Finite Group Databasebeta

← #30610210

Subgroups — #30610210

Order 15616.

960 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#21462495C211yesmaximal, characteristic
2C2×#16840783C211yesmaximal, characteristic
3#21461098C214yesmaximal
4#21461093C212yesmaximal, complemented
5#21461092C212yesmaximal, complemented
6#21461081C214yesmaximal, complemented
7C2×#16840315C211yesmaximal, characteristic
8#16840783—21no—
9#16840783—21no—
10#16840783C2212yes—
11#16840783C2212yes—
12#16840783C2212yes—
13#16840782—21no—
14#16840779C2212yes—
15#16840778—21no—
16#16840765—21no—
17C2×C4⋊#92420—21no—
18#16840732C2212yes—
19C2×C22⋊#92420C2212yes—
20C4×#11758217—21no—
21C2×#14519832—21no—
22#16840608C2218yes—
23#16840607C2218yes—
24#16840315—21no—
25#16840315—21no—
26#16840315—21no—
27#16840315—21no—
28#16840315—21no—
29#16840315—21no—
30#16840315—21no—
31#16840315—21no—
32C2×#14519776C411yescharacteristic
33C2×#14519776C411yescharacteristic
34C2×#14519768C2211yescharacteristic
35C2×#14519768C2211yescharacteristic
36C2×#14519754C412yes—
37C2×#14519754C2212yes—
38C2×C4×Dic122C412yes—
39C2×C4×Dic122C2212yes—
40C2×#14519736C411yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C2×#117×C61C411yescharacteristic
43C2×#11758217—22no—
44C22×#92420—22no—
45#14519844—22no—
46C4⋊#92420—22no—
47C4⋊#92420—22no—
48C4⋊#92420—22no—
49C22⋊#92420—22no—
50C22⋊#92420—22no—
51C22⋊#92420C2314yes—
52C22⋊#92420C2314yes—
53#14519832—22no—
54#14519832—22no—
55#14519832—22no—
56C4×#92420—22no—
57C22×Dic122C2×C412yes—
58C22×Dic122C2×C412yes—
59C23×Dic61C2×C411yescharacteristic
60C23×Dic61C2311yescharacteristic
61#14519776—21no—
62#14519776—21no—
63#14519776—21no—
64#14519776—21no—
65#14519776—21no—
66#14519776—21no—
67#14519776—21no—
68#14519776—21no—
69#14519768—21no—
70#14519768—21no—
71#14519768—21no—
72#14519768—21no—
73#14519768—21no—
74#14519768—21no—
75#14519768—21no—
76#14519768—21no—
77#14519754—22no—
78#14519754—22no—
79#14519754—22no—
80#14519754—22no—
81#14519754—22no—
82#14519754—22no—
83#14519754—22no—
84#14519754—22no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122—22no—
92C4×Dic122—22no—
93#14519736—21no—
94#14519736—21no—
95#14519736—21no—
96#14519736—21no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C412yes—
100C2×C4⋊Dic61C2312yes—
101C2×#11758196C2×C412yes—
102C2×#11758196C2×C412yes—
103C2×#11758196C2×C412yes—
104C2×#11758196C2312yes—
105C2×C22⋊Dic61C2×C412yes—
106C2×C4×Dic61C2×C412yes—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C23×C4×C61C2×C411yescharacteristic
120#117×C61—21no—
121#117×C61—21no—
122#117×C61—21no—
123#117×C61—21no—
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C412yes—
127C2×C42×C61C2×C412yes—
128C24×C61C22×C411yescharacteristic
129C22×C4×C61—24no—
130C22×C4×C61C22⋊C411yescharacteristic
131C22×C4×C61C22⋊C411yescharacteristic
132C22×C4×C61C22⋊C411yescharacteristic
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22×C412yes—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C412yes—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C22×C412yes—
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C412yes—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2411yescharacteristic
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122—44no—
159C2×Dic122—44no—
160#11758217—44no—
161C2×#92420—24no—
162C2×#92420—24no—
163C2×#92420—44no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C42×C61—22no—
171C42×C61—22no—
172C22⋊Dic61—22no—
173C22⋊Dic61—22no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182#11758196—22no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192C4×Dic61C22⋊C411yescharacteristic
193C4×Dic61C22⋊C411yescharacteristic
194C4×Dic61C22⋊C411yescharacteristic
195C4×Dic61C22⋊C411yescharacteristic
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×C61—22no—
209C23×C61—22no—
210C23×C61—41no—
211C23×C61C2×C22⋊C411yescharacteristic
212C23×C61C2×C22⋊C411yescharacteristic
213C23×C61C23×C411yescharacteristic
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—42no—
223C2×C4×C61#10114yes—
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—24no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—42no—
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C22×D411yescharacteristic
251C2×Dic61C22×D411yescharacteristic
252Dic122—44no—
253Dic122—44no—
254Dic122—44no—
255Dic122—44no—
256#92420—44no—
257#92420—44no—
258#17404—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—44no—
267C22×C61C2×#10112yes—
268C22×C61C22×C22⋊C411yescharacteristic
269C22×C61#56812yes—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—42no—
273C4×C61—42no—
