Finite Group Databasebeta

← #21459816

Subgroups — #21459816

Order 7808.

1122 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
1#16840488C211yesmaximal, characteristic, complemented
2#16840459C213yesmaximal, complemented
3#16840458C213yesmaximal, complemented
4#16840432C213yesmaximal, complemented
5#16840431C211yesmaximal, characteristic, complemented
6#16840431C211yesmaximal, characteristic, complemented
7#16840412C213yesmaximal, complemented
8#16840366C213yesmaximal, complemented
9#16840365C213yesmaximal, complemented
10#16840307C213yesmaximal, complemented
11#16840292C213yesmaximal, complemented
12#16840245C211yesmaximal, characteristic, complemented
13#16840244C211yesmaximal, characteristic, complemented
14#41×Dic61C211yesmaximal, characteristic, complemented
15C61×#550C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2216yes—
18#14519776C2213yes—
19#14519773C2213yes—
20#14519773C2213yes—
21#14519772C2213yes—
22#14519770C2213yes—
23#14519769C2213yes—
24#14519768C2213yes—
25#14519767C2211yescharacteristic
26#14519763C2213yes—
27#14519761C2213yes—
28#14519759C2216yes—
29#14519758C2216yes—
30#14519758C2213yes—
31#14519754C2213yes—
32#14519751C2213yes—
33#14519751C2213yes—
34#14519749C2216yes—
35#14519749C2213yes—
36#14519749C2216yes—
37#14519748C2216yes—
38#14519748C2213yes—
39#14519748C2213yes—
40Q8×Dic61C2211yescharacteristic
41Q8×Dic61C2211yescharacteristic
42Q8×Dic61C2211yescharacteristic
43C4×Dic122C2213yes—
44C4×D244C2213yes—
45D4×Dic61C2213yes—
46D4×Dic61C2213yes—
47D4×Dic61C2213yes—
48D4×Dic61C2213yes—
49#14519739C2213yes—
50C4×C22⋊D61C2213yes—
51C4×C22⋊D61C2213yes—
52#14519737C2216yes—
53#14519736C2213yes—
54#14519736C2213yes—
55#14519734C2213yes—
56C2×C4⋊Dic61C2213yes—
57C4⋊C4×D61C2213yes—
58C2×C4×Dic61C2213yes—
59C2×#41×C61C2211yescharacteristic
60C2×#41×C61C2211yescharacteristic
61#127×C61C2213yes—
62#121×C61C2213yes—
63#121×C61C2213yes—
64C4×Q8×C61C2211yescharacteristic
65C4×D4×C61C2213yes—
66#41×C61—24no—
67#41×C61—24no—
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61C2313yes—
70C2×D4×C61C2313yes—
71C2×D4×C61C2316yes—
72C2×D4×C61C2313yes—
73C22×C4×C61C2313yes—
74C22×C4×C61C2313yes—
75C2×C22⋊D61C2313yes—
76C2×C22⋊D61C2316yes—
77C2×C22⋊D61C2316yes—
78C2×C22⋊D61C2313yes—
79C22×Dic61C2313yes—
80C22×Dic61C2316yes—
81C22×Dic61C2313yes—
82#11758226—24no—
83#11758224—412no—
84C2×D244C2313yes—
85C2×C4×D61C2313yes—
86C2×C4×D61C2316yes—
87C2×Dic122C2313yes—
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2313yes—
90C22⋊C4×C61C2313yes—
91C22⋊C4×C61C2313yes—
92C42×C61C2313yes—
93C22⋊Dic61C2313yes—
94C22⋊Dic61C2316yes—
95C22⋊Dic61C2313yes—
96C22⋊Dic61C2313yes—
97C22⋊Dic61C2313yes—
98#11758198C2313yes—
99#11758198C2313yes—
100#11758198C2313yes—
101#11758198C2313yes—
102C4⋊Dic61C2313yes—
