Finite Group Databasebeta

← #21458539

Subgroups — #21458539

Order 7808.

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

normal subgroups only

This group has 372 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#16840485C211yesmaximal, characteristic, complemented
2Q8×D244C211yesmaximal, characteristic, complemented
3#16840122C212yesmaximal, complemented
4#16840113C211yesmaximal, characteristic, complemented
5#16840058C212yesmaximal, complemented
6#16840043C211yesmaximal, characteristic, complemented
7#16839978C212yesmaximal
8#16839968C211yesmaximal, characteristic, complemented
9#16839864C212yesmaximal, complemented
10C4×D488C211yesmaximal, characteristic
11C61×#446C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13C2×#11758190C2212yes—
14C2×D488C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519777C2211yescharacteristic
17#14519777C2212yes—
18#14519772—22no—
19#14519765C2212yes—
20#14519757—21no—
21#14519757—22no—
22#14519753—21no—
23C4×Dic122C2212yes—
24C4×D244C2211yescharacteristic
25C4×D244C2211yescharacteristic
26C4×D244C2212yes—
27#14519735—21no—
28#14519711C2212yes—
29#14519711C2211yescharacteristic
30#14519702C2212yes—
31#14519702C2212yes—
32#14519702C2212yes—
33#14519699C2212yes—
34#14519699C2211yescharacteristic
35#14519699C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42Q8×D61—44no—
43C2×D244C2311yescharacteristic
44C2×D244C2311yescharacteristic
45C2×C4×D61—22no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×Dic122—22no—
49C2×Dic122—21no—
50C2×Dic122C2312yes—
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2312yes—
54C4⋊C4×C61D411yescharacteristic
55C4⋊C4×C61D412yes—
56C42×C61C2311yescharacteristic
57C42×C61C2312yes—
58#11758198—22no—
59#11758198—22no—
60#11758198—21no—
61#11758198—21no—
62#11758198—22no—
63C4⋊Dic61—21no—
64C4⋊Dic61—22no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—22no—
71C4×Dic61—22no—
72D488—22no—
73#11758190—24no—
74C22×D61—21no—
75C22×D61—21no—
76Q8×C61—22no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86D244—21no—
87D244—21no—
88D244—21no—
89D244#4112yes—
90C4×D61—44no—
91C4×D61—42no—
92C4×D61—42no—
93Dic122—22no—
94Dic122—22no—
95Dic122—44no—
96Dic122—42no—
97C8×C61—22no—
98C8×C61—21no—
99C8×C61—21no—
100C22×C61C22×D411yescharacteristic
101C2×D61—22no—
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—41no—
107C4×C61—22no—
108C4×C61—22no—
109C4×C61—21no—
110C4×C61AGL(1,ℤ/8)12yes—
111C4×C61C2×#4111yescharacteristic
112C4×C612−1+411yescharacteristic
113Dic61—42no—
114Dic61—41no—
115Dic61—42no—
116Dic61—41no—
117#3367—611nomaximal, Sylow
118C2×C61#54811yescharacteristic
119C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C61#57811yescharacteristic
121D61—42no—
122D61—81no—
123#556—611no—
124D4×Q8—611no—
125#489—612no—
126#487—611no—
127#477—612no—
128#474—611no—
129#463—612no—
130#461—611no—
131#446D6111yescharacteristic, complemented
132#440—612no—
133C4×D8—611no—
134C61#336711yescharacteristic, complemented, Sylow
135C22×Q8—1221no—
136C2×SD16—612no—
137C2×D8—611no—
138C4⋊Q8—611no—
139C4⋊Q8—612no—
140C4⋊Q8—611no—
141#126—1222no—
142#124—612no—
143C22⋊Q8—1221no—
144C22⋊Q8—1221no—
145C22⋊Q8—1222no—
146C4×Q8—612no—
147C4×Q8C2×D6111yescharacteristic
148C4×D4—611no—
149C4×D4—612no—
150C4×D4—611no—
151#117—1221no—
152#107—611no—
153#107—612no—
154C4⋊C8C2×D6111yescharacteristic
155C4⋊C8C2×D6112yes—
156#103—612no—
157#103—612no—
158#103—612no—
159#102—611no—
160#102—611no—
161#102—612no—
162#97C2×D6112yes—
163C4×C8C2×D6111yescharacteristic
164C2×Q8—612no—
165C2×Q8—1222no—
166C2×Q8—1221no—
167C2×Q8—2444no—
168C2×Q8D24411yescharacteristic
169C2×D4—611no—
170C2×D4—611no—
171C22×C4—1221no—
172C22×C4—1222no—
173C22×C4—1221no—
174SD16—1224no—
175D8—1222no—
176C2×C8C22×D6111yescharacteristic
177C2×C8C22×D6111yescharacteristic
178C2×C8C22×D6112yes—
179C4⋊C4—611no—
180C4⋊C4—612no—
181C4⋊C4—611no—
182C4⋊C4—1222no—
183C4⋊C4—1221no—
184C4⋊C4—1222no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4D24411yescharacteristic
188C4⋊C4D24412yes—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1222no—
194C42—1222no—
195C42C22×D6111yescharacteristic
196C42C22×D6112yes—
197C23—1221no—
198C23—1221no—
199Q8—22no—
200Q8—1222no—
201Q8—1222no—
202Q8—2444no—
203Q8—2442no—
204D4—612no—
205D4—1221no—
206D4—1221no—
207D4—1221no—
208C2×C4—1221no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—2444no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4C2×D24412yes—
216C2×C4C2×D24411yescharacteristic
217C2×C4C2×D24412yes—
218C2×C4C2×D24411yescharacteristic
219C2×C4C23×D6111yescharacteristic
220C8—21no—
221C8—22no—
222C8—21no—
223C22—1222no—
224C22—2441no—
225C22—2441no—
226C22—2441no—
227C22—2441no—
228C22—2441no—
229C22C22×D24411yescharacteristic
230C4—22no—
231C4—22no—
232C4—21no—
233C4—2441no—
234C4—2442no—
235C4—2441no—
236C4—2442no—
237C4#1451980512yes—
238C4#41×D6111yescharacteristic
239C4#1451982511yescharacteristic
240C2—4881no—
241C2—2442no—
242C2#1684042411yescharacteristic
243C2C2×#1451980511yescharacteristic
244C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3367
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. #16840485C2semidirect
2. Q8×D244C2semidirect
3. #16840122C2semidirect
4. #16840113C2semidirect
5. #16840058C2semidirect
6. #16840043C2semidirect
8. #16839968C2semidirect
9. #16839864C2semidirect
11. C61×#446C2semidirect
131. #446D61semidirect
134. C61#3367semidirect