Finite Group Databasebeta

← #22591183

Subgroups — #22591183

Order 9088.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556085C211yesmaximal, characteristic, complemented
2C22×(C2×D71)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D71C211yesmaximal, characteristic
4#17985890C211yesmaximal, characteristic, complemented
5#17985890C211yesmaximal, characteristic, complemented
6#17985888C211yesmaximal, characteristic, complemented
7#17985888C211yesmaximal, characteristic, complemented
8#17985872C211yesmaximal, characteristic, complemented
9#17985871C211yesmaximal, characteristic, complemented
10#17985861C211yesmaximal, characteristic, complemented
11#17985858C211yesmaximal, characteristic, complemented
12#17985854C211yesmaximal, characteristic
13C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C24×D71C2211yescharacteristic
17C23×Dic71C2211yescharacteristic
18C22×C4×D71C2211yescharacteristic
19C22×C4×D71C2211yescharacteristic
20#14556085—24no—
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
38C22⋊C4×D71C418yescomplemented
39C2×C4×Dic71C2211yescharacteristic, complemented
40C2×C4×Dic71C2211yescharacteristic, complemented
41C71⋊#95C2211yescharacteristic, complemented
42C71⋊#95C2211yescharacteristic, complemented
43C71⋊#95C2211yescharacteristic, complemented
44C71⋊#95C2211yescharacteristic, complemented
45C71⋊#95C2211yescharacteristic, complemented
46C71⋊#95C2211yescharacteristic, complemented
47C23×C4×C71C2211yescharacteristic
48C2×C22⋊C4×C71C2211yescharacteristic
49C2×C22⋊C4×C71C2211yescharacteristic
50C2×C42×C71C2211yescharacteristic, complemented
51C2×C42×C71C2211yescharacteristic, complemented
52#95×C71C2211yescharacteristic, complemented
53#95×C71C2211yescharacteristic, complemented
54C23×D71—22no—
55C23×D71—22no—
56C23×D71—22no—
57C23×D71—22no—
58C23×D71—41no—
59C23×D71—41no—
60C23×D71C2×C414yes—
61C23×D71C2311yescharacteristic
62C23×D71C2311yescharacteristic
63C22×Dic71—22no—
64C22×Dic71—22no—
65C22×Dic71—41no—
66C22×Dic71C2311yescharacteristic
67C22×Dic71C2311yescharacteristic
68C22×Dic71C2311yescharacteristic
69C22×Dic71C2311yescharacteristic
70C22×Dic71C2311yescharacteristic
71C22×Dic71C2311yescharacteristic
72C2×C4×D71—22no—
73C2×C4×D71—22no—
74C2×C4×D71—41no—
75C2×C4×D71—41no—
76C2×C4×D71C2×C414yescomplemented
77C2×C4×D71C2×C414yescomplemented
78Dic71⋊C4—22no—
79Dic71⋊C4—22no—
80Dic71⋊C4—41no—
81Dic71⋊C4—41no—
82C22⋊Dic71—22no—
83C22⋊Dic71C2×C414yes—
84(C2×D71)⋊C4—22no—
85(C2×D71)⋊C4—22no—
86(C2×D71)⋊C4—22no—
87(C2×D71)⋊C4—22no—
88(C2×D71)⋊C4—22no—
89(C2×D71)⋊C4—41no—
90(C2×D71)⋊C4—41no—
91(C2×D71)⋊C4C2×C414yescomplemented
92(C2×D71)⋊C4C2×C414yescomplemented
93(C2×D71)⋊C4D414yes—
94C4×Dic71—22no—
95C4×Dic71—41no—
96C24×C71C2311yescharacteristic
97C22×C4×C71—22no—
98C22×C4×C71—22no—
99C22×C4×C71—41no—
100C22×C4×C71C2311yescharacteristic
101C22×C4×C71C2311yescharacteristic
102C22×C4×C71C2311yescharacteristic
103C22×C4×C71C2311yescharacteristic
104C22×C4×C71C2311yescharacteristic
105C22×C4×C71C2311yescharacteristic
106C22⋊C4×C71—22no—
107C22⋊C4×C71C2×C414yes—
108C42×C71—22no—
109C42×C71—41no—
110C23×C71—21no—
111C23×C71—21no—
112C23×C71—21no—
113C23×C71—21no—
114C23×C71C22×C412yes—
115C23×C71#4112yes—
116C23×C71#4112yes—
117C23×C71C2411yescharacteristic
118C22×D71—21no—
119C22×D71—21no—
120C22×D71—21no—
121C22×D71—21no—
122C22×D71—28no—
123C22×D71—21no—
124C22×D71—21no—
125C22×D71—21no—
126C22×D71—21no—
127C22×D71—21no—
128C22×D71—21no—
129C22×D71—28no—
130C22×D71—44no—
131C22×D71—44no—
