Finite Group Databasebeta

← #21459435

Subgroups — #21459435

Order 7808.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840488C211yesmaximal, characteristic, complemented
2#16840481C213yesmaximal, complemented
3#16840452C213yesmaximal, complemented
4#16840446C213yesmaximal, complemented
5Q8×C22⋊D61C211yesmaximal, characteristic, complemented
6#16840419C211yesmaximal, characteristic, complemented
7#16840412C213yesmaximal, complemented
8#16840314C213yesmaximal, complemented
9#16840293C213yesmaximal, complemented
10#16840291C213yesmaximal, complemented
11#41×Dic61C211yesmaximal, characteristic, complemented
12C4×#11758224C213yesmaximal, complemented
13C2×Q8×Dic61C211yesmaximal, characteristic, complemented
14C4×Q8×D61C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic, complemented
16C2×#11758224C2213yes—
17C2×Q8×D61C2211yescharacteristic
18#14519776C2213yes—
19#14519775C2213yes—
20#14519770C2216yes—
21#14519770C2216yes—
22#14519769C2213yes—
23#14519768C2213yes—
24#14519767C2216yes—
25#14519764C2213yes—
26#14519759C2216yes—
27#14519758C2216yes—
28#14519756C2213yes—
29#14519756C2213yes—
30#14519754C2216yes—
31#14519753C2213yes—
32#14519748C2213yes—
33Q8×Dic61C2211yescharacteristic
34Q8×Dic61C2213yes—
35Q8×Dic61C2211yescharacteristic
36Q8×Dic61C2213yes—
37Q8×Dic61C2211yescharacteristic
38C4×Dic122C2213yes—
39C4×Dic122C2213yes—
40#14519742C2213yes—
41#14519742C2213yes—
42D4×Dic61C2213yes—
43D4×Dic61C2213yes—
44D4×Dic61C2213yes—
45C4×C22⋊D61C2213yes—
46C4×C22⋊D61C2213yes—
47#14519737C2211yescharacteristic
48#14519737C2213yes—
49#14519736C2213yes—
50#14519735C2213yes—
51#14519733C2213yes—
52#14519733C2213yes—
53#14519733C2216yes—
54C2×C4⋊Dic61C2213yes—
55C4⋊C4×D61C2213yes—
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⋊D61C2311yescharacteristic
76C22×Dic61C2313yes—
77C22×Dic61C2313yes—
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2313yes—
80Q8×D61—24no—
81#11758224—212no—
82C2×C4×D61C2313yes—
83C2×C4×D61C2313yes—
84C2×C4×D61C2311yescharacteristic
85C2×Dic122C2313yes—
86C2×Dic122C2313yes—
87C4⋊C4×C61C2313yes—
88C4⋊C4×C61C2313yes—
89C22⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61C2313yes—
91C22⋊C4×C61C2316yes—
92C42×C61C2313yes—
93C22⋊Dic61C2313yes—
94C22⋊Dic61C2313yes—
95C22⋊Dic61C2316yes—
96C22⋊Dic61C2316yes—
97#11758198C2311yescharacteristic
98#11758198C2313yes—
99C4⋊Dic61C2313yes—
100C4⋊Dic61C2313yes—
101C4⋊Dic61C2316yes—
102C4⋊Dic61C2313yes—
103C4⋊Dic61C2313yes—
104#11758196C2316yes—
105#11758196C2311yescharacteristic
106#11758196C2313yes—
107#11758196C2313yes—
108#11758196C2313yes—
109#11758196C2316yes—
110#11758196C2316yes—
111C4×Dic61C2313yes—
112C4×Dic61C2313yes—
113C4×Dic61C2313yes—
114C4×Dic61C2311yescharacteristic
115C4×Dic61C2313yes—
116C4×Dic61C2313yes—
117C4×Dic61C2313yes—
118C4×Dic61C2313yes—
119C4×Dic61C2313yes—
120C23×C61C2413yes—
121C23×C61C2411yescharacteristic
122C22×D61C2411yescharacteristic
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×C61C2411yescharacteristic
131C2×C4×C61C2413yes—
132C2×C4×C61C2413yes—
133C2×C4×C61C2413yes—
134C22⋊D61—26no—
135C22⋊D61#4114yescomplemented
136C2×Dic61—26no—
137C2×Dic61—26no—
138C2×Dic61—22no—
139C2×Dic61—26no—
140C2×Dic61C2411yescharacteristic
141C2×Dic61C2413yes—
142C2×Dic61C2413yes—
143C2×Dic61C2413yes—
144C2×Dic61C2413yes—
145C2×Dic61C2411yescharacteristic
146C2×Dic61C2411yescharacteristic
147C4×D61—26no—
148C4×D61—26no—
149C4×D61—22no—
150Dic122—26no—
151Dic122—26no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—23no—
155C22×C61—23no—
156C22×C61—23no—
157C22×C61C2×#4112yes—
158C22×C61C2511yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61C2×#4112yes—
162C4×C61—23no—
163C4×C61—21no—
164C4×C61—23no—
165C4×C61—21no—
166C4×C61C2×#4116yes—
167Dic61—23no—
168Dic61—23no—
169Dic61—23no—
170Dic61—21no—
171Dic61—23no—
172Dic61C2×#4112yes—
173Dic612−1+412yes—
174#3482—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61—43no—
