614no—
515C2×C4—611no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1224no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2444no—
537C2×C4—2444no—
538C2×C4—2444no—
539C2×C4—2444no—
540C2×C4—2441no—
541C2×C4—2442no—
542C2×C4C2×C22⋊#692311yescharacteristic
543C2×C4C2×C22⋊#692311yescharacteristic
544C2×C4C2×C22⋊#692311yescharacteristic
545C2×C4C2×C22⋊#692311yescharacteristic
546C2×C4C2×C22⋊#692311yescharacteristic
547C2×C4C2×C22⋊#692311yescharacteristic
548C8—2444no—
549C8—2444no—
550C22—21no—
551C22—21no—
552C22—612no—
553C22—612no—
554C22—1228no—
555C22—1221no—
556C22—1221no—
557C22—1221no—
558C22—1221no—
559C22C22×C22⋊#692311yescharacteristic
560C22#1684084112yes—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—42no—
567C4—42no—
568C4—612no—
569C4—1221no—
570C4—1221no—
571C4—1221no—
572C4—1221no—
573C4—1221no—
574C4—2442no—
575C4—2442no—
576C4D61⋊#10112yes—
577C2—22no—
578C2—1222no—
579C2—1222no—
580C2#2146240411yescharacteristic
581C2D61⋊#41011yescharacteristic
582C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#125×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenterC2×#125#6923
hypocenterC61#17394
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #21461093C2semidirect
4. #21461092C2semidirect
5. #21461091C2semidirect
334. C61#17394semidirect

Maximal subgroups

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

subgroupindex
#214624982
#214624962
#214610932
#214610922
#214610912
#214610682
C2×#125×D612
#1739461