Finite Group Databasebeta

← #21458690

Subgroups — #21458690

Order 7808.

338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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
2#16840161C212yesmaximal, complemented
3#16840158C211yesmaximal, characteristic, complemented
4#16840069C212yesmaximal, complemented
5#16840059C212yesmaximal
6#16840057C211yesmaximal, characteristic, complemented
7#16840039C211yesmaximal, characteristic
8Q8×#92418C211yesmaximal, characteristic, complemented
9C4×#11758201C211yesmaximal, characteristic
10C4×#11758201C212yesmaximal
11C61×#557C211yesmaximal, characteristic, complemented
12C2×#11758201C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519769C2212yes—
15#14519755—22no—
16#14519753—21no—
17C4×D244C2211yescharacteristic
18C4×D244C2212yes—
19C4⋊C4×D61—21no—
20#14519710C2212yes—
21#14519710C2212yes—
22#14519708C2212yes—
23#14519708C2212yes—
24#14519708C2211yescharacteristic
25C4⋊#92418C2211yescharacteristic
26C4⋊#92418C2212yes—
27#14519701C2212yes—
28#14519701C2211yescharacteristic
29#14519697C2212yes—
30#14519697C2211yescharacteristic
31C4×#92418C2211yescharacteristic
32C4×#92418C2212yes—
33C4⋊Q8×C61—21no—
34C4⋊Q8×C61C2211yescharacteristic
35#125×C61—22no—
36#125×C61C2212yes—
37C4×Q8×C61—21no—
38C4×Q8×C61C2211yescharacteristic
39C4×Q8×C61C2212yes—
40C4×Q8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61D411yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×D244C2311yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—22no—
47C2×Dic122—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61D411yescharacteristic
54C4⋊C4×C61D412yes—
55C4⋊C4×C61C2311yescharacteristic
56C4⋊C4×C61C2312yes—
57C42×C61—22no—
58C42×C61—21no—
59C42×C61C2312yes—
60C42×C61C2311yescharacteristic
61#11758201Q814yescomplemented
62#11758198—22no—
63#11758198—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2311yescharacteristic
67#11758196—22no—
68#11758196—22no—
69C2×#92418C2311yescharacteristic
70C2×#92418C2312yes—
71C2×#92418C2311yescharacteristic
72C22×D61—21no—
73Q8×C61—22no—
74Q8×C61—21no—
75Q8×C61—42no—
76Q8×C61C2×Q812yes—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C2×Dic61—21no—
86C2×Dic61—22no—
87D244—21no—
88D244C2×Q812yes—
89C4×D61—42no—
90C4×D61—82no—
91Dic122—81no—
92#92418—21no—
93#92418—22no—
94#92418C2×Q812yes—
95C22×C61C22×D411yescharacteristic
96C2×D61—22no—
97C2×D61—41no—
98C2×D61—41no—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—42no—
104C4×C61—41no—
105C4×C61#13512yes—
106C4×C61C22×Q811yescharacteristic
107C4×C612−1+411yescharacteristic
108Dic61—41no—
109Dic61—42no—
110#3381—611nomaximal, Sylow
111C2×C61D4×Q811yescharacteristic
112C2×C61C2×#13511yescharacteristic
113C2×C61#57711yescharacteristic
114D61—42no—
115#557D6111yescharacteristic, complemented
116#554—611no—
117#499—612no—
118#498—611no—
119#479—612no—
120#478—612no—
121#477—611no—
122#474—611no—
123C8×Q8—611no—
124C4×SD16—611no—
125C4×SD16—612no—
126C61#338111yescharacteristic, complemented, Sylow
127C2×SD16—611no—
128C4⋊Q8—21no—
129C4⋊Q8—611no—
130C4⋊Q8C2×D6111yescharacteristic
131#125—22no—
132#125—612no—
133#125C2×D6112yes—
134C22⋊Q8—1221no—
135C22⋊Q8—1222no—
136C4×Q8—21no—
137C4×Q8C2×D6111yescharacteristic
138C4×Q8C2×D6112yes—
139C4×Q8C2×D6111yescharacteristic
140C4×D4—611no—
141C4×D4—612no—
142C2×C4⋊C4—1221no—
143#107—612no—
144#107—612no—
145#106—612no—
146#106—611no—
147#106—612no—
148C4⋊C8—611no—
149C4⋊C8—612no—
150#103—612no—
151#103—611no—
152#102—612no—
153#102—611no—
154C4×C8—611no—
155C4×C8—612no—
156C2×Q8—21no—
157C2×Q8—1221no—
158C2×Q8C22⋊D6111yescharacteristic
159C2×Q8C22×D6111yescharacteristic
160C2×D4—611no—
161C22×C4—1222no—
162C22×C4—1221no—
163SD16—614no—
164C2×C8—611no—
165C2×C8—611no—
166C2×C8—612no—
167C4⋊C4—22no—
168C4⋊C4—21no—
169C4⋊C4—22no—
170C4⋊C4—21no—
171C4⋊C4—22no—
172C4⋊C4—612no—
173C4⋊C4—611no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1222no—
177C4⋊C4C22⋊D6111yescharacteristic
178C4⋊C4C22⋊D6112yes—
179C4⋊C4C22×D6112yes—
180C4⋊C4C22×D6111yescharacteristic
181C22⋊C4—1221no—
182C22⋊C4—1222no—
183C42—22no—
184C42—21no—
185C42C22×D6112yes—
186C42C22×D6111yescharacteristic
187C23—1221no—
188Q8—21no—
189Q8—22no—
190Q8—42no—
191Q8—4881no—
192Q8Q8×D6112yes—
193D4—612no—
194D4—1221no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—4882no—
201C2×C4—2442no—
202C2×C4C2×C22⋊D6112yes—
203C2×C4C2×C22⋊D6112yes—
204C2×C4C2×C22⋊D6111yescharacteristic
205C2×C4C2×C22⋊D6111yescharacteristic
206C2×C4C23×D6111yescharacteristic
207C8—612no—
208C8—1221no—
209C8—1222no—
210C22—1222no—
211C22—2441no—
212C22—2441no—
213C22C22×C22⋊D6111yescharacteristic
214C4—22no—
215C4—22no—
216C4—21no—
217C4—22no—
218C4—42no—
219C4—41no—
220C4—2441no—
221C4—2442no—
222C4#1451979712yes—
223C4C2×Q8×D6111yescharacteristic
224C4#1451982511yescharacteristic
225C2—2442no—
226C2Q8×C22⋊D6111yescharacteristic
227C2C2×#1451979711yescharacteristic
228C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3381
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
2. #16840161C2semidirect
3. #16840158C2semidirect
4. #16840069C2semidirect
6. #16840057C2semidirect
8. Q8×#92418C2semidirect
11. C61×#557C2semidirect
61. #11758201Q8semidirect
115. #557D61semidirect
126. C61#3381semidirect