Finite Group Databasebeta

← #22598352

Subgroups — #22598352

Order 9088.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#11765865C211yesmaximal, characteristic, complemented
2#17986337C211yesmaximal, characteristic, complemented
3#17986320C211yesmaximal, characteristic, complemented
4#17986303C211yesmaximal, characteristic, complemented
5#17986296C211yesmaximal, characteristic, complemented
6#17986218C211yesmaximal, characteristic, complemented
7#17986211C211yesmaximal, characteristic, complemented
8#17986159C211yesmaximal, characteristic, complemented
9#17986142C211yesmaximal, characteristic
10C4×#11765855C211yesmaximal, characteristic, complemented
11C4×#11765852C211yesmaximal, characteristic, complemented
12C4×#11765853C211yesmaximal, characteristic, complemented
13C4×#11765850C211yesmaximal, characteristic, complemented
14#17986052C211yesmaximal, characteristic, complemented
15#529×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×#11765855C2211yescharacteristic
18C2×#11765853C2211yescharacteristic
19C2×#11765852C2211yescharacteristic
20C2×#11765850C2211yescharacteristic
21C4×Dic142C2211yescharacteristic
22C4×Dic142C2211yescharacteristic
23C4×D284C2211yescharacteristic
24C4×D284C2211yescharacteristic
25C4×C22⋊D71—21no—
26C4×C22⋊D71—21no—
27#14556087C2211yescharacteristic
28#14556085—21no—
29C42×D71—21no—
30#14556061C2211yescharacteristic
31#14556061C2211yescharacteristic
32#14556059C2211yescharacteristic
33#14556059C2211yescharacteristic
34C4⋊(C71⋊C8)C2211yescharacteristic
35C4⋊(C71⋊C8)C2211yescharacteristic
36#14556052C2211yescharacteristic
37#14556052C2211yescharacteristic
38#14556051C2211yescharacteristic
39#14556051C2211yescharacteristic
40#14556049C2211yescharacteristic
41#14556049C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46C4×C71⋊C8C2211yescharacteristic
47C4×C71⋊C8C2211yescharacteristic
48#126×C71—21no—
49#125×C71C2211yescharacteristic
50#124×C71C2211yescharacteristic
51#123×C71—21no—
52C22⋊Q8×C71C2211yescharacteristic
53#121×C71C2211yescharacteristic
54C4×Q8×C71C2211yescharacteristic
55C4×D4×C71—21no—
56C4×D4×C71C2211yescharacteristic
57#117×C71—21no—
58C2×C42×C71C2211yescharacteristic
59#11765865—22no—
60#11765865—22no—
61C2×Dic142C2311yescharacteristic
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C2×C4×D71—21no—
65C2×C4×D71—21no—
66C2×C4×D71—21no—
67#11765855—22no—
68#11765853—22no—
69#11765852—22no—
70#11765850—22no—
71C2×C71⋊C8C2311yescharacteristic
72C2×C71⋊C8C2311yescharacteristic
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C4⋊Dic71C2311yescharacteristic
76C4⋊Dic71C2311yescharacteristic
77Dic71⋊C4—21no—
78Dic71⋊C4—21no—
79C22⋊Dic71—21no—
80(C2×D71)⋊C4—21no—
81(C2×D71)⋊C4—21no—
82C4×Dic71—21no—
83C4×Dic71—21no—
84C4×Dic71—21no—
85C2×Q8×C71C2311yescharacteristic
86C2×D4×C71—21no—
87C2×D4×C71C2311yescharacteristic
88C22×C4×C71—21no—
89C22×C4×C71D411yescharacteristic
90C22×C4×C71D411yescharacteristic
91C22×C4×C71C2311yescharacteristic
92C4⋊C4×C71—21no—
93C4⋊C4×C71—21no—
94C4⋊C4×C71—21no—
95C4⋊C4×C71—21no—
96C4⋊C4×C71C2311yescharacteristic
97C4⋊C4×C71C2311yescharacteristic
98C22⋊C4×C71—21no—
99C22⋊C4×C71—21no—
100C22⋊C4×C71—21no—
101C22⋊C4×C71—21no—
102C22⋊C4×C71—21no—
103C42×C71—21no—
104C42×C71D411yescharacteristic
105C42×C71D411yescharacteristic
106C42×C71C2311yescharacteristic
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111Q8×C71—21no—
112Q8×C71—21no—
113D4×C71—21no—
114D4×C71—21no—
115D4×C71—42no—
116C2×C4×C71—22no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—41no—
123C2×C4×C71—42no—
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2×D411yescharacteristic
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2411yescharacteristic
130C22⋊D71—24no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134D284—21no—
135D284#4112yes—
136C4×D71—24no—
137C4×D71—42no—
138C4×D71—42no—
139Dic142—21no—
140Dic142#4112yes—
141C71⋊C8—21no—
142C71⋊C8—21no—
143C71⋊C8—21no—
144C71⋊C8—21no—
145C22×C71—21no—
146C22×C71—21no—
147C22×C71—21no—
148C22×C71—41no—
149C22×C71—41no—
150C22×C71—41no—
151C22×C71C22×D411yescharacteristic
152C2×D71—22no—
153C2×D71—41no—
