Finite Group Databasebeta

← #21456986

Subgroups — #21456986

Order 7808.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840293C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic, complemented
3#16840162C212yesmaximal, complemented
4#16840115C212yesmaximal, complemented
5#16840097C211yesmaximal, characteristic, complemented
6#16840093C211yesmaximal, characteristic, complemented
7#16840073C211yesmaximal, characteristic
8#16840072C212yesmaximal, complemented
9#16840064C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#481C211yesmaximal, characteristic
12#14519770—21no—
13#14519768—21no—
14#14519768—21no—
15#14519768C2212yes—
16#14519768C2212yes—
17#14519768C2211yescharacteristic
18#14519764C2211yescharacteristic
19#14519758—21no—
20#14519756C2211yescharacteristic
21#14519742C2211yescharacteristic
22D4×Dic61—21no—
23D4×Dic61C2211yescharacteristic
24#14519733—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61C2211yescharacteristic
29#14519710C2212yes—
30#14519710C2212yes—
31#14519709C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519700C2212yes—
35#14519698C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yes—
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61D411yescharacteristic
50C22×Dic61D411yescharacteristic
51C2×Dic122C2311yescharacteristic
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C4⋊C4×C61C2311yescharacteristic
56C22⋊C4×C61—21no—
57C22⋊Dic61—21no—
58C22⋊Dic61—21no—
59C22⋊Dic61—21no—
60C22⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—22no—
69#11758196—22no—
70#11758196—21no—
71#11758196—21no—
72C4×Dic61—21no—
73C4×Dic61D411yescharacteristic
74C4×Dic61D411yescharacteristic
75C4×Dic61C2311yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C23×C61—21no—
79C23×C61C2×D411yescharacteristic
80D4×C61—22no—
81D4×C61—42no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—42no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—41no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99Dic122—22no—
100C8×C61—22no—
101#92418—22no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61#13512yes—
108C22×C61C22×D411yescharacteristic
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—42no—
112C4×C612−1+412yes—
113Dic61—21no—
114Dic61—21no—
115Dic61—21no—
116Dic61—21no—
117Dic61—41no—
118Dic61—42no—
119Dic61—41no—
120#3232—611nomaximal, Sylow
121C2×C61—22no—
122C2×C61—81no—
123C2×C61#53611yescharacteristic
124C2×C61C2×#13511yescharacteristic
125C2×C61#57511yescharacteristic
126#529—611no—
127C2×#125—611no—
128#499—612no—
129#488—612no—
130#484—611no—
131#483—611no—
132#481D6111yescharacteristic
133#480—611no—
134#479—612no—
135#478—612no—
136#431—611no—
137C61#323211yescharacteristic, complemented, Sylow
138#126—1221no—
139#125—612no—
140#125—612no—
141#125—611no—
142#125—1221no—
143#125—1221no—
144#124—611no—
145#123—1221no—
146C22⋊Q8—611no—
147#121C2×D6111yescharacteristic
148C4×Q8—611no—
149C4×D4—611no—
150C4×D4—1221no—
151#117—1221no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C42—611no—
157#107—612no—
158#107—612no—
159#106—612no—
160#106C2×D6112yes—
161C4⋊C8—612no—
162#103—612no—
163#103—612no—
164#102—612no—
165#102C2×D6112yes—
166C22⋊C8—611no—
167C22⋊C8C2×D6111yescharacteristic
168C4×C8—612no—
169C2×Q8—611no—
170C2×D4—21no—
171C2×D4C22×D6111yescharacteristic
172C22×C4—21no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178C2×C8—612no—
179C2×C8C22×D6112yes—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4C22×D6112yes—
193C4⋊C4C22×D6111yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C42—611no—
200C42—611no—
201C42—611no—
202C42—611no—
203C42—1221no—
204C23—21no—
205C23D4×D6111yescharacteristic
206Q8—1222no—
207D4—22no—
208D4—42no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—2441no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4D4×D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—22no—
227C8—1222no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22#1451979812yes—
234C22C2×D4×D6111yescharacteristic
235C4—21no—
236C4—41no—
237C4—42no—
238C4—1221no—
239C4—1221no—
240C4—1221no—
241C4—1221no—
242C4—2442no—
243C4—2441no—
244C4—2441no—
245C4#1451982412yes—
246C2—22no—
247C2—81no—
248C2#1684033411yescharacteristic
249C2C2×#1451979811yescharacteristic
250C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3232
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#14519768C2semidirect
3. #16840162C2semidirect
4. #16840115C2semidirect
5. #16840097C2semidirect
6. #16840093C2semidirect
8. #16840072C2semidirect
9. #16840064C2semidirect
10. #16839812C2semidirect
137. C61#3232semidirect