Finite Group Databasebeta

← #21446953

Subgroups — #21446953

Order 7808.

326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519698C211yesmaximal, characteristic
3#16839665C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×Dic122—21no—
9C22×#92418C2211yescharacteristic
10#14519776—22no—
11#14519776—22no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C22⋊Dic61—21no—
16C2×C22⋊Dic61—21no—
17C2×C4×Dic61C2211yescharacteristic
18#14519698—22no—
19C22×D4×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22#102×C61—22no—
23C24×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61Q812yescomplemented
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61D411yescharacteristic
35C22×Dic61D411yescharacteristic
36C2×Dic122—24no—
37C2×Dic122—42no—
38C2×Dic122—42no—
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61D412yes—
44C22⋊Dic61—42no—
45C22⋊Dic61—42no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61D412yes—
50#11758196—24no—
51C4×Dic61—21no—
52C4×Dic61—21no—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C23×C61—22no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61C2×D411yescharacteristic
64D4×C61—22no—
65D4×C61—22no—
66D4×C61—41no—
67D4×C61—41no—
68C2×C4×C61—22no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×Q811yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—22no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61D812yes—
88C2×Dic61SD1612yes—
89Dic122—48no—
90C8×C61—41no—
91#92418—41no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—81no—
96C22×C61—81no—
97C22×C61—81no—
98C22×C61—81no—
99C22×C61#12011yescharacteristic
100C22×C61C22⋊Q811yescharacteristic
101C22×C61#12411yescharacteristic
102C22×C61C2×D811yescharacteristic
103C22×C61C2×SD1611yescharacteristic
104C22×C61AGL(1,ℤ/8)11yescharacteristic
105C22×C61#13711yescharacteristic
106C4×C61—42no—
107C4×C61C22⋊Q811yescharacteristic
108C4×C61C22⋊Q811yescharacteristic
109C4×C61#12411yescharacteristic
110C4×C61#12411yescharacteristic
111Dic61—22no—
112Dic61—22no—
113Dic61—42no—
114Dic61—81no—
115#2023—611nomaximal, Sylow
116C2×C61—82no—
117C2×C61#39311yescharacteristic
118C2×C61#44711yescharacteristic
119C2×C61#44811yescharacteristic
120C2×C61#47411yescharacteristic
121C2×C61#47611yescharacteristic
122C2×C61#48611yescharacteristic
123C2×C61#48911yescharacteristic
124C2×C4⋊Q8—611no—
125C2×#102—611no—
126C2×#102D6111yescharacteristic
127#390—611no—
128#340—611no—
129#340—611no—
130#336—611no—
131C61#202311yescharacteristic, complemented, Sylow
132C22×Q8—1221no—
133C22×D4C2×D6111yescharacteristic
134C22×C8—611no—
135C22×C8C2×D6111yescharacteristic
136C4⋊Q8—1222no—
137C4⋊Q8—1222no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—611no—
140C2×C4⋊C4—1221no—
141C2×C4⋊C4C2×D6111yescharacteristic
142C2×C22⋊C4—1221no—
143C2×C22⋊C4—1221no—
144C2×C42—611no—
145#102—22no—
146#102—1222no—
147C24—21no—
148C2×Q8—1224no—
149C2×Q8—2442no—
150C2×Q8—2442no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4Dic12212yescomplemented
157C22×C4—21no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—1221no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1221no—
167C2×C8—1221no—
168C2×C8—1221no—
169C4⋊C4—21no—
170C4⋊C4—612no—
171C4⋊C4—1224no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C4⋊C4C22⋊D6112yes—
176C22⋊C4—2442no—
177C22⋊C4—2442no—
178C42—1221no—
179C42—1221no—
180C23—22no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23D4×D6111yescharacteristic
188Q8—2448no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—612no—
197C2×C4—612no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4C2×Dic12211yescharacteristic
209C2×C4#1175822211yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4#1175822411yescharacteristic
212C2×C4#1175822411yescharacteristic
213C2×C4C2×C22⋊D6111yescharacteristic
214C8—41no—
215C8—2441no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22—81no—
223C22#1451974511yescharacteristic
224C22#1451975411yescharacteristic
225C22#1451976311yescharacteristic
226C22D8×D6111yescharacteristic
227C22SD16×D6111yescharacteristic
228C22#1451980111yescharacteristic
229C22#1451980611yescharacteristic
230C4—42no—
231C4—1222no—
232C4—1222no—
233C4—4881no—
234C4—2442no—
235C4#1451975411yescharacteristic
236C4#1451975611yescharacteristic
237C4#1451976311yescharacteristic
238C4#1451976411yescharacteristic
239C2—82no—
240C2#1683967411yescharacteristic
241C2#1683989411yescharacteristic
242C2#1683989911yescharacteristic
243C2#1684004011yescharacteristic
244C2#1684005011yescharacteristic
245C2#1684010711yescharacteristic
246C2#1684012011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#2023
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
4. #16839525C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
29. C2×D4×C61Q8semidirect
131. C61#2023semidirect
156. C2×D4Dic122semidirect