103C4⋊Dic61C2313yes—
104C4⋊Dic61C2313yes—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2313yes—
107C4⋊Dic61C2313yes—
108#11758196C2313yes—
109#11758196C2311yescharacteristic
110#11758196C2316yes—
111#11758196C2311yescharacteristic
112#11758196C2311yescharacteristic
113#11758196C2311yescharacteristic
114#11758196C2313yes—
115C4×Dic61C2311yescharacteristic
116C4×Dic61C2313yes—
117C4×Dic61C2313yes—
118C4×Dic61C2313yes—
119C4×Dic61C2313yes—
120C23×C61C2413yes—
121C23×C61C2413yes—
122C22×D61C2413yes—
123Q8×C61#4114yescomplemented
124D4×C61—26no—
125D4×C61—26no—
126D4×C61—46no—
127D4×C61—43no—
128C2×C4×C61—26no—
129C2×C4×C61—26no—
130C2×C4×C61C2411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C2×C4×C61C2413yes—
133C2×C4×C61C2411yescharacteristic
134C2×C4×C61C2413yes—
135C22⋊D61—26no—
136C22⋊D61—46no—
137C22⋊D61—46no—
138C22⋊D61—43no—
139C2×Dic61—26no—
140C2×Dic61—46no—
141C2×Dic61—43no—
142C2×Dic61C2411yescharacteristic
143C2×Dic61C2411yescharacteristic
144C2×Dic61C2413yes—
145C2×Dic61C2413yes—
146C2×Dic61C2413yes—
147C2×Dic61C2411yescharacteristic
148C2×Dic61C2411yescharacteristic
149D244—26no—
150C4×D61—26no—
151C4×D61—46no—
152Dic122—26no—
153C22×C61—23no—
154C22×C61—23no—
155C22×C61—23no—
156C22×C61—23no—
157C22×C61—23no—
158C22×C61—23no—
159C22×C61C2511yescharacteristic
160C2×D61—23no—
161C2×D61—23no—
162C2×D61—23no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—23no—
166C4×C61—21no—
167C4×C61C2×#4116yes—
168Dic61—21no—
169Dic61—23no—
170Dic61—23no—
171Dic61—21no—
172Dic61—23no—
173Dic61—21no—
174Dic61H(5,𝔽2)12yes—
175#3517—611nomaximal, Sylow
176C2×C61—43no—
177C2×C61—43no—
178C2×C61C22×#4111yescharacteristic
179C2×C61C2×H(5,𝔽2)11yescharacteristic
180C2×C61#58511yescharacteristic
181D61—43no—
182#557—611no—
183#553—613no—
184#553—613no—
185#550—611no—
186#550—611no—
187#550—613no—
188#550D6111yescharacteristic, complemented
189#547—613no—
190#540—613no—
191#540—613no—
192#532—613no—
193#529—613no—
194#520—611no—
195#520—611no—
196C4×#41—611no—
197C61#351711yescharacteristic, complemented, Sylow
198C2×#41—611no—
199C2×#41—616no—
200C2×#41C2×D6111yescharacteristic
201C2×#41C2×D6111yescharacteristic
202C4⋊Q8—613no—
203#127—613no—
204#127—613no—
205#127C2×D6113yes—
206#126—613no—
207#126—613no—
208#125—611no—
209#125—613no—
210#125—613no—
211#124—613no—
212#123—613no—
213#123—616no—
214#123—613no—
215#123—616no—
216C22⋊Q8—613no—
217#121—613no—
218#121—616no—
219#121—613no—
220#121—616no—
221#121—613no—
222#121—616no—
223#121—613no—
224#121—613no—
225#121C2×D6113yes—
226#121C2×D6113yes—
227C4×Q8—611no—
228C4×Q8—611no—
229C4×Q8—611no—
230C4×Q8—613no—
231C4×Q8C2×D6111yescharacteristic
232C4×D4—613no—
233C4×D4—613no—
234C4×D4—613no—
235C4×D4—613no—
236C4×D4—613no—
237C4×D4—613no—
