Finite Group Databasebeta

← #29663983

Subgroups — #29663983

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840108C211yesmaximal, characteristic, complemented
2#21455306C211yesmaximal, characteristic, complemented
3#41×#92418C211yesmaximal, characteristic, complemented
4#21445261C214yesmaximal, complemented
5#21445254C214yesmaximal, complemented
6#21444577C211yesmaximal, characteristic, complemented
7#21444492C211yesmaximal, characteristic, complemented
8#21444487C211yesmaximal, characteristic, complemented
9C61×#3038C211yesmaximal, characteristic
10C2×#14519807—21no—
11C2×#14519777C2211yescharacteristic
12#16840108—21no—
13#16840108—21no—
14#16840108C2214yes—
15#16839972—21no—
16#16839972C2212yescomplemented
17#16839967—21no—
18#16839967C2212yescomplemented
19Q8×#92418C2212yescomplemented
20D4×#92418—22no—
21D4×#92418C2212yescomplemented
22#16839815—21no—
23#16839815C2211yescharacteristic
24#16839786C2211yescharacteristic
25#16839770—21no—
26C2×#14519698—22no—
27C2×C4×#92418—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839514C2214yescomplemented
30#16839509C2214yescomplemented
31#16839506C2214yes—
32C2×AGL(1,ℤ/8)×C61—21no—
33C2×#127×C61C2211yescharacteristic
34C4×#41×C61C2211yescharacteristic
35C61×#460—21no—
36C61×#460C2212yes—
37C61×#459—21no—
38C61×#459C2212yes—
39C61×#423C2211yescharacteristic
40C61×#418—21no—
41C22×Dic122—21no—
42#14519807—44no—
43C2×#11758202—22no—
44C2×#11758200—22no—
45C2×#11758194—21no—
46C22×#92418—22no—
47C22×#92418D412yes—
48#14519777—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777C2312yes—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C4⋊#92418—21no—
55C4⋊#92418—22no—
56C4⋊#92418C2312yes—
57C4⋊#92418C2312yes—
58#14519700—22no—
59#14519700—22no—
60#14519698—24no—
61#14519698—24no—
62C22⋊#92418—21no—
63C22⋊#92418—22no—
64C4×#92418—21no—
65C4×#92418—22no—
66C4×#92418D411yescharacteristic
67C4×#92418D411yescharacteristic
68C4×#92418C2312yes—
69C2×#41×C61D411yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73AGL(1,ℤ/8)×C61—44no—
74C2×SD16×C61—22no—
75C2×D8×C61—22no—
76C2×M16×C61—21no—
77#127×C61—21no—
78#127×C61—21no—
79#127×C61—21no—
80#127×C61C2312yes—
81C4×Q8×C61D411yescharacteristic
82C4×Q8×C61C2311yescharacteristic
83C4×D4×C61—21no—
84C4×D4×C61—21no—
85C4×D4×C61D411yescharacteristic
86C4×D4×C61C2311yescharacteristic
87#117×C61—21no—
88#117×C61D411yescharacteristic
89C2×C42×C61—21no—
90C2×C42×C61C2311yescharacteristic
91C4⋊C8×C61—21no—
92C4⋊C8×C61C2312yes—
93#102×C61—22no—
94#102×C61—22no—
95C24×C61—41no—
96#41×C61—22no—
97#41×C61D814yes—
98C2×Q8×C61C2×D411yescharacteristic
99C2×D4×C61—21no—
100C2×D4×C61—22no—
101C2×D4×C61—22no—
102C2×D4×C61—22no—
103C2×D4×C61—44no—
104C2×D4×C61—41no—
105C2×D4×C61—41no—
106C2×D4×C61—41no—
107C2×D4×C61—42no—
108C2×D4×C61—42no—
109C2×D4×C61—82no—
110C2×D4×C61C2×D411yescharacteristic
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×Dic61—41no—
118C2×Dic122—22no—
119C2×Dic122—42no—
120C2×Dic122—42no—
121C2×Dic122—41no—
122SD16×C61—44no—
123D8×C61—44no—
124M16×C61—42no—
125C2×C8×C61—22no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61C2×D411yescharacteristic
129C4⋊C4×C61C2×D411yescharacteristic
130C22⋊C4×C61—21no—
131C22⋊C4×C61—21no—
132C22⋊C4×C61—21no—
133C42×C61—21no—
134C42×C61—21no—
135C42×C61—21no—
