Finite Group Databasebeta

← #29658202

Subgroups — #29658202

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457156C212yesmaximal, complemented
2#21456193C211yesmaximal, characteristic, complemented
3#21445019C212yesmaximal, complemented
4#21445012C212yesmaximal, complemented
5#21445005C212yesmaximal, complemented
6#21444998C212yesmaximal, complemented
7C2×#16839506C211yesmaximal, characteristic, complemented
8#21444232C212yesmaximal, complemented
9C61×#3543C211yesmaximal, characteristic
10#16840319C2211yescharacteristic, complemented
11#16840126—22no—
12#16840108C2212yes—
13#16840108C2212yescomplemented
14#16840066—22no—
15#16840047C2212yescomplemented
16#16840042C2212yescomplemented
17#16840001—22no—
18#16839989—22no—
19#16839981—22no—
20#16839972C2212yescomplemented
21#16839967C2212yescomplemented
22C2×C4⋊#92418C2212yescomplemented
23#16839767—22no—
24C4×#11758194C2211yescharacteristic, complemented
25#16839506C2212yes—
26#16839506C2211yescharacteristic, complemented
27#16839506C2211yescharacteristic, complemented
28Q8⋊#92418C2212yescomplemented
29Q8⋊#92418C2212yescomplemented
30D4⋊#92418C2212yescomplemented
31D4⋊#92418C2212yescomplemented
32C61×#560—22no—
33C61×#559C2211yescharacteristic
34C61×#550C2212yes—
35C61×#546—22no—
36D42×C61—22no—
37D42×C61C2211yescharacteristic
38C61×#540—22no—
39C61×#535—22no—
40C61×#534—22no—
41C2×#127×C61C2211yescharacteristic
42C61×#529C2212yes—
43C2×#11758202—22no—
44C2×#11758200—22no—
45C2×#11758194—21no—
46C22×#92418—22no—
47#14519777C2312yes—
48#14519769—21no—
49#14519756—22no—
50C4×Dic122—22no—
51#14519736—21no—
52#14519710—22no—
53#14519708—22no—
54C4⋊#92418—22no—
55C4⋊#92418C2312yes—
56C4⋊#92418C2312yes—
57#14519701—22no—
58#14519700—22no—
59#14519700—22no—
60#14519698—22no—
61#14519698—24no—
62#14519698—24no—
63#14519688—21no—
64C4×#92418C2312yes—
65C2×#41×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61D412yes—
70#127×C61—22no—
71#127×C61—22no—
72#127×C61D412yes—
73#127×C61C2311yescharacteristic
74#127×C61C2311yescharacteristic
75#126×C61—22no—
76#125×C61D412yes—
77#124×C61—22no—
78#124×C61D412yes—
79#123×C61—22no—
80#123×C61—24no—
81#123×C61—22no—
82#123×C61—22no—
83C22⋊Q8×C61D412yes—
84#121×C61—24no—
85#121×C61—24no—
86#121×C61—24no—
87#121×C61—24no—
88#121×C61—22no—
89#121×C61—22no—
90#121×C61D412yes—
91#120×C61—22no—
92#120×C61—24no—
93#120×C61—24no—
94#120×C61—22no—
95C4×Q8×C61C2312yes—
96C4×D4×C61—22no—
97C4×D4×C61—22no—
98C4×D4×C61—22no—
99C4×D4×C61C2312yes—
100#117×C61—22no—
101C2×C22⋊C4×C61—22no—
102C2×C42×C61C2311yescharacteristic
103C24×C61—22no—
104C24×C61—22no—
105#41×C61—82no—
106#41×C61—82no—
107C2×Q8×C61C2×D412yes—
108C2×D4×C61—22no—
109C2×D4×C61—24no—
110C2×D4×C61—24no—
111C2×D4×C61—24no—
112C2×D4×C61—22no—
113C2×D4×C61—24no—
114C2×D4×C61—22no—
115C2×D4×C61—22no—
116C2×D4×C61—44no—
117C2×D4×C61—82no—
118C2×D4×C61—82no—
119C2×D4×C61—82no—
120C2×D4×C61—82no—
121C2×D4×C61—84no—
122C2×D4×C61C2×D412yes—
123C2×D4×C61C2×D412yes—
124C2×D4×C61C2×D412yes—
125C22×C4×C61—24no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61C2×D412yes—
129C22×C4×C61C2×D411yescharacteristic
130C2×Dic122—22no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61C2×D412yes—
136C4⋊C4×C61C2×D412yes—
137C22⋊C4×C61—22no—
138C22⋊C4×C61—22no—
