Finite Group Databasebeta

← #21451571

Subgroups — #21451571

Order 7808.

728 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14519773C211yesmaximal, characteristic, complemented
2C2×#14519750C212yesmaximal, complemented
3C2×#14519735C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839678C212yesmaximal, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839671C212yesmaximal, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839662C212yesmaximal, complemented
10#16839626C211yesmaximal, characteristic, complemented
11C61×#394C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15C22×C22⋊D61C2212yes—
16C22×C22⋊D61C2212yes—
17C22×C4×D61C2211yescharacteristic
18#14519773—24no—
19#14519750—28no—
20#14519735—24no—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31#14519684C2211yescharacteristic
32#14519684C2212yes—
33C22×D4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36C2×C22⋊C4×C61C2212yes—
37#95×C61C2211yescharacteristic
38C24×C61C2312yes—
39C23×D61C2312yes—
40C23×D61C2311yescharacteristic
41C2×D4×C61—22no—
42C2×D4×C61—42no—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—24no—
50C2×C22⋊D61—24no—
51C2×C22⋊D61—24no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—42no—
54C2×C22⋊D61—42no—
55C2×C22⋊D61—42no—
56C22×Dic61C2312yes—
57C22×Dic61C2311yescharacteristic
58C22×Dic61C2311yescharacteristic
59C22×Dic61C2311yescharacteristic
60C2×D244—24no—
61C2×D244—22no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—42no—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61D414yescomplemented
68C4⋊C4×C61—22no—
69C22⋊C4×C61—24no—
70C22⋊C4×C61—42no—
71C22⋊Dic61—42no—
72#11758198—22no—
73#11758198—24no—
74#11758198—22no—
75#11758198—42no—
76#11758198—42no—
77C4⋊Dic61—22no—
78#11758196—24no—
79C4×Dic61—22no—
80C4×Dic61D414yescomplemented
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—22no—
88C23×C61C2411yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—22no—
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—22no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61C2×D412yes—
101D4×C61—44no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61C2×D412yes—
111C2×C4×C61C2×D412yes—
112C22⋊D61—48no—
113C22⋊D61—48no—
114C22⋊D61—48no—
115C2×Dic61—22no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61C2×D412yes—
122C2×Dic61C2×D412yes—
123C2×Dic61C2×D412yes—
124C2×Dic61#4112yes—
125D244—44no—
126D244—48no—
127C4×D61—28no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61—42no—
133C22×C61—42no—
134C22×C61—42no—
135C22×C61C22×D411yescharacteristic
136C22×C61C22×D411yescharacteristic
137C22×C61C2×#4111yescharacteristic
138C22×C61H(5,𝔽2)12yes—
139C22×C61H(5,𝔽2)12yes—
140C2×D61—22no—
141C2×D61—24no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—42no—
145C2×D61—42no—
146C2×D61—42no—
147C2×D61—42no—
148C2×D61—42no—
149C2×D61—42no—
150C2×D61—42no—
151C2×D61—42no—
152C4×C61—22no—
153C4×C61—22no—
154C4×C61—42no—
155C4×C61—41no—
156Dic61—22no—
157Dic61—41no—
158Dic61—42no—
159Dic61#12114yes—
160#2619—611nomaximal, Sylow
161C2×C61—82no—
162C2×C61C2×#12111yescharacteristic
163C2×C61#53511yescharacteristic
164C2×C61#53512yes—
165C2×C61#53511yescharacteristic
166C2×C61#54012yes—
167D61—42no—
168D61—82no—
169C2×#127—611no—
170C2×#121—612no—
171C2×#117—611no—
172#394—611no—
173#394—612no—
174#394D6111yescharacteristic, complemented
175#392—611no—
176#392—612no—
177#392—611no—
178#390—612no—
179#382—611no—
180C61#261911yescharacteristic, complemented, Sylow
181C22×D4—612no—
182C22×D4—612no—
183C22×D4—612no—
184C22×D4—612no—
185C22×D4—611no—
186C22×D4C2×D6111yescharacteristic
187C23×C4—611no—
188#127—1224no—
189#121—1228no—
190#117—1224no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—612no—
193C2×C4⋊C4C2×D6111yescharacteristic
194C2×C22⋊C4—611no—
195C2×C22⋊C4—611no—
196C2×C22⋊C4—612no—
197C2×C22⋊C4—612no—
198C2×C22⋊C4—612no—
199C2×C22⋊C4—612no—
200C2×C22⋊C4C2×D6112yes—
201C2×C22⋊C4C2×D6112yes—
202C2×C42—611no—
203C2×C42—611no—
204#95—612no—
205#95—611no—
206#95C2×D6111yescharacteristic
207C24—611no—
208C24—612no—
209C24C22×D6112yes—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—1224no—
213C2×D4—1224no—
214C2×D4—1224no—
215C2×D4—1224no—
216C2×D4—1224no—
217C2×D4—1224no—
218C2×D4—1222no—
219C2×D4—2442no—
220C2×D4—2442no—
221C2×D4—2442no—
222C2×D4—2442no—
223C2×D4—2442no—
224C2×D4—2442no—
225C2×D4—2442no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—614no—
229C22×C4—612no—
230C22×C4—611no—
231C22×C4—1222no—
232C22×C4—1222no—
233C22×C4C22×D6112yes—
234C22×C4C22×D6111yescharacteristic
235C22×C4C22×D6111yescharacteristic
236C22×C4C22×D6111yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—1224no—
239C4⋊C4—1222no—
240C22⋊C4—24no—
241C22⋊C4—42no—
242C22⋊C4—1222no—
243C22⋊C4—1222no—
244C22⋊C4—1224no—
245C22⋊C4—2442no—
246C22⋊C4—2442no—
247C22⋊C4—2442no—
248C42—614no—
249C42—1222no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—612no—
258C23—1221no—
259C23—1221no—
260C23—1222no—
261C23—1222no—
262C23—1222no—
263C23—1222no—
264C23—1222no—
265C23—1222no—
266C23—1222no—
267C23—1222no—
268C23—1222no—
269C23C23×D6111yescharacteristic
270D4—44no—
271D4—2444no—
272D4—2448no—
273D4—2448no—
274D4—2448no—
275D4—2448no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—612no—
285C2×C4—612no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—1228no—
289C2×C4—1222no—
290C2×C4—1221no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4D4×D6112yes—
296C2×C4D4×D6112yes—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—1222no—
305C22—1224no—
306C22—2442no—
307C22—2442no—
308C22—2442no—
309C22—2442no—
310C22—2442no—
311C22—2442no—
312C22—2442no—
313C22—2441no—
314C22—2441no—
315C22—2442no—
316C22C2×D4×D6111yescharacteristic
317C22C2×D4×D6111yescharacteristic
318C22#41×D6111yescharacteristic
319C22#1451982212yes—
320C22#1451982312yes—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—42no—
325C4—614no—
326C4—1222no—
327C4—2442no—
328C4—2441no—
329C2—82no—
330C2—4882no—
331C2—2442no—
332C2#121×D6111yescharacteristic
333C2#1684032711yescharacteristic
334C2#1684032812yes—
335C2#1684033011yescharacteristic
336C2#1684036412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2619
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519735C2semidirect
4. #16839679C2semidirect
5. #16839678C2semidirect
6. #16839672C2semidirect
7. #16839671C2semidirect
8. #16839670C2semidirect
9. #16839662C2semidirect
10. #16839626C2semidirect
11. C61×#394C2semidirect
67. C2×C4×D61D4semidirect
80. C4×Dic61D4semidirect
174. #394D61semidirect
180. C61#2619semidirect