Finite Group Databasebeta

← #22599434

Subgroups — #22599434

Order 9088.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986620C211yesmaximal, characteristic, complemented
2#17986386C211yesmaximal, characteristic, complemented
3#17986381C211yesmaximal, characteristic, complemented
4#17986358C211yesmaximal, characteristic, complemented
5#17986345C211yesmaximal, characteristic, complemented
6#17986218C211yesmaximal, characteristic, complemented
7#17986211C211yesmaximal, characteristic, complemented
8#17986196C211yesmaximal, characteristic, complemented
9#17986191C211yesmaximal, characteristic, complemented
10#17986161C211yesmaximal, characteristic, complemented
11#17986150C211yesmaximal, characteristic, complemented
12#17986144C211yesmaximal, characteristic, complemented
13#17986133C211yesmaximal, characteristic, complemented
14#17986060C211yesmaximal, characteristic, complemented
15#535×C71C211yesmaximal, characteristic, complemented
16C2×#11765855C2211yescharacteristic, complemented
17C2×#11765853C2211yescharacteristic
18C2×#11765853C2211yescharacteristic
19C2×#11765853C2211yescharacteristic, complemented
20C2×#11765852C2211yescharacteristic, complemented
21C2×#11765850C2211yescharacteristic
22C2×#11765850C2211yescharacteristic
23C2×#11765850C2211yescharacteristic, complemented
24#14556128C2211yescharacteristic, complemented
25#14556123—21no—
26#14556116C2211yescharacteristic, complemented
27#14556114—21no—
28#14556110—21no—
29#14556107C2211yescharacteristic
30#14556106—21no—
31#14556102C2211yescharacteristic
32C4×Dic142C2211yescharacteristic, complemented
33C4×D284C2211yescharacteristic, complemented
34C4⋊(C71⋊C8)C2211yescharacteristic, complemented
35C4⋊(C71⋊C8)C2211yescharacteristic, complemented
36#14556052C2211yescharacteristic, complemented
37#14556052C2211yescharacteristic, complemented
38#14556049C2211yescharacteristic
39#14556049C2211yescharacteristic
40#14556049C2211yescharacteristic
41#14556049C2211yescharacteristic
42#14556049C2211yescharacteristic, complemented
43#14556049C2211yescharacteristic, complemented
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46#14556039C2211yescharacteristic, complemented
47C4×C71⋊C8C2211yescharacteristic, complemented
48C2×#41×C71C2211yescharacteristic
49C22×D4×C71C2211yescharacteristic
50#127×C71C2211yescharacteristic
51#127×C71C2211yescharacteristic
52#124×C71C2211yescharacteristic
53#124×C71C2211yescharacteristic
54#121×C71—21no—
55#121×C71—21no—
56#120×C71—21no—
57#120×C71—21no—
58#117×C71C2211yescharacteristic
59C2×Dic142—21no—
60C2×Dic142C2311yescharacteristic
61C2×D284C2311yescharacteristic
62C2×C22⋊D71—21no—
63C2×C4×D71—21no—
64#11765855—41no—
65#11765853—41no—
66#11765853—41no—
67#11765853—41no—
68#11765852—41no—
69#11765850—41no—
70#11765850—41no—
71#11765850—41no—
72C2×C71⋊C8C2311yescharacteristic
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C4⋊Dic71—21no—
77C4⋊Dic71C2311yescharacteristic
78C4⋊Dic71C2311yescharacteristic
79Dic71⋊C4—21no—
80Dic71⋊C4—21no—
81C22⋊Dic71—21no—
82(C2×D71)⋊C4—21no—
83(C2×D71)⋊C4—21no—
84(C2×D71)⋊C4—21no—
85(C2×D71)⋊C4—21no—
86C4×Dic71—21no—
87C24×C71—21no—
88#41×C71—41no—
89#41×C71—41no—
90C2×Q8×C71C2311yescharacteristic
