Finite Group Databasebeta

← #21459906

Subgroups — #21459906

Order 7808.

992 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840488C211yesmaximal, characteristic, complemented
2#16840487C213yesmaximal, complemented
3#16840483C213yesmaximal, complemented
4#16840454C213yesmaximal, complemented
5#16840452C213yesmaximal, complemented
6Q8×C22⋊D61C211yesmaximal, characteristic, complemented
7Q8×C22⋊D61C211yesmaximal, characteristic, complemented
8#16840373C213yesmaximal, complemented
9#16840372C213yesmaximal, complemented
10#16840314C213yesmaximal, complemented
11#16840292C213yesmaximal
12#16840240C211yesmaximal, characteristic, complemented
13#16840238C211yesmaximal, characteristic, complemented
14C2×Q8×Dic61C211yesmaximal, characteristic, complemented
15D4×Q8×C61C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17#14519776C2213yes—
18#14519775C2213yes—
19#14519775C2213yes—
20#14519772C2216yes—
21#14519772C2213yes—
22#14519770C2216yes—
23#14519770C2213yes—
24#14519769C2213yes—
25#14519768C2216yes—
26#14519768C2213yes—
27#14519767C2216yes—
28#14519767C2213yes—
29#14519767C2216yes—
30#14519763C2213yes—
31#14519761C2213yes—
32#14519758C2213yes—
33#14519756C2213yes—
34#14519756C2213yes—
35#14519754C2213yes—
36#14519753C2213yes—
37#14519753C2213yes—
38#14519749C2211yescharacteristic
39Q8×Dic61C2213yes—
40Q8×Dic61C2213yes—
41Q8×Dic61C2211yescharacteristic
42Q8×Dic61C2211yescharacteristic
43Q8×Dic61C2213yes—
44Q8×Dic61C2211yescharacteristic
45Q8×Dic61C2213yes—
46C4×Dic122C2213yes—
47C4×Dic122C2213yes—
48#14519742C2216yes—
49#14519742C2213yes—
50C4×C22⋊D61C2213yes—
51C4×C22⋊D61C2213yes—
52#14519736C2213yes—
53#14519736C2213yes—
54#14519735C2213yes—
55#14519734C2213yes—
56#14519733C2216yes—
57C2×C4⋊Dic61C2213yes—
58C2×C4×Dic61C2213yes—
59C22×Q8×C61C2211yescharacteristic
60C22×Q8×C61C2211yescharacteristic
61C4⋊Q8×C61C2213yes—
62C22⋊Q8×C61C2213yes—
63C22⋊Q8×C61C2213yes—
64C4×Q8×C61C2211yescharacteristic
65C4×D4×C61C2213yes—
66C2×Q8×C61—24no—
67C2×Q8×C61—24no—
68C2×Q8×C61C2313yes—
69C2×Q8×C61C2313yes—
70C2×Q8×C61C2311yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C22×C4×C61C2313yes—
73C22×C4×C61C2313yes—
74C2×C22⋊D61C2311yescharacteristic
75C2×C22⋊D61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2313yes—
78Q8×D61—24no—
79C2×C4×D61C2313yes—
80C2×Dic122C2313yes—
81C2×Dic122C2313yes—
82C4⋊C4×C61C2313yes—
83C4⋊C4×C61C2313yes—
84C4⋊C4×C61C2316yes—
85C22⋊C4×C61C2313yes—
86C22⋊C4×C61C2313yes—
87C42×C61C2313yes—
88C22⋊Dic61C2313yes—
89C22⋊Dic61C2311yescharacteristic
90C22⋊Dic61C2313yes—
91C22⋊Dic61C2313yes—
92#11758198C2311yescharacteristic
93#11758198C2313yes—
94#11758198C2313yes—
95#11758198C2313yes—
