Finite Group Databasebeta

← #22592539

Subgroups — #22592539

Order 9088.

540 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556106C211yesmaximal, characteristic, complemented
2C2×#14556086C211yesmaximal, characteristic, complemented
3#17985939C211yesmaximal, characteristic, complemented
4#17985926C211yesmaximal, characteristic, complemented
5#17985916C211yesmaximal, characteristic
6#17985912C211yesmaximal, characteristic, complemented
7#17985904C211yesmaximal, characteristic, complemented
8#17985891C211yesmaximal, characteristic, complemented
9#17985890C211yesmaximal, characteristic, complemented
10#17985884C211yesmaximal, characteristic, complemented
11#17985877C211yesmaximal, characteristic
12#17985877C211yesmaximal, characteristic
13#17985873C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
15#387×C71C211yesmaximal, characteristic, complemented
16C22×Dic142C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C22×C4×D71C2211yescharacteristic
19C22×C4×D71C2211yescharacteristic
20#14556106—24no—
21#14556086—24no—
22C2×C4⋊Dic71C2211yescharacteristic
23C2×C4⋊Dic71C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊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
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C71⋊#95C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C4⋊C4×C71C2211yescharacteristic
48C2×C42×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52#95×C71C2211yescharacteristic
53C23×D71C2311yescharacteristic
54C23×D71C2311yescharacteristic
55C2×Dic142—22no—
56C2×Dic142—22no—
57C2×Dic142—41no—
58C2×D284—22no—
59C2×D284—22no—
60C2×D284—41no—
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C22×Dic71C2311yescharacteristic
64C22×Dic71C2311yescharacteristic
65C22×Dic71C2311yescharacteristic
66C22×Dic71C2311yescharacteristic
67C2×C4×D71—22no—
68C2×C4×D71—22no—
69C2×C4×D71—22no—
70C2×C4×D71—22no—
71C2×C4×D71—22no—
72C2×C4×D71—41no—
73C4⋊Dic71—22no—
74C4⋊Dic71—22no—
75Dic71⋊C4—22no—
76Dic71⋊C4—22no—
77(C2×D71)⋊C4—22no—
78(C2×D71)⋊C4—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—
87C4×Dic71—22no—
88C4×Dic71—22no—
89C22×C4×C71C2311yescharacteristic
90C22×C4×C71C2311yescharacteristic
91C22×C4×C71C2311yescharacteristic
92C22×C4×C71C2311yescharacteristic
93C22×C4×C71C2311yescharacteristic
94C22×C4×C71C2311yescharacteristic
95C22×C4×C71C2311yescharacteristic
96C4⋊C4×C71—41no—
97C4⋊C4×C71D414yescomplemented
98C42×C71—41no—
99C23×C71C2411yescharacteristic
100C22×D71—21no—
101C22×D71—21no—
102C22×D71—21no—
103C22×D71—21no—
104C22×D71—21no—
105C22×D71—21no—
106C22×D71—21no—
107C22×D71—21no—
108C22×D71—21no—
109C22×D71—21no—
110C22×D71—21no—
111C22×D71—21no—
112C22×D71#4112yes—
113C22×D71#4112yes—
114C2×C4×C71—21no—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
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×C71C2×D412yes—
133C2×C4×C71C2×D412yes—
134C2×C4×C71C2×D412yes—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71—21no—
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71—21no—
142C2×Dic71—21no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—21no—
150C2×Dic71—21no—
151C2×Dic71#4112yes—
152C2×Dic71#4112yes—
153D284—44no—
154C4×D71—28no—
155C4×D71—44no—
156Dic142—44no—
157C22×C71C22×D411yescharacteristic
158C22×C71C2×#4111yescharacteristic
159C22×C71C2×#4111yescharacteristic
160C22×C71C2×#4111yescharacteristic
161C22×C71C2×#4111yescharacteristic
162C22×C71H(5,𝔽2)11yescharacteristic
163C22×C712−1+411yescharacteristic
164C2×D71—22no—
165C2×D71—22no—
166C2×D71—22no—
167C2×D71—22no—
168C2×D71—22no—
169C2×D71—22no—
170C2×D71—41no—
171C2×D71—41no—
172C2×D71—41no—
173C2×D71—41no—
174C2×D71—41no—
175C2×D71—41no—
176C2×D71—41no—
177C2×D71—41no—
178C4×C71—22no—
179C4×C71—22no—
180C4×C71—22no—
181C4×C71—41no—
182C4×C71—41no—
183C4×C71—41no—
184C4×C71—41no—
185Dic71—22no—
186Dic71—22no—
187Dic71—41no—
188Dic71—41no—
189Dic71—41no—
190Dic71—41no—
191C2×C71#52511yescharacteristic
192C2×C71#52911yescharacteristic
193C2×C71#54211yescharacteristic
194C2×C71#54611yescharacteristic
195C2×C71#54811yescharacteristic
196C2×C71#55111yescharacteristic
197C2×C71#55211yescharacteristic