91C2×D4×C71—21no—
92C2×D4×C71—21no—
93C2×D4×C71—21no—
94C2×D4×C71—21no—
95C2×D4×C71—21no—
96C2×D4×C71—21no—
97C2×D4×C71—41no—
98C2×D4×C71—41no—
99C2×D4×C71C2311yescharacteristic
100C2×D4×C71C2311yescharacteristic
101C2×D4×C71C2311yescharacteristic
102C22×C4×C71—21no—
103C22×C4×C71C2311yescharacteristic
104C4⋊C4×C71D411yescharacteristic
105C4⋊C4×C71D411yescharacteristic
106C22⋊C4×C71—21no—
107C22⋊C4×C71—21no—
108C22⋊C4×C71—21no—
109C22⋊C4×C71—21no—
110C22⋊C4×C71D411yescharacteristic
111C22⋊C4×C71D411yescharacteristic
112C42×C71C2311yescharacteristic
113C42×C71C2311yescharacteristic
114C23×C71—21no—
115C23×C71—21no—
116C23×C71—21no—
117C23×C71—42no—
118C23×C71—81no—
119C23×C71—81no—
120C23×C71C2×D411yescharacteristic
121C22×D71—21no—
122Q8×C71—21no—
123Q8×C71—21no—
124D4×C71—21no—
125D4×C71—21no—
126D4×C71—21no—
127D4×C71—21no—
128D4×C71—21no—
129D4×C71—21no—
130D4×C71—42no—
131D4×C71—42no—
132D4×C71—81no—
133D4×C71—81no—
134D4×C71—81no—
135D4×C71—81no—
136C2×C4×C71—21no—
137C2×C4×C71—21no—
138C2×C4×C71—21no—
139C2×C4×C71—42no—
140C2×C4×C71C2×D411yescharacteristic
141C2×C4×C71C2×D411yescharacteristic
142C2×C4×C71C2×D411yescharacteristic
143C2×C4×C71C2×D411yescharacteristic
144C2×C4×C71C2×D411yescharacteristic
145C2×C4×C71C2411yescharacteristic
146C22⋊D71—81no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—21no—
150D284—21no—
151D284—21no—
152C4×D71—81no—
153Dic142—21no—
154Dic142—21no—
155Dic142—81no—
156C71⋊C8—21no—
157C71⋊C8—21no—
158C71⋊C8—21no—
159C71⋊C8—21no—
160C22×C71—21no—
161C22×C71—21no—
162C22×C71—21no—
163C22×C71—41no—
164C22×C71—41no—
165C22×C71—41no—
166C22×C71—41no—
167C22×C71—41no—
168C22×C71—41no—
169C22×C71—41no—
170C22×C71—41no—
171C22×C71—41no—
172C22×C71—84no—
173C22×C71C22×D411yescharacteristic
174C2×D71—41no—
175C2×D71—41no—
176C2×D71—41no—
177C4×C71—21no—
178C4×C71—21no—
179C4×C71—21no—
180C4×C71—21no—
181C4×C71—21no—
182C4×C71—41no—
183C4×C71H(5,𝔽2)11yescharacteristic
184C4×C71H(5,𝔽2)11yescharacteristic
185Dic71—41no—
186Dic71—41no—
187Dic71—41no—
188C2×C71—41no—
189C2×C71—81no—
190C2×C71—81no—
191C2×C71—81no—
192C2×C71#53511yescharacteristic
193C2×C71#57611yescharacteristic
194C2×C71#57711yescharacteristic
195D71—81no—
196#3224—711nomaximal, Sylow
197C71#322411yescharacteristic, complemented, Sylow
198#542—711no—
199#535D7111yescharacteristic, complemented
200#496—711no—
201#495—711no—
202#489—711no—
203#486—711no—
204#464—711no—
205#463—711no—
206#460—711no—
207#459—711no—
208#452—711no—
209#450—711no—
210#449—711no—
211#447—711no—
212#433—711no—
213C2×#41C2×D7111yescharacteristic
214C22×D4C2×D7111yescharacteristic
215C2×Q16—711no—
216C2×SD16—711no—
217C2×SD16—711no—
218C2×SD16—711no—
219C2×SD16—711no—
220C2×D8—711no—
221C2×D8—711no—
222C2×D8—711no—
223C4⋊Q8—711no—
224#127C2×D7111yescharacteristic
225#127C2×D7111yescharacteristic
226#126—1421no—
227#124—711no—
228#124—1421no—
229#124C2×D7111yescharacteristic
230#124C2×D7111yescharacteristic
231#123—1421no—
232C22⋊Q8—711no—
233C22⋊Q8—1421no—
234#121—21no—
235#121—21no—
236#121—711no—
237#120—21no—
238#120—21no—
239C4×Q8—711no—
240C4×D4—711no—
241#117C2×D7111yescharacteristic
242C4⋊C8—711no—
243C4⋊C8—711no—
244#103—711no—
245#103—711no—
