Finite Group Databasebeta

← #21451559

Subgroups — #21451559

Order 7808.

824 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519749C211yesmaximal, characteristic, complemented
2C2×#14519747C211yesmaximal, characteristic, complemented
3C2×#14519745C211yesmaximal, characteristic, complemented
4C22×#11758198C211yesmaximal, characteristic, complemented
5#16839691C212yesmaximal, complemented
6#16839680C212yesmaximal, complemented
7#16839677C212yesmaximal, complemented
8#16839671C212yesmaximal, complemented
9#16839641C211yesmaximal, characteristic, complemented
10#16839620C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×D244C2212yes—
14C22×C22⋊D61C2211yescharacteristic
15C22×C22⋊D61C2212yes—
16C22×C22⋊D61C2211yescharacteristic, complemented
17C23×Dic61C2211yescharacteristic
18#14519749—24no—
19#14519747—24no—
20#14519745—24no—
21C2×#11758196C2211yescharacteristic, complemented
22C2×#11758196C2212yescomplemented
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic, complemented
25C2×#11758198—24no—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30C2×#11758198C2211yescharacteristic, complemented
31C2×#11758198C2212yescomplemented
32#14519684C2212yescomplemented
33#14519684C2212yescomplemented
34C22×D4×C61C2211yescharacteristic
35C23×C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2212yescomplemented
38#95×C61C2212yescomplemented
39C24×C61C2311yescharacteristic
40C24×C61C2311yescharacteristic
41C23×D61—22no—
42C23×D61—22no—
43C23×D61—42no—
44C23×D61—42no—
45C23×D61D414yescomplemented
46C23×D61C2311yescharacteristic
47C23×D61C2312yes—
48C2×D4×C61—22no—
49C2×D4×C61—22no—
50C2×D4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—42no—
53C22×C4×C61C2312yes—
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2312yes—
56C2×C22⋊D61—22no—
57C2×C22⋊D61—22no—
58C2×C22⋊D61—22no—
59C2×C22⋊D61—24no—
60C2×C22⋊D61—22no—
61C2×C22⋊D61—42no—
62C2×C22⋊D61—42no—
63C2×C22⋊D61—42no—
64C22×Dic61—42no—
65C22×Dic61D414yescomplemented
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2312yes—
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C2×D244—24no—
71C2×D244—42no—
72C2×D244—42no—
73C22⋊C4×C61—22no—
74C22⋊C4×C61—42no—
75C22⋊Dic61—22no—
76C22⋊Dic61—22no—
77#11758198—24no—
78#11758198—24no—
79#11758198—24no—
80#11758198—24no—
81#11758198—22no—
82#11758198—42no—
83#11758196—22no—
84#11758196—42no—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—22no—
91C23×C61—22no—
92C23×C61C2×D412yes—
93C23×C61C2×D412yes—
94C23×C61#4112yes—
95C23×C61C2411yescharacteristic
96C22×D61—28no—
97C22×D61—22no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—22no—
102C22×D61—22no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—22no—
107C22×D61—22no—
108C22×D61—48no—
109C22×D61—44no—
110C22×D61—44no—
111C22×D61—48no—
112C22×D61C2×D414yes—
113D4×C61—44no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—44no—
124C22⋊D61—44no—
125C22⋊D61—48no—
126C22⋊D61—44no—
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—44no—
136C2×Dic61C2×D412yes—
137C2×Dic61C2×D412yes—
138D244—48no—
139C22×C61—22no—
140C22×C61—24no—
141C22×C61—22no—
142C22×C61—24no—
143C22×C61—41no—
144C22×C61—42no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—42no—
148C22×C61#12114yes—
149C22×C61C22×D411yescharacteristic
150C22×C61C22×D411yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61H(5,𝔽2)12yes—
153C22×C61H(5,𝔽2)12yes—
154C2×D61—24no—
155C2×D61—24no—
156C2×D61—24no—
157C2×D61—416no—
158C2×D61—42no—
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—42no—
162C2×D61—41no—
163C2×D61—42no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—42no—
167C4×C61—41no—
168C4×C61—42no—
169C4×C61—42no—
170Dic61—22no—
171Dic61—22no—
172Dic61—41no—
173Dic61—42no—
174#2617—611nomaximal, Sylow
175C2×C61—24no—
176C2×C61—81no—
177C2×C61C2×#12111yescharacteristic
178C2×C61#53412yes—
179C2×C61#53411yescharacteristic
180C2×C61#53511yescharacteristic
181C2×C61#53812yes—
182D61—44no—
183D61—81no—
184C2×#121—611no—
185C2×#120—611no—
