Finite Group Databasebeta

← #21456209

Subgroups — #21456209

Order 7808.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840310C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840120C214yesmaximal, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840108C211yesmaximal, characteristic, complemented
7#16839760C214yesmaximal, complemented
8C4×#11758189C211yesmaximal, characteristic, complemented
9C61×#486C211yesmaximal, characteristic, complemented
10C2×#11758224C2212yes—
11C2×Q8×D61—21no—
12C2×#11758189C2212yes—
13#14519777C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776C2212yes—
17#14519775—21no—
18#14519764C2212yes—
19#14519748—21no—
20#14519748—21no—
21D4×Dic61—21no—
22D4×Dic61—21no—
23C4⋊C4×D61—21no—
24C4⋊C4×D61C2212yes—
25C42×D61C2211yescharacteristic
26#14519702C2214yes—
27#14519700C2214yes—
28#14519698C2214yes—
29#14519687C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32#127×C61C2211yescharacteristic
33#102×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C2×C22⋊D61—22no—
40C22×Dic61—22no—
41Q8×D61—44no—
42#11758224—28no—
43C2×C4×D61—22no—
44C2×C4×D61D411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61C2311yescharacteristic
47C2×Dic122—21no—
48C2×Dic122—22no—
49C2×Dic122C2312yes—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55C22⋊Dic61—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61D411yescharacteristic
63C4×Dic61D411yescharacteristic
64C4×Dic61C2311yescharacteristic
65C2×#92418C2312yes—
66#11758189—24no—
67C23×C61—22no—
68C22×D61C2×D411yescharacteristic
69Q8×C61—42no—
70D4×C61—24no—
71D4×C61—42no—
72D4×C61—42no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—44no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—44no—
81C2×Dic61C2×D411yescharacteristic
82C2×Dic61C2×D411yescharacteristic
83C2×Dic61C2×D411yescharacteristic
84C4×D61—22no—
85C4×D61—22no—
86C4×D61—44no—
87C4×D61#4114yes—
88Dic122—24no—
89Dic122—44no—
90Dic122—42no—
91C8×C61—22no—
92#92418—22no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61C22×D411yescharacteristic
97C2×D61—21no—
98C2×D61—21no—
99C2×D61#12412yes—
100C4×C61—42no—
101C4×C61AGL(1,ℤ/8)12yes—
102C4×C61#13712yes—
103C4×C61C2×#4112yes—
104Dic61—21no—
105Dic61—21no—
106Dic61—42no—
107Dic61—42no—
108Dic61#12412yes—
109#3141—611nomaximal, Sylow
110C2×C61—82no—
111C2×C61C2×#12411yescharacteristic
112C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
113C2×C61C2×#13711yescharacteristic
114D61—22no—
115#532—611no—
116C2×C4⋊Q8—611no—
117#489—614no—
118#487—611no—
119#487—611no—
120#486—611no—
121#486D6111yescharacteristic, complemented
122#417—614no—
123C4×M16—611no—
124C61#314111yescharacteristic, complemented, Sylow
125C2×#41—612no—
126C22×Q8—1221no—
127C2×M16—612no—
128C4⋊Q8—612no—
129C4⋊Q8—611no—
130C4⋊Q8—611no—
131C4⋊Q8—1221no—
132C4⋊Q8—1221no—
133C4⋊Q8C2×D6111yescharacteristic
134#127C2×D6111yescharacteristic
135#124—612no—
136#121—1221no—
137#121—1221no—
138C4×D4—1221no—
139C4×D4—1221no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—1221no—
142C2×C42—611no—
143#103—614no—
144#103—614no—
145#102—614no—
146#102C2×D6114yes—
147#97—612no—
148C4×C8—611no—
149C4×C8C2×D6111yescharacteristic
150#41—1228no—
151C2×Q8—21no—
152C2×Q8—612no—
153C2×Q8—1222no—
154C2×Q8—1221no—
155C2×Q8—2444no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—1222no—
159C2×D4C22×D6112yes—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—1222no—
164C22×C4—1222no—
165M16—1224no—
166C2×C8—612no—
167C2×C8C22×D6112yes—
168C4⋊C4—21no—
169C4⋊C4—612no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C4⋊C4C22×D6112yes—
176C22⋊C4—1222no—
177C22⋊C4—1222no—
178C42—611no—
179C42—611no—
180C42—611no—
181C42C22×D6111yescharacteristic
182C23—22no—
183C23—611no—
184Q8—42no—
185Q8—1224no—
186Q8—2444no—
187Q8—2442no—
188D4—24no—
189D4—42no—
190D4—42no—
191D4—2444no—
192C2×C4—22no—
193C2×C4—611no—
194C2×C4—614no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—2444no—
202C2×C4—2444no—
203C2×C4D4×D6111yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C2×C4C23×D6111yescharacteristic
206C8—22no—
207C8—1222no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—612no—
212C22—1221no—
213C22—1221no—
214C22C2×D4×D6111yescharacteristic
215C4—42no—
216C4—612no—
217C4—1221no—
218C4—1221no—
219C4—2442no—
220C4—2442no—
221C4#1451980112yes—
222C4#1451980612yes—
223C4#41×D6112yes—
224C2—82no—
225C2—1222no—
226C2#124×D6111yescharacteristic
227C2C2×#1451980111yescharacteristic
228C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3141
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
3. #16840120C2semidirect
4. #16840114C2semidirect
5. #16840113C2semidirect
6. #16840108C2semidirect
7. #16839760C2semidirect
8. C4×#11758189C2semidirect
9. C61×#486C2semidirect
121. #486D61semidirect
124. C61#3141semidirect