Finite Group Databasebeta

← #21456830

Subgroups — #21456830

Order 7808.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840319C211yesmaximal, characteristic, complemented
2#16840157C212yesmaximal, complemented
3#16840121C212yesmaximal, complemented
4#16839969C212yesmaximal, complemented
5#16839959C212yesmaximal, complemented
6#16839924C214yesmaximal, complemented
7#16839819C211yesmaximal, characteristic, complemented
8C61×#532C211yesmaximal, characteristic
9C2×#11758202C2214yes—
10C2×#11758200C2214yes—
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519769—21no—
14#14519756—21no—
15#14519756C2212yes—
16C4×Dic122—21no—
17C4×Dic122C2212yes—
18#14519736—21no—
19C4⋊#92418C2212yes—
20#14519701C2214yes—
21#14519698C2214yes—
22C22⋊#92418C2212yes—
23#14519688C2212yes—
24C2×#41×C61C2212yes—
25C4⋊Q8×C61C2211yescharacteristic
26#127×C61C2211yescharacteristic
27#124×C61C2212yes—
28#121×C61—21no—
29#121×C61—21no—
30C4×D4×C61—21no—
31C4×D4×C61—21no—
32C2×C42×C61C2211yescharacteristic
33#41×C61—44no—
34C2×Q8×C61C2312yes—
35C2×D4×C61—22no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C22×C4×C61—22no—
40C22×C4×C61D411yescharacteristic
41C22×C4×C61D411yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×Dic122—21no—
44C2×Dic122C2312yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47C22⋊C4×C61—22no—
48C22⋊C4×C61—22no—
49C42×C61D411yescharacteristic
50C42×C61D411yescharacteristic
51C42×C61C2311yescharacteristic
52C42×C61C2311yescharacteristic
53C22⋊Dic61—22no—
54#11758202—44no—
55#11758200—44no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61—22no—
63C2×#92418C2314yes—
64C23×C61—22no—
65C23×C61C2×D411yescharacteristic
66Q8×C61—24no—
67D4×C61—24no—
68D4×C61—42no—
69D4×C61—44no—
70D4×C61—42no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—41no—
75C2×C4×C61—44no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—22no—
83C2×Dic61—22no—
84Dic122—22no—
85Dic122—22no—
86Dic122—42no—
87#92418—24no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61C22×D411yescharacteristic
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61#13712yes—
101C4×C61H(5,𝔽2)12yes—
102Dic61—42no—
103Dic61—42no—
104#3216—611nomaximal, Sylow
105C2×C61—41no—
106C2×C61—82no—
107C2×C61#53511yescharacteristic
108C2×C61C2×#13711yescharacteristic
109C2×C61#57511yescharacteristic
110#533—611no—
111#532D6111yescharacteristic
112#497—612no—
113#489—612no—
114#462—612no—
115#460—612no—
116#452—614no—
117#432—611no—
118C61#321611yescharacteristic, complemented, Sylow
119C2×#41C2×D6112yes—
120C2×Q16—614no—
121C2×SD16—614no—
122C4⋊Q8—611no—
123C4⋊Q8—611no—
124C4⋊Q8C2×D6111yescharacteristic
125#127C2×D6111yescharacteristic
126#125—1221no—
127#124C2×D6112yes—
128C22⋊Q8—612no—
129C22⋊Q8—1221no—
130#121—21no—
131#121—21no—
132C4×Q8—612no—
133C4×Q8—1221no—
134C4×D4—21no—
135C4×D4—21no—
136#117—1221no—
137C2×C42C2×D6111yescharacteristic
138C4⋊C8—612no—
139#103—614no—
140#102—614no—
141C22⋊C8—612no—
142#97—612no—
143#41—44no—
144C2×Q8—612no—
145C2×Q8—1221no—
146C2×Q8C22×D6112yes—
147C2×D4—22no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4C22×D6112yes—
151C22×C4—22no—
152C22×C4C22⋊D6111yescharacteristic
153C22×C4C22⋊D6111yescharacteristic
154C22×C4C22×D6111yescharacteristic
155Q16—2444no—
156SD16—2444no—
157C2×C8—614no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—612no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C22⋊C4—22no—
167C22⋊C4—22no—
168C22⋊C4—1222no—
169C42—1222no—
170C42C22⋊D6111yescharacteristic
171C42C22⋊D6111yescharacteristic
172C42C22×D6111yescharacteristic
173C42C22×D6111yescharacteristic
174C23—22no—
175C23C2×C22⋊D6111yescharacteristic
176Q8—24no—
177Q8—1222no—
178Q8—1222no—
179Q8—2442no—
180D4—24no—
181D4—42no—
182D4—44no—
183D4—42no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—44no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4C2×C22⋊D6111yescharacteristic
192C2×C4C2×C22⋊D6111yescharacteristic
193C2×C4C2×C22⋊D6111yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C23×D6111yescharacteristic
197C8—1224no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22C22×C22⋊D6111yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—42no—
210C4—2442no—
211C4—2442no—
212C4#1451980712yes—
213C4#1451982212yes—
214C2—41no—
215C2—82no—
216C2#1684032911yescharacteristic
217C2C2×#1451980711yescharacteristic
218C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#532C2
socleC22×C61C22×D4
hypercenter#532D61
hypocenterC61#3216
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
2. #16840157C2semidirect
3. #16840121C2semidirect
4. #16839969C2semidirect
5. #16839959C2semidirect
6. #16839924C2semidirect
7. #16839819C2semidirect
118. C61#3216semidirect