Finite Group Databasebeta

← #21453819

Subgroups — #21453819

Order 7808.

578 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519760C211yesmaximal, characteristic, complemented
2#16839700C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic, complemented
4#16839685C212yesmaximal, complemented
5#16839678C212yesmaximal, complemented
6#16839676C211yesmaximal, characteristic, complemented
7#16839676C212yesmaximal, complemented
8#16839670C212yesmaximal, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839622C211yesmaximal, characteristic, complemented
11C2×#121×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14#14519760—24no—
15C2×C4⋊Dic61C2212yes—
16C2×#11758196C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2211yescharacteristic
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27#14519684C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31C22×D4×C61C2212yes—
32C22×D4×C61C2211yescharacteristic
33C23×C4×C61C2211yescharacteristic
34#121×C61—24no—
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2212yes—
37C24×C61C2312yes—
38C24×C61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C2×D4×C61—24no—
41C2×D4×C61—22no—
42C2×D4×C61—42no—
43C2×D4×C61—42no—
44C2×D4×C61—42no—
45C22×C4×C61—42no—
46C22×C4×C61D414yescomplemented
47C22×C4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—22no—
51C2×C22⋊D61—42no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—42no—
54C2×C22⋊D61—42no—
55C22×Dic61C2312yes—
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2311yescharacteristic
58C22×Dic61C2312yes—
59C22×Dic61C2311yescharacteristic
60C4⋊C4×C61—22no—
61C22⋊C4×C61—24no—
62C22⋊Dic61—22no—
63C22⋊Dic61—42no—
64C22⋊Dic61—42no—
65C22⋊Dic61—42no—
66C22⋊Dic61—42no—
67#11758198—22no—
68#11758198—22no—
69#11758198—42no—
70C4⋊Dic61—42no—
71#11758196—22no—
72#11758196—22no—
73#11758196—42no—
74C23×C61—21no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—21no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61C2×D412yes—
86C23×C61C2411yescharacteristic
87C22×D61—21no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—21no—
91C22×D61—21no—
92D4×C61—44no—
93D4×C61—48no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—44no—
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2×D412yes—
102C22⋊D61—44no—
103C22⋊D61—48no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—21no—
117C22×C61—22no—
118C22×C61—22no—
119C22×C61—22no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61C22×D411yescharacteristic
130C22×C61H(5,𝔽2)12yes—
131C22×C61H(5,𝔽2)12yes—
132C22×C61H(5,𝔽2)11yescharacteristic
133C22×C612−1+411yescharacteristic
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—42no—
142Dic61—41no—
143Dic61—41no—
144Dic61—41no—
145Dic61—42no—
146Dic61—42no—
147#2813—611nomaximal, Sylow
148C2×C61—42no—
149C2×C61—82no—
150C2×C61#53411yescharacteristic
151C2×C61#53511yescharacteristic
152C2×C61#53711yescharacteristic
153C2×C61#56012yes—
154C2×C61#56212yes—
155D61—81no—
156C2×#123—611no—
157C2×#121D6111yescharacteristic, complemented
158#400—611no—
159#399—611no—
160#396—612no—
161#394—611no—
162#394—612no—
163#394—612no—
164#392—611no—
165#392—612no—
166#380—611no—
167C61#281311yescharacteristic, complemented, Sylow
168C22×D4—611no—
169C22×D4—612no—
170C22×D4C2×D6112yes—
171C22×D4C2×D6111yescharacteristic
172C23×C4C2×D6111yescharacteristic
173#123—1224no—
174#121—24no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4C2×D6111yescharacteristic
180C2×C22⋊C4—611no—
181C2×C22⋊C4—611no—
182C2×C22⋊C4—611no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4—612no—
188C2×C22⋊C4C2×D6112yes—
189#95—611no—
190#95—611no—
191#95—612no—
192#95—612no—
193C24—611no—
194C24C22×D6112yes—
195C24C22×D6111yescharacteristic
196C2×D4—24no—
197C2×D4—22no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—1222no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2442no—
205C2×D4—2442no—
206C22×C4—42no—
207C22×C4—612no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—612no—
211C22×C4—611no—
212C22×C4C22⋊D6114yescomplemented
213C22×C4C22×D6112yes—
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—1222no—
218C4⋊C4—1222no—
219C4⋊C4—2442no—
220C4⋊C4—2442no—
221C22⋊C4—24no—
222C22⋊C4—1222no—
223C22⋊C4—1222no—
224C22⋊C4—1222no—
225C22⋊C4—2442no—
226C22⋊C4—2442no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C22⋊C4—2442no—
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—1221no—
242C23—1222no—
243C23—1222no—
244C23—1221no—
245C23—1221no—
246C23C2×C22⋊D6112yes—
247C23C23×D6111yescharacteristic
248D4—44no—
249D4—48no—
250D4—2444no—
251D4—2448no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—1221no—
271C2×C4C2×C22⋊D6112yes—
272C2×C4C2×C22⋊D6112yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—2442no—
286C22—2442no—
287C22—2441no—
288C22—2441no—
289C22—2441no—
290C22C22×C22⋊D6111yescharacteristic
291C22#1451982212yes—
292C22#1451982212yes—
293C22#1451982311yescharacteristic
294C22#1451982411yescharacteristic
295C4—22no—
296C4—22no—
297C4—42no—
298C4—2442no—
299C4—2442no—
300C4—2441no—
301C4—2441no—
302C4—2441no—
303C2—42no—
304C2—82no—
305C2—4881no—
306C2#1684032111yescharacteristic
307C2#1684032911yescharacteristic
308C2#1684034011yescharacteristic
309C2#1684050012yes—
310C2#1684050712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2813
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519760C2semidirect
2. #16839700C2semidirect
3. #16839697C2semidirect
4. #16839685C2semidirect
5. #16839678C2semidirect
6. #16839676C2semidirect
7. #16839676C2semidirect
8. #16839670C2semidirect
9. #16839670C2semidirect
10. #16839622C2semidirect
11. C2×#121×C61C2semidirect
46. C22×C4×C61D4semidirect
157. C2×#121D61semidirect
167. C61#2813semidirect
212. C22×C4C22⋊D61semidirect