Finite Group Databasebeta

← #21459921

Subgroups — #21459921

Order 7808.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840494C213yesmaximal, complemented
2#16840488C211yesmaximal, characteristic, complemented
3#16840476C213yesmaximal, complemented
4#16840458C213yesmaximal, complemented
5#16840454C213yesmaximal, complemented
6#16840431C211yesmaximal, characteristic, complemented
7#16840423C211yesmaximal, characteristic, complemented
8#16840385C213yesmaximal, complemented
9#16840365C213yesmaximal, complemented
10#16840294C213yesmaximal, complemented
11#16840291C213yesmaximal, complemented
12#16840245C211yesmaximal, characteristic, complemented
13#16840240C211yesmaximal, characteristic, complemented
14C4×#11758226C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17#14519776C2213yes—
18#14519773C2213yes—
19#14519772C2216yes—
20#14519770C2213yes—
21#14519770C2211yescharacteristic
22#14519769C2213yes—
23#14519768C2213yes—
24#14519768C2213yes—
25#14519766C2213yes—
26#14519764C2213yes—
27#14519763C2216yes—
28#14519761C2216yes—
29#14519759C2213yes—
30#14519759C2213yes—
31#14519759C2216yes—
32#14519757C2213yes—
33#14519753C2213yes—
34#14519751C2213yes—
35#14519751C2213yes—
36#14519749C2216yes—
37#14519748C2213yes—
38#14519748C2213yes—
39Q8×Dic61C2213yes—
40Q8×Dic61C2211yescharacteristic
41Q8×Dic61C2211yescharacteristic
42Q8×Dic61C2211yescharacteristic
43Q8×Dic61C2213yes—
44C4×Dic122C2213yes—
45C4×D244C2213yes—
46D4×Dic61C2213yes—
47D4×Dic61C2213yes—
48#14519739C2213yes—
49C4×C22⋊D61C2213yes—
50C4×C22⋊D61C2213yes—
51#14519737C2216yes—
52#14519736C2213yes—
53#14519736C2213yes—
54#14519736C2213yes—
55#14519735C2213yes—
56#14519733C2216yes—
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⋊D61C2316yes—
75C2×C22⋊D61C2313yes—
76C2×C22⋊D61C2313yes—
77C22×Dic61C2316yes—
78#11758226—24no—
79C2×D244C2313yes—
80C2×C4×D61C2313yes—
81C2×C4×D61C2313yes—
82C2×C4×D61C2313yes—
83C2×Dic122C2313yes—
84C4⋊C4×C61C2313yes—
85C4⋊C4×C61C2313yes—
86C22⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61C2313yes—
88C22⋊C4×C61C2316yes—
89C42×C61C2313yes—
90C22⋊Dic61C2313yes—
91C22⋊Dic61C2311yescharacteristic
92C22⋊Dic61C2313yes—
93C22⋊Dic61C2313yes—
94C22⋊Dic61C2313yes—
95C22⋊Dic61C2311yescharacteristic
96#11758198C2316yes—
97#11758198C2316yes—
98#11758198C2313yes—
99#11758198C2313yes—
100C4⋊Dic61C2313yes—
101C4⋊Dic61C2313yes—
102C4⋊Dic61C2313yes—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2313yes—
105C4⋊Dic61C2313yes—
106C4⋊Dic61C2313yes—
107C4⋊Dic61C2313yes—
108#11758196C2313yes—
109#11758196C2316yes—
110#11758196C2313yes—
111#11758196C2311yescharacteristic
112#11758196C2311yescharacteristic
113C4×Dic61C2311yescharacteristic
114C4×Dic61C2313yes—
115C4×Dic61C2313yes—
116C4×Dic61C2316yes—
117C4×Dic61C2313yes—
118C4×Dic61C2313yes—
119C23×C61C2411yescharacteristic
120C23×C61C2413yes—
121C22×D61C2413yes—
122Q8×C61—26no—
123Q8×C61#4114yes—
124D4×C61—26no—
125D4×C61—43no—
126C2×C4×C61—26no—
127C2×C4×C61—26no—
128C2×C4×C61C2413yes—
129C2×C4×C61C2411yescharacteristic
130C2×C4×C61C2413yes—
131C2×C4×C61C2411yescharacteristic
132C2×C4×C61C2413yes—
133C22⋊D61—46no—
134C22⋊D61—43no—
135C22⋊D61—43no—
136C2×Dic61—46no—
137C2×Dic61C2411yescharacteristic
138C2×Dic61C2413yes—
139C2×Dic61C2411yescharacteristic
140C2×Dic61C2413yes—
141C2×Dic61C2411yescharacteristic
142C2×Dic61C2411yescharacteristic
143C2×Dic61C2413yes—
144D244—26no—
145C4×D61—26no—
146C4×D61—43no—
147C4×D61—43no—
148Dic122—43no—
149C22×C61—21no—
150C22×C61—23no—
151C22×C61—23no—
152C22×C61—21no—
153C22×C61—23no—
154C22×C61—21no—
155C22×C61C2511yescharacteristic
156C2×D61—23no—
157C2×D61—23no—
158C2×D61—23no—
159C4×C61—21no—
160C4×C61—23no—
161C4×C61—23no—
162C4×C61—21no—
163C4×C61C2×#4116yes—
164Dic61—21no—
165Dic61—21no—
166Dic61—23no—
167Dic61—21no—
168Dic61—23no—
169Dic61—23no—