154C2×D71—41no—
155C4×C71—21no—
156C4×C71—21no—
157C4×C71—21no—
158C4×C71—21no—
159C4×C71—41no—
160C4×C71—41no—
161C4×C71—41no—
162C4×C71#13512yes—
163C4×C71C2×#4111yescharacteristic
164C4×C71C2×#4111yescharacteristic
165Dic71—22no—
166Dic71—41no—
167Dic71—41no—
168C2×C71—41no—
169C2×C71—81no—
170C2×C71#52511yescharacteristic
171C2×C71C2×#13511yescharacteristic
172C2×C71#57511yescharacteristic
173D71—42no—
174#3102—711nomaximal, Sylow
175C71#310211yescharacteristic, complemented, Sylow
176#529D7111yescharacteristic, complemented
177C4×#41—711no—
178#485—711no—
179#482—711no—
180#479—711no—
181#478—711no—
182#464—711no—
183#463—711no—
184#452—711no—
185#449—711no—
186C4×Q16—711no—
187C4×SD16—711no—
188C4×SD16—711no—
189C4×D8—711no—
190#431—711no—
191C2×#41—711no—
192C2×Q16—711no—
193C2×SD16—711no—
194C2×SD16—711no—
195C2×D8—711no—
196#126—21no—
197#125C2×D7111yescharacteristic
198#124C2×D7111yescharacteristic
199#123—21no—
200C22⋊Q8C2×D7111yescharacteristic
201#121C2×D7111yescharacteristic
202C4×Q8—711no—
203C4×Q8—711no—
204C4×Q8C2×D7111yescharacteristic
205C4×D4—21no—
206C4×D4—711no—
207C4×D4—711no—
208C4×D4—1421no—
209C4×D4—1421no—
210C4×D4C2×D7111yescharacteristic
211#117—21no—
212#117—711no—
213#117—1421no—
214C2×C42—1421no—
215C2×C42C2×D7111yescharacteristic
216#107—711no—
217#107—711no—
218#106—711no—
219#106—711no—
220C4⋊C8—711no—
221C4⋊C8—711no—
222#103—711no—
223#103—711no—
224#103—711no—
225#103—711no—
226#102—711no—
227#102—711no—
228#102—711no—
229#102—711no—
230C22⋊C8—711no—
231C22⋊C8—711no—
232C4×C8—711no—
233C4×C8—711no—
234#41—1422no—
235#41—1422no—
236C2×Q8—711no—
237C2×Q8C22×D7111yescharacteristic
238C2×D4—21no—
239C2×D4—711no—
240C2×D4—1421no—
241C2×D4C22×D7111yescharacteristic
242C22×C4—21no—
243C22×C4—1421no—
244C22×C4—1421no—
245C22×C4—1421no—
246C22×C4C22⋊D7111yescharacteristic
247C22×C4C22⋊D7111yescharacteristic
248C22×C4C22×D7111yescharacteristic
249Q16—1422no—
250SD16—1422no—
251SD16—1422no—
252D8—1422no—
253C2×C8—711no—
254C2×C8—711no—
255C2×C8—711no—
256C2×C8—711no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—711no—
262C4⋊C4—711no—
263C4⋊C4—1421no—
264C4⋊C4—1421no—
265C4⋊C4C22×D7111yescharacteristic
266C4⋊C4C22×D7111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—1421no—
273C22⋊C4—1421no—
274C22⋊C4—1421no—
275C42—21no—
276C42—1421no—
277C42—1421no—
278C42—1421no—
279C42C22⋊D7111yescharacteristic
280C42C22⋊D7111yescharacteristic
281C42C22×D7111yescharacteristic
282C42C22×D7111yescharacteristic
283C23—21no—
284C23—1421no—
285C23C2×C22⋊D7111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—712no—
289Q8—1421no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—712no—
294D4—1424no—
295D4—1421no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—2842no—
305C2×C4—2842no—
306C2×C4—1424no—
307C2×C4—1421no—
308C2×C4—1421no—
309C2×C4—1421no—
310C2×C4C2×C22⋊D7111yescharacteristic
311C2×C4C2×C22⋊D7111yescharacteristic
312C2×C4C2×C22⋊D7111yescharacteristic
313C2×C4C2×C22⋊D7111yescharacteristic
314C2×C4C2×C22⋊D7111yescharacteristic
315C2×C4C23×D7111yescharacteristic
316C8—1421no—
317C8—1421no—
318C8—1421no—
319C8—1421no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2841no—
327C22—2841no—
328C22—1422no—
329C22C22×C22⋊D7111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2841no—
338C4—2841no—
339C4—1422no—
340C4#1455614812yes—
341C4#41×D7111yescharacteristic
342C4#41×D7111yescharacteristic
343C2—41no—
344C2—81no—
345C2—2842no—
346C2#1798650611yescharacteristic
347C2C2×#1455614811yescharacteristic
348C2#1798679711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#529×C71C2
socleC22×C71C22×D4
hypercenter#529D71
hypocenterC71#3102
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#11765865C2semidirect
2. #17986337C2semidirect
3. #17986320C2semidirect
4. #17986303C2semidirect
5. #17986296C2semidirect
6. #17986218C2semidirect
7. #17986211C2semidirect
8. #17986159C2semidirect
10. C4×#11765855C2semidirect
11. C4×#11765852C2semidirect
12. C4×#11765853C2semidirect
13. C4×#11765850C2semidirect
14. #17986052C2semidirect
15. #529×C71C2semidirect
175. C71#3102semidirect
176. #529D71semidirect