96C4⋊Dic61C2313yes—
97C4⋊Dic61C2313yes—
98C4⋊Dic61C2316yes—
99C4⋊Dic61C2313yes—
100C4⋊Dic61C2313yes—
101C4⋊Dic61C2313yes—
102C4⋊Dic61C2313yes—
103#11758196C2316yes—
104#11758196C2316yes—
105#11758196C2313yes—
106#11758196C2313yes—
107#11758196C2313yes—
108#11758196C2313yes—
109#11758196C2316yes—
110#11758196C2311yescharacteristic
111#11758196C2313yes—
112C4×Dic61C2313yes—
113C4×Dic61C2313yes—
114C4×Dic61C2313yes—
115C4×Dic61C2313yes—
116C4×Dic61C2316yes—
117C4×Dic61C2316yes—
118C4×Dic61C2313yes—
119C23×C61C2411yescharacteristic
120C23×C61C2411yescharacteristic
121C22×D61C2411yescharacteristic
122Q8×C61—26no—
123Q8×C61—26no—
124Q8×C61#4114yes—
125D4×C61—22no—
126C2×C4×C61—26no—
127C2×C4×C61—26no—
128C2×C4×C61C2413yes—
129C2×C4×C61C2413yes—
130C2×C4×C61C2413yes—
131C2×C4×C61C2411yescharacteristic
132C2×C4×C61C2413yes—
133C22⋊D61—22no—
134C22⋊D61—22no—
135C2×Dic61—26no—
136C2×Dic61—22no—
137C2×Dic61C2411yescharacteristic
138C2×Dic61C2413yes—
139C2×Dic61C2413yes—
140C2×Dic61C2411yescharacteristic
141C2×Dic61C2413yes—
142C2×Dic61C2413yes—
143C2×Dic61C2411yescharacteristic
144C4×D61—26no—
145Dic122—26no—
146Dic122—26no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C612−1+412yes—
153C22×C61C2511yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C4×C61—23no—
158C4×C61—23no—
159C4×C61—23no—
160C4×C61—21no—
161C4×C61C2×#4116yes—
162Dic61—23no—
163Dic61—23no—
164Dic61—21no—
165Dic61—23no—
166Dic61—23no—
167Dic61—21no—
168Dic612−1+412yes—
169#3523—611nomaximal, Sylow
170C2×C61—22no—
171C2×C61—41no—
172C2×C61C22×#4111yescharacteristic
173C2×C61C2×2−1+411yescharacteristic
174C2×C61C2×2−1+411yescharacteristic
175D61—41no—
176#557—613no—
177#557—611no—
178#556—613no—
179#552—613no—
180#552—613no—
181D4×Q8—611no—
182D4×Q8—611no—
183D4×Q8D6111yescharacteristic, complemented
184#541—613no—
185#541—613no—
186#533—613no—
187#529—613no—
188#519—611no—
189#519—611no—
190C2×C4×Q8—611no—
191C61#352311yescharacteristic, complemented, Sylow
192C22×Q8—611no—
193C22×Q8C2×D6111yescharacteristic
194C22×Q8C2×D6111yescharacteristic
195C4⋊Q8—613no—
196C4⋊Q8—613no—
197C4⋊Q8—613no—
198C4⋊Q8C2×D6113yes—
199#126—613no—
200#126—616no—
201#126—613no—
202#126—616no—
203#125—613no—
204#125—616no—
205#125—616no—
206#125—616no—
207#125—613no—
208#125—613no—
209#124—613no—
210#123—613no—
211#123—613no—
212C22⋊Q8—613no—
213C22⋊Q8—613no—
214C22⋊Q8—613no—
215C22⋊Q8—613no—
216C22⋊Q8—613no—
217C22⋊Q8C2×D6113yes—
218C22⋊Q8C2×D6113yes—
219#121—611no—
220C4×Q8—611no—
221C4×Q8—613no—
222C4×Q8—611no—
223C4×Q8—613no—
224C4×Q8—613no—
225C4×Q8—611no—
226C4×Q8—613no—
227C4×Q8—613no—
228C4×Q8—616no—
229C4×Q8—613no—
230C4×Q8—613no—
