Finite Group Databasebeta

← #22592586

Subgroups — #22592586

Order 9088.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556122C211yesmaximal, characteristic, complemented
2C22×(C2×D71)⋊C4C211yesmaximal, characteristic
3#17985928C211yesmaximal, characteristic, complemented
4#17985928C211yesmaximal, characteristic, complemented
5#17985928C211yesmaximal, characteristic, complemented
6#17985923C211yesmaximal, characteristic, complemented
7#17985890C211yesmaximal, characteristic, complemented
8#17985890C211yesmaximal, characteristic, complemented
9#17985890C211yesmaximal, characteristic, complemented
10#17985872C211yesmaximal, characteristic, complemented
11#17985871C211yesmaximal, characteristic, complemented
12#17985857C211yesmaximal, characteristic, complemented
13#17985854C211yesmaximal, characteristic
14#17985854C211yesmaximal, characteristic
15C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C24×D71C2211yescharacteristic
17C23×Dic71C2211yescharacteristic
18#14556122—24no—
19C2×Dic71⋊C4C2211yescharacteristic, complemented
20C2×Dic71⋊C4C2211yescharacteristic, complemented
21C2×Dic71⋊C4C2211yescharacteristic, complemented
22C2×Dic71⋊C4C2211yescharacteristic, complemented
23C2×Dic71⋊C4C2211yescharacteristic, complemented
24C2×Dic71⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic71C2211yescharacteristic
26C2×C22⋊Dic71C2211yescharacteristic
27C2×(C2×D71)⋊C4—24no—
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×(C2×D71)⋊C4C2211yescharacteristic
38C2×(C2×D71)⋊C4C2211yescharacteristic
39C2×(C2×D71)⋊C4C2211yescharacteristic
40C71⋊#95C2211yescharacteristic, complemented
41C71⋊#95C2211yescharacteristic, complemented
42C71⋊#95C2211yescharacteristic, complemented
43C71⋊#95C2211yescharacteristic, complemented
44C71⋊#95C2211yescharacteristic, complemented
45C71⋊#95C2211yescharacteristic, complemented
46C23×C4×C71C2211yescharacteristic
47C2×C22⋊C4×C71C2211yescharacteristic
48C2×C22⋊C4×C71C2211yescharacteristic
49C2×C42×C71C2211yescharacteristic, complemented
50C2×C42×C71C2211yescharacteristic, complemented
51#95×C71C2211yescharacteristic, complemented
52#95×C71C2211yescharacteristic, complemented
53C23×D71—22no—
54C23×D71—22no—
55C23×D71—22no—
56C23×D71—22no—
57C23×D71—22no—
58C23×D71—41no—
59C23×D71—41no—
60C23×D71C2311yescharacteristic
61C23×D71C2311yescharacteristic
62C22×Dic71—22no—
63C22×Dic71—22no—
64C22×Dic71—41no—
65C22×Dic71C2311yescharacteristic
66C22×Dic71C2311yescharacteristic
67C22×Dic71C2311yescharacteristic
68C22×Dic71C2311yescharacteristic
69C22×Dic71C2311yescharacteristic
70C22×Dic71C2311yescharacteristic
71Dic71⋊C4—22no—
72Dic71⋊C4—22no—
73Dic71⋊C4—22no—
74Dic71⋊C4—41no—
75Dic71⋊C4—41no—
76Dic71⋊C4—41no—
77C22⋊Dic71—22no—
78C22⋊Dic71—22no—
79(C2×D71)⋊C4—22no—
80(C2×D71)⋊C4—22no—
81(C2×D71)⋊C4—22no—
82(C2×D71)⋊C4—22no—
83(C2×D71)⋊C4—22no—
84(C2×D71)⋊C4—22no—
85(C2×D71)⋊C4—22no—
86(C2×D71)⋊C4—41no—
87(C2×D71)⋊C4—41no—
88(C2×D71)⋊C4—41no—
89(C2×D71)⋊C4—41no—
90(C2×D71)⋊C4D414yes—
91C24×C71C2311yescharacteristic
92C22×C4×C71—22no—
93C22×C4×C71—22no—
94C22×C4×C71—41no—
95C22×C4×C71C2311yescharacteristic
96C22×C4×C71C2311yescharacteristic
97C22×C4×C71C2311yescharacteristic
98C22×C4×C71C2311yescharacteristic
99C22×C4×C71C2311yescharacteristic
100C22×C4×C71C2311yescharacteristic
101C22⋊C4×C71—22no—
102C22⋊C4×C71—22no—
103C42×C71—22no—
104C42×C71—41no—
105C23×C71—21no—
106C23×C71—21no—
107C23×C71—21no—
108C23×C71—21no—
109C23×C71#4112yes—
110C23×C71#4112yes—
111C23×C71#4112yes—
