Finite Group Databasebeta

← #22599222

Subgroups — #22599222

Order 9088.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986577C211yesmaximal, characteristic
2#17986340C211yesmaximal, characteristic, complemented
3#17986332C211yesmaximal, characteristic, complemented
4#17986327C211yesmaximal, characteristic, complemented
5#17986323C211yesmaximal, characteristic, complemented
6#17986255C211yesmaximal, characteristic, complemented
7#17986247C211yesmaximal, characteristic, complemented
8#17986238C211yesmaximal, characteristic, complemented
9#17986230C211yesmaximal, characteristic, complemented
10#17986159C211yesmaximal, characteristic, complemented
11#17986159C211yesmaximal, characteristic, complemented
12#17986155C211yesmaximal, characteristic, complemented
13#17986138C211yesmaximal, characteristic, complemented
14#17985966C211yesmaximal, characteristic, complemented
15#536×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×#11765855C2211yescharacteristic
18C2×#11765855C2211yescharacteristic
19C2×#11765852C2211yescharacteristic
20C2×#11765852C2211yescharacteristic
21C2×#11765849C2211yescharacteristic
22C22×C71⋊C8C2211yescharacteristic
23#14556107C2211yescharacteristic
24#14556107C2211yescharacteristic
25#14556104—21no—
26#14556102C2211yescharacteristic
27#14556102C2211yescharacteristic
28#14556100—21no—
29#14556100—21no—
30#14556099—21no—
31C2×C4⋊Dic71C2211yescharacteristic
32#14556061C2211yescharacteristic
33#14556061C2211yescharacteristic
34#14556059C2211yescharacteristic
35#14556059C2211yescharacteristic
36#14556052C2211yescharacteristic
37#14556052C2211yescharacteristic
38#14556052C2211yescharacteristic
39#14556052C2211yescharacteristic
40#14556051C2211yescharacteristic
41#14556051C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46C22⋊(C71⋊C8)C2211yescharacteristic
47C22⋊(C71⋊C8)C2211yescharacteristic
48C2×#41×C71C2211yescharacteristic
49C22×Q8×C71C2211yescharacteristic
50C4⋊Q8×C71—21no—
51#124×C71—21no—
52#123×C71—21no—
53#123×C71—21no—
54C22⋊Q8×C71C2211yescharacteristic
55C22⋊Q8×C71C2211yescharacteristic
56C22⋊Q8×C71C2211yescharacteristic
57C22⋊Q8×C71C2211yescharacteristic
58#117×C71C2211yescharacteristic
59#11765865—41no—
60#11765865—41no—
61C2×Dic142C2311yescharacteristic
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C2×C22⋊D71—21no—
65C2×C22⋊D71—21no—
66C22×Dic71—21no—
67C2×C4×D71—21no—
68#11765855—41no—
69#11765855—41no—
70#11765852—41no—
71#11765852—41no—
72#11765849—41no—
73C2×C71⋊C8—41no—
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C2×C71⋊C8C2311yescharacteristic
77C2×C71⋊C8C2311yescharacteristic
78C4⋊Dic71—21no—
79C4⋊Dic71C2311yescharacteristic
80C4⋊Dic71C2311yescharacteristic
81Dic71⋊C4—21no—
82Dic71⋊C4—21no—
83C22⋊Dic71—21no—
84C22⋊Dic71—21no—
85(C2×D71)⋊C4—21no—
86(C2×D71)⋊C4—21no—
87#41×C71—41no—
88#41×C71—41no—
89C2×Q8×C71—21no—
90C2×Q8×C71—41no—
91C2×Q8×C71—41no—
92C2×Q8×C71D411yescharacteristic
93C2×Q8×C71C2311yescharacteristic
94C2×Q8×C71C2311yescharacteristic
95C2×D4×C71D411yescharacteristic
96C2×D4×C71D411yescharacteristic
97C2×D4×C71D411yescharacteristic
98C22×C4×C71—21no—
99C22×C4×C71C2311yescharacteristic
100C22×C4×C71C2311yescharacteristic
101C22×C4×C71C2311yescharacteristic
102C4⋊C4×C71—21no—
103C4⋊C4×C71—21no—
104C4⋊C4×C71—21no—
105C4⋊C4×C71—21no—
106C4⋊C4×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C22⋊C4×C71—21no—
109C22⋊C4×C71—21no—
110C22⋊C4×C71—21no—
111C22⋊C4×C71—21no—
112C22⋊C4×C71—21no—
113C42×C71—21no—
114C23×C71C2×D411yescharacteristic
115C23×C71C2×D411yescharacteristic
116C23×C71C2×D411yescharacteristic
117C22×D71—21no—
118Q8×C71—21no—
119Q8×C71—21no—
120Q8×C71—21no—
121Q8×C71—21no—
122Q8×C71—41no—
123Q8×C71—42no—
124D4×C71—41no—
125D4×C71—41no—
126D4×C71—41no—
127C2×C4×C71—21no—
128C2×C4×C71—21no—
129C2×C4×C71—21no—
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71—21no—
133C2×C4×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71—42no—
138C2×C4×C71C2×D411yescharacteristic
139C2×C4×C71C2×D411yescharacteristic
140C2×C4×C71C2×D411yescharacteristic
141C2×C4×C71C2411yescharacteristic
142C22⋊D71—42no—
143C22⋊D71—81no—
144C22⋊D71—81no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—81no—
149D284—21no—
150D284—21no—
151C4×D71—42no—
152Dic142—21no—
153Dic142—21no—
154C71⋊C8—21no—
155C71⋊C8—21no—
156C71⋊C8—21no—
157C71⋊C8—21no—
158C22×C71—21no—
159C22×C71—21no—
160C22×C71—21no—