246#102—711no—
247#102—711no—
248#102—711no—
249#102—711no—
250#102—711no—
251#102—711no—
252C22⋊C8—711no—
253C22⋊C8—711no—
254#97—711no—
255C4×C8—711no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—711no—
260C2×Q8—1421no—
261C2×Q8C22×D7111yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—711no—
271C2×D4—1421no—
272C2×D4C22×D7111yescharacteristic
273C2×D4C22×D7111yescharacteristic
274C2×D4C22×D7111yescharacteristic
275C22×C4—21no—
276C22×C4—1421no—
277C22×C4C22×D7111yescharacteristic
278Q16—2841no—
279SD16—2841no—
280SD16—2841no—
281SD16—2841no—
282SD16—2841no—
283D8—2841no—
284D8—2841no—
285D8—2841no—
286C2×C8—711no—
287C2×C8—711no—
288C2×C8—711no—
289C2×C8—711no—
290C4⋊C4—711no—
291C4⋊C4—711no—
292C4⋊C4—1421no—
293C4⋊C4—1421no—
294C4⋊C4—1421no—
295C4⋊C4C22⋊D7111yescharacteristic
296C4⋊C4C22⋊D7111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1421no—
302C22⋊C4—1421no—
303C22⋊C4—1421no—
304C22⋊C4—1421no—
305C22⋊C4—1421no—
306C22⋊C4C22⋊D7111yescharacteristic
307C22⋊C4C22⋊D7111yescharacteristic
308C42—1421no—
309C42C22×D7111yescharacteristic
310C42C22×D7111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1421no—
318C23C2×C22⋊D7111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—5681no—
322Q8—1421no—
323Q8—1421no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—5681no—
337D4—1421no—
338D4—1421no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—5681no—
344C2×C4—1421no—
345C2×C4—1421no—
346C2×C4—1421no—
347C2×C4C2×C22⋊D7111yescharacteristic
348C2×C4C2×C22⋊D7111yescharacteristic
349C2×C4C2×C22⋊D7111yescharacteristic
350C2×C4C2×C22⋊D7111yescharacteristic
351C2×C4C2×C22⋊D7111yescharacteristic
352C2×C4C23×D7111yescharacteristic
353C8—1421no—
354C8—1421no—
355C8—1421no—
356C8—1421no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—2841no—
371C22—2841no—
372C22—2841no—
373C22C22×C22⋊D7111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—2841no—
381C4—2841no—
382C4—2841no—
383C4#1455617311yescharacteristic
384C4#1455617311yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—5681no—
390C2#1798656611yescharacteristic
391C2#1798680211yescharacteristic
392C2#1798681011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#535×C71C2
socleC22×C71C22×D4
hypercenter#535D71
hypocenterC71#3224
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #17986620C2semidirect
2. #17986386C2semidirect
3. #17986381C2semidirect
4. #17986358C2semidirect
5. #17986345C2semidirect
6. #17986218C2semidirect
7. #17986211C2semidirect
8. #17986196C2semidirect
9. #17986191C2semidirect
10. #17986161C2semidirect
11. #17986150C2semidirect
12. #17986144C2semidirect
13. #17986133C2semidirect
14. #17986060C2semidirect
15. #535×C71C2semidirect
16. C2×#11765855C22semidirect
19. C2×#11765853C22semidirect
20. C2×#11765852C22semidirect
23. C2×#11765850C22semidirect
24. #14556128C22semidirect
26. #14556116C22semidirect
32. C4×Dic142C22semidirect
33. C4×D284C22semidirect
34. C4⋊(C71⋊C8)C22semidirect
35. C4⋊(C71⋊C8)C22semidirect
36. #14556052C22semidirect
37. #14556052C22semidirect
42. #14556049C22semidirect
43. #14556049C22semidirect
46. #14556039C22semidirect
47. C4×C71⋊C8C22semidirect
197. C71#3224semidirect
199. #535D71semidirect