139C22⋊C4×C61—24no—
140C22⋊C4×C61—24no—
141C22⋊C4×C61—22no—
142C22⋊C4×C61—22no—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—22no—
145C22⋊C4×C61—22no—
146C42×C61—22no—
147C42×C61C2×D412yes—
148C42×C61C2×D411yescharacteristic
149C42×C61C2411yescharacteristic
150C22⋊Dic61—41no—
151#11758202—82no—
152#11758200—82no—
153C4⋊Dic61—22no—
154C4⋊Dic61—22no—
155#11758196—42no—
156C4×Dic61—41no—
157#11758194—42no—
158C2×#92418—22no—
159C2×#92418—22no—
160C2×#92418—22no—
161C2×#92418—82no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—44no—
166C23×C61—84no—
167C23×C61—84no—
168C23×C61—82no—
169C23×C61#12011yescharacteristic
170Q8×C61—22no—
171Q8×C61—22no—
172D4×C61—22no—
173D4×C61—22no—
174D4×C61—42no—
175D4×C61—42no—
176D4×C61—44no—
177D4×C61—42no—
178D4×C61—42no—
179D4×C61—42no—
180D4×C61—42no—
181D4×C61—82no—
182D4×C61—84no—
183D4×C61—84no—
184D4×C61—84no—
185D4×C61—84no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—82no—
195C2×C4×C61—84no—
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#12012yes—
198C2×C4×C61C22×D411yescharacteristic
199C2×C4×C61C22×D412yes—
200C2×Dic61—42no—
201Dic122—42no—
202Dic122—42no—
203#92418—42no—
204#92418—42no—
205#92418—42no—
206#18720—611nomaximal, Sylow
207C22×C61—22no—
208C22×C61—42no—
209C22×C61—44no—
210C22×C61—42no—
211C22×C61—44no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—164no—
216C22×C61—164no—
217C22×C61#45512yes—
218C22×C61C2×#12011yescharacteristic
219C4×C61—22no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—42no—
223C4×C61—42no—
224C4×C61—42no—
225C4×C61#57612yes—
226C4×C61#57712yes—
227Dic61—82no—
228#3543D6111yescharacteristic
229#3248—612no—
230#3138—611no—
231#1642—612no—
232#1641—612no—
233#1640—612no—
234#1639—612no—
235C2×#331—611no—
236#1483—612no—
237C2×C61—22no—
238C2×C61—82no—
239C2×C61—82no—
240C2×C61—82no—
241C2×C61#301212yes—
242C2×C61C2×#45511yescharacteristic
243#560—22no—
244#559C2×D6111yescharacteristic
245#550C2×D6112yes—
246#546—22no—
247D42—22no—
248D42C2×D6111yescharacteristic
249#540—22no—
250#535—22no—
251#534—22no—
252#533—611no—
253C2×#127C2×D6111yescharacteristic
254#529C2×D6112yes—
255#490—1222no—
256#486—612no—
257#486—612no—
258#479—1222no—
259#475—612no—
260#474—612no—
261#467—1222no—
262#465—1222no—
263#464—1222no—
264#462—612no—
265#461—612no—
266C2×C4⋊C8—612no—
267#418—1222no—
268C4×M16—611no—
269#331—612no—
270#331—611no—
271#331—611no—
272Q8⋊C8—612no—
273Q8⋊C8—612no—
274D4⋊C8—612no—
275D4⋊C8—612no—
276C61#1872011yescharacteristic, complemented, Sylow
277C2×#41—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4C22⋊D6112yes—
282C2×Q16—1222no—
283C2×SD16—1222no—
284C2×M16—1221no—
285C22×C8—1222no—
286C4⋊Q8—612no—
287#127—22no—
288#127—22no—
289#127C22⋊D6112yes—
290#127C22×D6111yescharacteristic
291#127C22×D6111yescharacteristic
292#126—22no—
293#125—1221no—
294#125C22⋊D6112yes—
295#124—22no—
296#124C22⋊D6112yes—
297#123—22no—
298#123—24no—
299#123—22no—
300#123—22no—
301C22⋊Q8—1222no—
302C22⋊Q8C22⋊D6112yes—
303#121—24no—
304#121—24no—
305#121—24no—
306#121—24no—
307#121—22no—
308#121—22no—
309#121C22⋊D6112yes—
310#120—22no—
311#120—24no—
312#120—24no—
313#120—22no—
314C4×Q8—1222no—
315C4×Q8C22×D6112yes—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4C22×D6112yes—
