Finite Group Databasebeta

← #29600388

Subgroups — #29600388

Order 15616.

334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456202C211yesmaximal, characteristic
2#355×D61C211yesmaximal, characteristic
3#354×D61C211yesmaximal, characteristic
4#21443995C211yesmaximal, characteristic, complemented
5#21443994C211yesmaximal, characteristic, complemented
6#21443993C211yesmaximal, characteristic, complemented
7C61×#1414C211yesmaximal, characteristic, complemented
8#16840318C411yescharacteristic, complemented
9#124×D61C2211yescharacteristic
10#16840123—21no—
11#16840120—21no—
12#16840119C411yescharacteristic, complemented
13#16840117C411yescharacteristic, complemented
14#16840116C2211yescharacteristic
15#16839769—21no—
16#16839765—21no—
17#101×D61—21no—
18#99×D61—21no—
19C4×#11758189C411yescharacteristic, complemented
20#16839559C2211yescharacteristic
21#16839558—21no—
22#16839557C2211yescharacteristic
23#16839556—21no—
24C61×#488C2211yescharacteristic
25C61×#355C2211yescharacteristic
26C61×#354C2211yescharacteristic
27C2×Q8×D61D411yescharacteristic
28C2×D4×D61D411yescharacteristic
29C2×#11758189—21no—
30M16×D61—41no—
31#14519776—21no—
32#14519769C2×C411yescharacteristic, complemented
33#14519766D411yescharacteristic
34#14519765C2×C411yescharacteristic
35#14519764D411yescharacteristic
36#14519763—41no—
37#14519755—41no—
38#14519742—41no—
39#14519735—21no—
40C22⋊C4×D61—41no—
41C22⋊C4×D61—41no—
42C42×D61C2×C411yescharacteristic
43#14519702—21no—
44#14519701—21no—
45#14519700—21no—
46#14519699—21no—
47#14519698—21no—
48#14519697—21no—
49#14519696—21no—
50#14519695—41no—
51#14519692—21no—
52#14519691—41no—
53#14519687—21no—
54C4×#92418C2×C411yescharacteristic, complemented
55#125×C61C2×C411yescharacteristic, complemented
56#124×C61C2311yescharacteristic
57#103×C61—21no—
58#102×C61—21no—
59#101×C61—21no—
60#99×C61—21no—
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C2×Q8×C61C2×D411yescharacteristic
64C2×D4×C61C2×D411yescharacteristic
65C2×C22⋊D61—21no—
66Q8×D61—41no—
67Q8×D61—41no—
68D4×D61—41no—
69D4×D61—41no—
70C2×D244C22⋊C411yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—81no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×Dic122—21no—
76C2×Dic122—41no—
77C2×Dic122C22⋊C411yescharacteristic
78M16×C61—41no—
79C2×C8×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C42×C61C22×C411yescharacteristic
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—81no—
91C4⋊Dic61—21no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—21no—
95C4×Dic61—41no—
96C4×Dic61C22⋊C411yescharacteristic
97#11758194—41no—
98C2×#92418—21no—
99#11758189—41no—
100#11758189—41no—
101#11758189—81no—
102C8×D61—81no—
103C23×C61—21no—
104C22×D61—21no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—82no—
108C22×D61#9911yescharacteristic
109Q8×C61—41no—
110D4×C61—41no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C22⋊D61—81no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—41no—
120C2×Dic61—81no—
121C2×Dic61#9911yescharacteristic
122D244—41no—
123C4×D61—21no—
124C4×D61—21no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—81no—
128C4×D61—162no—
129Dic122—41no—
130Dic122—81no—
131Dic122—82no—
132C8×C61—41no—
133C8×C61—81no—
134#92418—41no—
135#92418—81no—
136#13603—611nomaximal, Sylow
137C22×C61—41no—
138C22×C61—81no—
139C22×C61C2×#9911yescharacteristic
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—82no—
143C2×D61—81no—
144C2×D61—161no—
145C2×D61#35411yescharacteristic
146C2×D61#35411yescharacteristic
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—81no—
151C4×C61—161no—
152Dic61—21no—
153Dic61—41no—
154Dic61—41no—
155Dic61—81no—
156Dic61—161no—
157#3140—611no—
158C2×#355—611no—
159C2×#354—611no—
160#1414—611no—
161#1414—611no—