136C42×C61C2×D411yescharacteristic
137C42×C61C2×D411yescharacteristic
138C42×C61#4111yescharacteristic
139C42×C61C2411yescharacteristic
140#11758202—44no—
141#11758200—44no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146#11758194—42no—
147C2×#92418—22no—
148C2×#92418—22no—
149C2×#92418—42no—
150C2×#92418—44no—
151C2×#92418C2×D412yes—
152C2×#92418C2×D412yes—
153C23×C61—21no—
154C23×C61—42no—
155C23×C61—82no—
156C23×C61—82no—
157C23×C61—82no—
158C23×C61#12111yescharacteristic
159Q8×C61—21no—
160Q8×C61C2×D812yes—
161D4×C61—24no—
162D4×C61—21no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—44no—
166D4×C61—82no—
167D4×C61—82no—
168D4×C61—82no—
169D4×C61—82no—
170D4×C61C2×D812yes—
171C2×C4×C61—21no—
172C2×C4×C61—22no—
173C2×C4×C61—24no—
174C2×C4×C61—22no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61C2×D812yes—
183C2×C4×C61#13512yes—
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C2×#4111yescharacteristic
187C2×Dic61—42no—
188C2×Dic61—82no—
189Dic122—42no—
190Dic122—42no—
191Dic122—82no—
192C8×C61—42no—
193#92418—22no—
194#92418—22no—
195#92418—42no—
196#92418—42no—
197#19276—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—22no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—82no—
204C22×C61—82no—
205C22×C61—82no—
206C22×C61—164no—
207C22×C61#46612yes—
208C22×C61C2×#12111yescharacteristic
209C4×C61—21no—
210C4×C61—22no—
211C4×C61—21no—
212C4×C61—41no—
213C4×C61—41no—
214C4×C61#46612yes—
215C4×C61#47112yes—
216C4×C61C22×D811yescharacteristic
217C4×C61C2×#13511yescharacteristic
218C4×C61#57512yes—
219Dic61—82no—
220C2×#486—611no—
221#3039—611no—
222#3038D6111yescharacteristic
223C8×#41—611no—
224#1682—614no—
225#1681—614no—
226#1567—611no—
227#1546—611no—
228#1545—611no—
229C2×C61—22no—
230C2×C61—42no—
231C2×C61—162no—
232C2×C61#304011yescharacteristic
233C2×C61C2×#46611yescharacteristic
234C2×C61C2×#47111yescharacteristic
235C2×#137—1221no—
236C2×AGL(1,ℤ/8)—21no—
237C2×C4⋊Q8—611no—
238C2×#127C2×D6111yescharacteristic
239C4×#41C2×D6111yescharacteristic
240#486—614no—
241#486—1221no—
242#486—1221no—
243#462—612no—
244#462—1221no—
245#461—612no—
246#461—1221no—
247#460—21no—
248#460C2×D6112yes—
249#459—21no—
250#459C2×D6112yes—
251C8×Q8—612no—
252C8×D4—612no—
253C8×D4—1222no—
254#431—611no—
255#431—1221no—
256#423—611no—
257#423C2×D6111yescharacteristic
258#419—1221no—
259#418—21no—
260C2×#102—1222no—
261C2×C4×C8—611no—
262C2×C4×C8—1221no—
263#335—614no—
264#332—614no—
265#331—614no—
266C61#1927611yescharacteristic, complemented, Sylow
267C2×#41C22⋊D6111yescharacteristic
268C22×Q8—1221no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272#137—2444no—
273AGL(1,ℤ/8)—44no—
274C2×Q16—1222no—
275C2×SD16—22no—
276C2×SD16—1222no—
277C2×D8—22no—
278C2×M16—21no—
279C2×M16—1221no—
280C22×C8—612no—
281C22×C8—1222no—
282C4⋊Q8—612no—
283C4⋊Q8—1221no—
284C4⋊Q8—1221no—
285C4⋊Q8—1221no—
286#127—21no—
287#127—21no—
288#127—21no—
289#127C22×D6112yes—
290C4×Q8C22⋊D6111yescharacteristic
291C4×Q8C22×D6111yescharacteristic
292C4×D4—21no—
293C4×D4—21no—
294C4×D4C22⋊D6111yescharacteristic
295C4×D4C22×D6111yescharacteristic
296#117—21no—
297#117C22⋊D6111yescharacteristic
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1221no—
300C2×C42—21no—
301C2×C42C22×D6111yescharacteristic
302C4⋊C8—21no—
303C4⋊C8—612no—
