Finite Group Databasebeta

← #21461669

Subgroups — #21461669

Order 7808.

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

normal subgroups only

This group has 588 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#16840760C212yesmaximal, complemented
2#16840754C212yesmaximal, complemented
3#16840748C211yesmaximal, characteristic, complemented
4#16840741C211yesmaximal, characteristic, complemented
5C2×#14519822C211yesmaximal, characteristic
6D61⋊M16C2212yescomplemented
7#14519856C2212yescomplemented
8#14519841—24no—
9#14519839—24no—
10#14519838—21no—
11#14519837—21no—
12#14519836—21no—
13#14519835—21no—
14#14519822—24no—
15#14519822—24no—
16C2×#11758222C411yescharacteristic, complemented
17C2×#11758222C2211yescharacteristic
18C2×#11758224—21no—
19C2×#11758224C411yescharacteristic, complemented
20C2×#11758224C2211yescharacteristic
21C22×C22⋊D61—21no—
22C22×C22⋊D61—21no—
23C2×D4×D61—21no—
24C2×D4×D61C411yescharacteristic, complemented
25C2×D4×D61C2211yescharacteristic
26C22×D4×C61C411yescharacteristic, complemented
27C24×C61—21no—
28C23×D61—21no—
29C23×D61—21no—
30C2×D4×C61—22no—
31C2×D4×C61—22no—
32C2×D4×C61—21no—
33C2×D4×C61C2×C411yescharacteristic
34C2×D4×C61C2×C411yescharacteristic
35C22×C4×C61C2×C411yescharacteristic
36C2×C22⋊D61—28no—
37C2×C22⋊D61—28no—
38C2×C22⋊D61—21no—
39C2×C22⋊D61—21no—
40C2×C22⋊D61—21no—
41C2×C22⋊D61—21no—
42C2×C22⋊D61—21no—
43C2×C22⋊D61D411yescharacteristic
44C2×C22⋊D61D411yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—21no—
47#11758224—28no—
48#11758224—22no—
49#11758224—22no—
50#11758224—22no—
51#11758224D414yes—
52D4×D61—28no—
53D4×D61—22no—
54D4×D61—22no—
55D4×D61—22no—
56D4×D61D414yes—
57#11758222—22no—
58#11758222—22no—
59#11758222—22no—
60#11758222—22no—
61C2×D244C2×C411yescharacteristic
62C2×D244D411yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61C2×C411yescharacteristic
65C2×C4×D61C2311yescharacteristic
66C2×Dic122C2×C411yescharacteristic
67C2×Dic122D411yescharacteristic
68C22⋊#6923—22no—
69#11758217—22no—
70C4⋊#6923—22no—
71C4×#6923—22no—
72#11758213—22no—
73D61⋊C8—22no—
74C23×C61—24no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—82no—
78C23×C61C22⋊C411yescharacteristic
79C22×D61—21no—
80C22×D61—24no—
81C22×D61—24no—
82C22×D61—82no—
83C22×D61—82no—
84C22×D61C22⋊C411yescharacteristic
85C22×D61C2×D411yescharacteristic
86C2×#6923—42no—
87D4×C61—24no—
88D4×C61—21no—
89D4×C61—21no—
90D4×C61C22⋊C412yes—
91D4×C61C22⋊C412yes—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61C22⋊C411yescharacteristic
95C2×C4×C61C22×C411yescharacteristic
96C22⋊D61—24no—
97C22⋊D61—24no—
98C22⋊D61—24no—
99C22⋊D61—22no—
100C22⋊D61—24no—
101C22⋊D61—22no—
102C22⋊D61—24no—
103C2×Dic61—24no—
104C2×Dic61—21no—
105C2×Dic61—24no—
106C2×Dic61C22⋊C411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108D244—22no—
109D244—21no—
110D244C22⋊C412yes—
111C4×D61—24no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61C2×D412yes—
115C4×D61C2×D412yes—
116Dic122—21no—
117Dic122—22no—
118Dic122C22⋊C412yes—
119#92420—42no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—21no—
123C22×C61—41no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—84no—
127C22×C61C2×C22⋊C411yescharacteristic
128C2×D61—21no—
129C2×D61—22no—
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—41no—
133C2×D61—84no—
134C2×D61—84no—
135C2×D61#12012yes—
136#6923—82no—
137C4×C61—21no—
