Finite Group Databasebeta

← #21458528

Subgroups — #21458528

Order 7808.

396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840472C211yesmaximal, characteristic, complemented
2#16840434C211yesmaximal, characteristic, complemented
3#16840127C212yesmaximal, complemented
4#16840109C211yesmaximal, characteristic, complemented
5#16840063C212yesmaximal, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16839958C211yesmaximal, characteristic, complemented
8#16839958C212yesmaximal, complemented
9#16839875C212yesmaximal, complemented
10C4×D488C211yesmaximal, characteristic, complemented
11C61×#446C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×D488C2211yescharacteristic
14C2×D488C2212yes—
15#14519777C2211yescharacteristic
16#14519774C2211yescharacteristic
17#14519774C2212yes—
18#14519769C2212yes—
19#14519755—22no—
20#14519753—21no—
21#14519752—21no—
22#14519752—22no—
23C4×D244C2211yescharacteristic
24C4×D244C2212yes—
25C4×D244C2211yescharacteristic
26C4×D244C2212yes—
27C4⋊C4×D61—21no—
28#14519711C2211yescharacteristic
29#14519709C2212yes—
30#14519699C2212yes—
31#14519699C2212yes—
32#14519699C2212yes—
33#14519699C2211yescharacteristic
34#14519699C2211yescharacteristic
35#14519699C2212yes—
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42#11758226—44no—
43C2×D244—22no—
44C2×D244—21no—
45C2×D244—22no—
46C2×D244—21no—
47C2×D244C2311yescharacteristic
48C2×D244C2312yes—
49C2×D244C2311yescharacteristic
50C2×C4×D61—22no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×Dic122—21no—
55C2×C8×C61C2311yescharacteristic
56C2×C8×C61C2311yescharacteristic
57C2×C8×C61C2312yes—
58C4⋊C4×C61D411yescharacteristic
59C4⋊C4×C61D412yes—
60C42×C61C2311yescharacteristic
61C42×C61C2312yes—
62#11758198—22no—
63#11758198—21no—
64#11758198—22no—
65#11758198—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—22no—
71#11758196—22no—
72D488—22no—
73D488—24no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—21no—
77Q8×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—21no—
86D244—21no—
87D244—22no—
88D244—21no—
89D244—21no—
90D244—22no—
91D244—44no—
92D244—42no—
93D244—81no—
94D244—82no—
95D244#4112yescomplemented
96C4×D61—44no—
97C4×D61—42no—
98C4×D61—42no—
99C4×D61—82no—
100Dic122—81no—
101C8×C61—21no—
102C8×C61—22no—
103C8×C61—21no—
104C22×C61C22×D411yescharacteristic
105C2×D61—22no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—42no—
109C2×D61—41no—
110C2×D61—42no—
111C2×D61—41no—
112C2×D61—42no—
113C2×D61—41no—
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—22no—
117C4×C61AGL(1,ℤ/8)12yes—
118C4×C61C2×#4111yescharacteristic
119C4×C612−1+411yescharacteristic
120Dic61—41no—
121Dic61—41no—
122Dic61—42no—
123#3366—611nomaximal, Sylow
124C2×C61#54811yescharacteristic
125C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C61#57611yescharacteristic
127D61—42no—
128D61—82no—
129D61—81no—
130#554—611no—
131#550—611no—
132#490—612no—
133#486—611no—
134#478—612no—
135#476—611no—
136#459—612no—
137#459—611no—
138#446D6111yescharacteristic, complemented
139#442—612no—
140C4×D8—611no—
141C61#336611yescharacteristic, complemented, Sylow
142C2×#41—1221no—
143C2×D8—611no—
144C2×D8—612no—
145C4⋊Q8—611no—
146#127—611no—
147#127—612no—
148#125—612no—
149C22⋊Q8—1221no—
150C22⋊Q8—1222no—
151#121—1221no—
152#121—1222no—
153C4×Q8C2×D6111yescharacteristic
154C4×D4—611no—
155C4×D4—612no—
156C4×D4—611no—
157C4×D4—612no—
158C2×C4⋊C4—1221no—
159#107—611no—
160#106—612no—
161C4⋊C8C2×D6111yescharacteristic
162C4⋊C8C2×D6112yes—
163#102—611no—
164#102—611no—
165#102—612no—
166#102—612no—
167#102—612no—
168#102—612no—
169#97C2×D6112yes—
170C4×C8C2×D6111yescharacteristic
171#41—2444no—
172C2×Q8—1221no—
173C2×Q8D24411yescharacteristic
174C2×D4—611no—
175C2×D4—611no—
176C2×D4—612no—
177C2×D4—1221no—
178C2×D4—1222no—
179C2×D4—1222no—
180C2×D4—1221no—
181C22×C4—1222no—
182C22×C4—1221no—
183C22×C4—1222no—
184C22×C4—1221no—
185D8—1222no—
186D8—1224no—
187C2×C8C22×D6111yescharacteristic
188C2×C8C22×D6111yescharacteristic
189C2×C8C22×D6112yes—
190C4⋊C4—612no—
191C4⋊C4—611no—
192C4⋊C4—611no—
193C4⋊C4—1222no—
194C4⋊C4—1221no—
195C4⋊C4—1222no—
196C4⋊C4D24411yescharacteristic
197C4⋊C4D24412yes—
198C22⋊C4—1221no—
199C22⋊C4—1222no—
200C22⋊C4—1221no—
201C22⋊C4—1222no—
202C42C22×D6111yescharacteristic
203C42C22×D6112yes—
204C23—1221no—
205C23—1222no—
206C23—1221no—
207Q8—22no—
208Q8—4881no—
209D4—612no—
210D4—1221no—
211D4—1222no—
212D4—1221no—
213D4—1221no—
214D4—1222no—
215D4—4882no—
216D4—4881no—
217D4—2444no—
218D4—2442no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—4882no—
223C2×C4—2444no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4C2×D24411yescharacteristic
227C2×C4C2×D24412yes—
228C2×C4C2×D24412yes—
229C2×C4C2×D24411yescharacteristic
230C2×C4C23×D6111yescharacteristic
231C8—21no—
232C8—22no—
233C8—21no—
234C22—1222no—
235C22—2442no—
236C22—2441no—
237C22—2441no—
238C22—2442no—
239C22—2442no—
240C22—2441no—
241C22—2441no—
242C22—2441no—
243C22C22×D24411yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—2441no—
248C4—2441no—
249C4—2442no—
250C4#1451980512yes—
251C4#41×D6111yescharacteristic
252C4#1451982511yescharacteristic
253C2—4882no—
254C2—4881no—
255C2—2442no—
256C2#1684042411yescharacteristic
257C2C2×#1451980511yescharacteristic
258C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3366
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #16840472C2semidirect
2. #16840434C2semidirect
3. #16840127C2semidirect
4. #16840109C2semidirect
5. #16840063C2semidirect
6. #16840053C2semidirect
7. #16839958C2semidirect
8. #16839958C2semidirect
9. #16839875C2semidirect
10. C4×D488C2semidirect
11. C61×#446C2semidirect
95. D244#41semidirect
138. #446D61semidirect
141. C61#3366semidirect