198D71—42no—
199D71—42no—
200#2477—711nomaximal, Sylow
201C71#247711yescharacteristic, complemented, Sylow
202C2×C22⋊Q8—711no—
203C2×#117—711no—
204#400—711no—
205#397—711no—
206#394—711no—
207#393—711no—
208#391—711no—
209#388—711no—
210#388—711no—
211#387—711no—
212#387D7111yescharacteristic, complemented
213#386—711no—
214#386—711no—
215#385—711no—
216C4×C22⋊C4—711no—
217C22×Q8—711no—
218C22×D4—711no—
219C23×C4—711no—
220C23×C4—711no—
221C22⋊Q8—1424no—
222#117—1424no—
223C2×C4⋊C4—711no—
224C2×C4⋊C4—711no—
225C2×C4⋊C4—711no—
226C2×C4⋊C4—711no—
227C2×C4⋊C4C2×D7111yescharacteristic
228C2×C4⋊C4C2×D7111yescharacteristic
229C2×C22⋊C4—711no—
230C2×C22⋊C4—711no—
231C2×C22⋊C4—711no—
232C2×C22⋊C4—711no—
233C2×C22⋊C4—711no—
234C2×C22⋊C4—711no—
235C2×C22⋊C4—711no—
236C2×C22⋊C4—711no—
237C2×C22⋊C4—711no—
238C2×C22⋊C4—711no—
239C2×C42—711no—
240C2×C42—711no—
241C2×C42C2×D7111yescharacteristic
242#95—711no—
243#95—711no—
244#95—711no—
245#95—711no—
246#95—711no—
247#95—711no—
248#95—711no—
249#95—711no—
250#95C2×D7111yescharacteristic
251#95C2×D7111yescharacteristic
252#95C2×D7111yescharacteristic
253#95C2×D7111yescharacteristic
254C24—711no—
255C24—711no—
256C2×Q8—2841no—
257C2×Q8—1422no—
258C2×Q8—1422no—
259C2×D4—2841no—
260C2×D4—1422no—
261C2×D4—1422no—
262C22×C4—2841no—
263C22×C4—711no—
264C22×C4—711no—
265C22×C4—711no—
266C22×C4—711no—
267C22×C4—711no—
268C22×C4—711no—
269C22×C4—1422no—
270C22×C4—1422no—
271C22×C4—1422no—
272C22×C4—1422no—
273C22×C4—1422no—
274C22×C4C22×D7111yescharacteristic
275C22×C4C22×D7111yescharacteristic
276C22×C4C22×D7111yescharacteristic
277C22×C4C22×D7111yescharacteristic
278C22×C4C22×D7111yescharacteristic
279C22×C4C22×D7111yescharacteristic
280C22×C4C22×D7111yescharacteristic
281C4⋊C4—41no—
282C4⋊C4—1422no—
283C4⋊C4—1422no—
284C4⋊C4—1422no—
285C4⋊C4—1422no—
286C4⋊C4D28414yescomplemented
287C22⋊C4—2841no—
288C22⋊C4—1422no—
289C22⋊C4—1422no—
290C22⋊C4—1422no—
291C22⋊C4—1422no—
292C22⋊C4—1422no—
293C22⋊C4—1422no—
294C22⋊C4—1422no—
295C22⋊C4—1422no—
296C22⋊C4—1422no—
297C42—41no—
298C42—1422no—
299C42—1422no—
300C23—712no—
301C23—712no—
302C23—1421no—
303C23—1421no—
304C23—1421no—
305C23—1421no—
306C23—1421no—
307C23—1421no—
308C23—1421no—
309C23—1421no—
310C23—1421no—
311C23—1421no—
312C23—1421no—
313C23—1421no—
314C23C23×D7111yescharacteristic
315Q8—2844no—
316D4—2844no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—2844no—
336C2×C4—712no—
337C2×C4—712no—
338C2×C4—1428no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4—1421no—
345C2×C4—1421no—
346C2×C4—1421no—
347C2×C4—1421no—
348C2×C4—1421no—
349C2×C4—1421no—
350C2×C4—1421no—
351C2×C4—1421no—
352C2×C4—1421no—
353C2×C4—1421no—
354C2×C4—1421no—
355C2×C4C2×D28412yes—
356C2×C4C2×D28412yes—
357C2×C4C2×D28412yes—
358C22—2841no—
359C22—2841no—
360C22—2841no—
361C22—2841no—
362C22—2841no—
363C22—2841no—
364C22—2841no—
365C22—2841no—
366C22—1422no—
367C22—1422no—
368C22—1422no—
369C22—1422no—
370C22—1422no—
371C22—1422no—
372C22C22×D28411yescharacteristic
373C22#41×D7111yescharacteristic
374C22#41×D7111yescharacteristic
375C22#41×D7111yescharacteristic
376C22#41×D7111yescharacteristic
377C22#1455617311yescharacteristic
378C22#1455617611yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—2841no—
387C4—2841no—
388C4—2841no—
389C4—2841no—
390C4—1422no—
391C4—1422no—
392C2—2842no—
393C2—2842no—
394C2#1798651111yescharacteristic
395C2#1798653211yescharacteristic
396C2#1798661911yescharacteristic
397C2#1798664411yescharacteristic
398C2#1798666111yescharacteristic
399C2#1798667711yescharacteristic
400C2#1798668111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#387×C71C2
hypercenter#387D71
hypocenterC71#2477
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14556106C2semidirect
2. C2×#14556086C2semidirect
3. #17985939C2semidirect
4. #17985926C2semidirect
6. #17985912C2semidirect
7. #17985904C2semidirect
8. #17985891C2semidirect
9. #17985890C2semidirect
10. #17985884C2semidirect
13. #17985873C2semidirect
14. C4×(C2×D71)⋊C4C2semidirect
15. #387×C71C2semidirect
97. C4⋊C4×C71D4semidirect
201. C71#2477semidirect
212. #387D71semidirect
286. C4⋊C4D284semidirect