170Dic61—21no—
171#3524—611nomaximal, Sylow
172C2×C61—41no—
173C2×C61—43no—
174C2×C61C22×#4111yescharacteristic
175C2×C61#58511yescharacteristic
176C2×C61#58511yescharacteristic
177D61—43no—
178#559—613no—
179#557—611no—
180#555—613no—
181#553—613no—
182#552—613no—
183#550—611no—
184#548—611no—
185#548D6111yescharacteristic, complemented
186#542—613no—
187#540—613no—
188#529—613no—
189#529—613no—
190#520—611no—
191#519—611no—
192C4×#41—611no—
193C61#352411yescharacteristic, complemented, Sylow
194C2×#41—611no—
195C2×#41C2×D6111yescharacteristic
196C22×Q8C2×D6111yescharacteristic
197C4⋊Q8—613no—
198#127—613no—
199#126—616no—
200#126—611no—
201#126—613no—
202#125—613no—
203#125—613no—
204#125—613no—
205#124—613no—
206#124—613no—
207#124—616no—
208#124C2×D6113yes—
209#123—616no—
210#123—613no—
211#123—613no—
212#123—616no—
213C22⋊Q8—613no—
214C22⋊Q8—613no—
215C22⋊Q8C2×D6113yes—
216#121—613no—
217#121—613no—
218#121—616no—
219#121—613no—
220#121—613no—
221#121C2×D6113yes—
222C4×Q8—611no—
223C4×Q8—613no—
224C4×Q8—611no—
225C4×Q8—613no—
226C4×Q8—611no—
227C4×Q8—613no—
228C4×Q8C2×D6111yescharacteristic
229C4×D4—613no—
230C4×D4—613no—
231C4×D4—613no—
232C4×D4—613no—
233C4×D4—613no—
234C4×D4—616no—
235C4×D4—613no—
236C4×D4C2×D6113yes—
237#117—613no—
238#117—613no—
239#117—613no—
240#117—613no—
241#117—616no—
242C2×C4⋊C4—613no—
243C2×C42—613no—
244#41—24no—
245#41—1224no—
246C2×Q8—24no—
247C2×Q8—613no—
248C2×Q8C22×D6113yes—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—613no—
251C2×D4—616no—
252C2×D4—613no—
253C2×D4—613no—
254C2×D4C22×D6113yes—
255C2×D4C22×D6113yes—
256C22×C4—616no—
257C22×C4—613no—
258C22×C4—613no—
259C22×C4—613no—
260C22×C4C22×D6113yes—
261C22×C4C22×D6113yes—
262C4⋊C4—613no—
263C4⋊C4—613no—
264C4⋊C4—613no—
265C4⋊C4—613no—
266C4⋊C4—616no—
267C4⋊C4—611no—
268C4⋊C4—613no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—613no—
272C4⋊C4—613no—
273C4⋊C4—613no—
274C4⋊C4—613no—
275C4⋊C4C22×D6113yes—
276C4⋊C4C22×D6113yes—
277C22⋊C4—611no—
278C22⋊C4—613no—
279C22⋊C4—613no—
280C22⋊C4—613no—
281C22⋊C4—613no—
282C22⋊C4—611no—
283C22⋊C4—616no—
284C22⋊C4—613no—
285C22⋊C4—616no—
286C22⋊C4—613no—
287C22⋊C4C22×D6116yes—
288C22⋊C4C22×D6113yes—
289C22⋊C4C22×D6111yescharacteristic
290C42—611no—
291C42—613no—
292C42—613no—
293C42—616no—
294C42—613no—
295C42—613no—
296C42C22×D6113yes—
297C23—613no—
298C23C23×D6111yescharacteristic
299C23C23×D6113yes—
300Q8—26no—
301Q8—2443no—
302Q8#1175822414yes—
303D4—26no—
304D4—43no—
305D4—1226no—
306D4—2446no—
307D4—2443no—
308D4—2443no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—613no—
314C2×C4—611no—
315C2×C4—613no—
316C2×C4—611no—
317C2×C4—613no—
318C2×C4—1226no—
319C2×C4—2443no—
320C2×C4—2443no—
321C2×C4—2446no—
322C2×C4C23×D6113yes—
323C2×C4C23×D6111yescharacteristic
324C2×C4C23×D6113yes—
325C2×C4C23×D6111yescharacteristic
326C2×C4C23×D6113yes—
327C22—21no—
328C22—23no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22—1223no—
334C22—1223no—
335C22—1223no—
336C22C24×D6111yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—1221no—
342C4—1221no—
343C4—1223no—
344C4—1221no—
345C4—1223no—
346C4—1223no—
347C4—1221no—
348C4C2×#1175822416yes—
349C2—41no—
350C2—43no—
351C2—2443no—
352C2C22×#1175822411yescharacteristic
353C2#1684059811yescharacteristic
354C2#1684059911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#548C2
hypercenter#548D61
hypocenterC61#3524
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. #16840476C2semidirect
4. #16840458C2semidirect
5. #16840454C2semidirect
6. #16840431C2semidirect
7. #16840423C2semidirect
8. #16840385C2semidirect
9. #16840365C2semidirect
10. #16840294C2semidirect
11. #16840291C2semidirect
12. #16840245C2semidirect
13. #16840240C2semidirect
14. C4×#11758226C2semidirect
15. C61×#548C2semidirect
185. #548D61semidirect
193. C61#3524semidirect