138C4×C61C2×C22⋊C411yescharacteristic
139C4×C61C2×C22⋊C411yescharacteristic
140Dic61—21no—
141Dic61—22no—
142Dic61#12012yes—
143#1795—611nomaximal, Sylow
144C2×C61—21no—
145C2×C61—42no—
146C2×C61—42no—
147C2×C61—41no—
148C2×C61#37911yescharacteristic
149D61—22no—
150D61—42no—
151D61—41no—
152C2×H(5,𝔽2)—611no—
153#421—612no—
154#418—612no—
155#413—611no—
156#410—611no—
157C61#179511yescharacteristic, complemented, Sylow
158H(5,𝔽2)—1224no—
159H(5,𝔽2)—1224no—
160C2×#41—611no—
161C2×#41—611no—
162C2×#41—611no—
163C2×#41—611no—
164C2×#41—1221no—
165C22×D4—611no—
166C22×D4—611no—
167C22×D4—1221no—
168C22×D4—1221no—
169C22×D4—1221no—
170C22×D4#692311yescharacteristic, complemented
171C2×M16—612no—
172#117—612no—
173#104—1224no—
174#102—1224no—
175#101—1221no—
176#100—1221no—
177#99—1221no—
178#99—1221no—
179C24—21no—
180C24—1221no—
181C24—1221no—
182#41—614no—
183#41—1222no—
184#41—1222no—
185#41—1222no—
186#41—1222no—
187#41—1222no—
188#41—1222no—
189#41—1228no—
190#41—1222no—
191C2×Q8—611no—
192C2×Q8—611no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—21no—
196C2×D4—614no—
197C2×D4—611no—
198C2×D4—611no—
199C2×D4—611no—
200C2×D4—611no—
201C2×D4—1222no—
202C2×D4—1221no—
203C2×D4—1221no—
204C2×D4—1222no—
205C2×D4—1228no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—1228no—
209C2×D4—1228no—
210C2×D4—1221no—
211C2×D4—1222no—
212C2×D4C2×#692311yescharacteristic
213C2×D4C2×#692311yescharacteristic
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4C2×#692311yescharacteristic
220M16—1222no—
221M16—1222no—
222C2×C8—1222no—
223C4⋊C4—1222no—
224C22⋊C4—1222no—
225C42—1222no—
226C23—24no—
227C23—21no—
228C23—21no—
229C23—82no—
230C23—611no—
231C23—611no—
232C23—1224no—
233C23—1224no—
234C23—1221no—
235C23—4882no—
236C23—4882no—
237C23C22⋊#692311yescharacteristic
238Q8—612no—
239Q8—1222no—
240Q8—1221no—
241D4—24no—
242D4—21no—
243D4—21no—
244D4—612no—
245D4—1222no—
246D4—1222no—
247D4—1224no—
248D4—1222no—
249D4—1224no—
250D4—1224no—
251D4—1224no—
252D4—1224no—
253D4—1221no—
254D4C22⋊#692312yes—
255D4C22⋊#692312yes—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—611no—
259C2×C4—612no—
260C2×C4—612no—
261C2×C4—611no—
262C2×C4—1224no—
263C2×C4—1224no—
264C2×C4—1224no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—2442no—
269C2×C4C22⋊#692311yescharacteristic
270C2×C4C22×#692311yescharacteristic
271C8—2442no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—84no—
279C22—612no—
280C22—1222no—
281C22—1221no—
282C22—4884no—
283C22—4884no—
284C22—2441no—
285C22—2441no—
286C22—2442no—
287C22C2×C22⋊#692311yescharacteristic
288C4—21no—
289C4—612no—
290C4—1221no—
291C4—1222no—
292C4—4882no—
293C4C2×C22⋊#692311yescharacteristic
294C4C2×C22⋊#692311yescharacteristic
295C2—21no—
296C2—42no—
297C2—42no—
298C2—41no—
299C2—1222no—
300C2—2442no—
301C2—2441no—
302C2#1684070311yescharacteristic
subgroupG/H
centerC2#16840703
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×D4×C61C4
socleC2×C61#379
hypercenterC22×D4#6923
hypocenterC61#1795
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840760C2semidirect
2. #16840754C2semidirect
3. #16840748C2semidirect
4. #16840741C2semidirect
6. D61⋊M16C22semidirect
7. #14519856C22semidirect
16. C2×#11758222C4semidirect
19. C2×#11758224C4semidirect
24. C2×D4×D61C4semidirect
26. C22×D4×C61C4semidirect
157. C61#1795semidirect
170. C22×D4#6923semidirect