Finite Group Databasebeta

← #21456951

Subgroups — #21456951

Order 7808.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840165C211yesmaximal, characteristic, complemented
3#16840158C211yesmaximal, characteristic, complemented
4#16840108C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16840083C214yesmaximal, complemented
7#16840062C214yesmaximal, complemented
8#16839815C211yesmaximal, characteristic, complemented
9C61×#532C211yesmaximal, characteristic
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519769C2212yes—
13#14519756—21no—
14#14519756—21no—
15C4×Dic122—21no—
16C4×Dic122—21no—
17#14519736C2212yes—
18#14519710C2214yes—
19#14519708C2214yes—
20C4⋊#92418C2212yes—
21#14519698C2214yes—
22#14519698C2214yes—
23C22⋊#92418C2212yes—
24C4×#92418C2211yescharacteristic
25C4×#92418C2211yescharacteristic
26C2×#41×C61—21no—
27C4⋊Q8×C61C2211yescharacteristic
28#127×C61C2211yescharacteristic
29#124×C61—21no—
30#121×C61—21no—
31#121×C61C2212yes—
32C4×D4×C61—21no—
33C4×D4×C61C2212yes—
34C2×C42×C61C2211yescharacteristic
35#41×C61—44no—
36C2×Q8×C61—21no—
37C2×D4×C61—22no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61C2312yes—
41C22×C4×C61—22no—
42C22×C4×C61D411yescharacteristic
43C22×C4×C61D411yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×Dic122—21no—
46C2×Dic122—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61C2312yes—
49C22⋊C4×C61—22no—
50C22⋊C4×C61—22no—
51C42×C61D411yescharacteristic
52C42×C61D411yescharacteristic
53C42×C61C2311yescharacteristic
54C42×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61C2312yes—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61—22no—
63C2×#92418C2312yes—
64C2×#92418C2312yes—
65C23×C61—22no—
66C23×C61C2×D411yescharacteristic
67Q8×C61—42no—
68D4×C61—24no—
69D4×C61—44no—
70D4×C61—42no—
71D4×C61—42no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—44no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—22no—
84C2×Dic61—22no—
85Dic122—42no—
86Dic122—42no—
87#92418—22no—
88#92418—22no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61C22×D411yescharacteristic
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61#13512yes—
101C4×C61AGL(1,ℤ/8)12yes—
102C4×C612−1+412yes—
103Dic61—42no—
104Dic61—42no—
105#3228—611nomaximal, Sylow
106C2×C61—41no—
107C2×C61—82no—
108C2×C61#53611yescharacteristic
109C2×C61C2×#13511yescharacteristic
110C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
111#533—611no—
112#532D6111yescharacteristic
113#500—611no—
114#498—611no—
115#486—611no—
116#486—611no—
117#482—614no—
118#478—614no—
119#431—611no—
120C61#322811yescharacteristic, complemented, Sylow
121C2×#41—21no—
122C4⋊Q8—611no—
123C4⋊Q8—611no—
124C4⋊Q8C2×D6111yescharacteristic
125#127C2×D6111yescharacteristic
126#125—612no—
127#124—21no—
128C22⋊Q8—1221no—
129C22⋊Q8—1221no—
130#121—21no—
131#121C2×D6112yes—
132C4×Q8—1221no—
133C4×Q8—1221no—
134C4×D4—21no—
135C4×D4C2×D6112yes—
136#117—612no—
137C2×C42C2×D6111yescharacteristic
138#107—614no—
139#106—614no—
140C4⋊C8—612no—
141#102—614no—
142#102—614no—
143C22⋊C8—612no—
144C4×C8—611no—
145C4×C8—611no—
146#41—44no—
147C2×Q8—21no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×D4—22no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4C22×D6112yes—
154C22×C4—22no—
155C22×C4C22⋊D6111yescharacteristic
156C22×C4C22⋊D6111yescharacteristic
157C22×C4C22×D6111yescharacteristic
158C2×C8—612no—
159C2×C8—612no—
160C4⋊C4—21no—
161C4⋊C4—612no—
162C4⋊C4—612no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4C22×D6112yes—
168C22⋊C4—22no—
169C22⋊C4—22no—
170C22⋊C4—1222no—
171C42—1222no—
172C42C22⋊D6111yescharacteristic
173C42C22⋊D6111yescharacteristic
174C42C22×D6111yescharacteristic
175C42C22×D6111yescharacteristic
176C23—22no—
177C23C2×C22⋊D6111yescharacteristic
178Q8—42no—
179Q8—2442no—
180Q8—2442no—
181D4—24no—
182D4—44no—
183D4—42no—
184D4—42no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4C2×C22⋊D6111yescharacteristic
193C2×C4C2×C22⋊D6111yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C23×D6111yescharacteristic
198C8—1222no—
199C8—1222no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C22×C22⋊D6111yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—2442no—
212C4—2442no—
213C4#1451979712yes—
214C4#1451980312yes—
215C4#1451982412yes—
216C2—41no—
217C2—82no—
218C2#1684033311yescharacteristic
219C2C2×#1451979711yescharacteristic
220C2C2×#1451980311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#532C2
socleC22×C61C22×D4
hypercenter#532D61
hypocenterC61#3228
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. #16840165C2semidirect
3. #16840158C2semidirect
4. #16840108C2semidirect
5. #16840108C2semidirect
6. #16840083C2semidirect
7. #16840062C2semidirect
8. #16839815C2semidirect
120. C61#3228semidirect