Finite Group Databasebeta

← #21461832

Subgroups — #21461832

Order 7808.

380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×D61⋊C8C211yesmaximal, characteristic
2C2×#14519840C212yesmaximal, complemented
3#16840704C211yesmaximal, characteristic
4#16840635C212yesmaximal, complemented
5C22⋊Q8×D61C211yesmaximal, characteristic
6C2×D61⋊C8—21no—
7C2×D61⋊C8—24no—
8C2×D61⋊C8C2212yes—
9C22×#92420—21no—
10C2×C4⋊#6923C2212yes—
11C2×C22⋊#6923—21no—
12#14519840—24no—
13(C2×#6923)⋊C4—21no—
14C2×Q8×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519757C411yescharacteristic, complemented
17#14519756C411yescharacteristic, complemented
18#14519755—21no—
19#14519754—21no—
20#14519753C411yescharacteristic, complemented
21C4⋊C4×D61—21no—
22C4⋊C4×D61C2211yescharacteristic
23C22⋊C4×D61—21no—
24C22⋊Q8×C61C411yescharacteristic, complemented
25C23×D61D411yescharacteristic
26C22×#6923—22no—
27C2×Q8×C61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C22×Dic61D411yescharacteristic
30Q8×D61—22no—
31Q8×D61—22no—
32C2×C4×D61—22no—
33C2×C4×D61—22no—
34C2×C4×D61—21no—
35C2×C4×D61—21no—
36C2×C4×D61C2×C411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61C2311yescharacteristic
40C2×Dic122—21no—
41C2×Dic122C2×C411yescharacteristic
42C22⋊#6923—42no—
43C2×#92420—24no—
44C2×#92420—22no—
45C4⋊#6923—22no—
46C4⋊#6923—22no—
47D61⋊C8—24no—
48D61⋊C8—22no—
49D61⋊C8D414yes—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2×C411yescharacteristic
52C22⋊C4×C61—21no—
53C22⋊Dic61—21no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61C2×C411yescharacteristic
58#11758196—21no—
59#11758196—21no—
60#11758196—21no—
61C23×C61C22⋊C411yescharacteristic
62C22×D61—22no—
63C22×D61—22no—
64C22×D61C22⋊C411yescharacteristic
65C22×D61SD1612yes—
66C22×D61Q1612yes—
67C22×D61C2×D411yescharacteristic
68C2×#6923—42no—
69C2×#6923—42no—
70C2×#6923—42no—
71Q8×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61C22⋊C411yescharacteristic
76C2×C4×C61C22×C411yescharacteristic
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61C22⋊C411yescharacteristic
82C2×Dic61C2×D411yescharacteristic
83C4×D61—22no—
84C4×D61—22no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—42no—
88C4×D61—42no—
89C4×D61C2×D412yes—
90C4×D61#4112yes—
91Dic122—22no—
92Dic122—41no—
93Dic122—41no—
94#92420—24no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61#10312yescomplemented
98C22×C61C2×C22⋊C411yescharacteristic
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—24no—
102C2×D61—24no—
103C2×D61#10312yescomplemented
104C2×D61#12112yes—
105C2×D61C2×SD1611yescharacteristic
106C2×D61C2×Q1611yescharacteristic
107C2×D61#13512yes—
108#6923—82no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—41no—
112C4×C61C4×D412yes—
113Dic61—21no—
114Dic61—41no—
115Dic61—41no—
116Dic61#12011yescharacteristic
117Dic61#12311yescharacteristic
118#1892—611nomaximal, Sylow
119C2×C61—22no—
120C2×C61#38611yescharacteristic
121C2×C61C2×#10311yescharacteristic
122C2×C61#41611yescharacteristic
123D61—22no—
124D61#46512yes—
125D61#46712yes—
126C23×C8—611no—
127C2×C22⋊Q8—611no—
128C2×#103—612no—
129#380—611no—
130#340—612no—
131C61#189211yescharacteristic, complemented, Sylow
132C22×Q8—611no—
133C23×C4—611no—
134C22×C8—612no—
135C22×C8—1224no—
136C22×C8—1221no—
137C22×C8—1221no—
138C22⋊Q8—611no—
139C22⋊Q8—611no—
140C22⋊Q8—611no—
141C22⋊Q8—1221no—
142C22⋊Q8—1221no—
143C22⋊Q8#692311yescharacteristic, complemented
144C2×C4⋊C4—611no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—1221no—
147C2×C22⋊C4—1221no—
148C2×C22⋊C4—1221no—
149#103—1224no—
150#95—1221no—
151C24—611no—
152C2×Q8—611no—
153C2×Q8—1221no—
154C2×Q8—1222no—
155C2×Q8—1222no—
156C2×Q8C2×#692311yescharacteristic
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1222no—
163C22×C4—1222no—
164C22×C4—1221no—
165C22×C4—1221no—
166C22×C4—1222no—
167C22×C4C2×#692311yescharacteristic
168C2×C8—614no—
169C2×C8—1222no—
170C2×C8—1222no—
171C2×C8—1224no—
172C2×C8—1224no—
173C4⋊C4—21no—
174C4⋊C4—611no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1221no—
181C4⋊C4C2×#692311yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—1221no—
184C22⋊C4—1221no—
185C22⋊C4—1221no—
186C22⋊C4—2442no—
187C23—611no—
188C23—612no—
189C23—612no—
190C23—611no—
191C23—1222no—
192C23—1222no—
193C23C22⋊#692311yescharacteristic
194Q8—22no—
195Q8—1222no—
196Q8—2441no—
197Q8—2441no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—611no—
202C2×C4—612no—
203C2×C4—612no—
204C2×C4—611no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4C22⋊#692311yescharacteristic
219C2×C4C22×#692311yescharacteristic
220C8—1224no—
221C22—21no—
222C22—21no—
223C22—612no—
224C22—611no—
225C22—611no—
226C22—612no—
227C22—612no—
228C22—1224no—
229C22—1224no—
230C22—1221no—
231C22—1221no—
232C22#1451984012yescomplemented
233C22C2×C22⋊#692311yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—611no—
238C4—611no—
239C4—1221no—
240C4—4882no—
241C4—2441no—
242C4—2441no—
243C4D4×#692312yes—
244C2—22no—
245C2—612no—
246C2—612no—
247C2—1222no—
248C2#1684071011yescharacteristic
249C2C2×#1451984011yescharacteristic
250C2#1684075211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14519840C2semidirect
4. #16840635C2semidirect
16. #14519757C4semidirect
17. #14519756C4semidirect
20. #14519753C4semidirect
24. C22⋊Q8×C61C4semidirect
97. C22×C61#103semidirect
103. C2×D61#103semidirect
131. C61#1892semidirect
143. C22⋊Q8#6923semidirect
232. C22#14519840semidirect