304C4⋊C8—612no—
305C4⋊C8—1222no—
306C4⋊C8—1221no—
307C4⋊C8C22×D6112yes—
308#103—1222no—
309#103—1222no—
310#102—22no—
311#102—22no—
312#102—1224no—
313#102—1224no—
314C22⋊C8—1222no—
315C22⋊C8—1221no—
316C4×C8—611no—
317C4×C8—611no—
318C4×C8—612no—
319C4×C8—1222no—
320C4×C8—1221no—
321C24—41no—
322#41—22no—
323#41#1175819914yes—
324C2×Q8—1222no—
325C2×Q8—2442no—
326C2×Q8—2442no—
327C2×Q8—2441no—
328C2×Q8C2×C22⋊D6111yescharacteristic
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—82no—
340C2×D4C2×C22⋊D6111yescharacteristic
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—2441no—
345C22×C4D4×D6111yescharacteristic
346C22×C4#1175822411yescharacteristic
347C22×C4C2×C22⋊D6111yescharacteristic
348Q16—2444no—
349SD16—44no—
350SD16—2444no—
351D8—44no—
352M16—42no—
353M16—2442no—
354C2×C8—22no—
355C2×C8—612no—
356C2×C8—612no—
357C2×C8—1222no—
358C2×C8—1222no—
359C2×C8—2442no—
360C2×C8—2444no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—1222no—
364C4⋊C4—1222no—
365C4⋊C4—2441no—
366C4⋊C4—2441no—
367C4⋊C4C2×C22⋊D6111yescharacteristic
368C4⋊C4C2×C22⋊D6111yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C42—21no—
373C42—21no—
374C42—21no—
375C42D4×D6111yescharacteristic
376C42#1175822411yescharacteristic
377C42C2×C22⋊D6111yescharacteristic
378C42C23×D6111yescharacteristic
379C23—21no—
380C23—42no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23#1451974911yescharacteristic
385Q8—21no—
386Q8—4882no—
387Q8—2442no—
388Q8—2442no—
389Q8C2×#1175819912yes—
390D4—24no—
391D4—21no—
392D4—42no—
393D4—42no—
394D4—44no—
395D4—82no—
396D4—82no—
397D4—82no—
398D4—82no—
399D4C2×#1175819912yes—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—4882no—
409C2×C4—2442no—
410C2×C4#1451974911yescharacteristic
411C2×C4#1451974911yescharacteristic
412C2×C4#1451974911yescharacteristic
413C2×C4C2×#1175819912yes—
414C2×C4#1451979712yes—
415C2×C4C2×D4×D6111yescharacteristic
416C2×C4C22×C22⋊D6111yescharacteristic
417C2×C4C2×#1175822411yescharacteristic
418C8—42no—
419C8—1222no—
420C8—1222no—
421C8—2442no—
422C8—2442no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—164no—
432C22#1683999612yes—
433C22C2×#1451974911yescharacteristic
434C4—22no—
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—4882no—
440C4#1683999612yes—
441C4#1684002312yes—
442C4C22×#1175819911yescharacteristic
443C4C2×#1451979711yescharacteristic
444C4#1684055812yes—
445C2—22no—
446C2—42no—
447C2—162no—
448C2#2145531111yescharacteristic
449C2C2×#1683999611yescharacteristic
450C2C2×#1684002311yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3038C2
socleC22×C61C2×#121
hypercenter#3038D61
hypocenterC61#19276
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C2×#16840108C2semidirect
2. #21455306C2semidirect
3. #41×#92418C2semidirect
4. #21445261C2semidirect
5. #21445254C2semidirect
6. #21444577C2semidirect
7. #21444492C2semidirect
8. #21444487C2semidirect
16. #16839972C22semidirect
18. #16839967C22semidirect
19. Q8×#92418C22semidirect
21. D4×#92418C22semidirect
29. #16839514C22semidirect
30. #16839509C22semidirect
266. C61#19276semidirect

Maximal subgroups

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

subgroupindex
C2×#168401082
#214553062
#41×#924182
#214452612
#214452542
#214445772
#214444922
#214444872
C61×#30382
#1927661