112C23×C71C2411yescharacteristic
113C22×D71—28no—
114C22×D71—21no—
115C22×D71—21no—
116C22×D71—21no—
117C22×D71—21no—
118C22×D71—21no—
119C22×D71—21no—
120C22×D71—21no—
121C22×D71—21no—
122C22×D71—21no—
123C22×D71—21no—
124C22×D71—21no—
125C22×D71—21no—
126C22×D71—44no—
127C22×D71—44no—
128C22×D71—44no—
129C22×D71—44no—
130C22×D71—44no—
131C22×D71—44no—
132C22×D71C2×D412yes—
133C22×D71#4112yes—
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×C4×C71—21no—
147C2×C4×C71—21no—
148C2×C4×C71—21no—
149C2×C4×C71—21no—
150C2×C4×C71—21no—
151C2×C4×C71—44no—
152C2×C4×C71C2×D412yes—
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—
164C2×Dic71—21no—
165C2×Dic71—21no—
166C2×Dic71—21no—
167C2×Dic71—21no—
168C2×Dic71—21no—
169C2×Dic71—21no—
170C2×Dic71—44no—
171C2×Dic71C2×D412yes—
172C22×C71—22no—
173C22×C71—22no—
174C22×C71—22no—
175C22×C71—22no—
176C22×C71—22no—
177C22×C71—22no—
178C22×C71#12614yescomplemented
179C22×C71C22×D411yescharacteristic
180C22×C71C2×#4111yescharacteristic
181C22×C71C2×#4111yescharacteristic
182C22×C71C2×#4111yescharacteristic
183C22×C71C2×#4111yescharacteristic
184C22×C71H(5,𝔽2)11yescharacteristic
185C22×C71H(5,𝔽2)11yescharacteristic
186C2×D71—22no—
187C2×D71—22no—
188C2×D71—22no—
189C2×D71—22no—
190C2×D71—22no—
191C2×D71—22no—
192C2×D71—416no—
193C2×D71—41no—
194C2×D71—41no—
195C2×D71—41no—
196C2×D71—41no—
197C2×D71—41no—
198C2×D71—41no—
199C2×D71—41no—
200C2×D71—41no—
201C4×C71—22no—
202C4×C71—41no—
203C4×C71—41no—
204C4×C71—41no—
205C4×C71—41no—
206C4×C71—41no—
207Dic71—22no—
208Dic71—41no—
209Dic71—41no—
210Dic71—41no—
211Dic71—41no—
212Dic71—41no—
213C2×C71—24no—
214C2×C71#52511yescharacteristic
215C2×C71C2×#12611yescharacteristic
216C2×C71#53811yescharacteristic
217C2×C71#54611yescharacteristic
218C2×C71#54611yescharacteristic
219C2×C71#55111yescharacteristic
220C2×C71#55111yescharacteristic
221D71—42no—
222D71—42no—
223#2480—711nomaximal, Sylow
224C71#248011yescharacteristic, complemented, Sylow
225C2×#126—711no—
226C22×C22⋊C4—711no—
227#397—711no—
228#397—711no—
229#397—711no—
230#396—711no—
231#388—711no—
232#388—711no—
233#388—711no—
234#385—711no—
235#385—711no—
236#380—711no—
237#379—711no—
238#379—711no—
239C4×C22⋊C4D7111yescharacteristic, complemented
240C25—711no—
241C23×C4—711no—
242C23×C4C2×D7111yescharacteristic
243#126—1424no—
244C2×C4⋊C4—711no—
245C2×C4⋊C4—711no—
246C2×C4⋊C4—711no—
247C2×C4⋊C4—711no—
248C2×C4⋊C4—711no—
249C2×C4⋊C4—711no—
250C2×C22⋊C4—711no—
251C2×C22⋊C4—711no—
252C2×C22⋊C4—711no—
253C2×C22⋊C4—711no—
254C2×C22⋊C4—711no—
255C2×C22⋊C4—711no—
256C2×C22⋊C4—711no—
257C2×C22⋊C4—711no—
258C2×C22⋊C4—711no—
259C2×C22⋊C4—711no—
260C2×C22⋊C4—711no—
261C2×C22⋊C4—711no—
262C2×C22⋊C4—711no—
263C2×C22⋊C4—711no—
264C2×C22⋊C4—1424no—
265C2×C22⋊C4C2×D7111yescharacteristic
266C2×C22⋊C4C2×D7111yescharacteristic
267C2×C42C2×D7111yescharacteristic, complemented
268C2×C42C2×D7111yescharacteristic, complemented
269#95—711no—
270#95—711no—
271#95—711no—
272#95—711no—
273#95—711no—
274#95—711no—
275#95C2×D7111yescharacteristic, complemented
276#95C2×D7111yescharacteristic, complemented
277C24—2841no—
278C24—2841no—
279C24—711no—
280C24—711no—
281C24—1422no—
282C24—1422no—
283C24—1422no—
284C24—1422no—
285C24—1422no—
286C24C22×D7111yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—2841no—
291C22×C4—711no—
292C22×C4—711no—
293C22×C4—711no—
294C22×C4—711no—
295C22×C4—711no—
296C22×C4—711no—
297C22×C4—1422no—
298C22×C4—1422no—
299C22×C4C22×D7111yescharacteristic
300C22×C4C22×D7111yescharacteristic
