Finite Group Databasebeta

← #21458127

Subgroups — #21458127

Order 7808.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840417C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic, complemented
3#16840112C211yesmaximal, characteristic, complemented
4#16840096C212yesmaximal, complemented
5#16840043C211yesmaximal, characteristic, complemented
6#16840005C212yesmaximal, complemented
7#16839906C212yesmaximal, complemented
8C4×#11758199C211yesmaximal, characteristic, complemented
9#16839839C211yesmaximal, characteristic, complemented
10#16839762C212yesmaximal, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×#11758222—21no—
14C2×#11758199C2211yescharacteristic
15C2×#11758189C2212yes—
16#14519777C2211yescharacteristic
17#14519762—22no—
18#14519759—22no—
19#14519756—21no—
20#14519753C2212yes—
21#14519752—21no—
22#14519748C2212yes—
23C4×D244C2211yescharacteristic
24C4×D244C2211yescharacteristic
25C4⋊C4×D61—21no—
26C4⋊C4×D61C2212yes—
27#14519711C2212yes—
28#14519710C2211yescharacteristic
29#14519701C2212yes—
30#14519701C2212yes—
31#14519699C2212yes—
32#14519698C2211yescharacteristic
33#14519697C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C2×SD16×C61C2212yes—
37C4⋊Q8×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61C2312yes—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C2×C22⋊D61—22no—
45#11758226—24no—
46#11758226—42no—
47#11758222—44no—
48C2×D244—22no—
49C2×D244D411yescharacteristic
50C2×D244C2311yescharacteristic
51C2×C4×D61—22no—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61C2312yes—
55C2×Dic122—21no—
56SD16×C61—42no—
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—22no—
64#11758199—22no—
65#11758198—22no—
66#11758198—21no—
67#11758198D412yes—
68C4⋊Dic61—21no—
69C4⋊Dic61D411yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71C4⋊Dic61C2312yes—
72#11758196—22no—
73#11758196—22no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76#11758189—42no—
77C23×C61—21no—
78C22×D61—21no—
79C22×D61C2×D412yes—
80Q8×C61—22no—
81Q8×C61—22no—
82D4×C61—21no—
83D4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—42no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C22⋊D61—44no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61C2×D412yes—
94D244—22no—
95D244—21no—
96D244—44no—
97D244#4112yescomplemented
98C4×D61—22no—
99C4×D61—22no—
100C4×D61—44no—
101C4×D61—44no—
102C4×D61—42no—
103Dic122—42no—
104C8×C61—22no—
105#92418—21no—
106#92418—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61C22×D411yescharacteristic
111C2×D61—22no—
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—41no—
116C2×D61—41no—
117C4×C61—21no—
118C4×C61—42no—
119C4×C61—41no—
120C4×C61AGL(1,ℤ/8)12yes—
121C4×C61C2×#4111yescharacteristic
122C4×C61H(5,𝔽2)11yescharacteristic
123Dic61—22no—
124Dic61—42no—
125Dic61—41no—
126#3330—611nomaximal, Sylow
127C2×C61—81no—
128C2×C61#54611yescharacteristic
129C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C61#57811yescharacteristic
131D61—42no—
132D61—42no—
133#547—611no—
134#547—611no—
135#487—611no—
136#484—612no—
137#474—611no—
138#468—612no—
139#461D6111yescharacteristic, complemented
140#449—612no—
141C4×D8—611no—
142#436—611no—
143#417—612no—
144C61#333011yescharacteristic, complemented, Sylow
145C2×#41—612no—
146C2×#41—1221no—
147C2×SD16C2×D6112yes—
148C2×D8—611no—
149C2×M16—612no—
150C4⋊Q8—611no—
151C4⋊Q8C2×D6111yescharacteristic
152#123—1222no—
153#123—1222no—
154C22⋊Q8—612no—
155C22⋊Q8—1221no—
156#121—612no—
157#121—1221no—
158C4×D4—611no—
159C4×D4—611no—
160C4×D4C2×D6111yescharacteristic
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1221no—
163#107—612no—
164#107—611no—
165C4⋊C8C2×D6111yescharacteristic
166#103—612no—
167#103—612no—
168#103C2×D6112yes—
169#102—611no—
170#102—612no—
171#102—611no—
172C22⋊C8—612no—
173C4×C8—611no—
174#41—1224no—
175#41—2444no—
176#41—2442no—
177C2×Q8—1221no—
178C2×Q8C22×D6112yes—
179C2×D4—611no—
180C2×D4—611no—
181C2×D4—1222no—
182C2×D4—1222no—
183C2×D4C22×D6111yescharacteristic
184C22×C4—21no—
185C22×C4—612no—
186C22×C4—1222no—
187C22×C4—1222no—
188C22×C4—1221no—
189SD16—42no—
190D8—1222no—
191M16—2442no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8C22×D6112yes—
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—611no—
198C4⋊C4—612no—
199C4⋊C4—611no—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4—1221no—
203C4⋊C4C22×D6111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—612no—
206C22⋊C4—1222no—
207C22⋊C4—1222no—
208C22⋊C4—1221no—
209C42C22×D6111yescharacteristic
210C23—21no—
211C23—612no—
212C23—1221no—
213Q8—22no—
214Q8—22no—
215Q8—2442no—
216D4—21no—
217D4—21no—
218D4—612no—
219D4—1221no—
220D4—1222no—
221D4—2444no—
222D4—2444no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—612no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—1222no—
231C2×C4—2444no—
232C2×C4—2444no—
233C2×C4—2442no—
234C2×C4D4×D6111yescharacteristic
235C2×C4D4×D6111yescharacteristic
236C2×C4C23×D6111yescharacteristic
237C8—22no—
238C8—1221no—
239C8—1221no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—1222no—
244C22—1222no—
245C22—1222no—
246C22—1222no—
247C22—2441no—
248C22—2441no—
249C22C2×D4×D6111yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—1222no—
254C4—2441no—
255C4—2442no—
256C4#1451980412yes—
257C4#41×D6111yescharacteristic
258C4#1451982211yescharacteristic
259C2—81no—
260C2—2442no—
261C2—2442no—
262C2#1684040911yescharacteristic
263C2C2×#1451980411yescharacteristic
264C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3330
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840417C2semidirect
2. #16840415C2semidirect
3. #16840112C2semidirect
4. #16840096C2semidirect
5. #16840043C2semidirect
6. #16840005C2semidirect
7. #16839906C2semidirect
8. C4×#11758199C2semidirect
9. #16839839C2semidirect
10. #16839762C2semidirect
11. C61×#461C2semidirect
97. D244#41semidirect
139. #461D61semidirect
144. C61#3330semidirect