Finite Group Databasebeta

← #21456196

Subgroups — #21456196

Order 7808.

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

normal subgroups only

This group has 380 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#16840317C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic
3#16840129C214yesmaximal, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840112C211yesmaximal, characteristic, complemented
7#16839769C214yesmaximal
8C4×#11758189C211yesmaximal, characteristic
9C61×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D61C2212yes—
11C2×#11758189C2212yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519776—21no—
15#14519776—21no—
16#14519775C2212yes—
17#14519768C2212yes—
18#14519757—21no—
19#14519753—21no—
20Q8×Dic61—21no—
21#14519742—21no—
22#14519735C2212yes—
23C4⋊C4×D61—21no—
24C4⋊C4×D61—21no—
25C42×D61C2211yescharacteristic
26#14519702C2214yes—
27#14519701C2214yes—
28#14519700C2214yes—
29#14519687C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#103×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61C2312yes—
37Q8×D61—28no—
38C2×C4×D61—22no—
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61C2311yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—22no—
44C2×Dic122C2312yes—
45C2×C8×C61C2312yes—
46C4⋊C4×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61C2312yes—
50C42×C61C2311yescharacteristic
51#11758198—22no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65#11758189—24no—
66C22×D61C2×D411yescharacteristic
67Q8×C61—24no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61C2×D411yescharacteristic
79C4×D61—22no—
80C4×D61—22no—
81C4×D61—44no—
82C4×D61#4114yes—
83Dic122—24no—
84Dic122—42no—
85Dic122—44no—
86C8×C61—22no—
87#92418—22no—
88C22×C61C22×D411yescharacteristic
89C2×D61—21no—
90C2×D61—21no—
91C2×D61#12412yes—
92C4×C61—42no—
93C4×C61—42no—
94C4×C61#13712yes—
95C4×C61#13712yes—
96C4×C61C2×#4112yes—
97Dic61—21no—
98Dic61—21no—
99Dic61—42no—
100Dic61—42no—
101Dic61#12412yes—
102#3139—611nomaximal, Sylow
103C2×C61C2×#12411yescharacteristic
104C2×C61C2×#13711yescharacteristic
105C2×C61C2×#13711yescharacteristic
106D61—22no—
107#533—611no—
108C2×C4⋊Q8—611no—
109#491—614no—
110#487—611no—
111#487—611no—
112#487—611no—
113#487D6111yescharacteristic, complemented
114#419—614no—
115C4×M16—611no—
116C61#313911yescharacteristic, complemented, Sylow
117C22×Q8—612no—
118C2×M16—612no—
119C4⋊Q8—612no—
120C4⋊Q8—611no—
121C4⋊Q8—611no—
122C4⋊Q8—1221no—
123C4⋊Q8—1221no—
124C4⋊Q8C2×D6111yescharacteristic
125C4⋊Q8C2×D6111yescharacteristic
126#125—612no—
127C22⋊Q8—1221no—
128C22⋊Q8—1221no—
129C4×Q8—1221no—
130C4×Q8—1221no—
131#117—612no—
132C2×C4⋊C4—1221no—
133C2×C4⋊C4—1221no—
134C2×C42—611no—
135#103—614no—
136#103—614no—
137#103—614no—
138#103C2×D6114yes—
139#97—612no—
140C4×C8—611no—
141C4×C8C2×D6111yescharacteristic
142C2×Q8—21no—
143C2×Q8—612no—
144C2×Q8—1222no—
145C2×Q8—1228no—
146C2×Q8—1221no—
147C2×Q8C22×D6112yes—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—1222no—
152M16—1224no—
153C2×C8—612no—
154C2×C8C22×D6112yes—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—612no—
159C4⋊C4—1222no—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4C22×D6112yes—
167C22⋊C4—1222no—
168C42—611no—
169C42—611no—
170C42—611no—
171C42—1222no—
172C42C22×D6111yescharacteristic
173C23—611no—
174Q8—24no—
175Q8—42no—
176Q8—1224no—
177Q8—2444no—
178Q8—2442no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—611no—
182C2×C4—614no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—2444no—
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4C23×D6111yescharacteristic
193C8—22no—
194C8—1222no—
195C22—612no—
196C22—1221no—
197C22—1221no—
198C22C2×D4×D6111yescharacteristic
199C4—42no—
200C4—42no—
201C4—612no—
202C4—1221no—
203C4—1221no—
204C4—2442no—
205C4—2442no—
206C4#1451980612yes—
207C4#1451980912yes—
208C4#41×D6112yes—
209C2—1222no—
210C2#124×D6111yescharacteristic
211C2C2×#1451980611yescharacteristic
212C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3139
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16840129C2semidirect
4. #16840114C2semidirect
5. #16840113C2semidirect
6. #16840112C2semidirect
9. C61×#487C2semidirect
113. #487D61semidirect
116. C61#3139semidirect