Finite Group Databasebeta

← #21459409

Subgroups — #21459409

Order 7808.

1112 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#16840494C213yesmaximal, complemented
2#16840488C211yesmaximal, characteristic, complemented
3#16840483C213yesmaximal, complemented
4#16840464C213yesmaximal, complemented
5#16840458C213yesmaximal, complemented
6#16840431C211yesmaximal, characteristic, complemented
7#16840423C211yesmaximal, characteristic, complemented
8#16840307C213yesmaximal, complemented
9#16840298C213yesmaximal, complemented
10#16840291C213yesmaximal, complemented
11#41×Dic61C211yesmaximal, characteristic, complemented
12C4×#11758226C211yesmaximal, characteristic, complemented
13C4×#11758224C213yesmaximal, complemented
14C2×Q8×Dic61C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2213yes—
18#14519776C2213yes—
19#14519773C2213yes—
20#14519772C2216yes—
21#14519770C2216yes—
22#14519769C2213yes—
23#14519768C2213yes—
24#14519766C2213yes—
25#14519763C2216yes—
26#14519761C2216yes—
27#14519759C2216yes—
28#14519753C2213yes—
29#14519751C2213yes—
30#14519751C2213yes—
31#14519749C2216yes—
32#14519748C2213yes—
33Q8×Dic61C2213yes—
34Q8×Dic61C2211yescharacteristic
35Q8×Dic61C2211yescharacteristic
36Q8×Dic61C2213yes—
37Q8×Dic61C2211yescharacteristic
38C4×Dic122C2213yes—
39#14519742C2213yes—
40C4×D244C2213yes—
41D4×Dic61C2213yes—
42D4×Dic61C2213yes—
43D4×Dic61C2213yes—
44#14519739C2213yes—
45C4×C22⋊D61C2213yes—
46C4×C22⋊D61C2213yes—
47#14519737C2213yes—
48#14519737C2213yes—
49#14519737C2216yes—
50#14519736C2213yes—
51#14519735C2213yes—
52#14519735C2213yes—
53#14519733C2211yescharacteristic
54#14519733C2213yes—
55C2×C4⋊Dic61C2213yes—
56C2×C4×Dic61C2213yes—
57C2×C4×Dic61C2213yes—
58C42×D61C2213yes—
59C2×#41×C61C2211yescharacteristic
60C22×Q8×C61C2211yescharacteristic
61#124×C61C2213yes—
62C22⋊Q8×C61C2213yes—
63#121×C61C2213yes—
64C4×Q8×C61C2211yescharacteristic
65C4×D4×C61C2213yes—
66#41×C61—24no—
67C2×Q8×C61—24no—
68C2×Q8×C61C2313yes—
69C2×Q8×C61C2311yescharacteristic
70C2×D4×C61C2313yes—
71C2×D4×C61C2313yes—
72C22×C4×C61C2313yes—
73C22×C4×C61C2313yes—
74C2×C22⋊D61C2313yes—
75C2×C22⋊D61C2313yes—
76C2×C22⋊D61C2316yes—
77C22×Dic61C2313yes—
78C22×Dic61C2313yes—
79C22×Dic61C2313yes—
80C22×Dic61C2311yescharacteristic
81#11758226—24no—
82#11758224—212no—
83C2×D244C2313yes—
84C2×C4×D61C2313yes—
85C2×C4×D61C2313yes—
86C2×C4×D61C2313yes—
87C2×Dic122C2313yes—
88C4⋊C4×C61C2313yes—
89C4⋊C4×C61C2313yes—
90C22⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61C2313yes—
92C22⋊C4×C61C2316yes—
93C42×C61C2313yes—
94C22⋊Dic61C2311yescharacteristic
95C22⋊Dic61C2313yes—
96C22⋊Dic61C2316yes—
97#11758198C2313yes—
98#11758198C2313yes—
99#11758198C2316yes—
100#11758198C2316yes—
101C4⋊Dic61C2313yes—
102C4⋊Dic61C2313yes—
103C4⋊Dic61C2316yes—
104C4⋊Dic61C2313yes—
