Finite Group Databasebeta

← #21451746

Subgroups — #21451746

Order 7808.

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

normal subgroups only

This group has 576 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×#14519757C211yesmaximal, characteristic, complemented
2C2×#14519750C211yesmaximal, characteristic
3#16839704C212yesmaximal, complemented
4#16839688C211yesmaximal, characteristic, complemented
5#16839678C212yesmaximal, complemented
6#16839675C211yesmaximal, characteristic, complemented
7#16839674C211yesmaximal, characteristic, complemented
8#16839640C212yesmaximal, complemented
9#16839638C212yesmaximal, complemented
10#95×D61C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C22×C22⋊D61C2211yescharacteristic
16C22×C4×D61C2212yes—
17C22×C4×D61C2211yescharacteristic
18#14519757—24no—
19#14519750—24no—
20C2×C4⋊Dic61C2212yes—
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27#14519684C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—42no—
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C2×D244—22no—
53C2×D244—24no—
54C2×C4×D61—24no—
55C2×C4×D61—42no—
56C2×C4×D61—42no—
57C2×C4×D61—42no—
58C2×C4×D61D414yes—
59C2×Dic122—22no—
60C2×Dic122—42no—
61C4⋊C4×C61—22no—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—42no—
64C22⋊Dic61—42no—
65#11758198—24no—
66#11758198—22no—
67#11758198—42no—
68#11758198—42no—
69C4⋊Dic61—24no—
70#11758196—22no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61C2411yescharacteristic
77C22×D61—22no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—22no—
82C22×D61—21no—
83C22×D61—22no—
84C22×D61—21no—
85C22×D61C2×D412yes—
86C22×D61#4114yes—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C22⋊D61—44no—
98C22⋊D61—44no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61C2×D412yes—
109D244—44no—
110C4×D61—44no—
111C4×D61—48no—
112Dic122—44no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61C22×D411yescharacteristic
119C22×C61C2×#4112yes—
120C22×C61H(5,𝔽2)11yescharacteristic
121C22×C61H(5,𝔽2)12yes—
122C22×C612−1+411yescharacteristic
123C2×D61—22no—
124C2×D61—22no—
125C2×D61—24no—
126C2×D61—24no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61#12414yes—
133C4×C61—22no—
134C4×C61—41no—
135C4×C61—42no—
136C4×C61—42no—
137Dic61—22no—
138Dic61—41no—
139Dic61—42no—
140Dic61—42no—
141#2639—611nomaximal, Sylow
142C2×C61—81no—
143C2×C61C2×#12411yescharacteristic
144C2×C61#53411yescharacteristic
145C2×C61#53711yescharacteristic
146C2×C61#53812yes—
147C2×C61#53912yes—
148D61—24no—
149D61—81no—
150C2×C22⋊Q8—611no—
151C2×#121—611no—
152#400—612no—
153#397—611no—
154#397D6111yescharacteristic, complemented
155#394—612no—
156#393—611no—
157#393—611no—
158#386—612no—
159#386—612no—
160C2×#95—611no—
161C61#263911yescharacteristic, complemented, Sylow
162C22×Q8—611no—
163C22×D4—611no—
164C22×D4—611no—
165C22×D4—611no—
166C23×C4—611no—
167C23×C4—612no—
168C22⋊Q8—1224no—
169#121—1224no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—612no—
172C2×C4⋊C4C2×D6111yescharacteristic
173C2×C22⋊C4—611no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4C2×D6111yescharacteristic
179C2×C22⋊C4C2×D6112yes—
180#95—611no—
181#95—612no—
182#95—612no—
183#95—612no—
184#95—612no—
185#95C2×D6111yescharacteristic
186#95C2×D6112yes—
187C24—611no—
188C24—611no—
189C24C22×D6111yescharacteristic
190C2×Q8—1222no—
191C2×Q8—2442no—
192C2×D4—1222no—
193C2×D4—1224no—
194C2×D4—1222no—
195C2×D4—1222no—
196C2×D4—1224no—
197C2×D4—2442no—
198C22×C4—611no—
199C22×C4—614no—
200C22×C4—612no—
201C22×C4—611no—
202C22×C4—612no—
203C22×C4—1224no—
204C22×C4—2442no—
205C22×C4—2442no—
206C22×C4—2442no—
207C22×C4C22×D6112yes—
208C22×C4C22×D6111yescharacteristic
209C22×C4C22×D6112yes—
210C22×C4C22×D6111yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—1222no—
213C4⋊C4—1224no—
214C22⋊C4—22no—
215C22⋊C4—42no—
216C22⋊C4—1224no—
217C22⋊C4—1222no—
218C22⋊C4—2442no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—22no—
225C23—21no—
226C23—612no—
227C23—614no—
228C23—1221no—
229C23—1222no—
230C23—1221no—
231C23—1221no—
232C23—1222no—
233C23—1221no—
234C23—1222no—
235C23—1221no—
236C23C23×D6111yescharacteristic
237Q8—2444no—
238D4—2444no—
239D4—2444no—
240D4—2444no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—612no—
251C2×C4—1222no—
252C2×C4—1221no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—2444no—
261C2×C4—2448no—
262C2×C4D4×D6112yes—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—42no—
268C22—614no—
269C22—1222no—
270C22—1222no—
271C22—1224no—
272C22—1224no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22—2442no—
277C22—2442no—
278C22C2×D4×D6111yescharacteristic
279C22#41×D6112yes—
280C22#1451982211yescharacteristic
281C22#1451982312yes—
282C22#1451982411yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—42no—
287C4—1222no—
288C4—2441no—
289C4—2442no—
290C4—2442no—
291C2—81no—
292C2—1224no—
293C2—4881no—
294C2#124×D6111yescharacteristic
295C2#1684032311yescharacteristic
296C2#1684034111yescharacteristic
297C2#1684034812yes—
298C2#1684035312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2639
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
3. #16839704C2semidirect
4. #16839688C2semidirect
5. #16839678C2semidirect
6. #16839675C2semidirect
7. #16839674C2semidirect
8. #16839640C2semidirect
9. #16839638C2semidirect
10. #95×D61C2semidirect
11. C61×#397C2semidirect
154. #397D61semidirect
161. C61#2639semidirect