177C2×C61C22×#4111yescharacteristic
178C2×C61C22×#4111yescharacteristic
179C2×C61C2×2−1+411yescharacteristic
180D61—22no—
181#557—611no—
182#556—613no—
183#552—613no—
184#552—613no—
185D4×Q8—611no—
186#548—611no—
187#548D6111yescharacteristic, complemented
188#547—613no—
189#533—613no—
190#529—613no—
191#529—613no—
192C4×#41—611no—
193C4×#41—613no—
194C2×C4×Q8—611no—
195C2×C4×Q8—611no—
196C61#348211yescharacteristic, complemented, Sylow
197C2×#41—613no—
198C2×#41C2×D6111yescharacteristic
199C22×Q8—611no—
200C22×Q8C2×D6111yescharacteristic
201C4⋊Q8—613no—
202C4⋊Q8—613no—
203#126—616no—
204#126—616no—
205#125—613no—
206#125—616no—
207#125—613no—
208#124—613no—
209#124C2×D6113yes—
210#123—616no—
211#123—616no—
212C22⋊Q8—613no—
213C22⋊Q8—613no—
214C22⋊Q8—613no—
215C22⋊Q8—616no—
216C22⋊Q8C2×D6113yes—
217#121—613no—
218#121C2×D6113yes—
219C4×Q8—611no—
220C4×Q8—613no—
221C4×Q8—611no—
222C4×Q8—613no—
223C4×Q8—611no—
224C4×Q8—613no—
225C4×Q8—613no—
226C4×Q8—613no—
227C4×Q8—613no—
228C4×Q8C2×D6111yescharacteristic
229C4×D4—613no—
230C4×D4—613no—
231C4×D4—613no—
232C4×D4—613no—
233C4×D4—613no—
234C4×D4—611no—
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×C4⋊C4—613no—
244C2×C42—613no—
245C2×C42—613no—
246C2×C42—613no—
247#41—24no—
248#41—12212no—
249C2×Q8—24no—
250C2×Q8—613no—
251C2×Q8—613no—
252C2×Q8—1224no—
253C2×Q8C22×D6113yes—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—611no—
256C2×D4—613no—
257C2×D4C22×D6113yes—
258C2×D4C22×D6113yes—
259C22×C4—611no—
260C22×C4—613no—
261C22×C4—613no—
262C22×C4—613no—
263C22×C4—611no—
264C22×C4—613no—
265C22×C4—613no—
266C22×C4C22×D6113yes—
267C22×C4C22×D6113yes—
268C4⋊C4—613no—
269C4⋊C4—616no—
270C4⋊C4—613no—
271C4⋊C4—616no—
272C4⋊C4—611no—
273C4⋊C4—613no—
274C4⋊C4—613no—
275C4⋊C4—613no—
276C4⋊C4—616no—
277C4⋊C4—616no—
278C4⋊C4—613no—
279C4⋊C4—613no—
280C4⋊C4C22×D6113yes—
281C4⋊C4C22×D6113yes—
282C22⋊C4—613no—
283C22⋊C4—616no—
284C22⋊C4—613no—
285C22⋊C4—616no—
286C22⋊C4—611no—
287C22⋊C4—613no—
288C22⋊C4C22×D6111yescharacteristic
289C22⋊C4C22×D6113yes—
290C22⋊C4C22×D6116yes—
291C42—611no—
292C42—613no—
293C42—613no—
294C42—613no—
295C42—613no—
296C42—613no—
297C42—613no—
298C42—613no—
299C42—613no—
300C42C22×D6113yes—
301C23—611no—
302C23C23×D6113yes—
303C23C23×D6111yescharacteristic
304Q8—26no—
305Q8—1226no—
306Q8—1226no—
307Q8#1175822414yescomplemented
308D4—26no—
309D4—26no—
310D4—614no—
311D4—1226no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—613no—
318C2×C4—613no—
319C2×C4—613no—
320C2×C4—613no—
321C2×C4—1222no—
322C2×C4—1226no—
323C2×C4—1222no—
324C2×C4—1226no—
325C2×C4—1226no—
326C2×C4—1226no—
327C2×C4—1226no—
328C2×C4C23×D6111yescharacteristic
329C2×C4C23×D6111yescharacteristic
330C2×C4C23×D6113yes—
331C2×C4C23×D6113yes—
332C2×C4C23×D6113yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—612no—
339C22—1221no—
340C22—1221no—
341C22#41×D6112yes—
342C22C24×D6111yescharacteristic
343C4—23no—
344C4—21no—
345C4—23no—
346C4—21no—
347C4—612no—
348C4—612no—
349C4—1223no—
350C4—1223no—
351C4—1223no—
352C4—1221no—
353C4—1223no—
354C4C2×#1175822416yes—
355C2—22no—
356C2—43no—
357C2—1222no—
358C2C2×#41×D6111yescharacteristic
359C2C22×#1175822411yescharacteristic
360C22−1+4×D6111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#548C2
hypercenter#548D61
hypocenterC61#3482
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16840488C2semidirect
2. #16840481C2semidirect
3. #16840452C2semidirect
4. #16840446C2semidirect
5. Q8×C22⋊D61C2semidirect
6. #16840419C2semidirect
7. #16840412C2semidirect
8. #16840314C2semidirect
9. #16840293C2semidirect
10. #16840291C2semidirect
11. #41×Dic61C2semidirect
12. C4×#11758224C2semidirect
13. C2×Q8×Dic61C2semidirect
14. C4×Q8×D61C2semidirect
15. C61×#548C2semidirect
124. Q8×C61#41semidirect
135. C22⋊D61#41semidirect
187. #548D61semidirect
196. C61#3482semidirect
307. Q8#11758224semidirect