Finite Group Databasebeta

← #22591104

Subgroups — #22591104

Order 9088.

596 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556103C211yesmaximal, characteristic
2#17985901C211yesmaximal, characteristic, complemented
3#17985900C211yesmaximal, characteristic, complemented
4#17985891C211yesmaximal, characteristic, complemented
5#17985889C211yesmaximal, characteristic, complemented
6#17985885C211yesmaximal, characteristic, complemented
7#17985877C211yesmaximal, characteristic, complemented
8#17985877C211yesmaximal, characteristic, complemented
9#17985877C211yesmaximal, characteristic, complemented
10#17985877C211yesmaximal, characteristic, complemented
11#17985861C211yesmaximal, characteristic, complemented
12C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
13#17985846C211yesmaximal, characteristic, complemented
14#17985846C211yesmaximal, characteristic, complemented
15#387×C71C211yesmaximal, characteristic, complemented
16C22×D284C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C22×D284C2211yescharacteristic
19C22×C4×D71C2211yescharacteristic
20C22×C4×D71C2211yescharacteristic
21C22×C4×D71C2211yescharacteristic
22#14556103C418yescomplemented
23C2×C4⋊Dic71C2211yescharacteristic
24C2×(C2×D71)⋊C4C2211yescharacteristic
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×C4×Dic71C2211yescharacteristic
37C2×C4×Dic71C2211yescharacteristic
38C2×C4×Dic71C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C2×C4⋊C4×C71C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C42×C71C2211yescharacteristic
48#95×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52C23×D71C2311yescharacteristic
53C23×D71C2311yescharacteristic
54C23×D71C2311yescharacteristic
55C2×D284—41no—
56C2×D284—41no—
57C2×D284—41no—
58C2×D284—41no—
59C2×D284—41no—
60C2×D284—41no—
61C2×D284C2×C414yes—
62C2×D284C2×C414yescomplemented
63C2×D284C2×C414yescomplemented
64C22×Dic71C2311yescharacteristic
65C22×Dic71C2311yescharacteristic
66C22×Dic71C2311yescharacteristic
67C22×Dic71C2311yescharacteristic
68C22×Dic71C2311yescharacteristic
69C2×C4×D71—22no—
70C2×C4×D71—22no—
71C2×C4×D71—41no—
72C2×C4×D71—41no—
73C2×C4×D71—41no—
74C2×C4×D71—41no—
75C2×C4×D71—41no—
76C2×C4×D71—41no—
77C2×C4×D71C2×C414yescomplemented
78C4⋊Dic71—41no—
79(C2×D71)⋊C4—22no—
80(C2×D71)⋊C4—22no—
81(C2×D71)⋊C4—22no—
82(C2×D71)⋊C4—22no—
83(C2×D71)⋊C4—41no—
84(C2×D71)⋊C4—41no—
85(C2×D71)⋊C4—41no—
86(C2×D71)⋊C4—41no—
87(C2×D71)⋊C4—41no—
88(C2×D71)⋊C4—41no—
89(C2×D71)⋊C4C2×C414yescomplemented
90(C2×D71)⋊C4C2×C414yescomplemented
91C4×Dic71—41no—
92C4×Dic71—41no—
93C4×Dic71—41no—
94C22×C4×C71C2311yescharacteristic
95C22×C4×C71C2311yescharacteristic
96C22×C4×C71C2311yescharacteristic
97C22×C4×C71C2311yescharacteristic
98C22×C4×C71C2311yescharacteristic
99C22×C4×C71C2311yescharacteristic
100C22×C4×C71C2311yescharacteristic
101C4⋊C4×C71—41no—
102C4⋊C4×C71C2×C414yescomplemented
103C42×C71—41no—
104C23×C71C2411yescharacteristic
105C22×D71—21no—
106C22×D71—21no—
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—21no—
