Finite Group Databasebeta

← #21461671

Subgroups — #21461671

Order 7808.

536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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#16840761C212yesmaximal, complemented
2#16840755C212yesmaximal, complemented
3#16840748C211yesmaximal, characteristic, complemented
4#16840741C211yesmaximal, characteristic, complemented
5C2×#14519825C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7#14519856C2212yes—
8#14519842—24no—
9#14519840—24no—
10#14519838—21no—
11#14519837—21no—
12#14519836—21no—
13#14519835—21no—
14#14519825—24no—
15#14519825—24no—
16C2×#11758226—21no—
17C2×#11758226C411yescharacteristic, complemented
18C2×#11758226C2211yescharacteristic
19C2×#11758222—21no—
20C2×#11758222—21no—
21C2×#11758222C411yescharacteristic, complemented
22C2×#11758222C2211yescharacteristic
23C2×Q8×D61—21no—
24C2×Q8×D61C411yescharacteristic, complemented
25C2×Q8×D61C2211yescharacteristic
26C22×Q8×C61C411yescharacteristic, complemented
27C2×Q8×C61—22no—
28C2×Q8×C61—22no—
29C2×Q8×C61—21no—
30C2×Q8×C61C2×C411yescharacteristic
31C2×Q8×C61C2×C411yescharacteristic
32C22×C4×C61—21no—
33C22×C4×C61C2×C411yescharacteristic
34C2×C22⋊D61—21no—
35C2×C22⋊D61D411yescharacteristic
36C2×C22⋊D61D411yescharacteristic
37#11758226—28no—
38#11758226—22no—
39#11758226—22no—
40#11758226—22no—
41#11758226D414yes—
42Q8×D61—28no—
43Q8×D61—22no—
44Q8×D61—22no—
45Q8×D61—22no—
46Q8×D61D414yes—
47#11758222—28no—
48#11758222—28no—
49#11758222—22no—
50#11758222—22no—
51#11758222—22no—
52#11758222—22no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244C2×C411yescharacteristic
56C2×D244D411yescharacteristic
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61C2×C411yescharacteristic
63C2×C4×D61C2311yescharacteristic
64C2×Dic122—21no—
65C2×Dic122—21no—
66C2×Dic122C2×C411yescharacteristic
67C2×Dic122D411yescharacteristic
68C22⋊#6923—22no—
69#11758217—22no—
70C4⋊#6923—22no—
71C4×#6923—22no—
72#11758213—22no—
73D61⋊C8—22no—
74C23×C61C22⋊C411yescharacteristic
75C22×D61—21no—
76C22×D61C22⋊C411yescharacteristic
77C22×D61C2×D411yescharacteristic
78C2×#6923—42no—
79Q8×C61—24no—
80Q8×C61—21no—
81Q8×C61—21no—
82Q8×C61C22⋊C412yes—
83Q8×C61C22⋊C412yes—
84C2×C4×C61—24no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61C22⋊C411yescharacteristic
90C2×C4×C61C22×C411yescharacteristic
91C22⋊D61—24no—
92C22⋊D61—22no—
93C22⋊D61—22no—
94C2×Dic61—21no—
95C2×Dic61C22⋊C411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97D244—24no—
98D244—24no—
99D244—22no—
100D244—21no—
101D244C22⋊C412yes—
102C4×D61—24no—
103C4×D61—24no—
104C4×D61—24no—
105C4×D61—24no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—24no—
109C4×D61C2×D412yes—
110C4×D61C2×D412yes—
111Dic122—24no—
112Dic122—21no—
113Dic122—24no—
114Dic122—22no—
115Dic122C22⋊C412yes—
116#92420—42no—
117C22×C61—21no—
118C22×C61—41no—
119C22×C61C2×C22⋊C411yescharacteristic
120C2×D61—21no—
121C2×D61—22no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61—41no—
125C2×D61#12012yes—
126#6923—82no—
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—21no—
