Finite Group Databasebeta

← #21451947

Subgroups — #21451947

Order 7808.

598 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519751C211yesmaximal, characteristic, complemented
2#16839692C211yesmaximal, characteristic, complemented
3#16839687C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839677C212yesmaximal, complemented
6#16839671C211yesmaximal, characteristic, complemented
7#16839670C212yesmaximal, complemented
8#16839662C212yesmaximal, complemented
9#16839652C212yesmaximal, complemented
10C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
11C2×#123×C61C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C22⋊D61C2212yes—
15#14519751—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29C22×D4×C61C2211yescharacteristic
30C23×C4×C61C2211yescharacteristic
31#123×C61—24no—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C24×C61C2311yescharacteristic
39C23×D61C2312yes—
40C2×D4×C61—22no—
41C2×D4×C61—42no—
42C22×C4×C61—42no—
43C22×C4×C61D414yescomplemented
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—24no—
50C2×C22⋊D61—24no—
51C2×C22⋊D61—42no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—42no—
54C2×C22⋊D61—42no—
55C22×Dic61C2312yes—
56C22×Dic61C2312yes—
57C22×Dic61C2312yes—
58C2×D244—22no—
59C2×D244—42no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C22⋊C4×C61—22no—
65C22⋊Dic61—24no—
66C22⋊Dic61—42no—
67#11758198—24no—
68#11758198—24no—
69#11758198—42no—
70#11758198—42no—
71C4⋊Dic61—22no—
72#11758196—42no—
73C4×Dic61—42no—
74C23×C61—22no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—22no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—22no—
83C23×C61C2×D412yes—
84C23×C61C2411yescharacteristic
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92D4×C61—44no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—44no—
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D412yes—
105C22⋊D61—48no—
106C22⋊D61—48no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61#4114yes—
116D244—44no—
117C22×C61—22no—
118C22×C61—22no—
119C22×C61—22no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61C22×D411yescharacteristic
128C22×C61C2×#4112yes—
129C22×C61H(5,𝔽2)12yes—
130C22×C61H(5,𝔽2)11yescharacteristic
131C22×C61H(5,𝔽2)11yescharacteristic
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144Dic61—24no—
145Dic61—42no—
146Dic61—42no—
147#2661—611nomaximal, Sylow
148C2×C61—42no—
149C2×C61—81no—
150C2×C61#53211yescharacteristic
151C2×C61#53411yescharacteristic
152C2×C61#53511yescharacteristic
153C2×C61#53812yes—
154C2×C61#54012yes—
155D61—82no—
156C2×#123D6111yescharacteristic, complemented
157C2×#121—611no—
158#398—611no—
159#397—611no—
160#394—611no—
161#394—612no—
162#392—612no—
163#392—611no—
164#390—612no—
165#388—612no—
166C4×C22⋊C4—611no—
167C61#266111yescharacteristic, complemented, Sylow
168C22×D4—612no—
169C22×D4—612no—
170C22×D4—611no—
171C22×D4C2×D6111yescharacteristic
172C23×C4C2×D6111yescharacteristic
173#123—24no—
174#121—1224no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—612no—
177C2×C4⋊C4C2×D6111yescharacteristic
178C2×C4⋊C4C2×D6111yescharacteristic
179C2×C22⋊C4—612no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4C2×D6111yescharacteristic
186C2×C22⋊C4C2×D6111yescharacteristic
187C2×C22⋊C4C2×D6111yescharacteristic
188C2×C42—612no—
189#95—611no—
190#95—611no—
191#95—612no—
192#95—612no—
193C24—612no—
194C24C22×D6111yescharacteristic
195C24C22×D6111yescharacteristic
196C2×D4—22no—
197C2×D4—42no—
198C2×D4—1224no—
199C2×D4—1224no—
200C2×D4—1222no—
201C2×D4—2442no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2442no—
205C2×D4—2442no—
206C22×C4—42no—
207C22×C4—612no—
208C22×C4—612no—
209C22×C4—612no—
210C22×C4C22⋊D6114yescomplemented
211C22×C4C22×D6111yescharacteristic
212C22×C4C22×D6111yescharacteristic
213C22×C4C22×D6111yescharacteristic
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—1222no—
219C4⋊C4—2442no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—1224no—
224C22⋊C4—1224no—
225C22⋊C4—1224no—
226C22⋊C4—2442no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C42—2442no—
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—21no—
239C23—1222no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23C2×C22⋊D6112yes—
247C23C23×D6111yescharacteristic
248D4—44no—
249D4—2444no—
250D4—2448no—
251D4—2448no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—44no—
262C2×C4—614no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4C2×C22⋊D6112yes—
272C2×C4C2×C22⋊D6112yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—42no—
282C22—42no—
283C22—2442no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22C22×C22⋊D6111yescharacteristic
291C22#41×D6112yes—
292C22#1451982212yes—
293C22#1451982311yescharacteristic
294C22#1451982311yescharacteristic
295C4—22no—
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—1224no—
301C4—2442no—
302C4—2442no—
303C2—42no—
304C2—81no—
305C2—4882no—
306C2#1684030811yescharacteristic
307C2#1684032111yescharacteristic
308C2#1684032611yescharacteristic
309C2#1684034812yes—
310C2#1684036412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#123×C61C2
hypercenterC2×#123D61
hypocenterC61#2661
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. #16839692C2semidirect
3. #16839687C2semidirect
4. #16839679C2semidirect
5. #16839677C2semidirect
6. #16839671C2semidirect
7. #16839670C2semidirect
8. #16839662C2semidirect
9. #16839652C2semidirect
10. C4×C22⋊Dic61C2semidirect
11. C2×#123×C61C2semidirect
43. C22×C4×C61D4semidirect
156. C2×#123D61semidirect
167. C61#2661semidirect
210. C22×C4C22⋊D61semidirect