Finite Group Databasebeta

← #21455612

Subgroups — #21455612

Order 7808.

440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×C4×D244C211yesmaximal, characteristic
2#16840059C214yesmaximal, complemented
3#16840049C212yesmaximal, complemented
4#16840039C212yesmaximal, complemented
5#16839805C212yesmaximal, complemented
6#16839786C211yesmaximal, characteristic, complemented
7#16839766C212yesmaximal
8C61×#533C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C4×D61—21no—
11C2×#11758194C2212yes—
12C4×D244—21no—
13C4×D244—21no—
14C4×D244C2212yes—
15C4×D244C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758198—21no—
18#14519710C2214yescomplemented
19#14519708C2214yescomplemented
20C4⋊#92418C2212yescomplemented
21C4⋊#92418C2212yescomplemented
22#14519697C2214yes—
23#14519697C2214yes—
24C4⋊Q8×C61C2211yescharacteristic, complemented
25C4⋊Q8×C61C2211yescharacteristic, complemented
26#125×C61C2212yescomplemented
27C22⋊Q8×C61—21no—
28C22⋊Q8×C61—21no—
29C4×Q8×C61—21no—
30C4×Q8×C61—21no—
31#117×C61C2212yes—
32C2×C42×C61C2211yescharacteristic
33C23×D61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—21no—
36C22×C4×C61D411yescharacteristic
37C22×C4×C61D411yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—21no—
40C2×D244—21no—
41C2×D244—22no—
42C2×D244Q814yescomplemented
43C2×D244C2312yes—
44C2×C4×D61—22no—
45C2×C4×D61—22no—
46C2×C4×D61—44no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2312yes—
52C4⋊C4×C61C2312yes—
53C22⋊C4×C61—22no—
54C42×C61—22no—
55C42×C61D411yescharacteristic
56C42×C61D411yescharacteristic
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63#11758194—24no—
64C2×#92418C2314yes—
65C23×C61C2×D411yescharacteristic
66C22×D61—24no—
67C22×D61—22no—
68C22×D61—42no—
69C22×D61—42no—
70Q8×C61—42no—
71Q8×C61—42no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—41no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×Q812yes—
82C2×C4×C61#4112yes—
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—22no—
85C2×Dic61—42no—
86D244—24no—
87D244—22no—
88D244C2×Q814yes—
89C4×D61—44no—
90C4×D61—44no—
91#92418—24no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61C22⋊Q812yes—
95C22×C61C22×D411yescharacteristic
96C2×D61—24no—
97C2×D61—48no—
98C2×D61—42no—
99C2×D61—42no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—42no—
104C4×C61—42no—
105C4×C61C22⋊Q812yes—
106C4×C61AGL(1,ℤ/8)12yes—
107C4×C61C22×Q811yescharacteristic
108C4×C61C2×#4111yescharacteristic
109Dic61—42no—
110#3077—611nomaximal, Sylow
111C2×C61—22no—
112C2×C61C2×C22⋊Q811yescharacteristic
113C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
114C2×C61#57511yescharacteristic
115D61—44no—
116#533D6111yescharacteristic, complemented
117C2×C4×D4—611no—
118#478—614no—
119#476—612no—
120#474—612no—
121#428—612no—
122#423—611no—
123#418—612no—
124C61#307711yescharacteristic, complemented, Sylow
125C22×D4—611no—
126C23×C4—1221no—
127C2×M16—612no—
128C4⋊Q8C2×D6111yescharacteristic, complemented
129C4⋊Q8C2×D6111yescharacteristic, complemented
130#125C2×D6112yescomplemented
131C22⋊Q8—21no—
132C22⋊Q8—21no—
133C4×Q8—21no—
134C4×Q8—21no—
135C4×D4—612no—
136C4×D4—612no—
137C4×D4—1221no—
138C4×D4—1221no—
139#117C2×D6112yes—
140C2×C4⋊C4—611no—
141C2×C22⋊C4—1221no—
142C2×C42C2×D6111yescharacteristic
143#107—614no—
144#106—614no—
145C4⋊C8—612no—
146C4⋊C8—612no—
147#102—614no—
148#102—614no—
149C24—1221no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×D4—614no—
153C2×D4—612no—
154C2×D4—1222no—
155C2×D4—1221no—
156C22×C4—1221no—
157C22×C4—1222no—
158C22×C4—1222no—
159C22×C4—2444no—
160C22×C4C22⋊D6111yescharacteristic
161C22×C4C22⋊D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163M16—1224no—
164C2×C8—614no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—612no—
170C4⋊C4—1221no—
171C4⋊C4C22×D6112yes—
172C4⋊C4C22×D6112yes—
173C22⋊C4—22no—
174C22⋊C4—1222no—
175C22⋊C4—1222no—
176C42—22no—
177C42C22⋊D6111yescharacteristic
178C42C22⋊D6111yescharacteristic
179C42C22×D6111yescharacteristic
180C42C22×D6111yescharacteristic
181C23—1222no—
182C23—1224no—
183C23—2442no—
184C23—2442no—
185C23C2×C22⋊D6111yescharacteristic
186Q8—42no—
187Q8—42no—
188D4—614no—
189D4—1222no—
190D4—1224no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—1222no—
196C2×C4—2444no—
197C2×C4—2442no—
198C2×C4—2444no—
199C2×C4Q8×D6112yes—
200C2×C4#1175822612yes—
201C2×C4C2×C22⋊D6111yescharacteristic
202C2×C4C2×C22⋊D6111yescharacteristic
203C2×C4C2×C22⋊D6111yescharacteristic
204C2×C4C2×C22⋊D6111yescharacteristic
205C2×C4C2×C22⋊D6111yescharacteristic
206C2×C4C23×D6111yescharacteristic
207C8—1224no—
208C22—21no—
209C22—21no—
210C22—1224no—
211C22—2448no—
212C22—2442no—
213C22—2442no—
214C22#1451975312yes—
215C22C22×C22⋊D6111yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—2442no—
222C4#1451975312yes—
223C4#1451980212yes—
224C4C2×Q8×D6111yescharacteristic
225C4C2×#1175822611yescharacteristic
226C2—22no—
227C2—2444no—
228C2C2×#1451975311yescharacteristic
229C2C2×#1451980211yescharacteristic
230C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3077
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840059C2semidirect
3. #16840049C2semidirect
4. #16840039C2semidirect
5. #16839805C2semidirect
6. #16839786C2semidirect
8. C61×#533C2semidirect
18. #14519710C22semidirect
19. #14519708C22semidirect
20. C4⋊#92418C22semidirect
21. C4⋊#92418C22semidirect
24. C4⋊Q8×C61C22semidirect
25. C4⋊Q8×C61C22semidirect
26. #125×C61C22semidirect
42. C2×D244Q8semidirect
116. #533D61semidirect
124. C61#3077semidirect
128. C4⋊Q8C2×D61semidirect
129. C4⋊Q8C2×D61semidirect
130. #125C2×D61semidirect