Finite Group Databasebeta

← #29646336

Subgroups — #29646336

Order 15616.

916 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840481C211yesmaximal, characteristic
2#21454909C211yesmaximal, characteristic, complemented
3#21454906C211yesmaximal, characteristic, complemented
4#21444185C212yesmaximal, complemented
5#21444185C212yesmaximal, complemented
6#21444171C211yesmaximal, characteristic
7#21444162C211yesmaximal, characteristic, complemented
8#21444150C212yesmaximal, complemented
9#21444142C211yesmaximal, characteristic, complemented
10#21444130C212yesmaximal, complemented
11C61×#1469C211yesmaximal, characteristic
12#16840481—21no—
13#16840481—21no—
14#16840481—21no—
15#16840481—22no—
16#16840481—22no—
17#16840481—21no—
18C2×#14519775C411yescharacteristic
19C2×#14519770C412yes—
20C2×#14519770C2212yes—
21C2×#14519764C411yescharacteristic
22C2×#14519754C412yes—
23C2×Q8×Dic61C411yescharacteristic
24C2×C4×Dic122C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×D4×Dic61C411yescharacteristic
27C2×#14519733C2212yes—
28#16839892—21no—
29#16839891—22no—
30#16839890—22no—
31#16839889—21no—
32C8×Dic122—21no—
33#16839886—21no—
34#16839819C2211yescharacteristic
35#16839816C2212yes—
36#16839816C2212yes—
37#16839815C2211yescharacteristic
38#16839812C2212yes—
39#16839812C2212yes—
40#16839487C2211yescharacteristic
41#16839487C2212yes—
42#16839487C2211yescharacteristic
43#16839487C2211yescharacteristic
44#16839487C2211yescharacteristic
45#16839487C2212yes—
46#16839486C2212yes—
47#16839486C2212yes—
48C2×#124×C61C2211yescharacteristic
49C61×#432C2211yescharacteristic
50C61×#431C2211yescharacteristic
51C61×#323C2212yes—
52C61×#323C2212yes—
53C22×Dic122C2×C411yescharacteristic
54C22×Dic122C2×C411yescharacteristic
55C23×Dic61C2×C412yes—
56#14519775—21no—
57#14519775—21no—
58#14519775—22no—
59#14519770—22no—
60#14519770—22no—
61#14519770—22no—
62#14519770—22no—
63#14519770—22no—
64#14519770—22no—
65#14519770—22no—
66#14519770—22no—
67#14519764—21no—
68#14519764—21no—
69#14519764—22no—
70#14519754—22no—
71#14519754—22no—
72#14519754—22no—
73#14519754—22no—
74Q8×Dic61—22no—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77C4×Dic122—21no—
78C4×Dic122—21no—
79C4×Dic122—21no—
80C4×Dic122—21no—
81C4×Dic122D411yescharacteristic
82C4×Dic122D411yescharacteristic
83C4×Dic122D411yescharacteristic
84C4×Dic122D412yes—
85C4×Dic122D412yes—
86C4×Dic122D411yescharacteristic
87D4×Dic61—22no—
88D4×Dic61—21no—
89D4×Dic61—21no—
90#14519733—22no—
91#14519733—22no—
92#14519733—22no—
93#14519733—22no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C412yes—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196C2×C412yes—
98C2×#11758196C2×C412yes—
99C2×#11758196C2×C412yes—
100C2×#11758196C2311yescharacteristic
101C2×#11758196C2311yescharacteristic
102C2×C22⋊Dic61C2×C412yes—
103C2×C22⋊Dic61C2×C412yes—
104C2×C22⋊Dic61C2×C412yes—
105C2×C4×Dic61C2×C412yes—
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2312yes—
109C4⋊#92418—21no—
110C4⋊#92418—21no—
111#14519706—22no—
112#14519706—22no—
113#14519706—22no—
114#14519706—22no—
115C22⋊#92418C2311yescharacteristic
116C22⋊#92418C2312yes—
117C22⋊#92418C2311yescharacteristic
118#14519688—21no—
119#14519687—22no—
120#14519687—22no—
121C4×#92418—21no—
122C8×Dic61—22no—
123C8×Dic61—22no—
124C22×Q8×C61C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126#124×C61—21no—
127#124×C61—21no—
128#124×C61—21no—
129#124×C61—21no—
130C2×C22⋊C4×C61C2×C412yes—
131C2×C22⋊C4×C61C2312yes—
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C22⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2311yescharacteristic
138#97×C61—21no—
139C4×C8×C61—21no—
140C24×C61C22×C412yes—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—42no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—42no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2411yescharacteristic
