Finite Group Databasebeta

← #29600413

Subgroups — #29600413

Order 15616.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#21456905C211yesmaximal, characteristic
2#21447505C211yesmaximal, characteristic
3#21447492C211yesmaximal, characteristic
4#21443994C211yesmaximal, characteristic, complemented
5#21443980C211yesmaximal, characteristic, complemented
6#21443978C211yesmaximal, characteristic, complemented
7C61×#1414C211yesmaximal, characteristic, complemented
8#16840375C411yescharacteristic, complemented
9#16840332C2211yescharacteristic
10#16840157C2211yescharacteristic
11#16840142C411yescharacteristic, complemented
12#16840132C411yescharacteristic, complemented
13#16839983—21no—
14#16839971—21no—
15#16839925—21no—
16#16839919—21no—
17#16839821C411yescharacteristic, complemented
18#101×D61—21no—
19#16839734—21no—
20#16839560—21no—
21#16839559C2211yescharacteristic
22#16839557C2211yescharacteristic
23#16839556—21no—
24C61×#488C2211yescharacteristic
25C61×#355C2211yescharacteristic
26C61×#354C2211yescharacteristic
27C2×#11758224D411yescharacteristic
28C2×Q8×D61D411yescharacteristic
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×#11758202—21no—
32C2×#11758200—21no—
33M16×D61—41no—
34#14519777C2×C411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519775D411yescharacteristic
37#14519772—41no—
38#14519768—41no—
39#14519764D411yescharacteristic
40#14519759—41no—
41#14519757—21no—
42#14519754—41no—
43#14519742—21no—
44#14519734C2×C411yescharacteristic
45#14519733—41no—
46#14519706—21no—
47#14519700—21no—
48#14519700—21no—
49#14519696—21no—
50#14519695—41no—
51#14519692—21no—
52#14519691—41no—
53#14519689—21no—
54#14519688C2×C411yescharacteristic
55#125×C61C2×C411yescharacteristic
56#124×C61C2311yescharacteristic
57#103×C61—21no—
58#102×C61—21no—
59#101×C61—21no—
60#99×C61—21no—
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61C2×D411yescharacteristic
63C2×D4×C61C2×D411yescharacteristic
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66Q8×D61—81no—
67#11758224—81no—
68C2×C4×D61—21no—
69C2×C4×D61C22⋊C411yescharacteristic
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122C22⋊C411yescharacteristic
73C2×Dic122C22⋊C411yescharacteristic
74M16×C61—41no—
75C2×C8×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C42×C61C22×C411yescharacteristic
81C22⋊Dic61—41no—
82C22⋊Dic61—41no—
83#11758202—81no—
84#11758200—81no—
85#11758198—21no—
86#11758198—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—21no—
91#11758196—41no—
92#11758196—41no—
93#11758196—81no—
94C4×Dic61—41no—
95C4×Dic61—81no—
96C4×Dic61C22⋊C411yescharacteristic
97#11758194—41no—
98C2×#92418—21no—
99Dic244—81no—
100Dic244—81no—
101#11758189—81no—
102C8×D61—81no—
103C23×C61—21no—
104C22×D61#9911yescharacteristic
105Q8×C61—41no—
106D4×C61—41no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—81no—
111C2×C4×C61C2×C22⋊C411yescharacteristic
112C22⋊D61—81no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—81no—
120C2×Dic61#9911yescharacteristic
121C4×D61—41no—
122C4×D61—41no—
123C4×D61—41no—
124Dic122—41no—
125Dic122—41no—
126Dic122—41no—
127Dic122—41no—
128Dic122—81no—
129C8×C61—41no—
130C8×C61—81no—
131#92418—41no—
132#92418—81no—
133#13608—611nomaximal, Sylow
134C22×C61—41no—
135C22×C61—81no—
136C22×C61C2×#9911yescharacteristic
137C2×D61—21no—
138C2×D61—41no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—81no—