301C22×C4C22×D7111yescharacteristic
302C22×C4C22×D7111yescharacteristic
303C22×C4C22×D7111yescharacteristic
304C22×C4C22×D7111yescharacteristic
305C4⋊C4—2841no—
306C4⋊C4—2841no—
307C4⋊C4—2841no—
308C4⋊C4—1422no—
309C4⋊C4—1422no—
310C4⋊C4—1422no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—2841no—
314C22⋊C4—2841no—
315C22⋊C4—2841no—
316C22⋊C4—2841no—
317C22⋊C4—714no—
318C22⋊C4—1422no—
319C22⋊C4—1422no—
320C22⋊C4—1422no—
321C22⋊C4—1422no—
322C22⋊C4—1422no—
323C22⋊C4—1422no—
324C22⋊C4—1422no—
325C22⋊C4—1422no—
326C22⋊C4—1422no—
327C42—22no—
328C42—41no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—2844no—
334C23—2844no—
335C23—2844no—
336C23—2844no—
337C23—2844no—
338C23—2844no—
339C23—712no—
340C23—712no—
341C23—1428no—
342C23—1421no—
343C23—1421no—
344C23—1421no—
345C23—1421no—
346C23—1421no—
347C23—1421no—
348C23—1421no—
349C23—1421no—
350C23—1421no—
351C23—1421no—
352C23—1421no—
353C23—1421no—
354C23#1176586512yes—
355C23#1176586512yes—
356C23#1176586512yes—
357C23C23×D7111yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—2844no—
377C2×C4—712no—
378C2×C4—1421no—
379C2×C4—1421no—
380C2×C4—1421no—
381C2×C4—1421no—
382C2×C4—1421no—
383C2×C4—1421no—
384C2×C4—1421no—
385C2×C4—1421no—
386C2×C4—1421no—
387C2×C4—1421no—
388C2×C4—1421no—
389C2×C4—1421no—
390C2×C4—1421no—
391C2×C4—1421no—
392C2×C4—1421no—
393C2×C4—1421no—
394C2×C4—1421no—
395C2×C4D4×D7112yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—28416no—
403C22—2841no—
404C22—2841no—
405C22—2841no—
406C22—2841no—
407C22—2841no—
408C22—2841no—
409C22—2841no—
410C22—2841no—
411C22—1422no—
412C22—1422no—
413C22—1422no—
414C22—1422no—
415C22—1422no—
416C22—1422no—
417C22#1455612214yescomplemented
418C22C2×D4×D7111yescharacteristic
419C22#41×D7111yescharacteristic
420C22C2×#1176586511yescharacteristic
421C22C2×#1176586511yescharacteristic
422C22C2×#1176586511yescharacteristic
423C22#1455617311yescharacteristic
424C22#1455617411yescharacteristic
425C4—22no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—2841no—
432C4—2841no—
433C4—2841no—
434C4—2841no—
435C4—2841no—
436C4—1422no—
437C2—24no—
438C2—2842no—
439C2—2842no—
440C2#1798650811yescharacteristic
441C2C2×#1455612211yescharacteristic
442C2#1798658211yescharacteristic
443C2#1798663911yescharacteristic
444C2#1798664511yescharacteristic
445C2#1798667311yescharacteristic
446C2#1798667811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
FittingC4×C22⋊C4×C71C2
hypercenterC4×C22⋊C4D71
hypocenterC71#2480
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556122C2semidirect
3. #17985928C2semidirect
4. #17985928C2semidirect
5. #17985928C2semidirect
6. #17985923C2semidirect
7. #17985890C2semidirect
8. #17985890C2semidirect
9. #17985890C2semidirect
10. #17985872C2semidirect
11. #17985871C2semidirect
12. #17985857C2semidirect
15. C4×C22⋊C4×C71C2semidirect
19. C2×Dic71⋊C4C22semidirect
20. C2×Dic71⋊C4C22semidirect
21. C2×Dic71⋊C4C22semidirect
22. C2×Dic71⋊C4C22semidirect
23. C2×Dic71⋊C4C22semidirect
24. C2×Dic71⋊C4C22semidirect
40. C71⋊#95C22semidirect
41. C71⋊#95C22semidirect
42. C71⋊#95C22semidirect
43. C71⋊#95C22semidirect
44. C71⋊#95C22semidirect
45. C71⋊#95C22semidirect
49. C2×C42×C71C22semidirect
50. C2×C42×C71C22semidirect
51. #95×C71C22semidirect
52. #95×C71C22semidirect
178. C22×C71#126semidirect
224. C71#2480semidirect
239. C4×C22⋊C4D71semidirect
267. C2×C42C2×D71semidirect
268. C2×C42C2×D71semidirect
275. #95C2×D71semidirect
276. #95C2×D71semidirect
417. C22#14556122semidirect