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—24no—
154C22×Dic61—42no—
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C412yes—
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C412yes—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—22no—
164C2×Dic122—42no—
165C2×Dic122—41no—
166C2×Dic122C22⋊C411yescharacteristic
167C2×Dic122C22⋊C411yescharacteristic
168C2×Dic122C22⋊C412yes—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—22no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C22⋊Dic61—22no—
181C22⋊Dic61—22no—
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190C4⋊Dic61C22⋊C412yes—
191C4⋊Dic61C22⋊C411yescharacteristic
192C4⋊Dic61C22⋊C411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196C22⋊C412yes—
202#11758196C22⋊C412yes—
203#11758196C22⋊C412yes—
204#11758196C22⋊C412yes—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D412yes—
213C4×Dic61C2×D412yes—
214C4×Dic61C2×D412yes—
215C2×#92418—21no—
216C2×#92418—22no—
217C2×#92418—21no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61C23×C411yescharacteristic
224Q8×C61—42no—
225Q8×C61—42no—
226D4×C61—42no—
227D4×C61—42no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—42no—
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×Dic61—21no—
241C2×Dic61—22no—
242C2×Dic61—21no—
243C2×Dic61—22no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—42no—
250C2×Dic61—44no—
251C2×Dic61—44no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C2×C22⋊C412yes—
258C2×Dic61#13112yes—
259Dic122—22no—
260Dic122—22no—
261Dic122—42no—
262Dic122—42no—
263Dic122—42no—
264C8×C61—41no—
265C8×C61—41no—
266C8×C61—42no—
267#92418—41no—
268#92418—42no—
269#92418—41no—
270#17428—611nomaximal, Sylow
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—82no—
277C22×C61—82no—
278C22×C61C22×C22⋊C411yescharacteristic
279C22×C61C2×#13111yescharacteristic
280C22×C61#56811yescharacteristic
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—42no—
287C4×C61#41312yes—
288Dic61—22no—
289Dic61—22no—
290Dic61—22no—
291Dic61—22no—
292Dic61—22no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296C2×#556—611no—
297#2984—611no—
298#2984—611no—
299#1473—612no—
300#1473—612no—
301#1469—611no—
302#1469D6111yescharacteristic
303#1467—611no—
304#1464—612no—
305#1461—611no—
306#1458—612no—
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—82no—
310C2×C61#288011yescharacteristic
311C2×C61#288411yescharacteristic
312C2×C61C2×#41311yescharacteristic
313#556—1221no—
314#556—1221no—
315#556—1222no—
316#556—1222no—
317#556—1221no—
318#556—1221no—
319C2×C4⋊Q8—611no—
320C2×#126—612no—
321C2×#126—612no—
322C2×#124—611no—
323C2×#124C2×D6111yescharacteristic
324C2×C22⋊Q8—612no—
325C2×C4×Q8—611no—
326C2×C4×Q8—611no—
327C2×C4×Q8—611no—
328C2×C4×D4—611no—
329C2×#117—612no—
330#446—1221no—
331#446—1222no—
332#446—1221no—
333#446—1222no—
334C8×Q8—1221no—
335C8×Q8—1221no—
336#432—611no—
337#432—612no—
338#432—612no—
339#432C2×D6111yescharacteristic
340#431—611no—
341#431—612no—
342#431—612no—
343#431C2×D6111yescharacteristic
344#324—611no—
345#324—612no—
346#324—611no—
347#324—611no—
348#324—611no—
349#324—612no—
350#323—612no—
351#323—612no—
352#323C2×D6112yes—
353#323C2×D6112yes—
354C61#1742811yescharacteristic, complemented, Sylow
355C22×Q8—611no—
356C22×Q8—611no—
357C22×Q8C4×D6111yescharacteristic
358C22×D4C4×D6111yescharacteristic
359C23×C4—612no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362C4⋊Q8—1222no—
363#126—1222no—
364#126—1222no—
365#126—1222no—
366#126—1222no—
367#126—1222no—
368#126—1222no—
369#126—1222no—
370#126—1222no—
371#124—21no—
372#124—21no—
373#124—21no—
374#124—21no—
375#124—1221no—
376#124—1221no—
377#124—1222no—
378C22⋊Q8—1222no—
379C22⋊Q8—1222no—
380C22⋊Q8—1222no—
381C22⋊Q8—1222no—
382C4×Q8—611no—
383C4×Q8—611no—
384C4×Q8—612no—
385C4×Q8—612no—
386C4×Q8—611no—
387C4×Q8—611no—