274C4×C61C2×#10112yes—
275C4×C61C2×#10112yes—
276Dic61—21no—
277Dic61—21no—
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—21no—
282Dic61—21no—
283Dic61—42no—
284Dic61—42no—
285Dic61#41012yes—
286C2×#533—611no—
287#2920—611no—
288C2×#432—611no—
289#1472—614no—
290#1470—612no—
291#1470—612no—
292#1467—614no—
293C2×C61—22no—
294C2×C61—22no—
295C2×C61—41no—
296C2×C61#287911yescharacteristic
297C2×C61C2×#41011yescharacteristic
298C2×C61C22×#10111yescharacteristic
299#533—1221no—
300#533—1221no—
301#533—1221no—
302#533—1221no—
303#533—1221no—
304#533—1221no—
305#533—1221no—
306#533—1221no—
307C2×C4⋊Q8—611no—
308C2×C4⋊Q8—611no—
309C2×#125—611no—
310C2×#125—611no—
311C2×C22⋊Q8—612no—
312C2×C22⋊Q8—612no—
313C2×C4×Q8—612no—
314C2×C4×Q8—612no—
315C2×#117—611no—
316C2×#117#692311yescharacteristic
317C22×C42—611no—
318#432—612no—
319#432—612no—
320#432—612no—
321#432—1221no—
322#432—1221no—
323#432—1221no—
324#431—612no—
325#431—1221no—
326#423—1221no—
327C2×C4⋊C8—1221no—
328#407—612no—
329C2×C22⋊C8—612no—
330C4×M16—1221no—
331C2×#97—1221no—
332#324—618no—
333#324—618no—
334C61#1740411yescharacteristic, complemented, Sylow
335C22×Q8—612no—
336C22×Q8—612no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4C2×#692311yescharacteristic
340C2×M16—1222no—
341C22×C8—1222no—
342C4⋊Q8—1221no—
343C4⋊Q8—1221no—
344C4⋊Q8—1221no—
345C4⋊Q8—1221no—
346C4⋊Q8—1221no—
347C4⋊Q8—1221no—
348C4⋊Q8—1221no—
349C4⋊Q8—1221no—
350#125—1221no—
351#125—1221no—
352#125—1221no—
353#125—1221no—
354#125—1221no—
355#125—1221no—
356#125—1221no—
357#125—1221no—
358C22⋊Q8—1222no—
359C22⋊Q8—1222no—
360C22⋊Q8—1222no—
361C22⋊Q8—1222no—
362C22⋊Q8—1222no—
363C22⋊Q8—1222no—
364C22⋊Q8—1222no—
365C22⋊Q8—1222no—
366C4×Q8—1222no—
367C4×Q8—1222no—
368C4×Q8—1222no—
369C4×Q8—1222no—
370C4×Q8—1222no—
371C4×Q8—1222no—
372C4×Q8—1222no—
373C4×Q8—1222no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—1221no—
379#117—1221no—
380#117—1221no—
381#117—1221no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—612no—
385C2×C4⋊C4—612no—
386C2×C4⋊C4—612no—
387C2×C4⋊C4—612no—
388C2×C4⋊C4—612no—
389C2×C4⋊C4—612no—
390C2×C4⋊C4C2×#692311yescharacteristic
391C2×C4⋊C4C2×#692311yescharacteristic
392C2×C22⋊C4—612no—
393C2×C22⋊C4C2×#692312yes—
394C2×C42—611no—
395C2×C42—611no—
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—612no—
407C2×C42C2×#692312yes—
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—
418#97—1222no—
419C4×C8—1222no—
420C24C22×#692311yescharacteristic
421C2×Q8—1222no—
422C2×Q8—1222no—
423C2×Q8—1222no—
424C2×Q8—1222no—
425C2×Q8—2444no—
426C2×Q8—2444no—
427C22×C4—24no—
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—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4C22⋊#692311yescharacteristic
445C22×C4C22⋊#692311yescharacteristic
446C22×C4C22⋊#692311yescharacteristic
447C22×C4C22⋊#692311yescharacteristic
448C22×C4C22×#692312yes—
449C22×C4C22×#692311yescharacteristic
450C22×C4C22×#692311yescharacteristic
451C22×C4C22×#692312yes—
452M16—2444no—
453C2×C8—1224no—
454C2×C8—1224no—
455C2×C8—2444no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
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—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—1222no—
479C22⋊C4—1222no—
480C42—22no—
481C42—22no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—1222no—
499C42—1222no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23C2×C22⋊#692311yescharacteristic
504C23C2×C22⋊#692311yescharacteristic
505C23C23×#692311yescharacteristic
506Q8—2444no—
507Q8—2444no—
508Q8—2444no—
509Q8—2444no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1224no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2442no—
543C2×C4#1451983814yes—
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—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—44no—
558C22C2×#1451983812yes—
559C22C22×C22⋊#692311yescharacteristic
560C22#1684084112yes—
561C4—21no—
562C4—21no—
563C4—42no—
564C4—42no—
565C4—612no—
566C4—1221no—
567C4—1221no—
568C4—1221no—
569C4—1221no—
570C4—1221no—
571C4—1221no—
572C4—1221no—
573C4—2442no—
574C4—2442no—
575C4C2×#1451983812yes—
576C4C2×#1451983812yes—
577C2—22no—
578C2—22no—
579C2—41no—
580C2#2146240411yescharacteristic
581C2D61⋊#41011yescharacteristic
582C2C22×#1451983811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC2×#117#6923
hypocenterC61#17404
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
4. #21461093C2semidirect
5. #21461092C2semidirect
6. #21461081C2semidirect
334. C61#17404semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407832
#214610982
#214610932
#214610922
#214610812
C2×#168403152
#1740461