Finite Group Databasebeta

← #21457134

Subgroups — #21457134

Order 7808.

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

normal subgroups only

This group has 392 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#16840316C211yesmaximal, characteristic, complemented
2#16840313C211yesmaximal, characteristic
3#16840051C212yesmaximal, complemented
4#16840044C211yesmaximal, characteristic, complemented
5#16839994C212yesmaximal, complemented
6#16839992C212yesmaximal, complemented
7#16839966C212yesmaximal, complemented
8#16839963C211yesmaximal, characteristic, complemented
9#16839962C211yesmaximal, characteristic, complemented
10C4⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#475C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758190C2212yes—
14C2×#11758201C2212yes—
15C2×C8×D61C2212yes—
16#14519776C2211yescharacteristic
17#14519775C2211yescharacteristic
18#14519774C2211yescharacteristic
19#14519767—21no—
20#14519766—21no—
21#14519757C2211yescharacteristic
22#14519755—21no—
23#14519753C2211yescharacteristic
24#14519752—21no—
25#14519752C2212yes—
26C4×Dic122—21no—
27C4×Dic122C2211yescharacteristic
28#14519739—21no—
29#14519739C2212yes—
30#14519734—21no—
31C42×D61C2211yescharacteristic
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519700C2212yes—
36#14519699C2212yes—
37#14519697C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#106×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45#11758226—44no—
46C2×D244—22no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244C2312yes—
50C2×C4×D61—22no—
51C2×C4×D61D411yescharacteristic
52C2×C4×D61D411yescharacteristic
53C2×C4×D61C2311yescharacteristic
54C2×Dic122—21no—
55C2×Dic122C2311yescharacteristic
56C2×C8×C61C2312yes—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C4⋊C4×C61C2311yescharacteristic
61C42×C61—21no—
62C42×C61C2311yescharacteristic
63#11758201—42no—
64#11758198—21no—
65#11758198—21no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61—21no—
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75C4×Dic61—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80#11758190—42no—
81C8×D61—42no—
82C22×D61—22no—
83C22×D61C2×D411yescharacteristic
84Q8×C61—21no—
85Q8×C61—21no—
86Q8×C61—42no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98D244—22no—
99D244—22no—
100D244—42no—
101D244—44no—
102D244—42no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—41no—
106C4×D61—44no—
107C4×D61SD1614yescomplemented
108Dic122—21no—
109Dic122—21no—
110Dic122—42no—
111C8×C61—22no—
112#92418—22no—
113C22×C61C22×D411yescharacteristic
114C2×D61—21no—
115C2×D61—21no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61C2×SD1612yes—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—42no—
123C4×C61—41no—
124C4×C61C2×SD1612yes—
125C4×C61H(5,𝔽2)11yescharacteristic
126C4×C612−1+411yescharacteristic
127Dic61—21no—
128Dic61—21no—
129Dic61—41no—
130Dic61—41no—
131Dic61C2×SD1612yes—
132#3246—611nomaximal, Sylow
133C2×C61#53711yescharacteristic
134C2×C61C22×SD1611yescharacteristic
135C2×C61#57511yescharacteristic
136D61—22no—
137D61—82no—
138#533—611no—
139#532—611no—
140#476—612no—
141#475—611no—
142#475D6111yescharacteristic, complemented
143#465—612no—
144#465—612no—
145#461—612no—
146#460—611no—
147#460—611no—
148C2×C4⋊C8—611no—
149C61#324611yescharacteristic, complemented, Sylow
150C2×#41—1221no—
151C2×SD16—612no—
152C2×SD16—612no—
153C22×C8—612no—
154C4⋊Q8—611no—
155C4⋊Q8—611no—
156C4⋊Q8C2×D6111yescharacteristic
157#127—611no—
158#125—1221no—
159#124—1221no—
160C22⋊Q8—611no—
161C22⋊Q8—611no—
162C22⋊Q8—1221no—
163#121—612no—
164#121—1221no—
165C4×Q8—611no—
166C4×Q8—1221no—
167C4×Q8C2×D6111yescharacteristic
168C4×D4—612no—
169C4×D4—1221no—
170#117—1221no—
171C2×C42—611no—
172#106—612no—
173#106C2×D6112yes—
174C4⋊C8—612no—
175C4⋊C8—611no—
176C4⋊C8C2×D6111yescharacteristic
177#103—612no—
178#103C2×D6112yes—
179#102—612no—
180#102—612no—
181#41—2444no—
182C2×Q8—21no—
183C2×Q8—611no—
184C2×Q8—1221no—
185C2×Q8C22×D6111yescharacteristic
186C2×D4—612no—
187C2×D4—1222no—
188C2×D4—1221no—
189C2×D4—1221no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1222no—
194SD16—2442no—
195SD16—2442no—
196C2×C8—612no—
197C2×C8—2442no—
198C2×C8C22×D6112yes—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—611no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4C22×D6111yescharacteristic
209C4⋊C4C22×D6112yes—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C42—21no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—611no—
221C23—1222no—
222Q8—21no—
223Q8—21no—
224Q8—42no—
225Q8—1221no—
226Q8—1221no—
227Q8—2442no—
228D4—1222no—
229D4—1222no—
230D4—2442no—
231D4—2444no—
232D4—2442no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—611no—
237C2×C4—614no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—2441no—
245C2×C4—2444no—
246C2×C4D4×D6111yescharacteristic
247C2×C4D4×D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—22no—
250C8—1222no—
251C22—612no—
252C22—1221no—
253C22—1221no—
254C22—2442no—
255C22—2442no—
256C22—2442no—
257C22C2×D4×D6111yescharacteristic
258C4—21no—
259C4—42no—
260C4—41no—
261C4—41no—
262C4—612no—
263C4—1221no—
264C4—1221no—
265C4—2441no—
266C4—2441no—
267C4SD16×D6112yes—
268C4#1451982311yescharacteristic
269C4#1451982511yescharacteristic
270C2—1222no—
271C2—4882no—
272C2#1684034211yescharacteristic
273C2C2×SD16×D6111yescharacteristic
274C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3246
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840051C2semidirect
4. #16840044C2semidirect
5. #16839994C2semidirect
6. #16839992C2semidirect
7. #16839966C2semidirect
8. #16839963C2semidirect
9. #16839962C2semidirect
10. C4⋊C8×D61C2semidirect
11. C61×#475C2semidirect
107. C4×D61SD16semidirect
142. #475D61semidirect
149. C61#3246semidirect