120C22×D71—21no—
121C22×D71—21no—
122C22×D71—21no—
123C22×D71C22×C412yes—
124C22×D71C22×C412yes—
125C22×D71C22×C412yes—
126C2×C4×C71—21no—
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—21no—
138C2×C4×C71—21no—
139C2×C4×C71—21no—
140C2×C4×C71—21no—
141C2×C4×C71—21no—
142C2×C4×C71—21no—
143C2×C4×C71C22×C412yes—
144C2×C4×C71C22×C412yes—
145C2×C4×C71C22×C412yes—
146C2×C4×C71#4112yes—
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×Dic71C22×C412yes—
161C2×Dic71#4112yes—
162D284—44no—
163D284—44no—
164D284—44no—
165C4×D71—44no—
166C4×D71—44no—
167C4×D71—44no—
168C22×C71C23×C411yescharacteristic
169C22×C71C2×#4111yescharacteristic
170C22×C71C2×#4111yescharacteristic
171C22×C71H(5,𝔽2)11yescharacteristic
172C22×C71H(5,𝔽2)11yescharacteristic
173C22×C71H(5,𝔽2)11yescharacteristic
174C22×C71H(5,𝔽2)11yescharacteristic
175C2×D71—22no—
176C2×D71—22no—
177C2×D71—22no—
178C2×D71—22no—
179C2×D71—22no—
180C2×D71—22no—
181C2×D71—22no—
182C2×D71—22no—
183C2×D71—22no—
184C2×D71—41no—
185C2×D71—41no—
186C2×D71—41no—
187C2×D71—41no—
188C2×D71—41no—
189C2×D71—41no—
190C2×D71—41no—
191C2×D71—41no—
192C2×D71—41no—
193C2×D71—41no—
194C2×D71—41no—
195C2×D71—41no—
196C4×C71—22no—
197C4×C71—22no—
198C4×C71—22no—
199C4×C71—22no—
200C4×C71—41no—
201C4×C71—41no—
202C4×C71—41no—
203Dic71—22no—
204Dic71—22no—
205Dic71—41no—
206Dic71—41no—
207Dic71—41no—
208C2×C71C4×#4111yescharacteristic
209C2×C71#51811yescharacteristic
210C2×C71#51811yescharacteristic
211C2×C71#53811yescharacteristic
212C2×C71#53811yescharacteristic
213C2×C71#54011yescharacteristic
214C2×C71#54011yescharacteristic
215D71—42no—
216D71—42no—
217D71—42no—
218#2333—711nomaximal, Sylow
219C71#233311yescharacteristic, complemented, Sylow
220C2×#121—711no—
221#390—711no—
222#390—711no—
223#388—711no—
224#388—711no—
225#387—711no—
226#387D7111yescharacteristic, complemented
227#386—711no—
228#386—711no—
229#386—711no—
230#386—711no—
231#381—711no—
232C4×C22⋊C4—711no—
233C4×C22⋊C4—711no—
234C4×C22⋊C4—711no—
235C22×D4—711no—
236C22×D4—711no—
237C22×D4—711no—
238C23×C4—711no—
239C23×C4—711no—
240C23×C4—711no—
241#121—718no—
242C2×C4⋊C4—711no—
243C2×C4⋊C4C2×D7111yescharacteristic
244C2×C4⋊C4C2×D7111yescharacteristic
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⋊C4—711no—
255C2×C22⋊C4—711no—
256C2×C22⋊C4—711no—
257C2×C42—711no—
258C2×C42—711no—
259C2×C42—711no—
260C2×C42C2×D7111yescharacteristic
261#95—711no—
262#95—711no—
263#95—711no—
264#95—711no—
265#95—711no—
266#95—711no—
267#95C2×D7111yescharacteristic
268#95C2×D7111yescharacteristic
269#95C2×D7111yescharacteristic
270#95C2×D7111yescharacteristic
271C24—711no—
272C24—711no—
273C24—711no—
274C2×D4—2841no—
275C2×D4—2841no—
276C2×D4—2841no—
277C2×D4—2841no—
278C2×D4—2841no—
279C2×D4—2841no—
280C2×D4—714no—
281C2×D4—714no—
282C2×D4—714no—
283C22×C4—2841no—
284C22×C4—2841no—
285C22×C4—2841no—
286C22×C4—2841no—
287C22×C4—2841no—
288C22×C4—2841no—
289C22×C4—714no—
290C22×C4—711no—
291C22×C4—711no—
292C22×C4—711no—
293C22×C4—711no—
294C22×C4—711no—
295C22×C4—1422no—
