Finite Group Databasebeta

← #29600411

Subgroups — #29600411

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#21456897C211yesmaximal, characteristic
2#21447505C211yesmaximal, characteristic
3#21447492C211yesmaximal, characteristic
4#21443995C211yesmaximal, characteristic, complemented
5#21443993C211yesmaximal, characteristic, complemented
6#21443979C211yesmaximal, characteristic, complemented
7C61×#1407C211yesmaximal, characteristic, complemented
8#16840373C411yescharacteristic, complemented
9#16840332C2211yescharacteristic
10#16840141C411yescharacteristic, complemented
11#16840131C411yescharacteristic, complemented
12#16840116C2211yescharacteristic
13#16839982—21no—
14#16839970—21no—
15#16839921—21no—
16#16839916—21no—
17#16839824C411yescharacteristic, complemented
18#101×D61—21no—
19#16839734—21no—
20#16839560—21no—
21#16839559C2211yescharacteristic
22#16839557C2211yescharacteristic
23#16839556—21no—
24C61×#497C2211yescharacteristic
25C61×#355C2211yescharacteristic
26C61×#354C2211yescharacteristic
27C2×#11758224D411yescharacteristic
28C2×Q8×D61D411yescharacteristic
29C2×#11758202—21no—
30C2×#11758202—21no—
31M16×D61—41no—
32#14519777C2×C411yescharacteristic
33#14519775D411yescharacteristic
34#14519772—41no—
35#14519769C2×C411yescharacteristic
36#14519767—41no—
37#14519764D411yescharacteristic
38#14519759—41no—
39#14519754—41no—
40#14519753—21no—
41Q8×Dic61—21no—
42#14519734C2×C411yescharacteristic
43#14519733—41no—
44#14519706—21no—
45#14519702—21no—
46#14519702—21no—
47#14519701—21no—
48#14519698—21no—
49#14519696—21no—
50#14519695—41no—
51#14519692—21no—
52#14519691—41no—
53#14519689—21no—
54C4×#92418C2×C411yescharacteristic
55C2×Q16×C61—21no—
56C2×SD16×C61—21no—
57C4⋊Q8×C61C2×C411yescharacteristic
58#124×C61C2311yescharacteristic
59#101×C61—21no—
60#99×C61—21no—
61#97×C61C2×C411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61C2×D411yescharacteristic
64C2×D4×C61C2×D411yescharacteristic
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67Q8×D61—81no—
68#11758224—81no—
69C2×C4×D61—21no—
70C2×C4×D61C22⋊C411yescharacteristic
71C2×Dic122—21no—
72C2×Dic122C22⋊C411yescharacteristic
73C2×Dic122C22⋊C411yescharacteristic
74Q16×C61—81no—
75SD16×C61—81no—
76M16×C61—41no—
77C2×C8×C61—21no—
78C4⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C42×C61C22×C411yescharacteristic
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84#11758202—81no—
85#11758202—81no—
86#11758198—21no—
87#11758198—41no—
88C4⋊Dic61—21no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—21no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95#11758196—81no—
96C4×Dic61—41no—
97C4×Dic61—81no—
98C4×Dic61C22⋊C411yescharacteristic
99#11758194—41no—
100C2×#92418—21no—
101#11758189—81no—
102C8×D61—81no—
103C23×C61—21no—
104C22×D61#9911yescharacteristic
105Q8×C61—41no—
106Q8×C61—41no—
107Q8×C61—41no—
108D4×C61—41no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—81no—
113C2×C4×C61C2×C22⋊C411yescharacteristic
114C22⋊D61—81no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—81no—
122C2×Dic61#9911yescharacteristic
123C4×D61—41no—
124C4×D61—41no—
125C4×D61—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#1414—611no—
155#1407—611no—
156#1407D6111yescharacteristic, complemented
157C2×C61—21no—
158C2×C61—81no—
159C2×C61#212711yescharacteristic
160D61—41no—
161#541—611no—
162#536—611no—
163#497C2×D6111yescharacteristic
164#494—611no—
165#491—611no—
166#488—611no—
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—21no—
184C2×Q16—1221no—
185C2×Q16—1221no—
186C2×SD16—21no—
187C2×M16—2441no—
188C4⋊Q8—611no—
189C4⋊Q8—611no—
190C4⋊Q8C4×D6111yescharacteristic
191#126—2441no—
192#125—611no—
193#125—2441no—
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—1221no—
204#103—1221no—
205#103—1221no—
206#102—1221no—
207#101—21no—
208#101—1221no—
209#101—2441no—
210#99—21no—
211#99—1221no—
212#99—2441no—
213C22⋊C8—1221no—
214#97C4×D6111yescharacteristic
215C4×C8—611no—
216#41—4881no—
217C2×Q8—21no—
218C2×Q8—611no—
219C2×Q8—611no—
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—81no—
229Q16—4881no—
230Q16—4881no—
231SD16—81no—
232M16—41no—
233M16—4881no—
234M16—2441no—
235C2×C8—21no—
236C2×C8—1221no—
237C2×C8—4881no—
238C4⋊C4—41no—
239C4⋊C4—1221no—
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—41no—
261Q8—41no—
262Q8—4881no—
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#2144748511yescharacteristic
subgroupG/H
centerC2#21447485
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1407C2
socleC2×C61#2127
prime radicalC2×#11758224D4
cosocle#124×C61C23
hypercenter#1407D61
hypocenterC61#13608
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1407

Complements

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

NH ≅ G/Ntype
4. #21443995C2semidirect
5. #21443993C2semidirect
6. #21443979C2semidirect
7. C61×#1407C2semidirect
8. #16840373C4semidirect
10. #16840141C4semidirect
11. #16840131C4semidirect
17. #16839824C4semidirect
156. #1407D61semidirect
180. C61#13608semidirect

Maximal subgroups

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

subgroupindex
#214568972
#214475052
#214474922
#214439952
#214439932
#214439792
C61×#14072
#1360861