Finite Group Databasebeta

← #21458706

Subgroups — #21458706

Order 7808.

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

normal subgroups only

This group has 324 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#16840490C211yesmaximal, characteristic
2#16840165C211yesmaximal, characteristic
3#16840161C212yesmaximal
4#16840069C212yesmaximal
5#16840066C212yesmaximal
6#16840047C211yesmaximal, characteristic
7#16840044C211yesmaximal, characteristic
8Q8×#92418C211yesmaximal, characteristic
9C4×#11758202C211yesmaximal, characteristic
10C4×#11758202C212yesmaximal
11C61×#557C211yesmaximal, characteristic
12C2×#11758202C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519775—21no—
15#14519769C2212yes—
16#14519767—22no—
17C4×Dic122C2211yescharacteristic
18C4×Dic122C2212yes—
19#14519742—21no—
20#14519710C2212yes—
21#14519710C2211yescharacteristic
22#14519710C2212yes—
23#14519708C2212yes—
24#14519708C2212yes—
25C4⋊#92418C2211yescharacteristic
26C4⋊#92418C2212yes—
27#14519701C2212yes—
28#14519701C2211yescharacteristic
29#14519700C2212yes—
30#14519700C2211yescharacteristic
31C4×#92418C2212yes—
32C4×#92418C2211yescharacteristic
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×Dic122—21no—
45C2×Dic122C2311yescharacteristic
46C4⋊C4×C61—22no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61D411yescharacteristic
52C4⋊C4×C61D412yes—
53C4⋊C4×C61C2311yescharacteristic
54C4⋊C4×C61C2312yes—
55C42×C61—22no—
56C42×C61—21no—
57C42×C61C2312yes—
58C42×C61C2311yescharacteristic
59#11758202Q814yescomplemented
60C4⋊Dic61—21no—
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2312yes—
63#11758196—22no—
64#11758196—21no—
65#11758196—22no—
66#11758196—22no—
67C4×Dic61—22no—
68C4×Dic61—21no—
69C2×#92418C2312yes—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72Q8×C61—22no—
73Q8×C61—21no—
74Q8×C61—42no—
75Q8×C61C2×Q812yes—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87Dic122—21no—
88Dic122—42no—
89Dic122C2×Q812yes—
90#92418—22no—
91#92418—21no—
92#92418C2×Q812yes—
93C22×C61C22×D411yescharacteristic
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—21no—
98C4×C61—42no—
99C4×C61—41no—
100C4×C61#13512yes—
101C4×C61C22×Q811yescharacteristic
102C4×C612−1+411yescharacteristic
103Dic61—22no—
104Dic61—42no—
105Dic61—41no—
106#3383—611nomaximal, Sylow
107C2×C61D4×Q811yescharacteristic
108C2×C61C2×#13511yescharacteristic
109C2×C61#57811yescharacteristic
110#557—611no—
111#557D6111yescharacteristic
112#500—611no—
113#499—612no—
114#479—612no—
115#479—612no—
116#475—611no—
117#475—611no—
118C8×Q8—611no—
119C4×Q16—612no—
120C4×Q16—611no—
121C61#338311yescharacteristic, complemented, Sylow
122C2×Q16—611no—
123C4⋊Q8—21no—
124C4⋊Q8—611no—
125C4⋊Q8—1221no—
126C4⋊Q8C2×D6111yescharacteristic
127#125—22no—
128#125—612no—
129#125—1222no—
130#125C2×D6112yes—
131C4×Q8—21no—
132C4×Q8—611no—
133C4×Q8—612no—
134C4×Q8—1221no—
135C4×Q8C2×D6111yescharacteristic
136C4×Q8C2×D6112yes—
137C4×Q8C2×D6111yescharacteristic
138#107—611no—
139#107—612no—
140#107—612no—
141#106—612no—
142#106—612no—
143C4⋊C8—611no—
144C4⋊C8—612no—
145#103—612no—
146#103—611no—
147#103—612no—
148#103—611no—
149C4×C8—612no—
150C4×C8—611no—
151C2×Q8—21no—
152C2×Q8—611no—
153C2×Q8—1221no—
154C2×Q8C22⋊D6111yescharacteristic
155C2×Q8C22×D6111yescharacteristic
156Q16—614no—
157C2×C8—611no—
158C2×C8—612no—
159C2×C8—611no—
160C4⋊C4—22no—
161C4⋊C4—21no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—611no—
166C4⋊C4—612no—
167C4⋊C4—1221no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1221no—
172C4⋊C4C22⋊D6111yescharacteristic
173C4⋊C4C22⋊D6112yes—
174C4⋊C4C22×D6111yescharacteristic
175C4⋊C4C22×D6112yes—
176C42—22no—
177C42—21no—
178C42—1222no—
179C42—1221no—
180C42C22×D6112yes—
181C42C22×D6111yescharacteristic
182Q8—21no—
183Q8—22no—
184Q8—42no—
185Q8—612no—
186Q8—1221no—
187Q8—2442no—
188Q8Q8×D6112yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1222no—
195C2×C4C2×C22⋊D6112yes—
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C2×C22⋊D6112yes—
198C2×C4C2×C22⋊D6111yescharacteristic
199C2×C4C23×D6111yescharacteristic
200C8—612no—
201C8—1222no—
202C8—1221no—
203C22C22×C22⋊D6111yescharacteristic
204C4—22no—
205C4—22no—
206C4—21no—
207C4—22no—
208C4—42no—
209C4—41no—
210C4—1222no—
211C4—2442no—
212C4—2441no—
213C4#1451979712yes—
214C4C2×Q8×D6111yescharacteristic
215C4#1451982511yescharacteristic
216C2Q8×C22⋊D6111yescharacteristic
217C2C2×#1451979711yescharacteristic
218C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3383
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
59. #11758202Q8semidirect
121. C61#3383semidirect