105C4⋊Dic61C2313yes—
106#11758196C2311yescharacteristic
107#11758196C2313yes—
108#11758196C2311yescharacteristic
109#11758196C2313yes—
110#11758196C2316yes—
111C4×Dic61C2311yescharacteristic
112C4×Dic61C2313yes—
113C4×Dic61C2313yes—
114C4×Dic61C2311yescharacteristic
115C4×Dic61C2313yes—
116C4×Dic61C2313yes—
117C4×Dic61C2313yes—
118C4×Dic61C2313yes—
119C4×Dic61C2313yes—
120C23×C61C2413yes—
121C23×C61C2411yescharacteristic
122C22×D61C2413yes—
123Q8×C61—26no—
124Q8×C61#4114yescomplemented
125D4×C61—26no—
126D4×C61—26no—
127C2×C4×C61—26no—
128C2×C4×C61—26no—
129C2×C4×C61C2411yescharacteristic
130C2×C4×C61C2413yes—
131C2×C4×C61C2411yescharacteristic
132C2×C4×C61C2413yes—
133C2×C4×C61C2413yes—
134C22⋊D61—26no—
135C22⋊D61—26no—
136C22⋊D61—46no—
137C2×Dic61—26no—
138C2×Dic61—43no—
139C2×Dic61—43no—
140C2×Dic61#4114yescomplemented
141C2×Dic61C2411yescharacteristic
142C2×Dic61C2411yescharacteristic
143C2×Dic61C2413yes—
144C2×Dic61C2413yes—
145C2×Dic61C2413yes—
146C2×Dic61C2411yescharacteristic
147C2×Dic61C2411yescharacteristic
148D244—26no—
149C4×D61—26no—
150C4×D61—26no—
151C4×D61—43no—
152Dic122—26no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—23no—
156C22×C61—23no—
157C22×C61—23no—
158C22×C61C2×#4112yes—
159C22×C61C2511yescharacteristic
160C2×D61—23no—
161C2×D61—23no—
162C2×D61—23no—
163C4×C61—23no—
164C4×C61—21no—
165C4×C61—23no—
166C4×C61—21no—
167C4×C61C2×#4116yes—
168Dic61—23no—
169Dic61—21no—
170Dic61—23no—
171Dic61—21no—
172Dic61—23no—
173Dic61C2×#4112yes—
174Dic61C2×#4112yes—
175#3480—611nomaximal, Sylow
176C2×C61—22no—
177C2×C61—43no—
178C2×C61C22×#4111yescharacteristic
179C2×C61C22×#4111yescharacteristic
180C2×C61#58511yescharacteristic
181D61—43no—
182#559—613no—
183#557—611no—
184#556—613no—
185#553—613no—
186#553—613no—
187#550—611no—
188#548—611no—
189#548D6111yescharacteristic, complemented
190#532—613no—
191#529—613no—
192#529—613no—
193C4×#41—611no—
194C4×#41—611no—
195C4×#41—613no—
196C2×C4×Q8—611no—
197C61#348011yescharacteristic, complemented, Sylow
198C2×#41—611no—
199C2×#41—613no—
200C2×#41C2×D6111yescharacteristic
201C22×Q8C2×D6111yescharacteristic
202C4⋊Q8—613no—
203#127—613no—
204#126—616no—
205#126—616no—
206#125—613no—
207#125—613no—
208#124—613no—
209#124—616no—
210#124C2×D6113yes—
211#123—616no—
212#123—616no—
213C22⋊Q8—613no—
214C22⋊Q8C2×D6113yes—
215#121—613no—
216#121—616no—
217#121—613no—
218#121—613no—
219#121C2×D6113yes—
220C4×Q8—611no—
221C4×Q8—613no—
222C4×Q8—611no—
223C4×Q8—613no—
224C4×Q8—611no—
225C4×Q8—613no—
226C4×Q8—613no—
227C4×Q8C2×D6111yescharacteristic
228C4×D4—613no—
229C4×D4—613no—
230C4×D4—613no—
231C4×D4—613no—
232C4×D4—613no—
233C4×D4—613no—
234C4×D4—613no—
235C4×D4—613no—
236C4×D4—616no—
237C4×D4—613no—
238C4×D4C2×D6113yes—
239#117—613no—
240#117—613no—
241#117—613no—
242#117—611no—
