Finite Group Databasebeta

← #21458751

Subgroups — #21458751

Order 7808.

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

normal subgroups only

This group has 326 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
1Q8×Dic122C211yesmaximal, characteristic
2#16840172C212yesmaximal
3#16840158C211yesmaximal, characteristic
4#16840066C212yesmaximal
5#16840057C211yesmaximal, characteristic
6#16840047C212yesmaximal
7#16840044C211yesmaximal, characteristic
8#16839893C211yesmaximal, characteristic
9#16839867C212yesmaximal
10C4×#11758202C211yesmaximal, characteristic
11C61×#557C211yesmaximal, characteristic
12C2×#11758202C2211yescharacteristic
13#14519777C2212yes—
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776—22no—
17Q8×Dic61—21no—
18C4×Dic122C2211yescharacteristic
19C4×Dic122C2212yes—
20#14519710C2212yes—
21#14519710C2211yescharacteristic
22#14519708C2212yes—
23#14519708C2212yes—
24#14519708C2212yes—
25C4⋊#92418C2211yescharacteristic
26C4⋊#92418C2212yes—
27#14519701C2211yescharacteristic
28#14519701C2212yes—
29#14519700C2212yes—
30#14519700C2211yescharacteristic
31#14519688C2212yes—
32C4×#92418C2211yescharacteristic
33C4⋊Q8×C61—21no—
34C4⋊Q8×C61C2211yescharacteristic
35#125×C61—22no—
36#125×C61C2212yes—
37C4×Q8×C61—21no—
38C4×Q8×C61C2212yes—
39C4×Q8×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61D411yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×Dic122—22no—
45C2×Dic122—21no—
46C2×Dic122C2311yescharacteristic
47C4⋊C4×C61—22no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61D411yescharacteristic
53C4⋊C4×C61D412yes—
54C4⋊C4×C61C2311yescharacteristic
55C4⋊C4×C61C2312yes—
56C42×C61—22no—
57C42×C61—21no—
58C42×C61C2312yes—
59C42×C61C2311yescharacteristic
60#11758202Q814yescomplemented
61C4⋊Dic61—22no—
62C4⋊Dic61—21no—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2312yes—
65#11758196—22no—
66#11758196—21no—
67C4×Dic61—22no—
68C4×Dic61—21no—
69C2×#92418C2311yescharacteristic
70C2×#92418C2312yes—
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—22no—
86C2×Dic61—21no—
87Dic122—21no—
88Dic122—82no—
89Dic122—81no—
90Dic122C2×Q812yes—
91#92418—21no—
92#92418—22no—
93#92418C2×Q812yes—
94C22×C61C22×D411yescharacteristic
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—22no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61—41no—
101C4×C61#13712yes—
102C4×C61C22×Q811yescharacteristic
103C4×C612−1+411yescharacteristic
104Dic61—22no—
105Dic61—41no—
106Dic61—42no—
107#3387—611nomaximal, Sylow
108C2×C61D4×Q811yescharacteristic
109C2×C61C2×#13711yescharacteristic
110C2×C61#57711yescharacteristic
111Q82—611no—
112#557D6111yescharacteristic
113#501—612no—
114#498—611no—
115#479—612no—
116#477—611no—
117#475—611no—
118#475—612no—
119#446—611no—
120#441—612no—
121C4×Q16—611no—
122C61#338711yescharacteristic, complemented, Sylow
123C2×Q16—611no—
124C4⋊Q8—21no—
125C4⋊Q8—612no—
126C4⋊Q8—611no—
127C4⋊Q8—1221no—
128C4⋊Q8—1222no—
129C4⋊Q8C2×D6111yescharacteristic
130#125—22no—
131#125C2×D6112yes—
132C4×Q8—21no—
133C4×Q8—611no—
134C4×Q8—612no—
135C4×Q8—1221no—
136C4×Q8C2×D6111yescharacteristic
137C4×Q8C2×D6112yes—
138C4×Q8C2×D6111yescharacteristic
139#107—611no—
140#107—612no—
141#106—612no—
142#106—612no—
143#106—612no—
144C4⋊C8—611no—
145C4⋊C8—612no—
146#103—611no—
147#103—612no—
148#103—611no—
149#103—612no—
150#97—612no—
151C4×C8—611no—
152C2×Q8—21no—
153C2×Q8—611no—
154C2×Q8—1222no—
155C2×Q8—1221no—
156C2×Q8C22⋊D6111yescharacteristic
157C2×Q8C22×D6111yescharacteristic
158Q16—614no—
159C2×C8—611no—
160C2×C8—611no—
161C2×C8—612no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—21no—
166C4⋊C4—22no—
167C4⋊C4—611no—
168C4⋊C4—612no—
169C4⋊C4—1222no—
170C4⋊C4—1221no—
171C4⋊C4—1222no—
172C4⋊C4—1221no—
173C4⋊C4C22⋊D6111yescharacteristic
174C4⋊C4C22⋊D6112yes—
175C4⋊C4C22×D6112yes—
176C4⋊C4C22×D6111yescharacteristic
177C42—22no—
178C42—21no—
179C42—1222no—
180C42—1221no—
181C42C22×D6111yescharacteristic
182C42C22×D6112yes—
183Q8—21no—
184Q8—22no—
185Q8—42no—
186Q8—612no—
187Q8—1221no—
188Q8—4882no—
189Q8—4881no—
190Q8Q8×D6112yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—1221no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4C2×C22⋊D6112yes—
198C2×C4C2×C22⋊D6112yes—
199C2×C4C2×C22⋊D6111yescharacteristic
200C2×C4C2×C22⋊D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—612no—
203C8—1221no—
204C8—1222no—
205C22C22×C22⋊D6111yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—22no—
210C4—42no—
211C4—41no—
212C4—1222no—
213C4—2442no—
214C4—2441no—
215C4#1451980712yes—
216C4C2×Q8×D6111yescharacteristic
217C4#1451982511yescharacteristic
218C2Q8×C22⋊D6111yescharacteristic
219C2C2×#1451980711yescharacteristic
220C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3387
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
60. #11758202Q8semidirect
122. C61#3387semidirect