Finite Group Databasebeta

← #21455077

Subgroups — #21455077

Order 7808.

754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#11758222C211yesmaximal, characteristic
2C2×#14519808C212yesmaximal, complemented
3#16839922C214yesmaximal, complemented
4#16839917C212yesmaximal, complemented
5#16839912C212yesmaximal, complemented
6#16839761C212yesmaximal, complemented
7#16839726C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10C2×#11758222—21no—
11C2×#11758222—28no—
12C2×#11758222C2212yes—
13C2×#11758222C2212yes—
14C22×Dic122C2211yescharacteristic
15C22×D244C2211yescharacteristic
16C22×C22⋊D61—21no—
17C22×C4×D61—21no—
18#14519808—28no—
19C2×#11758202C2214yescomplemented
20C2×#11758201C2214yescomplemented
21C2×#11758194C2212yescomplemented
22#14519700C2214yescomplemented
23#14519697C2214yescomplemented
24C22⋊#92418C2212yes—
25C22⋊#92418C2212yescomplemented
26C22×Q8×C61C2211yescharacteristic, complemented
27C23×C4×C61C2211yescharacteristic
28C22⋊Q8×C61—21no—
29C22⋊Q8×C61—21no—
30C22⋊Q8×C61C2212yes—
31C22⋊Q8×C61C2212yescomplemented
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61C2211yescharacteristic, complemented
34C2×C22⋊C4×C61—21no—
35C24×C61D411yescharacteristic
36C23×D61—21no—
37C2×Q8×C61—21no—
38C2×Q8×C61—24no—
39C2×Q8×C61C2312yes—
40C22×C4×C61—24no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61D411yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—28no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C22×Dic61—21no—
53#11758222—28no—
54#11758222—28no—
55#11758222—24no—
56#11758222—24no—
57#11758222—24no—
58#11758222D418yes—
59C2×D244—21no—
60C2×D244—24no—
61C2×D244C2312yes—
62C2×C4×D61—28no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×Dic122—21no—
66C2×Dic122—24no—
67C2×Dic122C2312yes—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61C2312yes—
72C22⋊C4×C61—22no—
73C22⋊C4×C61—22no—
74#11758202—28no—
75#11758201—28no—
76#11758194—24no—
77C2×#92418C2314yes—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—41no—
81C23×C61C2×D411yescharacteristic
82C23×C61C2×D411yescharacteristic
83C23×C61C2×D411yescharacteristic
84C22×D61—24no—
85C22×D61—22no—
86C22×D61—42no—
87C22×D61—42no—
88Q8×C61—24no—
89Q8×C61—42no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D414yes—
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—28no—
105C22⋊D61—28no—
106C2×Dic61—24no—
107C2×Dic61—22no—
108D244—24no—
109D244—22no—
110D244C2×D414yes—
111C4×D61—28no—
112C4×D61—28no—
113Dic122—24no—
114Dic122—22no—
115Dic122C2×D414yes—
116#92418—24no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—44no—
125C22×C61#12012yes—
126C22×C61#13712yescomplemented
127C22×C61C22×D411yescharacteristic
128C2×D61—24no—
129C2×D61—48no—
130C2×D61—42no—
131C2×D61—42no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—42no—
135C4×C61—42no—
136C4×C61#12012yes—
137C4×C61C22×D412yes—
138Dic61—24no—
139#3007—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—22no—
142C2×C61—41no—
143C2×C61C2×#12011yescharacteristic
144C2×C61C2×#13711yescharacteristic
145C2×C61#57511yescharacteristic
146D61—44no—
147C22×#41—611no—
148C2×#137—612no—
149C2×C22⋊Q8D6111yescharacteristic, complemented
150#452—614no—
151#451—612no—
152#450—612no—
153#417—612no—
154#407—611no—
155C61#300711yescharacteristic, complemented, Sylow
