Finite Group Databasebeta

← #22600430

Subgroups — #22600430

Order 9088.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986654C211yesmaximal, characteristic
2#17986369C211yesmaximal, characteristic, complemented
3#17986340C211yesmaximal, characteristic, complemented
4#17986334C211yesmaximal, characteristic, complemented
5#17986296C211yesmaximal, characteristic, complemented
6#17986255C211yesmaximal, characteristic, complemented
7#17986238C211yesmaximal, characteristic, complemented
8#17986209C211yesmaximal, characteristic, complemented
9#17986159C211yesmaximal, characteristic, complemented
10#17986159C211yesmaximal, characteristic, complemented
11#17986097C211yesmaximal, characteristic, complemented
12#17986071C211yesmaximal, characteristic, complemented
13#17985998C211yesmaximal, characteristic, complemented
14#17985993C211yesmaximal, characteristic, complemented
15#552×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×#11765865C2211yescharacteristic
18C2×#11765855C2211yescharacteristic
19C2×#11765855C2211yescharacteristic
20C2×#11765852C2211yescharacteristic
21C2×#11765849C2211yescharacteristic
22C22×C71⋊C8C2211yescharacteristic
23#14556128C2211yescharacteristic
24#14556110—21no—
25#14556110—21no—
26#14556107C2211yescharacteristic
27#14556107C2211yescharacteristic
28#14556099—21no—
29C4×D284C2211yescharacteristic
30C4⋊C4×D71—21no—
31#14556061C2211yescharacteristic
32#14556061C2211yescharacteristic
33#14556059C2211yescharacteristic
34C4⋊(C71⋊C8)C2211yescharacteristic
35#14556052C2211yescharacteristic
36#14556051C2211yescharacteristic
37#14556051C2211yescharacteristic
38#14556051C2211yescharacteristic
39#14556051C2211yescharacteristic
40#14556051C2211yescharacteristic
41#14556051C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44#14556048C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46C22⋊(C71⋊C8)C2211yescharacteristic
47#14556039C2211yescharacteristic
48#126×C71—21no—
49#125×C71—21no—
50#125×C71C2211yescharacteristic
51#123×C71—21no—
52C22⋊Q8×C71C2211yescharacteristic
53C22⋊Q8×C71C2211yescharacteristic
54C4×Q8×C71C2211yescharacteristic
55C4×D4×C71C2211yescharacteristic
56#117×C71—21no—
57#117×C71C2211yescharacteristic
58C2×C4⋊C4×C71C2211yescharacteristic
59#11765865—22no—
60#11765865—22no—
61#11765865—41no—
62#11765865—41no—
63C2×Dic142C2311yescharacteristic
64C2×Dic142C2311yescharacteristic
65C2×D284C2311yescharacteristic
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68C2×C4×D71—21no—
69C2×C4×D71—21no—
70C2×C4×D71—21no—
71#11765855—41no—
72#11765855—41no—
73#11765852—22no—
74#11765849—41no—
75C2×C71⋊C8—41no—
76C2×C71⋊C8C2311yescharacteristic
77C2×C71⋊C8C2311yescharacteristic
78C2×C71⋊C8C2311yescharacteristic
79C2×C71⋊C8C2311yescharacteristic
80C4⋊Dic71—21no—
81C4⋊Dic71—21no—
82C4⋊Dic71C2311yescharacteristic
83Dic71⋊C4—21no—
84Dic71⋊C4—21no—
85C22⋊Dic71—21no—
86C22⋊Dic71—21no—
87(C2×D71)⋊C4—21no—
88C2×Q8×C71C2311yescharacteristic
89C2×D4×C71D411yescharacteristic
90C22×C4×C71—21no—
91C22×C4×C71C2311yescharacteristic
92C22×C4×C71C2311yescharacteristic
93C4⋊C4×C71—21no—
94C4⋊C4×C71—21no—
95C4⋊C4×C71—21no—
96C4⋊C4×C71—21no—
97C4⋊C4×C71—21no—
98C4⋊C4×C71—21no—
99C4⋊C4×C71D411yescharacteristic
100C4⋊C4×C71C2311yescharacteristic
101C4⋊C4×C71C2311yescharacteristic
102C4⋊C4×C71C2311yescharacteristic
103C22⋊C4×C71—21no—
104C22⋊C4×C71—21no—
105C22⋊C4×C71—21no—
106C22⋊C4×C71D411yescharacteristic
107C22⋊C4×C71D411yescharacteristic
108C42×C71—21no—
109C42×C71—21no—
110C42×C71C2311yescharacteristic
111C23×C71C2×D411yescharacteristic
112C23×C71C2×D411yescharacteristic
113C22×D71—21no—
114Q8×C71—21no—
115Q8×C71—21no—
116D4×C71—41no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—42no—
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2×D411yescharacteristic
130C2×C4×C71C2411yescharacteristic
131C22⋊D71—42no—
132C22⋊D71—42no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136D284—21no—
137D284#4112yes—
138C4×D71—42no—
139C4×D71—42no—
140C4×D71—42no—
141Dic142—21no—
142Dic142—21no—
143Dic142—21no—
144Dic142—21no—
145C71⋊C8—21no—
146C71⋊C8—21no—
147C71⋊C8—21no—
148C71⋊C8—21no—
149C22×C71—21no—
150C22×C71—21no—
151C22×C71—21no—
152C22×C71—21no—
153C22×C71—21no—
154C22×C71—21no—