231C4×Q8C2×D6111yescharacteristic
232C4×D4—613no—
233C4×D4—613no—
234C4×D4C2×D6113yes—
235#117—613no—
236#117—613no—
237#117—613no—
238#117—616no—
239#117—613no—
240C2×C4⋊C4—613no—
241C2×C42—613no—
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—613no—
245C2×Q8—613no—
246C2×Q8—1224no—
247C2×Q8C22×D6113yes—
248C2×Q8C22×D6113yes—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—611no—
251C2×D4—611no—
252C2×D4C22×D6111yescharacteristic
253C22×C4—611no—
254C22×C4—613no—
255C22×C4—613no—
256C22×C4C22×D6113yes—
257C22×C4C22×D6113yes—
258C4⋊C4—613no—
259C4⋊C4—613no—
260C4⋊C4—616no—
261C4⋊C4—613no—
262C4⋊C4—613no—
263C4⋊C4—616no—
264C4⋊C4—616no—
265C4⋊C4—613no—
266C4⋊C4—613no—
267C4⋊C4—611no—
268C4⋊C4—616no—
269C4⋊C4—613no—
270C4⋊C4—613no—
271C4⋊C4—613no—
272C4⋊C4—613no—
273C4⋊C4—613no—
274C4⋊C4C22×D6113yes—
275C4⋊C4C22×D6113yes—
276C4⋊C4C22×D6116yes—
277C22⋊C4—611no—
278C22⋊C4—613no—
279C22⋊C4—613no—
280C22⋊C4—613no—
281C22⋊C4—611no—
282C22⋊C4—613no—
283C22⋊C4—613no—
284C22⋊C4—613no—
285C22⋊C4C22×D6113yes—
286C22⋊C4C22×D6113yes—
287C42—613no—
288C42—613no—
289C42—613no—
290C42—613no—
291C42—616no—
292C42—616no—
293C42—613no—
294C42C22×D6113yes—
295C23—611no—
296C23C23×D6111yescharacteristic
297C23C23×D6111yescharacteristic
298Q8—26no—
299Q8—26no—
300Q8—1226no—
301Q8—1226no—
302Q8#1175822414yes—
303D4—22no—
304D4—1222no—
305D4—1222no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—613no—
311C2×C4—613no—
312C2×C4—611no—
313C2×C4—613no—
314C2×C4—613no—
315C2×C4—1222no—
316C2×C4—1226no—
317C2×C4—1226no—
318C2×C4C23×D6113yes—
319C2×C4C23×D6113yes—
320C2×C4C23×D6113yes—
321C2×C4C23×D6111yescharacteristic
322C2×C4C23×D6113yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1221no—
329C22—1221no—
330C22—1221no—
331C22#1451982512yes—
332C22C24×D6111yescharacteristic
333C4—23no—
334C4—23no—
335C4—23no—
336C4—21no—
337C4—612no—
338C4—1223no—
339C4—1221no—
340C4—1223no—
341C4—1223no—
342C4—1223no—
343C4—1221no—
344C4C2×#1175822416yes—
345C2—22no—
346C2—41no—
347C2—2441no—
348C2C22×#1175822411yescharacteristic
349C22−1+4×D6111yescharacteristic
350C2C2×#1451982511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingD4×Q8×C61C2
hypercenterD4×Q8D61
hypocenterC61#3523
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #16840488C2semidirect
2. #16840487C2semidirect
3. #16840483C2semidirect
4. #16840454C2semidirect
5. #16840452C2semidirect
6. Q8×C22⋊D61C2semidirect
7. Q8×C22⋊D61C2semidirect
8. #16840373C2semidirect
9. #16840372C2semidirect
10. #16840314C2semidirect
12. #16840240C2semidirect
13. #16840238C2semidirect
14. C2×Q8×Dic61C2semidirect
15. D4×Q8×C61C2semidirect
183. D4×Q8D61semidirect
191. C61#3523semidirect