388C4×Q8—1222no—
389C4×Q8—1221no—
390C4×Q8—1221no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×D4—1222no—
396C4×D4—1221no—
397C4×D4—1221no—
398#117—1222no—
399#117—1222no—
400#117—1222no—
401#117—1222no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—612no—
404C2×C4⋊C4—612no—
405C2×C4⋊C4—612no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C22⋊C4—612no—
411C2×C22⋊C4—612no—
412C2×C22⋊C4—612no—
413C2×C22⋊C4C4×D6112yes—
414C2×C22⋊C4C22×D6112yes—
415C2×C42—612no—
416C2×C42—612no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42C22×D6111yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—1222no—
423C4⋊C8—1222no—
424C4⋊C8—1222no—
425C4⋊C8—1222no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C22⋊C8—611no—
429C22⋊C8—612no—
430C22⋊C8—611no—
431C22⋊C8C22×D6111yescharacteristic
432C22⋊C8C22×D6112yes—
433C22⋊C8C22×D6111yescharacteristic
434#97—21no—
435#97—1222no—
436#97—1222no—
437#97—1221no—
438C4×C8—21no—
439C4×C8—1222no—
440C4×C8—1222no—
441C4×C8—1221no—
442C24C2×C4×D6112yes—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—42no—
446C2×Q8—611no—
447C2×Q8—611no—
448C2×Q8—612no—
449C2×Q8—1222no—
450C2×Q8—1221no—
451C2×Q8—1221no—
452C2×Q8—2441no—
453C2×Q8—2442no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—42no—
457C22×C4—612no—
458C22×C4—611no—
459C22×C4—612no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1224no—
466C22×C4—2442no—
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4C2×C4×D6112yes—
470C22×C4C23×D6111yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—1221no—
475C2×C8—1222no—
476C2×C8—1221no—
477C4⋊C4—612no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—612no—
481C4⋊C4—612no—
482C4⋊C4—611no—
483C4⋊C4—611no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C42—612no—
507C42—612no—
508C42—612no—
509C42—612no—
510C42—1222no—
511C42—1222no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42—1221no—
516C42D4×D6111yescharacteristic
517C42D4×D6111yescharacteristic
518C42D4×D6111yescharacteristic
519C42D4×D6111yescharacteristic
520C23—22no—
521C23—22no—
522C23—22no—
523C23—42no—
524C23—42no—
525C23C22×C4×D6111yescharacteristic
526Q8—42no—
527Q8—42no—
528Q8—1222no—
529Q8—1222no—
530Q8—2442no—
531Q8—2442no—
532Q8—2442no—
533D4—42no—
534D4—42no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—1221no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—2442no—
556C2×C4—2444no—
557C2×C4—2444no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4C22⋊C4×D6111yescharacteristic
561C2×C4C22⋊C4×D6111yescharacteristic
562C2×C4C22⋊C4×D6111yescharacteristic
563C2×C4C22⋊C4×D6111yescharacteristic
564C2×C4C2×D4×D6111yescharacteristic
565C2×C4C2×D4×D6111yescharacteristic
566C8—41no—
567C8—41no—
568C8—42no—
569C8—2441no—
570C8—2442no—
571C8—2441no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22C2×C22⋊C4×D6111yescharacteristic
580C22#131×D6111yescharacteristic
581C22#1684052711yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—42no—
588C4—1222no—
589C4—1222no—
590C4—1222no—
591C4—1222no—
592C4—1222no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4#1683974312yes—
597C2—21no—
598C2—21no—
599C2—82no—
600C2#2145426711yescharacteristic
601C2#2145428111yescharacteristic
602C2C2×#1683974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1469C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#1469D61
hypocenterC61#17428
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #21454909C2semidirect
3. #21454906C2semidirect
4. #21444185C2semidirect
5. #21444185C2semidirect
7. #21444162C2semidirect
8. #21444150C2semidirect
9. #21444142C2semidirect
10. #21444130C2semidirect
354. C61#17428semidirect

Maximal subgroups

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

subgroupindex
C2×#168404812
#214549092
#214549062
#214441852
#214441712
#214441622
#214441502
#214441422
#214441302
C61×#14692
#1742861