156C2×#41—612no—
157C2×#41—612no—
158C2×#41—1228no—
159C2×#41—1221no—
160C2×#41—1221no—
161C22×Q8—611no—
162C22×Q8C2×D6111yescharacteristic, complemented
163C22×D4—611no—
164C22×D4—1221no—
165C23×C4—1221no—
166C23×C4C2×D6111yescharacteristic
167#137—1228no—
168C2×Q16—614no—
169C2×SD16—614no—
170C2×M16—612no—
171C22⋊Q8—21no—
172C22⋊Q8—21no—
173C22⋊Q8C2×D6112yes—
174C22⋊Q8C2×D6112yescomplemented
175C2×C4⋊C4—21no—
176C2×C4⋊C4C2×D6111yescharacteristic, complemented
177C2×C22⋊C4—21no—
178#103—614no—
179#102—614no—
180C22⋊C8—612no—
181C22⋊C8—612no—
182C24—1221no—
183C24C22⋊D6111yescharacteristic
184#41—618no—
185#41—1224no—
186#41—1224no—
187#41—1228no—
188#41—1228no—
189#41—1224no—
190C2×Q8—21no—
191C2×Q8—24no—
192C2×Q8—612no—
193C2×Q8—1224no—
194C2×Q8—1221no—
195C2×Q8C22×D6112yes—
196C2×D4—612no—
197C2×D4—1224no—
198C2×D4—1228no—
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—1221no—
202C22×C4—24no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—1228no—
206C22×C4—1221no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4C22⋊D6111yescharacteristic
210C22×C4C22⋊D6111yescharacteristic
211C22×C4C22⋊D6111yescharacteristic
212C22×C4C22×D6111yescharacteristic
213C22×C4C22×D6111yescharacteristic
214C22×C4C22×D6111yescharacteristic
215Q16—1228no—
216SD16—1228no—
217M16—1224no—
218C2×C8—614no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—21no—
222C4⋊C4C22×D6112yes—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—1224no—
229C23—1222no—
230C23—2442no—
231C23—2442no—
232C23C2×C22⋊D6111yescharacteristic
233C23C2×C22⋊D6111yescharacteristic
234C23C2×C22⋊D6111yescharacteristic
235Q8—24no—
236Q8—42no—
237Q8—614no—
238Q8—1224no—
239Q8—1222no—
240D4—614no—
241D4—1224no—
242D4—1228no—
243D4—1228no—
244D4—1222no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—1228no—
255C2×C4—1224no—
256C2×C4—1222no—
257C2×C4—1228no—
258C2×C4D4×D6114yes—
259C2×C4C2×C22⋊D6111yescharacteristic
260C2×C4C2×C22⋊D6111yescharacteristic
261C2×C4C2×C22⋊D6111yescharacteristic
262C2×C4C23×D6111yescharacteristic
263C8—1224no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22—1224no—
273C22—2448no—
274C22—2442no—
275C22—2442no—
276C22#1451974512yes—
277C22#1451980812yescomplemented
278C22C22×C22⋊D6111yescharacteristic
279C4—21no—
280C4—21no—
281C4—42no—
282C4—42no—
283C4—1224no—
284C4#1451974512yes—
285C4C2×D4×D6112yes—
286C2—22no—
287C2—22no—
288C2—41no—
289C2—2444no—
290C2C2×#1451974511yescharacteristic
291C2C2×#1451980811yescharacteristic
292C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C22⋊Q8×C61C2
socleC22×C61C22×D4
hypercenterC2×C22⋊Q8D61
hypocenterC61#3007
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. #16839922C2semidirect
4. #16839917C2semidirect
5. #16839912C2semidirect
6. #16839761C2semidirect
7. #16839726C2semidirect
8. C2×C22⋊Q8×C61C2semidirect
19. C2×#11758202C22semidirect
20. C2×#11758201C22semidirect
21. C2×#11758194C22semidirect
22. #14519700C22semidirect
23. #14519697C22semidirect
25. C22⋊#92418C22semidirect
26. C22×Q8×C61C22semidirect
31. C22⋊Q8×C61C22semidirect
33. C2×C4⋊C4×C61C22semidirect
126. C22×C61#137semidirect
149. C2×C22⋊Q8D61semidirect
155. C61#3007semidirect
162. C22×Q8C2×D61semidirect
174. C22⋊Q8C2×D61semidirect
176. C2×C4⋊C4C2×D61semidirect
277. C22#14519808semidirect