Finite Group Databasebeta

← #21455852

Subgroups — #21455852

Order 7808.

428 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 127 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#16840313C211yesmaximal, characteristic
2C4×Q8×D61C211yesmaximal, characteristic, complemented
3#16840082C212yesmaximal, complemented
4#16840044C211yesmaximal, characteristic, complemented
5#16839963C211yesmaximal, characteristic, complemented
6#16839962C211yesmaximal, characteristic, complemented
7#16839902C212yesmaximal, complemented
8#16839849C212yesmaximal, complemented
9#16839847C212yesmaximal, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#475C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×Q8×D61C2211yescharacteristic
14C2×#11758190C2212yes—
15C2×#11758201C2212yes—
16#14519774C2211yescharacteristic
17#14519766—21no—
18#14519752—21no—
19#14519752C2212yes—
20Q8×Dic61C2211yescharacteristic
21C4×Dic122—21no—
22C4×Dic122C2211yescharacteristic
23#14519742—21no—
24#14519742C2211yescharacteristic
25#14519739—21no—
26#14519739C2212yes—
27C4⋊C4×D61—21no—
28C4⋊C4×D61C2211yescharacteristic
29C42×D61—21no—
30C42×D61C2211yescharacteristic
31#14519708C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519700C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#106×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45#11758226—44no—
46Q8×D61—22no—
47Q8×D61—22no—
48C2×D244—22no—
49C2×D244—21no—
50C2×D244—21no—
51C2×D244C2312yes—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—22no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×Dic122—21no—
59C2×Dic122C2311yescharacteristic
60C2×C8×C61C2312yes—
61C4⋊C4×C61—21no—
62C4⋊C4×C61—21no—
63C4⋊C4×C61C2312yes—
64C4⋊C4×C61C2311yescharacteristic
65C42×C61—21no—
66C42×C61C2311yescharacteristic
67#11758201—24no—
68#11758198—22no—
69#11758198—22no—
70C4⋊Dic61—21no—
71C4⋊Dic61C2311yescharacteristic
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82#11758190—24no—
83C22×D61—22no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—21no—
86Q8×C61—42no—
87Q8×C61#4112yescomplemented
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99D244—22no—
100D244—22no—
101D244—42no—
102D244—44no—
103D244—42no—
104C4×D61—24no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—41no—
108C4×D61—42no—
109C4×D61—44no—
110C4×D61SD1614yescomplemented
111Dic122—24no—
112Dic122—21no—
113Dic122#4112yescomplemented
114C8×C61—22no—
115#92418—22no—
116C22×C61C22×D411yescharacteristic
117C2×D61—21no—
118C2×D61—21no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61C2×SD1612yes—
123C4×C61—22no—
124C4×C61—21no—
125C4×C61—42no—
126C4×C61—41no—
127C4×C61C2×SD1612yes—
128C4×C61C2×#4111yescharacteristic
129C4×C61C2×#4111yescharacteristic
130Dic61—21no—
131Dic61—22no—
132Dic61—21no—
133Dic61—41no—
134Dic61C2×SD1612yes—
135#3103—611nomaximal, Sylow
136C2×C61#52511yescharacteristic
137C2×C61C22×SD1611yescharacteristic
138C2×C61#57511yescharacteristic
139D61—22no—
140D61—82no—
141#532—611no—
142C2×C4×Q8—611no—
143#481—612no—
144#475—611no—
145#475D6111yescharacteristic, complemented
146#460—611no—
147#460—611no—
148#448—612no—
149C4×SD16—612no—
150C4×SD16—612no—
151#431—611no—
152C61#310311yescharacteristic, complemented, Sylow
153C2×#41—1221no—
154C22×Q8—611no—
155C2×SD16—612no—
156C2×SD16—612no—
157C4⋊Q8C2×D6111yescharacteristic
158#127—611no—
159#124—1221no—
160#121—612no—
161#121—1221no—
162C4×Q8—611no—
163C4×Q8—611no—
164C4×Q8—611no—
165C4×Q8—1221no—
166C4×Q8—1221no—
167C4×Q8C2×D6111yescharacteristic
168C4×D4—612no—
169C4×D4—1221no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—1221no—
172C2×C42—611no—
173C2×C42—1221no—
174#106—612no—
175#106C2×D6112yes—
176C4⋊C8—611no—
177C4⋊C8C2×D6111yescharacteristic
178#103—612no—
179#103C2×D6112yes—
180#102—612no—
181#102—612no—
182C22⋊C8—612no—
183C4×C8—612no—
184#41—2444no—
185C2×Q8—21no—
186C2×Q8—611no—
187C2×Q8—1221no—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×Q8C22×D6111yescharacteristic
191C2×D4—612no—
192C2×D4—1222no—
193C2×D4—1221no—
194C2×D4—1221no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—1222no—
199C22×C4—1221no—
200C22×C4—1221no—
201SD16—1224no—
202SD16—1224no—
203C2×C8—612no—
204C2×C8C22×D6112yes—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—611no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4C22×D6111yescharacteristic
213C4⋊C4C22×D6112yes—
214C22⋊C4—1222no—
215C22⋊C4—1222no—
216C42—21no—
217C42—611no—
218C42—611no—
219C42—611no—
220C42—1221no—
221C42—1221no—
222C42—1221no—
223C42C22×D6111yescharacteristic
224C23—611no—
225C23—1222no—
226Q8—21no—
227Q8—42no—
228Q8—612no—
229Q8—1224no—
230Q8—1221no—
231Q8#1175822612yescomplemented
232D4—1222no—
233D4—1222no—
234D4—2442no—
235D4—2444no—
236D4—2442no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—611no—
241C2×C4—614no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1224no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—2441no—
250C2×C4—2444no—
251C2×C4—2442no—
252C2×C4D4×D6111yescharacteristic
253C2×C4D4×D6111yescharacteristic
254C2×C4C23×D6111yescharacteristic
255C8—22no—
256C8—1222no—
257C22—612no—
258C22—1221no—
259C22—1221no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22C2×D4×D6111yescharacteristic
264C4—22no—
265C4—21no—
266C4—42no—
267C4—41no—
268C4—612no—
269C4—1221no—
270C4—1222no—
271C4—1221no—
272C4—2441no—
273C4SD16×D6112yes—
274C4#41×D6111yescharacteristic
275C4C2×#1175822611yescharacteristic
276C2—1222no—
277C2—4882no—
278C2#1684027511yescharacteristic
279C2C2×SD16×D6111yescharacteristic
280C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3103
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D61C2semidirect
3. #16840082C2semidirect
4. #16840044C2semidirect
5. #16839963C2semidirect
6. #16839962C2semidirect
7. #16839902C2semidirect
8. #16839849C2semidirect
9. #16839847C2semidirect
10. #16839814C2semidirect
11. C61×#475C2semidirect
87. Q8×C61#41semidirect
110. C4×D61SD16semidirect
113. Dic122#41semidirect
145. #475D61semidirect
152. C61#3103semidirect
231. Q8#11758226semidirect