161C22×C71—21no—
162C22×C71—21no—
163C22×C71—21no—
164C22×C71—21no—
165C22×C71—21no—
166C22×C71—21no—
167C22×C71C22×D411yescharacteristic
168C2×D71—41no—
169C2×D71—41no—
170C2×D71—41no—
171C4×C71—21no—
172C4×C71—21no—
173C4×C71—21no—
174C4×C71—41no—
175C4×C71—41no—
176C4×C71—41no—
177C4×C71—41no—
178C4×C71H(5,𝔽2)11yescharacteristic
179C4×C71H(5,𝔽2)11yescharacteristic
180Dic71—41no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—41no—
184C2×C71—41no—
185C2×C71—41no—
186C2×C71#53411yescharacteristic
187C2×C71#57711yescharacteristic
188C2×C71#57811yescharacteristic
189D71—81no—
190#3201—711nomaximal, Sylow
191C71#320111yescharacteristic, complemented, Sylow
192#537—711no—
193#536D7111yescharacteristic, complemented
194#485—711no—
195#484—711no—
196#483—711no—
197#482—711no—
198#470—711no—
199#468—711no—
200#467—711no—
201#465—711no—
202#452—711no—
203#452—711no—
204#451—711no—
205#448—711no—
206#408—711no—
207C2×#41—711no—
208C2×#41C2×D7111yescharacteristic
209C22×Q8C2×D7111yescharacteristic
210C2×Q16—711no—
211C2×Q16—711no—
212C2×SD16—711no—
213C2×SD16—711no—
214C2×M16—711no—
215C22×C8—711no—
216C4⋊Q8—21no—
217#124—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—711no—
221C22⋊Q8—711no—
222C22⋊Q8—1421no—
223C22⋊Q8C2×D7111yescharacteristic
224C22⋊Q8C2×D7111yescharacteristic
225C22⋊Q8C2×D7111yescharacteristic
226C22⋊Q8C2×D7111yescharacteristic
227#121—711no—
228#121—711no—
229#121—1421no—
230#121—1421no—
231#121—1421no—
232#117C2×D7111yescharacteristic
233C2×C4⋊C4—711no—
234#107—711no—
235#107—711no—
236#106—711no—
237#106—711no—
238#103—711no—
239#103—711no—
240#103—711no—
241#103—711no—
242#103—711no—
243#103—711no—
244#102—711no—
245#102—711no—
246C22⋊C8—711no—
247C22⋊C8—711no—
248C22⋊C8—711no—
249C22⋊C8—711no—
250#41—41no—
251#41—41no—
252#41—2841no—
253#41—2841no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—711no—
258C2×Q8C22⋊D7111yescharacteristic
259C2×Q8C22×D7111yescharacteristic
260C2×Q8C22×D7111yescharacteristic
261C2×D4—711no—
262C2×D4—1421no—
263C2×D4—1421no—
264C2×D4—1421no—
265C2×D4C22⋊D7111yescharacteristic
266C2×D4C22⋊D7111yescharacteristic
267C2×D4C22⋊D7111yescharacteristic
268C22×C4—21no—
269C22×C4—1421no—
270C22×C4—1421no—
271C22×C4C22×D7111yescharacteristic
272C22×C4C22×D7111yescharacteristic
273C22×C4C22×D7111yescharacteristic
274Q16—2841no—
275Q16—2841no—
276SD16—2841no—
277SD16—2841no—
278M16—2841no—
279C2×C8—2841no—
280C2×C8—711no—
281C2×C8—711no—
282C2×C8—711no—
283C2×C8—711no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—711no—
289C4⋊C4—711no—
290C4⋊C4—1421no—
291C4⋊C4—1421no—
292C4⋊C4—1421no—
293C4⋊C4C22×D7111yescharacteristic
294C4⋊C4C22×D7111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1421no—
301C22⋊C4—1421no—
302C22⋊C4—1421no—
303C22⋊C4—1421no—
304C42—21no—
305C23—1421no—
306C23C2×C22⋊D7111yescharacteristic
307C23C2×C22⋊D7111yescharacteristic
308C23C2×C22⋊D7111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—1421no—
316Q8—1421no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—2842no—
321D4—5681no—
322D4—5681no—
323D4—1421no—
324D4—1421no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—2842no—
337C2×C4—5681no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4C2×C22⋊D7111yescharacteristic
342C2×C4C2×C22⋊D7111yescharacteristic
343C2×C4C2×C22⋊D7111yescharacteristic
344C2×C4C23×D7111yescharacteristic
345C8—1421no—
346C8—1421no—
347C8—1421no—
348C8—1421no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2841no—
359C22—2841no—
360C22—2841no—
361C22C22×C22⋊D7111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2841no—
370C4—2841no—
371C4—2841no—
372C4#1455617311yescharacteristic
373C4#1455617311yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—5681no—
378C2#1798655811yescharacteristic
379C2#1798680711yescharacteristic
380C2#1798681411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#536×C71C2
socleC22×C71C22×D4
hypercenter#536D71
hypocenterC71#3201
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #17986340C2semidirect
3. #17986332C2semidirect
4. #17986327C2semidirect
5. #17986323C2semidirect
6. #17986255C2semidirect
7. #17986247C2semidirect
8. #17986238C2semidirect
9. #17986230C2semidirect
10. #17986159C2semidirect
11. #17986159C2semidirect
12. #17986155C2semidirect
13. #17986138C2semidirect
14. #17985966C2semidirect
15. #536×C71C2semidirect
191. C71#3201semidirect
193. #536D71semidirect