Finite Group Databasebeta

← #22595378

Subgroups — #22595378

Order 9088.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985935C211yesmaximal, characteristic, complemented
2#17985928C211yesmaximal, characteristic, complemented
3#17985927C211yesmaximal, characteristic, complemented
4#17985925C211yesmaximal, characteristic, complemented
5#17985923C211yesmaximal, characteristic, complemented
6#17985921C211yesmaximal, characteristic, complemented
7#17985893C211yesmaximal, characteristic, complemented
8#17985891C211yesmaximal, characteristic, complemented
9#17985890C211yesmaximal, characteristic, complemented
10#17985890C211yesmaximal, characteristic, complemented
11#17985888C211yesmaximal, characteristic, complemented
12#17985854C211yesmaximal, characteristic
13#17985854C211yesmaximal, characteristic
14#17985854C211yesmaximal, characteristic
15#388×C71C211yesmaximal, characteristic, complemented
16C24×D71C2211yescharacteristic
17C2×C4⋊Dic71C2211yescharacteristic, complemented
18C2×Dic71⋊C4C2211yescharacteristic, complemented
19C2×Dic71⋊C4C2211yescharacteristic, complemented
20C2×Dic71⋊C4C2211yescharacteristic, complemented
21C2×Dic71⋊C4C2211yescharacteristic, complemented
22C2×C22⋊Dic71C2211yescharacteristic
23C2×C22⋊Dic71C2211yescharacteristic
24C2×C22⋊Dic71C2211yescharacteristic
25C2×(C2×D71)⋊C4C2211yescharacteristic
26C2×(C2×D71)⋊C4C2211yescharacteristic
27C2×(C2×D71)⋊C4C2211yescharacteristic
28C2×(C2×D71)⋊C4C2211yescharacteristic
29C2×(C2×D71)⋊C4C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×(C2×D71)⋊C4C2211yescharacteristic
33C2×(C2×D71)⋊C4C2211yescharacteristic
34C2×(C2×D71)⋊C4C2211yescharacteristic
35C2×(C2×D71)⋊C4C2211yescharacteristic
36C2×(C2×D71)⋊C4C2211yescharacteristic
37C2×C4×Dic71C2211yescharacteristic, complemented
38C71⋊#95C2211yescharacteristic, complemented
39C71⋊#95C2211yescharacteristic, complemented
40C71⋊#95C2211yescharacteristic, complemented
41C71⋊#95C2211yescharacteristic, complemented
42C71⋊#95C2211yescharacteristic, complemented
43C71⋊#95C2211yescharacteristic, complemented
44C2×C4⋊C4×C71C2211yescharacteristic, complemented
45C2×C22⋊C4×C71C2211yescharacteristic
46C2×C22⋊C4×C71C2211yescharacteristic
47C2×C22⋊C4×C71C2211yescharacteristic
48C2×C42×C71C2211yescharacteristic, complemented
49#95×C71C2211yescharacteristic, complemented
50#95×C71C2211yescharacteristic, complemented
51C23×D71—22no—
52C23×D71—22no—
53C23×D71—22no—
54C23×D71—41no—
55C23×D71—41no—
56C23×D71—41no—
57C23×D71—41no—
58C23×D71C2311yescharacteristic
59C23×D71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C22×Dic71C2311yescharacteristic
64C22×Dic71C2311yescharacteristic
65C22×Dic71C2311yescharacteristic
66C4⋊Dic71—41no—
67Dic71⋊C4—41no—
68Dic71⋊C4—41no—
69Dic71⋊C4—41no—
70Dic71⋊C4—41no—
71C22⋊Dic71—22no—
72C22⋊Dic71—41no—
73C22⋊Dic71—41no—
74(C2×D71)⋊C4—22no—
75(C2×D71)⋊C4—22no—
76(C2×D71)⋊C4—22no—
77(C2×D71)⋊C4—22no—
78(C2×D71)⋊C4—41no—
79(C2×D71)⋊C4—41no—
80(C2×D71)⋊C4—41no—
81(C2×D71)⋊C4—41no—
82(C2×D71)⋊C4—41no—
83(C2×D71)⋊C4—41no—
84(C2×D71)⋊C4—41no—
85(C2×D71)⋊C4—41no—
86C4×Dic71—41no—
87C24×C71C2311yescharacteristic
88C22×C4×C71C2311yescharacteristic
89C22×C4×C71C2311yescharacteristic
90C22×C4×C71C2311yescharacteristic
91C22×C4×C71C2311yescharacteristic
92C22×C4×C71C2311yescharacteristic
93C22×C4×C71C2311yescharacteristic
94C4⋊C4×C71—41no—
95C22⋊C4×C71—22no—
96C22⋊C4×C71—41no—
97C22⋊C4×C71—41no—
98C42×C71—41no—
99C23×C71—21no—
100C23×C71—21no—
