Finite Group Databasebeta

← #21461770

Subgroups — #21461770

Order 7808.

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C2×#14519856C211yesmaximal, characteristic
2C2×#14519846C211yesmaximal, characteristic, complemented
3C2×#14519845C211yesmaximal, characteristic, complemented
4#16840704C211yesmaximal, characteristic
5#16840636C211yesmaximal, characteristic, complemented
6#16840636C211yesmaximal, characteristic, complemented
7C22⋊C8×D61C211yesmaximal, characteristic
8#14519856—22no—
9#14519856—22no—
10C2×C4⋊#6923C2211yescharacteristic
11C2×C4⋊#6923C2211yescharacteristic
12C2×C4⋊#6923C2211yescharacteristic
13C2×C4⋊#6923C2211yescharacteristic
14C2×C22⋊#6923—21no—
15C2×C22⋊#6923—21no—
16C2×C4×#6923—21no—
17#14519846—22no—
18#14519845—22no—
19(C2×#6923)⋊C4—21no—
20C22×C4×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23C22⋊#92418C411yescharacteristic, complemented
24#14519689C411yescharacteristic, complemented
25#14519689C411yescharacteristic, complemented
26C22⋊C8×C61C411yescharacteristic, complemented
27C23×D61D411yescharacteristic
28C22×#6923—21no—
29C22×#6923—21no—
30C22×#6923—21no—
31C22×#6923—21no—
32C22×C4×C61C2×C411yescharacteristic
33C22×Dic61Q811yescharacteristic
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61C2×C411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61Q811yescharacteristic
41C2×C4×D61C2311yescharacteristic
42C22⋊#6923—24no—
43C22⋊#6923—42no—
44C4⋊#6923—21no—
45C4⋊#6923—21no—
46C4⋊#6923—21no—
47C4⋊#6923—21no—
48C4⋊#6923—21no—
49C4⋊#6923—21no—
50C4⋊#6923D412yes—
51C4⋊#6923D412yes—
52C4×#6923—24no—
53C2×C8×C61C2×C411yescharacteristic
54C2×C8×C61C2×C411yescharacteristic
55C2×#92418C2×C411yescharacteristic
56C2×#92418C2×C411yescharacteristic
57C8×D61—21no—
58C8×D61—21no—
59C8×D61—21no—
60C8×D61—21no—
61C23×C61C4⋊C411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61C4⋊C411yescharacteristic
69C22×D61C2×D411yescharacteristic
70C2×#6923—22no—
71C2×#6923—22no—
72C2×#6923—41no—
73C2×#6923—41no—
74C2×#6923—41no—
75C2×#6923—41no—
76C2×#6923—41no—
77C2×#6923—41no—
78C2×#6923—41no—
79C2×#6923—41no—
80C2×#6923—41no—
81C2×#6923—41no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61C4⋊C411yescharacteristic
85C2×C4×C61C22×C411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61C4⋊C411yescharacteristic
89C2×Dic61C2×Q811yescharacteristic
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—21no—
96C4×D61C2×D411yescharacteristic
97C4×D61C2×D411yescharacteristic
98C4×D61#4111yescharacteristic
99C4×D61#4111yescharacteristic
100C8×C61—21no—
101C8×C61—21no—
102#92418—21no—
103#92418—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61C2×C4⋊C411yescharacteristic
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C2×D61#12011yescharacteristic
116C2×D61#12311yescharacteristic
117C2×D61#13511yescharacteristic
118C2×D61#13511yescharacteristic
119C2×D61AGL(1,ℤ/8)11yescharacteristic
120C2×D61#13711yescharacteristic
121#6923—42no—
122#6923—42no—
123#6923—81no—
124#6923—81no—
125C4×C61—21no—
126C4×C61C4×D411yescharacteristic
127C4×C61C4×D411yescharacteristic
128Dic61—21no—
129Dic61C22⋊Q811yescharacteristic
130Dic61C22⋊Q811yescharacteristic
131#1854—611nomaximal, Sylow
132C2×C61—41no—
133C2×C61#38511yescharacteristic
134C2×C61#42711yescharacteristic
135C2×C61#42811yescharacteristic
136D61—41no—
137D61#44911yescharacteristic
138D61#45211yescharacteristic
139D61#48211yescharacteristic
140D61#48511yescharacteristic
141C2×#117—611no—
142C2×#107—611no—
143C2×#106—611no—
144C2×C22⋊C8—611no—
145#380—611no—
146#340—611no—
147#340—611no—
148C61#185411yescharacteristic, complemented, Sylow
149C23×C4—611no—
150C22×C8—611no—
151C22×C8—611no—
152#117—1222no—
153#117—1222no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C22⋊C4—1221no—
159C2×C22⋊C4—1221no—
160C2×C42—1221no—
161#107—1222no—
162#106—1222no—
163C22⋊C8—611no—
164C22⋊C8—611no—
165C22⋊C8—611no—
166C22⋊C8#692311yescharacteristic, complemented
167#95—1221no—
168C24—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4—1221no—
181C22×C4—1221no—
182C22×C4C2×#692311yescharacteristic
183C2×C8—611no—
184C2×C8—611no—
185C2×C8—1221no—
186C2×C8—1221no—
187C2×C8—1221no—
188C2×C8—1221no—
189C2×C8C2×#692311yescharacteristic
190C2×C8C2×#692311yescharacteristic
191C4⋊C4—612no—
192C4⋊C4—612no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C22⋊C4—1224no—
200C22⋊C4—2442no—
201C42—1224no—
202C23—611no—
203C23—611no—
204C23—1221no—
205C23—1221no—
206C23—1221no—
207C23—1221no—
208C23—1221no—
209C23—1221no—
210C23C4⋊#692311yescharacteristic
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—611no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4C4⋊#692311yescharacteristic
240C2×C4C22×#692311yescharacteristic
241C8—21no—
242C8—21no—
243C8—1221no—
244C8—1221no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—611no—
249C22—611no—
250C22—611no—
251C22—611no—
252C22—611no—
253C22—611no—
254C22—1221no—
255C22—1221no—
256C22—1221no—
257C22—2441no—
258C22—2441no—
259C22—2441no—
260C22—2441no—
261C22C2×C4⋊#692311yescharacteristic
262C4—21no—
263C4—611no—
264C4—611no—
265C4—1221no—
266C4—4881no—
267C4—4881no—
268C4—2442no—
269C4—2442no—
270C4D4×#692311yescharacteristic
271C4D4×#692311yescharacteristic
272C2—41no—
273C2—611no—
274C2—611no—
275C2—611no—
276C2—611no—
277C2—2441no—
278C2#1684070911yescharacteristic
279C2#1684077211yescharacteristic
280C2#1684077311yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC22⋊C8#6923
hypocenterC61#1854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14519846C2semidirect
3. C2×#14519845C2semidirect
5. #16840636C2semidirect
6. #16840636C2semidirect
23. C22⋊#92418C4semidirect
24. #14519689C4semidirect
25. #14519689C4semidirect
26. C22⋊C8×C61C4semidirect
148. C61#1854semidirect
166. C22⋊C8#6923semidirect