296C22×C4—1422no—
297C22×C4C22×D7111yescharacteristic
298C22×C4C22×D7111yescharacteristic
299C22×C4C22×D7111yescharacteristic
300C22×C4C22×D7111yescharacteristic
301C22×C4C22×D7111yescharacteristic
302C22×C4C22×D7111yescharacteristic
303C22×C4C22×D7111yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—2841no—
306C4⋊C4C4×D7114yescomplemented
307C22⋊C4—2841no—
308C22⋊C4—2841no—
309C22⋊C4—2841no—
310C22⋊C4—2841no—
311C22⋊C4—2841no—
312C22⋊C4—2841no—
313C22⋊C4—714no—
314C22⋊C4—714no—
315C22⋊C4—1422no—
316C22⋊C4—1422no—
317C22⋊C4—1422no—
318C22⋊C4—1422no—
319C42—41no—
320C42—2841no—
321C42—2841no—
322C42—2841no—
323C23—712no—
324C23—712no—
325C23—712no—
326C23—1421no—
327C23—1421no—
328C23—1421no—
329C23—1421no—
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—1421no—
343C23—1421no—
344C23C23×D7111yescharacteristic
345D4—2844no—
346D4—2844no—
347D4—2844no—
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—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—2844no—
366C2×C4—2844no—
367C2×C4—2844no—
368C2×C4—712no—
369C2×C4—712no—
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—
380C2×C4—1421no—
381C2×C4—1421no—
382C2×C4—1421no—
383C2×C4C2×C4×D7112yes—
384C2×C4C2×C4×D7112yes—
385C2×C4C2×C4×D7112yes—
386C2×C4#1176586612yes—
387C22—2841no—
388C22—2841no—
389C22—2841no—
390C22—2841no—
391C22—2841no—
392C22—2841no—
393C22—2841no—
394C22—2841no—
395C22—2841no—
396C22—2841no—
397C22—2841no—
398C22—2841no—
399C22—1422no—
400C22—1422no—
401C22—1422no—
402C22—1422no—
403C22—1422no—
404C22—1422no—
405C22—1422no—
406C22—1422no—
407C22—1422no—
408C22C22×C4×D7111yescharacteristic
409C22#41×D7111yescharacteristic
410C22C2×#1176586611yescharacteristic
411C22#1455617311yescharacteristic
412C22#1455617411yescharacteristic
413C22#1455617411yescharacteristic
414C22#1455617411yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—2841no—
423C4—2841no—
424C4—2841no—
425C4—1422no—
426C4—1422no—
427C2—2842no—
428C2—2842no—
429C2—2842no—
430C2C4×#1176586611yescharacteristic
431C2#1798647111yescharacteristic
432C2#1798647311yescharacteristic
433C2#1798658811yescharacteristic
434C2#1798658911yescharacteristic
435C2#1798660111yescharacteristic
436C2#1798660511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
Fitting#387×C71C2
socleC23×C71C24
hypercenter#387D71
hypocenterC71#2333
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #17985901C2semidirect
3. #17985900C2semidirect
4. #17985891C2semidirect
5. #17985889C2semidirect
6. #17985885C2semidirect
7. #17985877C2semidirect
8. #17985877C2semidirect
9. #17985877C2semidirect
10. #17985877C2semidirect
11. #17985861C2semidirect
12. C4×(C2×D71)⋊C4C2semidirect
13. #17985846C2semidirect
14. #17985846C2semidirect
15. #387×C71C2semidirect
22. #14556103C4semidirect
62. C2×D284C2×C4semidirect
63. C2×D284C2×C4semidirect
77. C2×C4×D71C2×C4semidirect
89. (C2×D71)⋊C4C2×C4semidirect
90. (C2×D71)⋊C4C2×C4semidirect
102. C4⋊C4×C71C2×C4semidirect
219. C71#2333semidirect
226. #387D71semidirect
306. C4⋊C4C4×D71semidirect