132C22×D71—44no—
133C22×D71—44no—
134C22×D71—44no—
135C22×D71C22×C412yes—
136C22×D71C22×C412yes—
137C22×D71C2×D412yes—
138C22×D71#4112yes—
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—21no—
152C2×C4×C71—21no—
153C2×C4×C71—21no—
154C2×C4×C71—44no—
155C2×C4×C71C22×C412yes—
156C2×C4×C71C22×C412yes—
157C2×C4×C71C2×D412yes—
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—21no—
171C2×Dic71—21no—
172C2×Dic71—21no—
173C2×Dic71—44no—
174C2×Dic71C22×C412yes—
175C2×Dic71C22×C412yes—
176C2×Dic71C2×D412yes—
177C4×D71—28no—
178C4×D71—44no—
179C22×C71—22no—
180C22×C71—22no—
181C22×C71—22no—
182C22×C71—22no—
183C22×C71—22no—
184C22×C71—22no—
185C22×C71#11714yescomplemented
186C22×C71C23×C411yescharacteristic
187C22×C71C22×D411yescharacteristic
188C22×C71C2×#4111yescharacteristic
189C22×C71C2×#4111yescharacteristic
190C22×C71C2×#4111yescharacteristic
191C22×C71H(5,𝔽2)11yescharacteristic
192C22×C71H(5,𝔽2)11yescharacteristic
193C2×D71—22no—
194C2×D71—22no—
195C2×D71—22no—
196C2×D71—22no—
197C2×D71—22no—
198C2×D71—22no—
199C2×D71—22no—
200C2×D71—22no—
201C2×D71—22no—
202C2×D71—416no—
203C2×D71—41no—
204C2×D71—41no—
205C2×D71—41no—
206C2×D71—41no—
207C2×D71C4×D414yes—
208C4×C71—22no—
209C4×C71—22no—
210C4×C71—22no—
211C4×C71—41no—
212C4×C71—41no—
213C4×C71—41no—
214Dic71—22no—
215Dic71—22no—
216Dic71—22no—
217Dic71—41no—
218Dic71—41no—
219Dic71—41no—
220C2×C71—24no—
221C2×C71C2×#11711yescharacteristic
222C2×C71C2×C4×D411yescharacteristic
223C2×C71#51811yescharacteristic
224C2×C71#54611yescharacteristic
225C2×C71#54611yescharacteristic
226C2×C71#55111yescharacteristic
227C2×C71#55111yescharacteristic
228D71—24no—
229D71—42no—
230#2342—711nomaximal, Sylow
231C71#234211yescharacteristic, complemented, Sylow
232C2×#117—711no—
233C22×C22⋊C4—711no—
234C22×C22⋊C4—711no—
235#388—711no—
236#388—711no—
237#388—711no—
238#388—711no—
239#385—711no—
240#385—711no—
241#381—711no—
242#380—711no—
243#379—711no—
244C4×C22⋊C4—711no—
245C4×C22⋊C4—711no—
246C4×C22⋊C4D7111yescharacteristic, complemented
247C25—711no—
248C23×C4—711no—
249C23×C4—711no—
250C23×C4—711no—
251C23×C4C2×D7111yescharacteristic
252#117—1424no—
253C2×C4⋊C4—711no—
254C2×C4⋊C4—711no—
255C2×C4⋊C4—711no—
256C2×C4⋊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—718no—
264C2×C22⋊C4—711no—
265C2×C22⋊C4—711no—
266C2×C22⋊C4—711no—
267C2×C22⋊C4—711no—
268C2×C22⋊C4—711no—
269C2×C22⋊C4—711no—
270C2×C22⋊C4—1424no—
271C2×C22⋊C4C2×D7111yescharacteristic
272C2×C22⋊C4C2×D7111yescharacteristic
273C2×C42—711no—
274C2×C42—711no—
275C2×C42C2×D7111yescharacteristic, complemented
276C2×C42C2×D7111yescharacteristic, complemented
277#95—711no—
278#95—711no—
279#95—711no—
280#95—711no—
281#95—711no—
282#95—711no—
283#95C2×D7111yescharacteristic, complemented
284#95C2×D7111yescharacteristic, complemented
285C24—2841no—
286C24—2841no—
287C24—714no—
288C24—711no—
289C24—711no—
290C24—1422no—
291C24—1422no—
292C24—1422no—
293C24—1422no—
294C24C22×D7111yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—2841no—
299C22×C4—2841no—
300C22×C4—2841no—
301C22×C4—714no—
302C22×C4—711no—
303C22×C4—711no—
304C22×C4—711no—
305C22×C4—714no—
306C22×C4—711no—
307C22×C4—711no—
308C22×C4—711no—
309C22×C4—1422no—
310C22×C4—1422no—
311C22×C4—1422no—
312C22×C4—1422no—
313C22×C4C22×D7111yescharacteristic
314C22×C4C22×D7111yescharacteristic
315C22×C4C22×D7111yescharacteristic
316C22×C4C22×D7111yescharacteristic
317C22×C4C22×D7111yescharacteristic
318C22×C4C22×D7111yescharacteristic
319C4⋊C4—2841no—