130C4×C61C2×C22⋊C411yescharacteristic
131C4×C61C2×C22⋊C411yescharacteristic
132Dic61—21no—
133Dic61—22no—
134Dic61#12012yes—
135#1796—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—41no—
138C2×C61#37911yescharacteristic
139D61—22no—
140D61—41no—
141D61—42no—
142C2×2−1+4—611no—
143#421—612no—
144#419—612no—
145#413—611no—
146#410—611no—
147C61#179611yescharacteristic, complemented, Sylow
1482−1+4—1224no—
1492−1+4—1224no—
150C2×#41—611no—
151C2×#41—611no—
152C2×#41—611no—
153C2×#41—611no—
154C2×#41—1221no—
155C2×#41—1221no—
156C2×#41—1221no—
157C22×Q8—611no—
158C22×Q8—611no—
159C22×Q8—1221no—
160C22×Q8#692311yescharacteristic, complemented
161C2×M16—612no—
162#117—612no—
163#104—1224no—
164#103—1224no—
165#101—1221no—
166#100—1221no—
167#99—1221no—
168#99—1221no—
169#41—614no—
170#41—1222no—
171#41—1222no—
172#41—1222no—
173#41—1222no—
174#41—1228no—
175#41—1228no—
176#41—1222no—
177#41—1222no—
178#41—1228no—
179#41—1222no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—611no—
184C2×Q8—614no—
185C2×Q8—611no—
186C2×Q8—1221no—
187C2×Q8—1221no—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×Q8—1228no—
191C2×Q8—1222no—
192C2×Q8C2×#692311yescharacteristic
193C2×Q8C2×#692311yescharacteristic
194C2×D4—611no—
195C2×D4—611no—
196C2×D4—611no—
197C2×D4—611no—
198C2×D4—1221no—
199C2×D4—1221no—
200C2×D4—1221no—
201C22×C4—21no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C2×#692311yescharacteristic
210M16—1222no—
211M16—1222no—
212C2×C8—1222no—
213C4⋊C4—1222no—
214C22⋊C4—1222no—
215C42—1222no—
216C23—611no—
217C23—611no—
218C23—1221no—
219C23C22⋊#692311yescharacteristic
220Q8—24no—
221Q8—21no—
222Q8—21no—
223Q8—612no—
224Q8—1224no—
225Q8—1222no—
226Q8—1224no—
227Q8—1221no—
228Q8C22⋊#692312yes—
229Q8C22⋊#692312yes—
230D4—612no—
231D4—1222no—
232D4—1224no—
233D4—1224no—
234D4—1222no—
235D4—1222no—
236D4—1224no—
237D4—1221no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—611no—
244C2×C4—612no—
245C2×C4—612no—
246C2×C4—611no—
247C2×C4—1224no—
248C2×C4—1224no—
249C2×C4—1224no—
250C2×C4—1224no—
251C2×C4—1224no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—2442no—
256C2×C4C22⋊#692311yescharacteristic
257C2×C4C22×#692311yescharacteristic
258C8—2442no—
259C22—21no—
260C22—41no—
261C22—612no—
262C22—1222no—
263C22—1221no—
264C22—2441no—
265C22—2441no—
266C22—2442no—
267C22C2×C22⋊#692311yescharacteristic
268C4—22no—
269C4—22no—
270C4—21no—
271C4—612no—
272C4—1221no—
273C4—1222no—
274C4—4882no—
275C4C2×C22⋊#692311yescharacteristic
276C4C2×C22⋊#692311yescharacteristic
277C2—21no—
278C2—41no—
279C2—1222no—
280C2—2442no—
281C2—2441no—
282C2#1684070311yescharacteristic
subgroupG/H
centerC2#16840703
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×Q8×C61C4
socleC2×C61#379
hypercenterC22×Q8#6923
hypocenterC61#1796
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #16840761C2semidirect
2. #16840755C2semidirect
3. #16840748C2semidirect
4. #16840741C2semidirect
17. C2×#11758226C4semidirect
21. C2×#11758222C4semidirect
24. C2×Q8×D61C4semidirect
26. C22×Q8×C61C4semidirect
147. C61#1796semidirect
160. C22×Q8#6923semidirect