143C4×C61—161no—
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147Dic61—41no—
148Dic61—81no—
149Dic61—161no—
150#3223—611no—
151#2133—611no—
152#2129—611no—
153#1414—611no—
154#1414D6111yescharacteristic, complemented
155#1407—611no—
156#1407—611no—
157C2×C61—21no—
158C2×C61—81no—
159C2×C61#212711yescharacteristic
160D61—41no—
161#541—611no—
162#536—611no—
163#497—611no—
164#494—611no—
165#491—611no—
166#488C2×D6111yescharacteristic
167#464—1221no—
168#462—1221no—
169#452—1221no—
170#451—1221no—
171#433—611no—
172C2×#101—1221no—
173#410—1221no—
174#356—1221no—
175#355—611no—
176#355C2×D6111yescharacteristic
177#354—611no—
178#354—1221no—
179#354C2×D6111yescharacteristic
180C61#1360811yescharacteristic, complemented, Sylow
181C2×#41—611no—
182C22×Q8—611no—
183C2×Q16—1221no—
184C2×Q16—1221no—
185C2×Q16—1221no—
186C2×SD16—1221no—
187C2×M16—2441no—
188C4⋊Q8—611no—
189C4⋊Q8—611no—
190C4⋊Q8—611no—
191#126—2441no—
192#125—2441no—
193#125C4×D6111yescharacteristic
194#124—611no—
195#124C22×D6111yescharacteristic
196#123—2441no—
197C22⋊Q8—1221no—
198C22⋊Q8—2441no—
199C4×Q8—1221no—
200#117—611no—
201#117—2441no—
202C4⋊C8—1221no—
203#103—21no—
204#103—1221no—
205#103—1221no—
206#102—21no—
207#101—21no—
208#101—1221no—
209#101—2441no—
210#99—21no—
211#99—1221no—
212#99—2441no—
213C22⋊C8—1221no—
214#97—611no—
215C4×C8C4×D6111yescharacteristic
216#41—4881no—
217C2×Q8—611no—
218C2×Q8—611no—
219C2×Q8—1221no—
220C2×Q8—1221no—
221C2×Q8—4881no—
222C2×Q8D4×D6111yescharacteristic
223C2×D4—1221no—
224C2×D4D4×D6111yescharacteristic
225C22×C4—611no—
226C22×C4—1221no—
227C22×C4—1221no—
228Q16—4881no—
229Q16—4881no—
230Q16—4881no—
231SD16—4881no—
232M16—41no—
233M16—4881no—
234M16—2441no—
235C2×C8—21no—
236C2×C8—1221no—
237C2×C8—4881no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—1221no—
241C4⋊C4—4881no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—1221no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C42—611no—
254C42—4881no—
255C42—2441no—
256C42C2×C4×D6111yescharacteristic
257C23—21no—
258C23—611no—
259Q8—41no—
260Q8—4881no—
261Q8—2441no—
262Q8—2441no—
263Q8—2441no—
264Q8—2441no—
265D4—41no—
266D4—4881no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—611no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—4881no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4C22⋊C4×D6111yescharacteristic
283C8—41no—
284C8—81no—
285C8—4881no—
286C8—2441no—
287C22—41no—
288C22—81no—
289C22—1221no—
290C22—2441no—
291C22#99×D6111yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—161no—
297C4—1221no—
298C4—9761no—
299C4—4881no—
300C4—2441no—
301C4—2441no—
302C4—2441no—
303C2—21no—
304C2—81no—
305C2—2441no—
306C2#2144748711yescharacteristic
subgroupG/H
centerC2#21447487
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1414C2
socleC2×C61#2127
prime radicalC2×#11758224D4
cosocle#124×C61C23
hypercenter#1414D61
hypocenterC61#13608
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. #21443994C2semidirect
5. #21443980C2semidirect
6. #21443978C2semidirect
7. C61×#1414C2semidirect
8. #16840375C4semidirect
11. #16840142C4semidirect
12. #16840132C4semidirect
17. #16839821C4semidirect
154. #1414D61semidirect
180. C61#13608semidirect

Maximal subgroups

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

subgroupindex
#214569052
#214475052
#214474922
#214439942
#214439802
#214439782
C61×#14142
#1360861