320C4⋊C4—2841no—
321C4⋊C4—1422no—
322C4⋊C4—1422no—
323C22⋊C4—22no—
324C22⋊C4—2841no—
325C22⋊C4—2841no—
326C22⋊C4—714no—
327C22⋊C4—714no—
328C22⋊C4—714no—
329C22⋊C4—714no—
330C22⋊C4—1422no—
331C22⋊C4—1422no—
332C22⋊C4—1422no—
333C22⋊C4—1422no—
334C22⋊C4—1422no—
335C22⋊C4—1422no—
336C22⋊C4C4×D7114yes—
337C42—22no—
338C42—41no—
339C42—2841no—
340C42—1422no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—2844no—
346C23—2844no—
347C23—2844no—
348C23—2844no—
349C23—2844no—
350C23—712no—
351C23—712no—
352C23—712no—
353C23—712no—
354C23—1428no—
355C23—1421no—
356C23—1421no—
357C23—1421no—
358C23—1421no—
359C23—1421no—
360C23—1421no—
361C23—1428no—
362C23—1421no—
363C23—1421no—
364C23—1421no—
365C23—1421no—
366C23C2×C4×D7112yes—
367C23#1176586512yes—
368C23#1176586512yes—
369C23C23×D7111yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—2844no—
387C2×C4—2844no—
388C2×C4—712no—
389C2×C4—712no—
390C2×C4—712no—
391C2×C4—1428no—
392C2×C4—1421no—
393C2×C4—1421no—
394C2×C4—1421no—
395C2×C4—1421no—
396C2×C4—1421no—
397C2×C4—1421no—
398C2×C4—1421no—
399C2×C4—1421no—
400C2×C4—1421no—
401C2×C4—1421no—
402C2×C4—1421no—
403C2×C4—1421no—
404C2×C4—1421no—
405C2×C4—1421no—
406C2×C4—1421no—
407C2×C4C2×C4×D7112yes—
408C2×C4C2×C4×D7112yes—
409C2×C4D4×D7112yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—28416no—
417C22—2841no—
418C22—2841no—
419C22—2841no—
420C22—2841no—
421C22—714no—
422C22—1422no—
423C22—1422no—
424C22—1422no—
425C22—1422no—
426C22—1422no—
427C22—1422no—
428C22—1422no—
429C22—1422no—
430C22—1422no—
431C22#1455608514yescomplemented
432C22C22×C4×D7111yescharacteristic
433C22C2×D4×D7111yescharacteristic
434C22#41×D7111yescharacteristic
435C22C2×#1176586511yescharacteristic
436C22C2×#1176586511yescharacteristic
437C22#1455617311yescharacteristic
438C22#1455617411yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—2841no—
446C4—2841no—
447C4—2841no—
448C4—1422no—
449C4—1422no—
450C4—1422no—
451C2—24no—
452C2—2842no—
453C2—1424no—
454C2C2×#1455608511yescharacteristic
455C2C4×D4×D7111yescharacteristic
456C2#1798647111yescharacteristic
457C2#1798663911yescharacteristic
458C2#1798664511yescharacteristic
459C2#1798667311yescharacteristic
460C2#1798667811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
FittingC4×C22⋊C4×C71C2
socleC23×C71C24
hypercenterC4×C22⋊C4D71
hypocenterC71#2342
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556085C2semidirect
4. #17985890C2semidirect
5. #17985890C2semidirect
6. #17985888C2semidirect
7. #17985888C2semidirect
8. #17985872C2semidirect
9. #17985871C2semidirect
10. #17985861C2semidirect
11. #17985858C2semidirect
13. C22⋊C4×Dic71C2semidirect
14. C4×(C2×D71)⋊C4C2semidirect
15. C4×C22⋊C4×C71C2semidirect
21. C2×Dic71⋊C4C22semidirect
22. C2×Dic71⋊C4C22semidirect
23. C2×Dic71⋊C4C22semidirect
24. C2×Dic71⋊C4C22semidirect
38. C22⋊C4×D71C4semidirect
39. C2×C4×Dic71C22semidirect
40. C2×C4×Dic71C22semidirect
41. C71⋊#95C22semidirect
42. C71⋊#95C22semidirect
43. C71⋊#95C22semidirect
44. C71⋊#95C22semidirect
45. C71⋊#95C22semidirect
46. C71⋊#95C22semidirect
50. C2×C42×C71C22semidirect
51. C2×C42×C71C22semidirect
52. #95×C71C22semidirect
53. #95×C71C22semidirect
76. C2×C4×D71C2×C4semidirect
77. C2×C4×D71C2×C4semidirect
91. (C2×D71)⋊C4C2×C4semidirect
92. (C2×D71)⋊C4C2×C4semidirect
185. C22×C71#117semidirect
231. C71#2342semidirect
246. C4×C22⋊C4D71semidirect
275. C2×C42C2×D71semidirect
276. C2×C42C2×D71semidirect
283. #95C2×D71semidirect
284. #95C2×D71semidirect
431. C22#14556085semidirect