238C4×D4—613no—
239C4×D4—616no—
240C4×D4—613no—
241C4×D4C2×D6113yes—
242#117—613no—
243#117—613no—
244#117—613no—
245C2×C4⋊C4—613no—
246C2×C4⋊C4—613no—
247C2×C42—613no—
248#41—24no—
249#41—24no—
250#41—1224no—
251#41—24412no—
252C2×Q8—613no—
253C2×Q8C22×D6111yescharacteristic
254C2×D4—613no—
255C2×D4—616no—
256C2×D4—613no—
257C2×D4—616no—
258C2×D4—613no—
259C2×D4C22×D6113yes—
260C2×D4C22×D6113yes—
261C2×D4C22×D6113yes—
262C2×D4C22×D6116yes—
263C22×C4—613no—
264C22×C4—613no—
265C22×C4—616no—
266C22×C4—613no—
267C22×C4—616no—
268C22×C4C22×D6113yes—
269C22×C4C22×D6113yes—
270C4⋊C4—613no—
271C4⋊C4—613no—
272C4⋊C4—613no—
273C4⋊C4—613no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—616no—
278C4⋊C4—611no—
279C4⋊C4—613no—
280C4⋊C4—611no—
281C4⋊C4—613no—
282C4⋊C4—613no—
283C4⋊C4C22×D6113yes—
284C4⋊C4C22×D6111yescharacteristic
285C22⋊C4—613no—
286C22⋊C4—616no—
287C22⋊C4—613no—
288C22⋊C4—613no—
289C22⋊C4—613no—
290C22⋊C4—613no—
291C22⋊C4—613no—
292C22⋊C4—613no—
293C22⋊C4—613no—
294C22⋊C4C22×D6113yes—
295C22⋊C4C22×D6113yes—
296C42—611no—
297C42—613no—
298C42—613no—
299C42—613no—
300C42—613no—
301C42C22×D6113yes—
302C23—613no—
303C23C23×D6113yes—
304C23C23×D6113yes—
305Q8—1226no—
306Q8#1175822414yescomplemented
307D4—26no—
308D4—26no—
309D4—43no—
310D4—46no—
311D4—1226no—
312D4—1226no—
313D4—2446no—
314D4—2443no—
315D4—2446no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—613no—
322C2×C4—613no—
323C2×C4—613no—
324C2×C4—611no—
325C2×C4—1226no—
326C2×C4—1226no—
327C2×C4—2446no—
328C2×C4—2443no—
329C2×C4—2446no—
330C2×C4C23×D6111yescharacteristic
331C2×C4C23×D6111yescharacteristic
332C2×C4C23×D6113yes—
333C2×C4C23×D6111yescharacteristic
334C2×C4C23×D6113yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—23no—
341C22—1223no—
342C22—1223no—
343C22—1223no—
344C22C24×D6111yescharacteristic
345C4—21no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—612no—
350C4—1221no—
351C4—1223no—
352C4—1223no—
353C4—1221no—
354C4—1223no—
355C4—1221no—
356C4C2×#1175822416yes—
357C2—43no—
358C2—43no—
359C2—2443no—
360C2C22×#1175822411yescharacteristic
361C2H(5,𝔽2)×D6111yescharacteristic
362C2#1684059811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#550C2
hypercenter#550D61
hypocenterC61#3517
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #16840488C2semidirect
2. #16840459C2semidirect
3. #16840458C2semidirect
4. #16840432C2semidirect
5. #16840431C2semidirect
6. #16840431C2semidirect
7. #16840412C2semidirect
8. #16840366C2semidirect
9. #16840365C2semidirect
10. #16840307C2semidirect
11. #16840292C2semidirect
12. #16840245C2semidirect
13. #16840244C2semidirect
14. #41×Dic61C2semidirect
15. C61×#550C2semidirect
123. Q8×C61#41semidirect
188. #550D61semidirect
197. C61#3517semidirect
306. Q8#11758224semidirect