Finite Group Databasebeta

← #21446199

Subgroups — #21446199

Order 7808.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic, complemented
2#16840308C211yesmaximal, characteristic
3#16839779C211yesmaximal, characteristic, complemented
4#16839735C211yesmaximal, characteristic, complemented
5#16839523C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519785—22no—
10#14519783—22no—
11C2×#11758194C2211yescharacteristic
12M16×D61—22no—
13#14519775C411yescharacteristic, complemented
14#14519773C411yescharacteristic, complemented
15#14519766C411yescharacteristic, complemented
16#14519764C411yescharacteristic, complemented
17#14519749—22no—
18C4×C22⋊D61—22no—
19#14519736C2211yescharacteristic
20C2×C4×Dic61C2211yescharacteristic
21#14519704—22no—
22#14519691—22no—
23C2×#41×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25#117×C61C2211yescharacteristic
26#104×C61—22no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31C2×Q8×C61C2×C411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61C2×C411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×C22⋊D61D412yes—
38C22×Dic61—21no—
39#11758222—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43C2×D244C2×C411yescharacteristic
44C2×C4×D61D412yes—
45C2×Dic122C2×C411yescharacteristic
46M16×C61—21no—
47M16×C61D412yescomplemented
48C2×C8×C61—21no—
49C4⋊C4×C61—21no—
50C22⋊C4×C61—21no—
51C42×C61—21no—
52C22⋊Dic61—22no—
53C22⋊Dic61—21no—
54#11758198—22no—
55C4⋊Dic61—21no—
56#11758196—22no—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C4×Dic61C2×C411yescharacteristic
60C4×Dic61C2×C411yescharacteristic
61#11758194—21no—
62#11758194D412yescomplemented
63C2×#92418—21no—
64#11758189—24no—
65C8×D61—24no—
66C23×C61—21no—
67C23×C61C2×D411yescharacteristic
68C22×D61C22⋊C412yes—
69Q8×C61—21no—
70Q8×C61—21no—
71D4×C61—21no—
72D4×C61—21no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C22×C411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C22⋊D61—22no—
86C22⋊D61—22no—
87C22⋊D61—44no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—42no—
91C2×Dic61—41no—
92C2×Dic61C22⋊C412yes—
93D244—21no—
94D244—21no—
95C4×D61—22no—
96C4×D61—22no—
97Dic122—21no—
98Dic122—21no—
99C8×C61—22no—
100#92418—22no—
101C22×C61—41no—
102C22×C61—42no—
103C22×C61—41no—
104C22×C61C2×C22⋊C411yescharacteristic
105C22×C61#12111yescharacteristic
106C22×C61#12111yescharacteristic
107C2×D61—22no—
108C2×D61—42no—
109C4×C61—41no—
110C4×C61—81no—
111C4×C61C4×D411yescharacteristic
112C4×C61C4×D411yescharacteristic
113C4×C61#12011yescharacteristic
114C4×C61#12311yescharacteristic
115Dic61—22no—
116Dic61—22no—
117Dic61—41no—
118Dic61—81no—
119#1884—611nomaximal, Sylow
120C2×C61—21no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—81no—
124C2×C61#38611yescharacteristic
125D61—42no—
126#568—611no—
127#532—611no—
128#421—611no—
129#421D6111yescharacteristic, complemented
130#410—611no—
131#339—611no—
132#339—611no—
133C61#188411yescharacteristic, complemented, Sylow
134C2×#41—611no—
135C2×#41C2×D6111yescharacteristic
136#131—1222no—
137#131—1222no—
138C2×M16—611no—
139C2×M16—1222no—
140C2×M16C2×D6111yescharacteristic
141C4⋊Q8—611no—
142#127—611no—
143#124—611no—
144#124—611no—
145#121—1222no—
146C4×D4—1222no—
147#117—611no—
148#117C2×D6111yescharacteristic
149C2×C42—611no—
150#104—22no—
151#104—1222no—
152#99—1222no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—1221no—
158#41—1221no—
159#41—1221no—
160#41—1221no—
161C2×Q8—611no—
162C2×Q8C4×D6111yescharacteristic
163C2×D4—21no—
164C2×D4—612no—
165C2×D4—611no—
166C2×D4—1222no—
167C2×D4C4×D6111yescharacteristic
168C22×C4—21no—
169C22×C4—612no—
170C22×C4—1221no—
171C22×C4C22×D6111yescharacteristic
172M16—21no—
173M16—612no—
174M16—1224no—
175M16—1221no—
176M16C22⋊D6112yescomplemented
177C2×C8—21no—
178C2×C8—1224no—
179C2×C8—1221no—
180C4⋊C4—21no—
181C4⋊C4—1222no—
182C4⋊C4—1221no—
183C22⋊C4—21no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1221no—
187C42—21no—
188C42—611no—
189C42—611no—
190C42—1221no—
191C42—1221no—
192C23—21no—
193C23—612no—
194C23D4×D6111yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—1221no—
198Q8—1221no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—1222no—
204D4—1222no—
205D4—1221no—
206D4—1221no—
207D4—2444no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—612no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—2442no—
218C2×C4—2441no—
219C2×C4C2×C4×D6111yescharacteristic
220C2×C4#1175822211yescharacteristic
221C2×C4D4×D6111yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4#1175822411yescharacteristic
224C2×C4C2×C22⋊D6111yescharacteristic
225C8—22no—
226C8—1222no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—1222no—
231C22—2442no—
232C22C22⋊C4×D6111yescharacteristic
233C22#1451974811yescharacteristic
234C22#1451975011yescharacteristic
235C4—41no—
236C4—81no—
237C4—1222no—
238C4—1222no—
239C4—4881no—
240C4—2441no—
241C4#1451973711yescharacteristic
242C4C4×C22⋊D6111yescharacteristic
243C4#1451974511yescharacteristic
244C4#1451975911yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—81no—
249C2—2442no—
250C2#1683963811yescharacteristic
subgroupG/H
centerC4#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#386
hypercenter#421D61
hypocenterC61#1884
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #16840528C2semidirect
3. #16839779C2semidirect
4. #16839735C2semidirect
5. #16839523C2semidirect
6. #16839521C2semidirect
7. C61×#421C2semidirect
13. #14519775C4semidirect
14. #14519773C4semidirect
15. #14519766C4semidirect
16. #14519764C4semidirect
47. M16×C61D4semidirect
62. #11758194D4semidirect
129. #421D61semidirect
133. C61#1884semidirect
176. M16C22⋊D61semidirect