Finite Group Databasebeta

← #21455789

Subgroups — #21455789

Order 7808.

386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 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#16840333C211yesmaximal, characteristic
2#16840245C211yesmaximal, characteristic
3#16840104C212yesmaximal, complemented
4#16840104C212yesmaximal, complemented
5#16840098C212yesmaximal, complemented
6#16840093C212yesmaximal, complemented
7#16839804C211yesmaximal, characteristic, complemented
8#16839800C211yesmaximal, characteristic, complemented
9#16839772C211yesmaximal, characteristic, complemented
10C2×#14519702C211yesmaximal, characteristic, complemented
11C61×#408C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519775—21no—
14#14519764—21no—
15#14519758—22no—
16#14519756C2212yes—
17#14519756C2212yes—
18Q8×Dic61—21no—
19D4×Dic61—22no—
20D4×Dic61—21no—
21#14519736C2211yescharacteristic
22#14519736C2212yes—
23#14519736C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2212yes—
26#14519711C2211yescharacteristic
27#14519711C2211yescharacteristic
28#14519711C2212yes—
29#14519709C2211yescharacteristic
30#14519709C2211yescharacteristic
31#14519709C2212yes—
32#14519702C2212yes—
33#14519702C2212yes—
34#14519702C2212yes—
35#14519702C2212yes—
36C2×#41×C61C2211yescharacteristic
37C2×M16×C61C2211yescharacteristic
38C22×C8×C61C2211yescharacteristic
39C22⋊C8×C61C2212yes—
40C22⋊C8×C61C2212yes—
41#41×C61—22no—
42#41×C61—22no—
43C2×Q8×C61D411yescharacteristic
44C2×D4×C61D412yes—
45C2×D4×C61D411yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C22×Dic61—21no—
49C22×Dic61—22no—
50C22×Dic61—21no—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—21no—
54C2×Dic122C2312yes—
55M16×C61—22no—
56C2×C8×C61—22no—
57C2×C8×C61C2311yescharacteristic
58C2×C8×C61C2311yescharacteristic
59C2×C8×C61C2312yes—
60C22⋊Dic61—22no—
61C22⋊Dic61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65C4⋊Dic61—22no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71C4⋊Dic61C2311yescharacteristic
72#11758196—22no—
73#11758196—22no—
74C4×Dic61—22no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C23×C61C2×D412yes—
78C23×C61C2×D411yescharacteristic
79Q8×C61—22no—
80D4×C61—24no—
81D4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61#4112yes—
87C2×C4×C61#4112yes—
88C2×C4×C61C2411yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—42no—
96C2×Dic61—81no—
97C2×Dic61—82no—
98Dic122—22no—
99Dic122—22no—
100Dic122—42no—
101C8×C61—21no—
102C8×C61—21no—
103C8×C61—22no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—22no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61#12312yes—
110C22×C61C22×D411yescharacteristic
111C4×C61—22no—
112C4×C61#12312yes—
113C4×C61C2×#4111yescharacteristic
114C4×C61C2×#4111yescharacteristic
115Dic61—42no—
116Dic61—41no—
117Dic61—42no—
118Dic61—41no—
119Dic61—41no—
120Dic61—41no—
121#3097—611nomaximal, Sylow
122C2×C61—22no—
123C2×C61—42no—
124C2×C61C2×#12311yescharacteristic
125C2×C61#57711yescharacteristic
126C2×C61#57811yescharacteristic
127#536—611no—
128#520—611no—
129#485—612no—
130#485—612no—
131#484—612no—
132#483—612no—
133#428—611no—
134#427—611no—
135#419—611no—
136C2×#103—611no—
137#408D6111yescharacteristic
138C61#309711yescharacteristic, complemented, Sylow
139C2×#41C2×D6111yescharacteristic
140C22×Q8—611no—
141C2×M16C2×D6111yescharacteristic
142C22×C8C2×D6111yescharacteristic
143C4⋊Q8—1221no—
144#124—1221no—
145#123—1222no—
146C22⋊Q8—612no—
147C22⋊Q8—612no—
148C4×Q8—1221no—
149C4×D4—1222no—
150C4×D4—1221no—
151#117—611no—
152#117—612no—
153#117—611no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—612no—
156#107—611no—
157#107—611no—
158#107—612no—
159#106—611no—
160#106—611no—
161#106—612no—
162#103—612no—
163#103—612no—
164#103—612no—
165#103—612no—
166C22⋊C8C2×D6112yes—
167C22⋊C8C2×D6112yes—
168#41—22no—
169#41—22no—
170C2×Q8—612no—
171C2×Q8—1221no—
172C2×Q8—1222no—
173C2×Q8—1222no—
174C2×Q8D24411yescharacteristic
175C2×D4D24412yes—
176C2×D4D24411yescharacteristic
177C22×C4—1222no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182M16—22no—
183C2×C8—22no—
184C2×C8C22×D6111yescharacteristic
185C2×C8C22×D6112yes—
186C2×C8C22×D6111yescharacteristic
187C4⋊C4—612no—
188C4⋊C4—611no—
189C4⋊C4—611no—
190C4⋊C4—611no—
191C4⋊C4—611no—
192C4⋊C4—1222no—
193C4⋊C4—1221no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C22⋊C4—1222no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C22⋊C4—1222no—
200C22⋊C4—1222no—
201C42—1222no—
202C42—1221no—
203C42—1221no—
204C23C2×D24412yes—
205C23C2×D24411yescharacteristic
206Q8—22no—
207Q8—1222no—
208Q8—1222no—
209Q8—2442no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—4881no—
221C2×C4—4882no—
222C2×C4—2442no—
223C2×C4C2×D24412yes—
224C2×C4C2×D24411yescharacteristic
225C2×C4#1175822412yes—
226C2×C4#1175822412yes—
227C2×C4C23×D6111yescharacteristic
228C8—21no—
229C8—21no—
230C8—22no—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22#1451976112yes—
237C22C22×D24411yescharacteristic
238C4—22no—
239C4—2442no—
240C4—2441no—
241C4—2442no—
242C4—2441no—
243C4—2441no—
244C4—2441no—
245C4#1451976112yes—
246C4C2×#1175822411yescharacteristic
247C4C2×#1175822411yescharacteristic
248C2—22no—
249C2—42no—
250C2C2×#1451976111yescharacteristic
251C2#1684057411yescharacteristic
252C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3097
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
3. #16840104C2semidirect
4. #16840104C2semidirect
5. #16840098C2semidirect
6. #16840093C2semidirect
7. #16839804C2semidirect
8. #16839800C2semidirect
9. #16839772C2semidirect
10. C2×#14519702C2semidirect
138. C61#3097semidirect