Finite Group Databasebeta

← #21453840

Subgroups — #21453840

Order 7808.

644 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519750C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3#16839690C212yesmaximal, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839687C211yesmaximal, characteristic, complemented
6#16839671C212yesmaximal, complemented
7#16839670C212yesmaximal, complemented
8#16839670C212yesmaximal, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839624C211yesmaximal, characteristic, complemented
11C61×#392C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C22⋊D61C2211yescharacteristic
15C22×C22⋊D61C2211yescharacteristic
16C22×C22⋊D61C2212yes—
17C22×C4×D61C2211yescharacteristic
18#14519750—24no—
19#14519748—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×C22⋊Dic61C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C22×D4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C24×C61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C2×D4×C61—22no—
42C2×D4×C61—42no—
43C2×D4×C61—42no—
44C2×D4×C61—42no—
45C2×D4×C61—42no—
46C22×C4×C61C2311yescharacteristic
47C22×C4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—24no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—42no—
54C2×C22⋊D61—42no—
55C2×C22⋊D61—42no—
56C2×C22⋊D61—42no—
57C2×C22⋊D61—42no—
58C2×C22⋊D61—42no—
59C22×Dic61C2312yes—
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2312yes—
62C22×Dic61C2311yescharacteristic
63C2×D244—22no—
64C2×D244—42no—
65C2×C4×D61—42no—
66C2×C4×D61D414yescomplemented
67C22⋊C4×C61—22no—
68C22⋊C4×C61—42no—
69C22⋊Dic61—24no—
70C22⋊Dic61—42no—
71C22⋊Dic61—42no—
72#11758198—22no—
73#11758198—42no—
74#11758198—42no—
75C4⋊Dic61—22no—
76#11758196—22no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—22no—
88C23×C61—21no—
89C23×C61C2411yescharacteristic
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—22no—
97C22×D61—22no—
98C22×D61—21no—
99C22×D61C2×D412yes—
100D4×C61—44no—
101D4×C61—48no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—22no—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61C2×D412yes—
109C22⋊D61—44no—
110C22⋊D61—44no—
111C22⋊D61—48no—
112C22⋊D61—48no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61C2×D412yes—
123D244—44no—
124C4×D61—44no—
125C22×C61—41no—
126C22×C61—42no—
127C22×C61—41no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—41no—
131C22×C61—42no—
132C22×C61—42no—
133C22×C61—42no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61—42no—
137C22×C61C22×D411yescharacteristic
138C22×C61H(5,𝔽2)12yes—
139C22×C61H(5,𝔽2)12yes—
140C22×C61H(5,𝔽2)11yescharacteristic
141C22×C61H(5,𝔽2)11yescharacteristic
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—42no—
146C2×D61—42no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—42no—
151C2×D61—42no—
152C4×C61—22no—
153C4×C61—41no—
154C4×C61—42no—
155Dic61—22no—
156Dic61—41no—
157Dic61—42no—
158Dic61—42no—
159#2815—611nomaximal, Sylow
160C2×C61—81no—
161C2×C61—82no—
162C2×C61#53411yescharacteristic
163C2×C61#53511yescharacteristic
164C2×C61#53511yescharacteristic
165C2×C61#56012yes—
166C2×C61#56012yes—
167D61—42no—
168D61—81no—
169C2×#121—611no—
170C2×#121—611no—
171#397—611no—
172#397—612no—
173#397—611no—
174#392—612no—
175#392—611no—
176#392—612no—
177#392—612no—
178#392D6111yescharacteristic, complemented
179#381—611no—
180C61#281511yescharacteristic, complemented, Sylow
181C22×D4—611no—
182C22×D4—612no—
183C22×D4—611no—
184C22×D4—612no—
185C22×D4—611no—
186C22×D4C2×D6111yescharacteristic
187C22×D4C2×D6112yes—
188C23×C4—611no—
189#121—1224no—
190#121—1224no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C22⋊C4—612no—
194C2×C22⋊C4—611no—
195C2×C22⋊C4—612no—
196C2×C22⋊C4—612no—
197C2×C22⋊C4—612no—
198C2×C22⋊C4—612no—
199C2×C22⋊C4C2×D6111yescharacteristic
200C2×C22⋊C4C2×D6112yes—
201#95—612no—
202#95—611no—
203#95—612no—
204#95—612no—
205#95C2×D6111yescharacteristic
206C24—611no—
207C24—611no—
208C24C22×D6111yescharacteristic
209C24C22×D6112yes—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—1222no—
216C2×D4—1222no—
217C2×D4—1222no—
218C2×D4—1224no—
219C2×D4—2442no—
220C2×D4—2442no—
221C2×D4—2442no—
222C2×D4—2442no—
223C2×D4—2442no—
224C2×D4—2442no—
225C2×D4—2442no—
226C2×D4—2442no—
227C22×C4—611no—
228C22×C4—614no—
229C22×C4—612no—
230C22×C4—611no—
231C22×C4—612no—
232C22×C4—2442no—
233C22×C4C22×D6112yes—
234C22×C4C22×D6111yescharacteristic
235C22×C4C22×D6111yescharacteristic
236C4⋊C4—1222no—
237C4⋊C4—1222no—
238C22⋊C4—22no—
239C22⋊C4—42no—
240C22⋊C4—1224no—
241C22⋊C4—1222no—
242C22⋊C4—2442no—
243C22⋊C4—2442no—
244C22⋊C4—2442no—
245C22⋊C4—2442no—
246C23—21no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—21no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—612no—
259C23—1222no—
260C23—1222no—
261C23—1221no—
262C23—1221no—
263C23—1221no—
264C23—1221no—
265C23—1222no—
266C23—1222no—
267C23—1221no—
268C23C23×D6111yescharacteristic
269D4—44no—
270D4—48no—
271D4—2444no—
272D4—2444no—
273D4—2444no—
274D4—2448no—
275D4—2448no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—612no—
283C2×C4—1222no—
284C2×C4—1221no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—1222no—
289C2×C4—1222no—
290C2×C4—1222no—
291C2×C4—1222no—
292C2×C4—2444no—
293C2×C4D4×D6112yes—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—1222no—
307C22—1222no—
308C22—1222no—
309C22—2442no—
310C22—2442no—
311C22—2441no—
312C22—2441no—
313C22—2441no—
314C22—2442no—
315C22—2442no—
316C22C2×D4×D6111yescharacteristic
317C22#1451982212yes—
318C22#1451982212yes—
319C22#1451982211yescharacteristic
320C22#1451982311yescharacteristic
321C4—22no—
322C4—42no—
323C4—41no—
324C4—1222no—
325C4—2442no—
326C4—2441no—
327C4—2442no—
328C2—82no—
329C2—81no—
330C2—4881no—
331C2—2442no—
332C2#1684032211yescharacteristic
333C2#1684032511yescharacteristic
334C2#1684032811yescharacteristic
335C2#1684050012yes—
336C2#1684050112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2815
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519750C2semidirect
2. C2×#14519748C2semidirect
3. #16839690C2semidirect
4. #16839689C2semidirect
5. #16839687C2semidirect
6. #16839671C2semidirect
7. #16839670C2semidirect
8. #16839670C2semidirect
9. #16839670C2semidirect
10. #16839624C2semidirect
11. C61×#392C2semidirect
66. C2×C4×D61D4semidirect
178. #392D61semidirect
180. C61#2815semidirect