155C22×C71C22×D411yescharacteristic
156C2×D71—22no—
157C2×D71—41no—
158C2×D71—41no—
159C4×C71—21no—
160C4×C71—21no—
161C4×C71—21no—
162C4×C71—21no—
163C4×C71—41no—
164C4×C71—41no—
165C4×C71—41no—
166C4×C71—41no—
167C4×C71C2×#4111yescharacteristic
168C4×C71H(5,𝔽2)11yescharacteristic
169Dic71—41no—
170Dic71—41no—
171Dic71—41no—
172C2×C71—41no—
173C2×C71—41no—
174C2×C71#54611yescharacteristic
175C2×C71#57511yescharacteristic
176C2×C71#57811yescharacteristic
177D71—42no—
178#3315—711nomaximal, Sylow
179C71#331511yescharacteristic, complemented, Sylow
180#552D7111yescharacteristic, complemented
181#547—711no—
182#491—711no—
183#485—711no—
184#484—711no—
185#478—711no—
186#470—711no—
187#467—711no—
188#462—711no—
189#452—711no—
190#452—711no—
191#440—711no—
192#435—711no—
193#417—711no—
194#416—711no—
195C2×#41—711no—
196C2×#41—711no—
197C2×Q16—711no—
198C2×Q16—711no—
199C2×SD16—711no—
200C2×M16—711no—
201C22×C8—711no—
202C4⋊Q8—711no—
203#126—21no—
204#125—21no—
205#125C2×D7111yescharacteristic
206#123—21no—
207#123—1421no—
208#123—1421no—
209C22⋊Q8—711no—
210C22⋊Q8—711no—
211C22⋊Q8C2×D7111yescharacteristic
212C22⋊Q8C2×D7111yescharacteristic
213#121—1421no—
214C4×Q8C2×D7111yescharacteristic
215C4×D4—711no—
216C4×D4C2×D7111yescharacteristic
217#117—21no—
218#117C2×D7111yescharacteristic
219C2×C4⋊C4—1421no—
220C2×C4⋊C4C2×D7111yescharacteristic
221#107—711no—
222#107—711no—
223#106—711no—
224C4⋊C8—711no—
225#103—711no—
226#103—711no—
227#103—711no—
228#103—711no—
229#103—711no—
230#103—711no—
231#103—711no—
232#102—711no—
233#102—711no—
234#102—711no—
235C22⋊C8—711no—
236C22⋊C8—711no—
237#97—711no—
238#41—2841no—
239#41—2841no—
240#41—1422no—
241#41—1422no—
242C2×Q8—711no—
243C2×Q8—711no—
244C2×Q8C22×D7111yescharacteristic
245C2×D4—711no—
246C2×D4—1421no—
247C2×D4—1421no—
248C2×D4C22⋊D7111yescharacteristic
249C22×C4—21no—
250C22×C4—1421no—
251C22×C4—1421no—
252C22×C4—1421no—
253C22×C4C22×D7111yescharacteristic
254C22×C4C22×D7111yescharacteristic
255Q16—2841no—
256Q16—2841no—
257SD16—1422no—
258M16—2841no—
259C2×C8—2841no—
260C2×C8—711no—
261C2×C8—711no—
262C2×C8—711no—
263C2×C8—711no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—711no—
271C4⋊C4—1421no—
272C4⋊C4—1421no—
273C4⋊C4—1421no—
274C4⋊C4—1421no—
275C4⋊C4C22⋊D7111yescharacteristic
276C4⋊C4C22×D7111yescharacteristic
277C4⋊C4C22×D7111yescharacteristic
278C4⋊C4C22×D7111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1421no—
283C22⋊C4—1421no—
284C22⋊C4—1421no—
285C22⋊C4C22⋊D7111yescharacteristic
286C22⋊C4C22⋊D7111yescharacteristic
287C42—21no—
288C42—21no—
289C42C22×D7111yescharacteristic
290C23—1421no—
291C23C2×C22⋊D7111yescharacteristic
292C23C2×C22⋊D7111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1421no—
296Q8—1421no—
297Q8—1421no—
298Q8—1421no—
299D4—41no—
300D4—2842no—
301D4—2842no—
302D4—712no—
303D4—1421no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—2842no—
314C2×C4—2842no—
315C2×C4—2842no—
316C2×C4—1421no—
317C2×C4—1421no—
318C2×C4—1421no—
319C2×C4C2×C22⋊D7111yescharacteristic
320C2×C4C2×C22⋊D7111yescharacteristic
321C2×C4C2×C22⋊D7111yescharacteristic
322C2×C4C2×C22⋊D7111yescharacteristic
323C2×C4C23×D7111yescharacteristic
324C8—1421no—
325C8—1421no—
326C8—1421no—
327C8—1421no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—2841no—
335C22—2841no—
336C22—1422no—
337C22C22×C22⋊D7111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2841no—
347C4—2841no—
348C4—2841no—
349C4#41×D7111yescharacteristic
350C4#1455617411yescharacteristic
351C2—41no—
352C2—41no—
353C2—2842no—
354C2#1798663711yescharacteristic
355C2#1798679711yescharacteristic
356C2#1798681411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#552×C71C2
socleC22×C71C22×D4
hypercenter#552D71
hypocenterC71#3315
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #17986369C2semidirect
3. #17986340C2semidirect
4. #17986334C2semidirect
5. #17986296C2semidirect
6. #17986255C2semidirect
7. #17986238C2semidirect
8. #17986209C2semidirect
9. #17986159C2semidirect
10. #17986159C2semidirect
11. #17986097C2semidirect
12. #17986071C2semidirect
13. #17985998C2semidirect
14. #17985993C2semidirect
15. #552×C71C2semidirect
179. C71#3315semidirect
180. #552D71semidirect