101C23×C71—21no—
102C23×C71—21no—
103C23×C71—21no—
104C23×C71—21no—
105C23×C71#4112yes—
106C23×C71C2411yescharacteristic
107C22×D71—21no—
108C22×D71—21no—
109C22×D71—21no—
110C22×D71—21no—
111C22×D71—21no—
112C22×D71—21no—
113C22×D71—21no—
114C22×D71—21no—
115C22×D71—21no—
116C22×D71—21no—
117C22×D71—21no—
118C22×D71—21no—
119C22×D71—44no—
120C22×D71—44no—
121C22×D71—44no—
122C22×D71—44no—
123C22×D71—44no—
124C22×D71—44no—
125C22×D71—44no—
126C22×D71#4112yes—
127C22×D71#4112yes—
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—21no—
138C2×C4×C71—21no—
139C2×C4×C71—21no—
140C2×C4×C71—21no—
141C2×C4×C71—21no—
142C2×C4×C71—21no—
143C2×C4×C71—21no—
144C2×C4×C71—21no—
145C2×C4×C71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—21no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152C2×Dic71—21no—
153C2×Dic71—21no—
154C2×Dic71—21no—
155C2×Dic71—21no—
156C2×Dic71—21no—
157C2×Dic71—21no—
158C2×Dic71—21no—
159C2×Dic71—21no—
160C2×Dic71—21no—
161C2×Dic71—21no—
162C2×Dic71—21no—
163C2×Dic71—21no—
164C22×C71—22no—
165C22×C71—22no—
166C22×C71—22no—
167C22×C71—41no—
168C22×C71—41no—
169C22×C71—41no—
170C22×C71—41no—
171C22×C71C2×#4111yescharacteristic
172C22×C71C2×#4111yescharacteristic
173C22×C71C2×#4111yescharacteristic
174C22×C71H(5,𝔽2)11yescharacteristic
175C22×C71H(5,𝔽2)11yescharacteristic
176C22×C71H(5,𝔽2)11yescharacteristic
177C22×C71H(5,𝔽2)11yescharacteristic
178C2×D71—22no—
179C2×D71—22no—
180C2×D71—22no—
181C2×D71—22no—
182C2×D71—22no—
183C2×D71—22no—
184C2×D71—416no—
185C2×D71—41no—
186C2×D71—41no—
187C2×D71—41no—
188C2×D71—41no—
189C2×D71—41no—
190C2×D71—41no—
191C2×D71—41no—
192C2×D71—41no—
193C4×C71—41no—
194C4×C71—41no—
195C4×C71—41no—
196C4×C71—41no—
197C4×C71—41no—
198C4×C71—41no—
199Dic71—41no—
200Dic71—41no—
201Dic71—41no—
202Dic71—41no—
203Dic71—41no—
204Dic71—41no—
205C2×C71—42no—
206C2×C71#53811yescharacteristic
207C2×C71#53811yescharacteristic
208C2×C71#53811yescharacteristic
209C2×C71#55111yescharacteristic
210C2×C71#55111yescharacteristic
211C2×C71#55111yescharacteristic
212C2×C71#56011yescharacteristic
213D71—42no—
214D71—42no—
215#2735—711nomaximal, Sylow
216C71#273511yescharacteristic, complemented, Sylow
217#399—711no—
218#397—711no—
219#397—711no—
220#397—711no—
221#396—711no—
222#396—711no—
223#388—711no—
224#388—711no—
225#388—711no—
226#388—711no—
227#388—711no—
228#388D7111yescharacteristic, complemented
229#379—711no—
230#379—711no—
231#379—711no—
232C25—711no—
233C2×C4⋊C4—711no—
234C2×C4⋊C4—711no—
235C2×C4⋊C4—711no—
236C2×C4⋊C4—711no—
237C2×C4⋊C4—711no—
238C2×C4⋊C4C2×D7111yescharacteristic, complemented
239C2×C22⋊C4—711no—
240C2×C22⋊C4—711no—
241C2×C22⋊C4—711no—
242C2×C22⋊C4—711no—
243C2×C22⋊C4—711no—
244C2×C22⋊C4—711no—
245C2×C22⋊C4—711no—
246C2×C22⋊C4—711no—
247C2×C22⋊C4—711no—
248C2×C22⋊C4—711no—
249C2×C22⋊C4—711no—
250C2×C22⋊C4—711no—
251C2×C22⋊C4—711no—
252C2×C22⋊C4—711no—
253C2×C22⋊C4—711no—
254C2×C22⋊C4C2×D7111yescharacteristic
255C2×C22⋊C4C2×D7111yescharacteristic
256C2×C22⋊C4C2×D7111yescharacteristic
257C2×C42—711no—
258C2×C42C2×D7111yescharacteristic, complemented
259#95—711no—
260#95—711no—
261#95—711no—
262#95—711no—
263#95—711no—
264#95—711no—
265#95C2×D7111yescharacteristic, complemented
266#95C2×D7111yescharacteristic, complemented
267C24—2841no—
268C24—2841no—
269C24—2841no—
270C24—2841no—
271C24—711no—
272C24—711no—
273C24—1422no—
274C24—1422no—
275C24—1422no—
276C24C22×D7111yescharacteristic
277C22×C4—711no—