162#1414—611no—
163#1414D6111yescharacteristic, complemented
164C2×C61—21no—
165C2×C61—81no—
166C2×C61C2×#35411yescharacteristic
167D61—21no—
168D61—21no—
169D61—81no—
170#533—611no—
171C2×#124—611no—
172#489—1221no—
173#489—1221no—
174#488—611no—
175#488—611no—
176#488—611no—
177#488C2×D6111yescharacteristic
178#419—1221no—
179#418—1221no—
180C2×#101—1221no—
181C2×#99—1221no—
182C4×M16—611no—
183#355—611no—
184#355—1221no—
185#355C2×D6111yescharacteristic
186#354—611no—
187#354—1221no—
188#354C2×D6111yescharacteristic
189C61#1360311yescharacteristic, complemented, Sylow
190C22×Q8—611no—
191C22×D4—611no—
192C2×M16—1221no—
193C2×M16—2441no—
194C4⋊Q8—1221no—
195#125—611no—
196#125C4×D6111yescharacteristic, complemented
197#124—611no—
198#124—611no—
199#124—611no—
200#124—2441no—
201#124C22×D6111yescharacteristic
202C22⋊Q8—2441no—
203C4×Q8—2441no—
204#117—1221no—
205C2×C22⋊C4—2441no—
206C2×C22⋊C4—2441no—
207C2×C42—611no—
208#103—21no—
209#103—1221no—
210#103—1221no—
211#103—1221no—
212#102—21no—
213#102—1221no—
214#102—1221no—
215#102—1221no—
216#101—21no—
217#101—1221no—
218#101—2441no—
219#99—21no—
220#99—1221no—
221#99—2441no—
222#97—1221no—
223C4×C8—611no—
224C4×C8C4×D6111yescharacteristic, complemented
225C24—1221no—
226C2×Q8—611no—
227C2×Q8—1221no—
228C2×Q8—2441no—
229C2×Q8—2441no—
230C2×Q8—2441no—
231C2×Q8D4×D6111yescharacteristic
232C2×D4—611no—
233C2×D4—1221no—
234C2×D4—2441no—
235C2×D4—2441no—
236C2×D4D4×D6111yescharacteristic
237C22×C4—611no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—4881no—
241M16—41no—
242M16—4881no—
243M16—2441no—
244M16—2441no—
245M16—2441no—
246C2×C8—21no—
247C2×C8—1221no—
248C2×C8—4881no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—1221no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—4881no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C22⋊C4—2441no—
260C22⋊C4—2441no—
261C22⋊C4—2441no—
262C42—611no—
263C42—1221no—
264C42—2441no—
265C42C2×C4×D6111yescharacteristic
266C23—21no—
267C23—611no—
268C23—1221no—
269C23—4882no—
270C23—2441no—
271C23—2441no—
272Q8—41no—
273Q8—4881no—
274Q8—4882no—
275Q8—2441no—
276D4—41no—
277D4—4881no—
278D4—2441no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—611no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—9762no—
289C2×C4—4881no—
290C2×C4—4881no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4C22⋊C4×D6111yescharacteristic
295C8—41no—
296C8—81no—
297C8—4881no—
298C8—2441no—
299C22—41no—
300C22—81no—
301C22—611no—
302C22—611no—
303C22—9761no—
304C22—4881no—
305C22—4882no—
306C22—2441no—
307C22—2441no—
308C22#99×D6111yescharacteristic
309C4—21no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—161no—
314C4—1221no—
315C4—9761no—
316C4—4881no—
317C4—2441no—
318C4—2441no—
319C2—21no—
320C2—81no—
321C2—1221no—
322C2—1221no—
323C2—4881no—
324C2#354×D6111yescharacteristic
subgroupG/H
centerC2#354×D61
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1414C2
socleC2×C61C2×#354
prime radicalC2×D4×D61D4
cosocle#124×C61C23
hypercenter#1414D61
hypocenterC61#13603
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1414

Complements

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

NH ≅ G/Ntype
4. #21443995C2semidirect
5. #21443994C2semidirect
6. #21443993C2semidirect
7. C61×#1414C2semidirect
8. #16840318C4semidirect
12. #16840119C4semidirect
13. #16840117C4semidirect
19. C4×#11758189C4semidirect
32. #14519769C2×C4semidirect
54. C4×#92418C2×C4semidirect
55. #125×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
163. #1414D61semidirect
189. C61#13603semidirect
196. #125C4×D61semidirect
224. C4×C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214562022
#355×D612
#354×D612
#214439952
#214439942
#214439932
C61×#14142
#1360361