Finite Group Databasebeta

← #21452641

Subgroups — #21452641

Order 7808.

450 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519776C211yesmaximal, characteristic, complemented
2#16839701C211yesmaximal, characteristic, complemented
3#16839693C211yesmaximal, characteristic, complemented
4#16839687C211yesmaximal, characteristic
5#16839685C211yesmaximal, characteristic
6#16839674C211yesmaximal, characteristic
7#16839674C211yesmaximal, characteristic
8#16839668C211yesmaximal, characteristic, complemented
9#16839667C211yesmaximal, characteristic, complemented
10#16839656C211yesmaximal, characteristic
11#16839650C211yesmaximal, characteristic
12#16839648C211yesmaximal, characteristic, complemented
13#16839646C211yesmaximal, characteristic, complemented
14#16839643C211yesmaximal, characteristic, complemented
15C2×#126×C61C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18#14519776—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31#14519684C2211yescharacteristic
32#14519684C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#126×C61—24no—
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×Dic122—22no—
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—22no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61D414yes—
77C22⋊C4×C61—22no—
78C22⋊C4×C61—22no—
79C22⋊C4×C61—22no—
80C42×C61—22no—
81C22⋊Dic61—22no—
82C22⋊Dic61—22no—
83C22⋊Dic61—41no—
84C22⋊Dic61—41no—
85C4⋊Dic61—22no—
86C4⋊Dic61—41no—
87#11758196—22no—
88#11758196—22no—
89#11758196—22no—
90#11758196—22no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61C2411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×D412yes—
117C2×C4×C61C2×D412yes—
118C2×C4×C61C2×D412yes—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61#4112yes—
142C2×Dic61#4112yes—
143Dic122—44no—
144Dic122—44no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61C2×#4111yescharacteristic
155C22×C61H(5,𝔽2)11yescharacteristic
156C22×C612−1+411yescharacteristic
157C22×C612−1+411yescharacteristic
158C22×C612−1+411yescharacteristic
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165Dic61—22no—
166Dic61—22no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173#2716—611nomaximal, Sylow
174C2×C61—81no—
175C2×C61#53611yescharacteristic
176C2×C61#54111yescharacteristic
177C2×C61#54211yescharacteristic
178C2×C61#54611yescharacteristic
179C2×C61#54811yescharacteristic
180C2×C61#55611yescharacteristic
181C2×C61#56311yescharacteristic
182C2×C4⋊Q8—611no—
183C2×#126D6111yescharacteristic
184#400—611no—
185#398—611no—
186#397—611no—
187#396—611no—
188#393—611no—
189#393—611no—
190#391—611no—
191#391—611no—
192#388—611no—
193#388—611no—
194#387—611no—
195#387—611no—
196#387—611no—
197C61#271611yescharacteristic, complemented, Sylow
198C22×Q8—611no—
199C22×Q8—611no—
200C4⋊Q8—1224no—
201#126—24no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4C2×D6111yescharacteristic
209C2×C4⋊C4C2×D6111yescharacteristic
210C2×C4⋊C4C2×D6111yescharacteristic
211C2×C22⋊C4—611no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4C2×D6111yescharacteristic
216C2×C22⋊C4C2×D6111yescharacteristic
217C2×C22⋊C4C2×D6111yescharacteristic
218C2×C42—611no—
219C2×C42—611no—
220C2×C42C2×D6111yescharacteristic
221#95—611no—
222#95—611no—
223#95—611no—
224#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95—611no—
233#95—611no—
234#95—611no—
235C24C22×D6111yescharacteristic
236C2×Q8—1222no—
237C2×Q8—1222no—
238C2×Q8—1222no—
239C2×Q8—1222no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—1222no—
259C4⋊C4—1222no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—2441no—
264C4⋊C4C22⋊D6114yes—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—1222no—
269C22⋊C4—1222no—
270C22⋊C4—2441no—
271C22⋊C4—2441no—
272C42—22no—
273C42—1222no—
274C42—2441no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23C23×D6111yescharacteristic
283Q8—2444no—
284Q8—2444no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4C2×C22⋊D6112yes—
325C2×C4C2×C22⋊D6112yes—
326C2×C4C2×C22⋊D6112yes—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C22×C22⋊D6111yescharacteristic
335C22#41×D6111yescharacteristic
336C22#41×D6111yescharacteristic
337C22#1451982311yescharacteristic
338C22#1451982411yescharacteristic
339C22#1451982411yescharacteristic
340C22#1451982411yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1222no—
348C4—1222no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4—2441no—
355C2—81no—
356C2#1684033311yescharacteristic
357C2#1684036911yescharacteristic
358C2#1684037811yescharacteristic
359C2#1684040011yescharacteristic
360C2#1684041911yescharacteristic
361C2#1684047911yescharacteristic
362C2#1684051411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#126×C61C2
hypercenterC2×#126D61
hypocenterC61#2716
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
2. #16839701C2semidirect
3. #16839693C2semidirect
8. #16839668C2semidirect
9. #16839667C2semidirect
12. #16839648C2semidirect
13. #16839646C2semidirect
14. #16839643C2semidirect
197. C61#2716semidirect