Finite Group Databasebeta

← #21458749

Subgroups — #21458749

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#16840491C211yesmaximal, characteristic
3#16840170C212yesmaximal
4#16840160C211yesmaximal, characteristic
5#16840067C212yesmaximal
6#16840057C211yesmaximal, characteristic
7#16840047C211yesmaximal, characteristic
8#16840045C212yesmaximal
9#16839892C211yesmaximal, characteristic
10#16839869C212yesmaximal
11C4×Q16×C61C211yesmaximal, characteristic
12#14519777—21no—
13#14519777—21no—
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519776—22no—
17#14519776C2212yes—
18#14519768—22no—
19#14519768C2212yes—
20Q8×Dic61C2212yes—
21Q8×Dic61C2212yes—
22C4×Dic122—21no—
23C4×Dic122—21no—
24C4×Dic122C2211yescharacteristic
25#14519710C2212yes—
26#14519709C2212yes—
27#14519709C2212yes—
28#14519708C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519701C2212yes—
32#14519701C2212yes—
33#14519687C2212yes—
34C2×Q16×C61C2211yescharacteristic
35C4×Q8×C61C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37#107×C61C2211yescharacteristic
38#103×C61C2211yescharacteristic
39#103×C61C2211yescharacteristic
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61C2311yescharacteristic
42C2×Q8×C61C2311yescharacteristic
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—22no—
46C2×Dic122D411yescharacteristic
47Q16×C61Q814yescomplemented
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2311yescharacteristic
53C4⋊C4×C61C2311yescharacteristic
54C42×C61—21no—
55C42×C61—21no—
56C42×C61C2311yescharacteristic
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2312yes—
64C4⋊Dic61C2312yes—
65#11758196—22no—
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72Q8×C61—21no—
73Q8×C61—21no—
74Q8×C61C2×Q812yes—
75Q8×C61C2×Q812yes—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61C2×D412yes—
86C2×Dic61C2×D412yes—
87Dic122—22no—
88Dic122—42no—
89Dic122—82no—
90Dic122—81no—
91C8×C61—21no—
92C8×C61C2×Q812yes—
93#92418—22no—
94C22×C61C22×D411yescharacteristic
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—41no—
100C4×C61#13712yes—
101C4×C61C22×Q811yescharacteristic
102C4×C612−1+411yescharacteristic
103Dic61—22no—
104Dic61—22no—
105Dic61—42no—
106Dic61—42no—
107#3387—611nomaximal, Sylow
108C2×C61D4×Q811yescharacteristic
109C2×C61C2×#13711yescharacteristic
110C2×C61#57711yescharacteristic
111Q82—611no—
112#557—611no—
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×Q16D6111yescharacteristic
122C61#338711yescharacteristic, complemented, Sylow
123C2×Q16C2×D6111yescharacteristic
124C4⋊Q8—612no—
125C4⋊Q8—611no—
126C4⋊Q8—611no—
127C4⋊Q8—1221no—
128C4⋊Q8—1221no—
129C4⋊Q8—1222no—
130#125—612no—
131#125—1222no—
132C4×Q8—611no—
133C4×Q8—612no—
134C4×Q8—612no—
135C4×Q8—1221no—
136C4×Q8—1221no—
137C4×Q8C2×D6111yescharacteristic
138C4×Q8C2×D6111yescharacteristic
139#107—612no—
140#107C2×D6111yescharacteristic
141#106—612no—
142#106—612no—
143#106—612no—
144C4⋊C8—612no—
145C4⋊C8—611no—
146#103—612no—
147#103—612no—
148#103C2×D6111yescharacteristic
149#103C2×D6111yescharacteristic
150#97—612no—
151C4×C8C2×D6111yescharacteristic
152C2×Q8—611no—
153C2×Q8—1222no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8C22×D6111yescharacteristic
157C2×Q8C22×D6111yescharacteristic
158Q16Dic12214yescomplemented
159C2×C8—612no—
160C2×C8C22×D6111yescharacteristic
161C2×C8C22×D6111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—612no—
165C4⋊C4—611no—
166C4⋊C4—612no—
167C4⋊C4—612no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C4⋊C4C22×D6111yescharacteristic
176C4⋊C4C22×D6111yescharacteristic
177C42—21no—
178C42—21no—
179C42—612no—
180C42—1222no—
181C42—1222no—
182C42C22×D6111yescharacteristic
183Q8—21no—
184Q8—21no—
185Q8—1222no—
186Q8—4881no—
187Q8—4882no—
188Q8—2442no—
189Q8C2×Dic12212yes—
190Q8C2×Dic12212yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4D4×D6111yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—21no—
203C8—1222no—
204C8C2×Dic12212yes—
205C22C2×D4×D6111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—41no—
210C4—41no—
211C4—1222no—
212C4—1222no—
213C4—2442no—
214C4—2442no—
215C4#1451980912yes—
216C4C22×Dic12211yescharacteristic
217C4#1451982411yescharacteristic
218C2D4×Dic12211yescharacteristic
219C2C2×#1451980911yescharacteristic
220C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#3387
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
47. Q16×C61Q8semidirect
122. C61#3387semidirect
158. Q16Dic122semidirect