278C22×C4—711no—
279C22×C4—711no—
280C22×C4—711no—
281C22×C4—711no—
282C22×C4—711no—
283C22×C4C22×D7111yescharacteristic
284C22×C4C22×D7111yescharacteristic
285C22×C4C22×D7111yescharacteristic
286C22×C4C22×D7111yescharacteristic
287C22×C4C22×D7111yescharacteristic
288C22×C4C22×D7111yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—2841no—
291C4⋊C4—2841no—
292C4⋊C4—2841no—
293C4⋊C4—2841no—
294C4⋊C4—2841no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—2841no—
299C22⋊C4—2841no—
300C22⋊C4—2841no—
301C22⋊C4—2841no—
302C22⋊C4—2841no—
303C22⋊C4—2841no—
304C22⋊C4—2841no—
305C22⋊C4—2841no—
306C22⋊C4—2841no—
307C22⋊C4—2841no—
308C22⋊C4—1422no—
309C22⋊C4—1422no—
310C22⋊C4—1422no—
311C22⋊C4—1422no—
312C22⋊C4—1422no—
313C42—41no—
314C42—2841no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—2844no—
322C23—2844no—
323C23—2844no—
324C23—2844no—
325C23—2844no—
326C23—2844no—
327C23—2844no—
328C23—712no—
329C23—712no—
330C23—1421no—
331C23—1421no—
332C23—1421no—
333C23—1421no—
334C23—1421no—
335C23—1421no—
336C23—1421no—
337C23—1421no—
338C23—1421no—
339C23—1421no—
340C23—1421no—
341C23—1421no—
342C23#1176586512yes—
343C23C23×D7111yescharacteristic
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—1421no—
363C2×C4—1421no—
364C2×C4—1421no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4—1421no—
370C2×C4—1421no—
371C2×C4—1421no—
372C2×C4—1421no—
373C2×C4—1421no—
374C2×C4—1421no—
375C2×C4—1421no—
376C2×C4—1421no—
377C2×C4—1421no—
378C2×C4—1421no—
379C2×C4—1421no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—28416no—
388C22—2841no—
389C22—2841no—
390C22—2841no—
391C22—2841no—
392C22—2841no—
393C22—2841no—
394C22—2841no—
395C22—2841no—
396C22—1422no—
397C22—1422no—
398C22—1422no—
399C22—1422no—
400C22—1422no—
401C22—1422no—
402C22#41×D7111yescharacteristic
403C22#41×D7111yescharacteristic
404C22C2×#1176586511yescharacteristic
405C22#1455617311yescharacteristic
406C22#1455617311yescharacteristic
407C22#1455617411yescharacteristic
408C22#1455617411yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—2841no—
416C4—2841no—
417C4—2841no—
418C4—2841no—
419C4—2841no—
420C4—2841no—
421C2—42no—
422C2—2842no—
423C2—2842no—
424C2#1798658111yescharacteristic
425C2#1798658211yescharacteristic
426C2#1798658311yescharacteristic
427C2#1798667311yescharacteristic
428C2#1798667411yescharacteristic
429C2#1798667811yescharacteristic
430C2#1798673911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#388×C71C2
hypercenter#388D71
hypocenterC71#2735
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #17985935C2semidirect
2. #17985928C2semidirect
3. #17985927C2semidirect
4. #17985925C2semidirect
5. #17985923C2semidirect
6. #17985921C2semidirect
7. #17985893C2semidirect
8. #17985891C2semidirect
9. #17985890C2semidirect
10. #17985890C2semidirect
11. #17985888C2semidirect
15. #388×C71C2semidirect
17. C2×C4⋊Dic71C22semidirect
18. C2×Dic71⋊C4C22semidirect
19. C2×Dic71⋊C4C22semidirect
20. C2×Dic71⋊C4C22semidirect
21. C2×Dic71⋊C4C22semidirect
37. C2×C4×Dic71C22semidirect
38. C71⋊#95C22semidirect
39. C71⋊#95C22semidirect
40. C71⋊#95C22semidirect
41. C71⋊#95C22semidirect
42. C71⋊#95C22semidirect
43. C71⋊#95C22semidirect
44. C2×C4⋊C4×C71C22semidirect
48. C2×C42×C71C22semidirect
49. #95×C71C22semidirect
50. #95×C71C22semidirect
216. C71#2735semidirect
228. #388D71semidirect
238. C2×C4⋊C4C2×D71semidirect
258. C2×C42C2×D71semidirect
265. #95C2×D71semidirect
266. #95C2×D71semidirect