Finite Group Databasebeta

← #21446884

Subgroups — #21446884

Order 7808.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840560C211yesmaximal, characteristic, complemented
2#16840273C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic, complemented
4#16839779C211yesmaximal, characteristic, complemented
5#16839726C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#525C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807—21no—
11#14519803—21no—
12#14519802—21no—
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519760—21no—
17#14519756—21no—
18#14519751—21no—
19#14519746—21no—
20C4×C22⋊D61—22no—
21#14519736C2211yescharacteristic
22#14519705—22no—
23#14519704—22no—
24C22⋊#92418—22no—
25C2×#41×C61C2211yescharacteristic
26C23×C4×C61C2211yescharacteristic
27#123×C61—21no—
28C22⋊Q8×C61—21no—
29#121×C61—21no—
30#120×C61—21no—
31C4×D4×C61—22no—
32#117×C61C2211yescharacteristic
33C24×C61D411yescharacteristic
34#41×C61—21no—
35#41×C61—21no—
36#41×C61—21no—
37#41×C61—21no—
38C2×Q8×C61D411yescharacteristic, complemented
39C2×D4×C61—22no—
40C2×D4×C61—21no—
41C2×D4×C61D411yescharacteristic, complemented
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61D411yescharacteristic
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—22no—
52C2×C22⋊D61—21no—
53#11758222—21no—
54#11758222—21no—
55#11758222—21no—
56#11758222—21no—
57C2×D244D411yescharacteristic, complemented
58C2×C4×D61—21no—
59C2×Dic122D411yescharacteristic, complemented
60C4⋊C4×C61—22no—
61C4⋊C4×C61—21no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C22⋊C4×C61—21no—
65C42×C61D412yescomplemented
66C22⋊Dic61—22no—
67C22⋊Dic61—21no—
68#11758202—22no—
69#11758201—22no—
70#11758200—22no—
71#11758199—22no—
72#11758198—22no—
73C4⋊Dic61—21no—
74#11758196—22no—
75C4×Dic61D412yescomplemented
76#11758194—21no—
77#11758194—21no—
78#11758194—21no—
79#11758194—21no—
80C2×#92418—21no—
81C2×#92418D412yescomplemented
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—42no—
87C23×C61C2×D411yescharacteristic
88C22×D61—21no—
89Q8×C61—21no—
90Q8×C61—21no—
91D4×C61—21no—
92D4×C61—21no—
93D4×C61—44no—
94D4×C61—41no—
95D4×C61—41no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61C2×D411yescharacteristic
108C2×C4×C61C2×D411yescharacteristic
109C2×C4×C61C2×D411yescharacteristic
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61#4111yescharacteristic
113C22⋊D61—44no—
114C22⋊D61—41no—
115C22⋊D61—41no—
116C2×Dic61—22no—
117C2×Dic61—21no—
118D244—21no—
119D244—21no—
120C4×D61—41no—
121C4×D61—41no—
122Dic122—21no—
123Dic122—21no—
124#92418—22no—
125#92418—41no—
126C22×C61—22no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—41no—
130C22×C61—41no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—42no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61#12011yescharacteristic
137C22×C61#12011yescharacteristic
138C22×C61#12111yescharacteristic
139C2×D61—42no—
140C2×D61—41no—
141C4×C61—42no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61#12011yescharacteristic
145C4×C61#12111yescharacteristic
146C4×C61#12111yescharacteristic
147C4×C61#12711yescharacteristic
148Dic61—42no—
149Dic61—41no—
150#2010—611nomaximal, Sylow
151C2×C61—21no—
152C2×C61—21no—
153C2×C61—21no—
154C2×C61—42no—
155C2×C61—81no—
156C2×C61#39211yescharacteristic
157D61—81no—
158#575—611no—
159#525—611no—
160#525D6111yescharacteristic, complemented
161#421—611no—
162#421—611no—
163#407—611no—
164H(3,ℤ/4)—611no—
165C61#201011yescharacteristic, complemented, Sylow
166C2×#41—611no—
167C2×#41C2×D6111yescharacteristic
168C23×C4C2×D6111yescharacteristic
169#137—1221no—
170#137—1221no—
171AGL(1,ℤ/8)—1221no—
172AGL(1,ℤ/8)—1221no—
173#135—1222no—
174C2×M16—611no—
175C2×M16—611no—
176#123—21no—
177#123—1221no—
178C22⋊Q8—21no—
179C22⋊Q8—1221no—
180#121—21no—
181#121—1221no—
182#120—21no—
183#120—1221no—
184C4×D4—22no—
185C4×D4—1222no—
186#117—611no—
187#117C2×D6111yescharacteristic
188#104—1222no—
189#104—1222no—
190C22⋊C8—1222no—
191C24C22⋊D6111yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—1221no—
197#41—1221no—
198#41—1221no—
199#41—1221no—
200C2×Q8—611no—
201C2×Q8C22⋊D6111yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—611no—
205C2×D4—1222no—
206C2×D4—1221no—
207C2×D4C22⋊D6111yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—1221no—
216C22×C4C22⋊D6111yescharacteristic
217C22×C4C22×D6111yescharacteristic
218Q16—1222no—
219SD16—1222no—
220SD16—1222no—
221D8—1222no—
222M16—1221no—
223M16—1221no—
224M16—1221no—
225M16—1221no—
226C2×C8—612no—
227C2×C8—1221no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—1222no—
231C4⋊C4—1221no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—1222no—
236C22⋊C4—1222no—
237C22⋊C4—1221no—
238C42—612no—
239C42C22⋊D6112yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—1221no—
246C23C2×C22⋊D6111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—1221no—
250Q8—1221no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—1221no—
257D4—1221no—
258D4—2444no—
259D4—2441no—
260D4—2441no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4D4×D6111yescharacteristic
277C2×C4D4×D6111yescharacteristic
278C2×C4D4×D6111yescharacteristic
279C2×C4#1175822411yescharacteristic
280C2×C4C2×C22⋊D6111yescharacteristic
281C2×C4C2×C22⋊D6111yescharacteristic
282C8—1222no—
283C8—2441no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—2442no—
295C22—2441no—
296C22#1451974511yescharacteristic
297C22#1451974611yescharacteristic
298C22#1451974911yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—2442no—
303C4—2441no—
304C4#1451974511yescharacteristic
305C4#1451974811yescharacteristic
306C4#1451974911yescharacteristic
307C4#1451977311yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—4881no—
314C2#1683967011yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#525C2
socleC2×C61#392
hypercenter#525D61
hypocenterC61#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. #16840273C2semidirect
3. #16839780C2semidirect
4. #16839779C2semidirect
5. #16839726C2semidirect
6. #16839518C2semidirect
7. C61×#525C2semidirect
38. C2×Q8×C61D4semidirect
41. C2×D4×C61D4semidirect
57. C2×D244D4semidirect
59. C2×Dic122D4semidirect
65. C42×C61D4semidirect
75. C4×Dic61D4semidirect
81. C2×#92418D4semidirect
160. #525D61semidirect
165. C61#2010semidirect
201. C2×Q8C22⋊D61semidirect
207. C2×D4C22⋊D61semidirect
239. C42C22⋊D61semidirect