243#117—613no—
244C2×C4⋊C4—613no—
245C2×C42—613no—
246C2×C42—613no—
247C2×C42—613no—
248#41—24no—
249#41—12212no—
250#41—1224no—
251C2×Q8—24no—
252C2×Q8—613no—
253C2×Q8C22×D6113yes—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—613no—
256C2×D4—613no—
257C2×D4—616no—
258C2×D4—613no—
259C2×D4C22×D6113yes—
260C2×D4C22×D6113yes—
261C22×C4—611no—
262C22×C4—613no—
263C22×C4—613no—
264C22×C4—613no—
265C22×C4—613no—
266C22×C4—613no—
267C22×C4—613no—
268C22×C4C22×D6113yes—
269C22×C4C22×D6113yes—
270C4⋊C4—613no—
271C4⋊C4—613no—
272C4⋊C4—616no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—613no—
276C4⋊C4—613no—
277C4⋊C4—616no—
278C4⋊C4—613no—
279C4⋊C4—613no—
280C4⋊C4C22×D6113yes—
281C4⋊C4C22×D6113yes—
282C22⋊C4—611no—
283C22⋊C4—613no—
284C22⋊C4—616no—
285C22⋊C4—613no—
286C22⋊C4—616no—
287C22⋊C4—613no—
288C22⋊C4—616no—
289C22⋊C4C22×D6111yescharacteristic
290C22⋊C4C22×D6113yes—
291C22⋊C4C22×D6116yes—
292C42—611no—
293C42—611no—
294C42—613no—
295C42—613no—
296C42—613no—
297C42—613no—
298C42—613no—
299C42—613no—
300C42—613no—
301C42C22×D6113yes—
302C23—613no—
303C23C23×D6113yes—
304C23C23×D6111yescharacteristic
305Q8—26no—
306Q8—1226no—
307Q8#1175822414yescomplemented
308D4—26no—
309D4—26no—
310D4—1226no—
311D4—1226no—
312D4—1226no—
313D4—2446no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—614no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—613no—
322C2×C4—613no—
323C2×C4—613no—
324C2×C4—1226no—
325C2×C4—1226no—
326C2×C4—1226no—
327C2×C4—2443no—
328C2×C4—2443no—
329C2×C4—2443no—
330C2×C4C23×D6111yescharacteristic
331C2×C4C23×D6113yes—
332C2×C4C23×D6111yescharacteristic
333C2×C4C23×D6113yes—
334C2×C4C23×D6113yes—
335C22—21no—
336C22—21no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—1223no—
341C22—1223no—
342C22—1223no—
343C22#41×D6112yes—
344C22C24×D6111yescharacteristic
345C4—23no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—612no—
350C4—612no—
351C4—1223no—
352C4—1221no—
353C4—1223no—
354C4—1221no—
355C4—1223no—
356C4C2×#1175822416yes—
357C2—22no—
358C2—43no—
359C2—2443no—
360C2C2×#41×D6111yescharacteristic
361C2C22×#1175822411yescharacteristic
362C2#1684059911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#548C2
hypercenter#548D61
hypocenterC61#3480
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16840494C2semidirect
2. #16840488C2semidirect
3. #16840483C2semidirect
4. #16840464C2semidirect
5. #16840458C2semidirect
6. #16840431C2semidirect
7. #16840423C2semidirect
8. #16840307C2semidirect
9. #16840298C2semidirect
10. #16840291C2semidirect
11. #41×Dic61C2semidirect
12. C4×#11758226C2semidirect
13. C4×#11758224C2semidirect
14. C2×Q8×Dic61C2semidirect
15. C61×#548C2semidirect
124. Q8×C61#41semidirect
140. C2×Dic61#41semidirect
189. #548D61semidirect
197. C61#3480semidirect
307. Q8#11758224semidirect