320#117—22no—
321#117—1221no—
322C2×C22⋊C4—22no—
323C2×C42C22×D6111yescharacteristic
324#107—1222no—
325#106—1222no—
326C4⋊C8—612no—
327C4⋊C8—612no—
328C4⋊C8—1222no—
329#103—1222no—
330#103—1222no—
331#103—1222no—
332#102—1224no—
333#102—1224no—
334#102—1222no—
335#97—1221no—
336C4×C8—612no—
337C24—22no—
338C24—22no—
339#41—82no—
340#41—82no—
341C2×Q8—1222no—
342C2×Q8C2×C22⋊D6112yes—
343C2×D4—22no—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—24no—
351C2×D4—44no—
352C2×D4—82no—
353C2×D4—82no—
354C2×D4—82no—
355C2×D4—82no—
356C2×D4—84no—
357C2×D4C2×C22⋊D6112yes—
358C2×D4C2×C22⋊D6112yes—
359C2×D4C2×C22⋊D6112yes—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4C2×C22⋊D6111yescharacteristic
364C22×C4C2×C22⋊D6112yes—
365Q16—4882no—
366SD16—4882no—
367M16—2442no—
368C2×C8—1222no—
369C2×C8—1222no—
370C2×C8—1222no—
371C2×C8—4882no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—1222no—
377C4⋊C4—1222no—
378C4⋊C4—2442no—
379C4⋊C4C2×C22⋊D6112yes—
380C4⋊C4C2×C22⋊D6112yes—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—2441no—
391C42—22no—
392C42—2441no—
393C42C2×C22⋊D6111yescharacteristic
394C42C2×C22⋊D6112yes—
395C42C23×D6111yescharacteristic
396C23—22no—
397C23—22no—
398C23—22no—
399C23—44no—
400C23—84no—
401C23—84no—
402C23—82no—
403C23#1451974611yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—2442no—
407Q8—2442no—
408D4—22no—
409D4—22no—
410D4—42no—
411D4—42no—
412D4—44no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—82no—
418D4—84no—
419D4—84no—
420D4—84no—
421D4—84no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4—84no—
432C2×C4—2442no—
433C2×C4#1451974611yescharacteristic
434C2×C4#1451974612yes—
435C2×C4C22×C22⋊D6111yescharacteristic
436C2×C4C22×C22⋊D6112yes—
437C8—2442no—
438C8—2442no—
439C8—2442no—
440C22—22no—
441C22—42no—
442C22—44no—
443C22—42no—
444C22—44no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—164no—
449C22—164no—
450C22#1683994012yes—
451C22C2×#1451974611yescharacteristic
452C4—22no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4—4882no—
459C4#1684056512yes—
460C4#1684057312yes—
461C2—22no—
462C2—82no—
463C2—82no—
464C2—82no—
465C2#2145512312yes—
466C2C2×#1683994011yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3543C2
socleC22×C61C2×#120
hypercenter#3543D61
hypocenterC61#18720
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3543

Complements

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

NH ≅ G/Ntype
1. #21457156C2semidirect
2. #21456193C2semidirect
3. #21445019C2semidirect
4. #21445012C2semidirect
5. #21445005C2semidirect
6. #21444998C2semidirect
7. C2×#16839506C2semidirect
8. #21444232C2semidirect
10. #16840319C22semidirect
13. #16840108C22semidirect
15. #16840047C22semidirect
16. #16840042C22semidirect
20. #16839972C22semidirect
21. #16839967C22semidirect
22. C2×C4⋊#92418C22semidirect
24. C4×#11758194C22semidirect
26. #16839506C22semidirect
27. #16839506C22semidirect
28. Q8⋊#92418C22semidirect
29. Q8⋊#92418C22semidirect
30. D4⋊#92418C22semidirect
31. D4⋊#92418C22semidirect
276. C61#18720semidirect

Maximal subgroups

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

subgroupindex
#214571562
#214561932
#214450192
#214450122
#214450052
#214449982
C2×#168395062
#214442322
C61×#35432
#1872061