Finite Group Databasebeta

← #21452835

Subgroups — #21452835

Order 7808.

528 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519755C212yesmaximal, complemented
2#16839697C212yesmaximal, complemented
3#16839696C212yesmaximal, complemented
4#16839684C212yesmaximal, complemented
5#16839668C211yesmaximal, characteristic, complemented
6#16839664C211yesmaximal, characteristic
7#16839640C212yesmaximal
8#16839633C212yesmaximal, complemented
9C61×#389C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519755—28no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C42×C61C2211yescharacteristic
31#95×C61C2212yes—
32C23×D61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×D244—41no—
42C2×D244—41no—
43C2×D244Q814yescomplemented
44C2×C4×D61—24no—
45C2×C4×D61—42no—
46C2×C4×D61—42no—
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×Dic122D414yescomplemented
50C4⋊C4×C61—24no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—41no—
53C42×C61—41no—
54#11758198—24no—
55#11758198—24no—
56#11758198—24no—
57#11758198—42no—
58#11758198—42no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61#11758196—24no—
62#11758196—24no—
63#11758196—42no—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61C2×Q814yes—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×Q812yes—
86C2×C4×C61#4112yes—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61C2×D414yes—
96D244—44no—
97C4×D61—48no—
98Dic122—44no—
99C22×C61C22×D411yescharacteristic
100C22×C61C22×Q811yescharacteristic
101C22×C61C2×#4111yescharacteristic
102C22×C61H(5,𝔽2)11yescharacteristic
103C22×C61H(5,𝔽2)11yescharacteristic
104C22×C61H(5,𝔽2)11yescharacteristic
105C22×C612−1+411yescharacteristic
106C2×D61—24no—
107C2×D61—24no—
108C2×D61—24no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—22no—
116C4×C61—42no—
117C4×C61—42no—
118Dic61—24no—
119Dic61—42no—
120Dic61—42no—
121#2732—611nomaximal, Sylow
122C2×C61#53411yescharacteristic
123C2×C61#53911yescharacteristic
124C2×C61#54311yescharacteristic
125C2×C61D4×Q811yescharacteristic
126C2×C61#55011yescharacteristic
127C2×C61#55411yescharacteristic
128C2×C61#56211yescharacteristic
129D61—44no—
130C2×C22⋊Q8—612no—
131#399—612no—
132#398—612no—
133#396—612no—
134#391—611no—
135#390—611no—
136#389D6111yescharacteristic, complemented
137#386—612no—
138#385—612no—
139C61#273211yescharacteristic, complemented, Sylow
140C22×Q8—611no—
141C22×D4—611no—
142C23×C4—612no—
143C22⋊Q8—1228no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4C2×D6112yes—
150C2×C4⋊C4C2×D6111yescharacteristic
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C42C2×D6111yescharacteristic
158#95—612no—
159#95—612no—
160#95—612no—
161#95C2×D6112yes—
162C24—612no—
163C2×Q8—614no—
164C2×Q8—2441no—
165C2×Q8—2441no—
166C2×D4—614no—
167C2×D4—2441no—
168C2×D4—2441no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4—1224no—
173C22×C4—2442no—
174C22×C4—2442no—
175C22×C4C22×D6112yes—
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6111yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—41no—
183C4⋊C4—1224no—
184C4⋊C4—1224no—
185C4⋊C4—2442no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C22⋊C4—1224no—
189C22⋊C4—1224no—
190C22⋊C4—1224no—
191C22⋊C4—2442no—
192C22⋊C4—2442no—
193C42—41no—
194C23—614no—
195C23—1222no—
196C23—1222no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23—1222no—
201C23C23×D6111yescharacteristic
202Q8—2444no—
203D4—2444no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—614no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—2448no—
226C2×C4#1175822212yes—
227C2×C4D4×D6112yes—
228C2×C4Q8×D6112yes—
229C22—1224no—
230C22—1224no—
231C22—1224no—
232C22—2442no—
233C22—2442no—
234C22—2442no—
235C22—2442no—
236C22C2×D4×D6111yescharacteristic
237C22C2×Q8×D6111yescharacteristic
238C22C2×#1175822211yescharacteristic
239C22#1451982211yescharacteristic
240C22#1451982311yescharacteristic
241C22#1451982311yescharacteristic
242C22#1451982511yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—42no—
247C4—42no—
248C4—1224no—
249C4—2442no—
250C4—2442no—
251C2—2444no—
252C2#1684032011yescharacteristic
253C2#1684035911yescharacteristic
254C2#1684038711yescharacteristic
255C2#1684042711yescharacteristic
256C2#1684043311yescharacteristic
257C2#1684047211yescharacteristic
258C2#1684051011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2732
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
2. #16839697C2semidirect
3. #16839696C2semidirect
4. #16839684C2semidirect
5. #16839668C2semidirect
8. #16839633C2semidirect
9. C61×#389C2semidirect
43. C2×D244Q8semidirect
49. C2×Dic122D4semidirect
136. #389D61semidirect
139. C61#2732semidirect