186C2×#120—611no—
187C22×C22⋊C4—611no—
188#397—612no—
189#394—612no—
190#394—612no—
191#392—612no—
192#386—611no—
193#386D6111yescharacteristic, complemented
194#380—611no—
195C61#261711yescharacteristic, complemented, Sylow
196C25—611no—
197C22×D4—611no—
198C22×D4—612no—
199C22×D4—611no—
200C22×D4—612no—
201C22×D4C2×D6111yescharacteristic
202C23×C4—611no—
203C23×C4C2×D6111yescharacteristic
204#121—1224no—
205#120—1224no—
206#120—1224no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—612no—
209C2×C22⋊C4—611no—
210C2×C22⋊C4—611no—
211C2×C22⋊C4—612no—
212C2×C22⋊C4—612no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4—612no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—612no—
217C2×C22⋊C4—1224no—
218C2×C22⋊C4C2×D6111yescharacteristic
219C2×C22⋊C4C2×D6112yescomplemented
220#95—612no—
221#95—612no—
222#95C2×D6112yescomplemented
223C24—612no—
224C24—614no—
225C24—611no—
226C24—1222no—
227C24—1222no—
228C24—2442no—
229C24—2442no—
230C24C22×D6111yescharacteristic
231C24C22×D6111yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—1224no—
236C2×D4—1222no—
237C2×D4—1224no—
238C2×D4—1222no—
239C2×D4—1222no—
240C2×D4—1222no—
241C2×D4—2442no—
242C2×D4—2442no—
243C2×D4—2442no—
244C2×D4—2442no—
245C2×D4—2442no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—614no—
251C22×C4—611no—
252C22×C4—612no—
253C22×C4—2442no—
254C22×C4C22×D6112yes—
255C22×C4C22×D6112yes—
256C22×C4C22×D6111yescharacteristic
257C4⋊C4—1222no—
258C4⋊C4—2442no—
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—1224no—
262C22⋊C4—1224no—
263C22⋊C4—1222no—
264C22⋊C4—1224no—
265C22⋊C4—1224no—
266C22⋊C4—1222no—
267C22⋊C4—1222no—
268C22⋊C4—2442no—
269C23—22no—
270C23—22no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—614no—
277C23—1222no—
278C23—1222no—
279C23—1222no—
280C23—1222no—
281C23—1222no—
282C23—1222no—
283C23—1228no—
284C23—1221no—
285C23—1221no—
286C23—1221no—
287C23—1222no—
288C23—1222no—
289C23—2448no—
290C23—2444no—
291C23—2444no—
292C23—2448no—
293C23#1175822212yes—
294C23D4×D6112yes—
295C23D4×D6112yes—
296C23C23×D6111yescharacteristic
297D4—44no—
298D4—2448no—
299D4—2444no—
300D4—2448no—
301D4—2444no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—44no—
312C2×C4—612no—
313C2×C4—612no—
314C2×C4—1222no—
315C2×C4—1222no—
316C2×C4—1221no—
317C2×C4—1222no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—2444no—
323C22—24no—
324C22—22no—
325C22—22no—
326C22—24no—
327C22—41no—
328C22—42no—
329C22—41no—
330C22—41no—
331C22—42no—
332C22—1224no—
333C22—1224no—
334C22—1224no—
335C22—24416no—
336C22—2441no—
337C22—2442no—
338C22—2441no—
339C22—2441no—
340C22—2442no—
341C22—2442no—
342C22—2442no—
343C22—2442no—
344C22—2442no—
345C22#1451975014yes—
346C22C2×D4×D6111yescharacteristic
347C22C2×D4×D6111yescharacteristic
348C22C2×#1175822211yescharacteristic
349C22#1451982212yes—
350C22#1451982312yes—
351C4—41no—
352C4—42no—
353C4—42no—
354C4—1222no—
355C4—1222no—
356C4—2441no—
357C4—2442no—
358C2—24no—
359C2—81no—
360C2—4881no—
361C2—2444no—
362C2C2×#1451975011yescharacteristic
363C2#1684032012yes—
364C2#1684032311yescharacteristic
365C2#1684032711yescharacteristic
366C2#1684034512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2617
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14519749C2semidirect
2. C2×#14519747C2semidirect
3. C2×#14519745C2semidirect
4. C22×#11758198C2semidirect
5. #16839691C2semidirect
6. #16839680C2semidirect
7. #16839677C2semidirect
8. #16839671C2semidirect
9. #16839641C2semidirect
10. #16839620C2semidirect
11. C61×#386C2semidirect
16. C22×C22⋊D61C22semidirect
21. C2×#11758196C22semidirect
22. C2×#11758196C22semidirect
24. C2×C22⋊Dic61C22semidirect
30. C2×#11758198C22semidirect
31. C2×#11758198C22semidirect
32. #14519684C22semidirect
33. #14519684C22semidirect
37. C2×C22⋊C4×C61C22semidirect
38. #95×C61C22semidirect
45. C23×D61D4semidirect
65. C22×Dic61D4semidirect
193. #386D61semidirect
195. C61#2617semidirect
219. C2×C22⋊C4C2×D61semidirect
222. #95C2×D61semidirect