Finite Group Databasebeta

← #21446885

Subgroups — #21446885

Order 7808.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840274C211yesmaximal, characteristic, complemented
3#16840269C211yesmaximal, characteristic, complemented
4#16839778C211yesmaximal, characteristic, complemented
5#16839725C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×C4×D61C2211yescharacteristic
10#14519808—21no—
11#14519807—21no—
12#14519803—21no—
13#14519802—21no—
14#14519797—22no—
15C2×#11758194C2211yescharacteristic
16#14519761—21no—
17#14519758—21no—
18#14519757—21no—
19#14519753—21no—
20#14519752—21no—
21#14519748—21no—
22#14519747—21no—
23#14519745—21no—
24C4×D244—22no—
25C4×C22⋊D61—22no—
26#14519736C2211yescharacteristic
27#14519703—22no—
28#14519689—22no—
29C2×#41×C61C2211yescharacteristic
30C2×M16×C61C2211yescharacteristic
31#117×C61C2211yescharacteristic
32#104×C61—22no—
33C23×D61D411yescharacteristic
34#41×C61—21no—
35#41×C61—21no—
36#41×C61—21no—
37#41×C61—21no—
38C2×Q8×C61D411yescharacteristic, complemented
39C2×D4×C61—21no—
40C2×D4×C61D411yescharacteristic, complemented
41C22×C4×C61—21no—
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—22no—
44C2×C22⋊D61—21no—
45C22×Dic61D411yescharacteristic
46#11758222—21no—
47#11758222—21no—
48#11758222—21no—
49#11758222—21no—
50C2×D244—22no—
51C2×D244D411yescharacteristic, complemented
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×Dic122D411yescharacteristic, complemented
60M16×C61—21no—
61M16×C61—21no—
62C2×C8×C61—21no—
63C4⋊C4×C61—21no—
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—
73#11758198—22no—
74#11758198—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—21no—
77#11758196—22no—
78C4×Dic61D412yescomplemented
79#11758194—21no—
80#11758194—21no—
81C2×#92418D412yescomplemented
82C23×C61—21no—
83C23×C61C2×D411yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—42no—
89Q8×C61—21no—
90Q8×C61—21no—
91D4×C61—21no—
92D4×C61—21no—
93D4×C61—41no—
94D4×C61—41no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61#4111yescharacteristic
105C22⋊D61—44no—
106C22⋊D61—41no—
107C22⋊D61—41no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113D244—21no—
114D244—21no—
115D244—44no—
116C4×D61—41no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—41no—
122Dic122—21no—
123Dic122—21no—
124C8×C61—41no—
125#92418—22no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—41no—
129C22×C61#12011yescharacteristic
130C22×C61#12011yescharacteristic
131C22×C61#12111yescharacteristic
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—42no—
140C2×D61—41no—
141C4×C61—42no—
142C4×C61—41no—
143C4×C61#12011yescharacteristic
144C4×C61#12111yescharacteristic
145C4×C61#12111yescharacteristic
146C4×C61#12711yescharacteristic
147Dic61—42no—
148Dic61—41no—
149Dic61—41no—
150#2010—611nomaximal, Sylow
151C2×C61—21no—
152C2×C61—21no—
153C2×C61—21no—
154C2×C61—81no—
155C2×C61#39211yescharacteristic
156D61—42no—
157D61—81no—
158#575—611no—
159#525—611no—
160#525—611no—
161#421—611no—
162#421D6111yescharacteristic, complemented
163#407—611no—
164H(3,ℤ/4)—611no—
165C61#201011yescharacteristic, complemented, Sylow
166C2×#41—611no—
167C2×#41C2×D6111yescharacteristic
168C23×C4—611no—
169#137—1221no—
170#137—1221no—
171AGL(1,ℤ/8)—1221no—
172AGL(1,ℤ/8)—1221no—
173#135—1222no—
174C2×M16—611no—
175C2×M16C2×D6111yescharacteristic
176#123—1221no—
177#123—1221no—
178C22⋊Q8—1221no—
179C22⋊Q8—1221no—
180#121—1221no—
181#121—1221no—
182#120—1221no—
183#120—1221no—
184C4×D4—1222no—
185C4×D4—1222no—
186#117—611no—
187#117C2×D6111yescharacteristic
188#104—22no—
189#104—1222no—
190C22⋊C8—1222no—
191C24—611no—
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×Q8D24411yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—611no—
204C2×D4—1222no—
205C2×D4—1222no—
206C2×D4—1221no—
207C2×D4D24411yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4C22×D6111yescharacteristic
218Q16—1222no—
219SD16—1222no—
220SD16—1222no—
221D8—1222no—
222M16—21no—
223M16—21no—
224M16—1221no—
225M16—1221no—
226C2×C8—21no—
227C2×C8—612no—
228C4⋊C4—21no—
229C4⋊C4—1222no—
230C4⋊C4—1222no—
231C4⋊C4—1221no—
232C22⋊C4—21no—
233C22⋊C4—1222no—
234C22⋊C4—1222no—
235C22⋊C4—1222no—
236C22⋊C4—1222no—
237C22⋊C4—1221no—
238C42—612no—
239C42C22⋊D6112yescomplemented
240C23—21no—
241C23—1221no—
242C23—1221no—
243C23—1221no—
244C23—1221no—
245C23—2442no—
246C23D4×D6111yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—1221no—
250Q8—1221no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—1221no—
256D4—1221no—
257D4—2444no—
258D4—2444no—
259D4—2441no—
260D4—2441no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4C2×D24411yescharacteristic
277C2×C4#1175822211yescharacteristic
278C2×C4D4×D6111yescharacteristic
279C2×C4D4×D6111yescharacteristic
280C2×C4D4×D6111yescharacteristic
281C2×C4C2×C22⋊D6111yescharacteristic
282C8—41no—
283C8—1222no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—1222no—
288C22—1222no—
289C22—1222no—
290C22—2442no—
291C22—2441no—
292C22—2441no—
293C22—2441no—
294C22—2441no—
295C22—2441no—
296C22#1451974511yescharacteristic
297C22#1451974711yescharacteristic
298C22#1451975011yescharacteristic
299C4—42no—
300C4—41no—
301C4—2442no—
302C4—2441no—
303C4—2441no—
304C4#1451974711yescharacteristic
305C4#1451975011yescharacteristic
306C4#1451975111yescharacteristic
307C4#1451977311yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—4881no—
313C2—2442no—
314C2#1683967111yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#392
hypercenter#421D61
hypocenterC61#2010
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. #16840274C2semidirect
3. #16840269C2semidirect
4. #16839778C2semidirect
5. #16839725C2semidirect
6. #16839518C2semidirect
7. C61×#421C2semidirect
38. C2×Q8×C61D4semidirect
40. C2×D4×C61D4semidirect
51. C2×D244D4semidirect
59. C2×Dic122D4semidirect
65. C42×C61D4semidirect
78. C4×Dic61D4semidirect
81. C2×#92418D4semidirect
162. #421D61semidirect
165. C61#2010semidirect
201. C2×Q8D244semidirect
207. C2×D4D244semidirect
239. C42C22⋊D61semidirect