Finite Group Databasebeta

← #22600682

Subgroups — #22600682

Order 9088.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986650C211yesmaximal, characteristic, complemented
2#17986649C211yesmaximal, characteristic, complemented
3#17986403C211yesmaximal, characteristic, complemented
4#17986314C211yesmaximal, characteristic, complemented
5#17986313C211yesmaximal, characteristic, complemented
6#17986311C211yesmaximal, characteristic, complemented
7#17986278C211yesmaximal, characteristic, complemented
8#17986277C211yesmaximal, characteristic, complemented
9#17986234C211yesmaximal, characteristic, complemented
10#17986233C211yesmaximal, characteristic, complemented
11#17986079C211yesmaximal, characteristic, complemented
12(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
13C2×#14556061C211yesmaximal, characteristic, complemented
14#107×D71C211yesmaximal, characteristic, complemented
15#480×C71C211yesmaximal, characteristic, complemented
16C2×#11765865—21no—
17C2×#11765864—21no—
18C2×#11765850C2211yescharacteristic
19C22×C71⋊C8C2211yescharacteristic
20C2×C8×D71C2211yescharacteristic
21#14556127C2211yescharacteristic
22#14556127C2211yescharacteristic
23#14556113—21no—
24#14556111—21no—
25#14556110—21no—
26#14556109—21no—
27#14556106—21no—
28#14556105—21no—
29#14556103C2211yescharacteristic
30#14556102C2211yescharacteristic
31#14556099C2211yescharacteristic
32D4×Dic71C2211yescharacteristic
33#14556090C2211yescharacteristic
34C4×C22⋊D71C2211yescharacteristic
35C2×C4⋊Dic71C2211yescharacteristic
36C4⋊C4×D71C2211yescharacteristic
37C4⋊C4×D71C2211yescharacteristic
38#14556062C2211yescharacteristic
39#14556062C2211yescharacteristic
40#14556061C2211yescharacteristic
41#14556061C2211yescharacteristic
42#14556061C2211yescharacteristic
43#14556061C2211yescharacteristic
44#14556061C2211yescharacteristic
45Dic71⋊C8C2211yescharacteristic
46#14556050C2211yescharacteristic
47#14556050C2211yescharacteristic
48#14556049C2211yescharacteristic
49#14556048C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic
51C8×Dic71C2211yescharacteristic
52#121×C71C2211yescharacteristic
53C2×C4⋊C4×C71C2211yescharacteristic
54#107×C71C2211yescharacteristic
55#107×C71C2211yescharacteristic
56#102×C71C2211yescharacteristic
57#102×C71C2211yescharacteristic
58C22⋊C8×C71C2211yescharacteristic
59#11765865—44no—
60#11765864—44no—
61C2×Dic142—21no—
62C2×Dic142—21no—
63C2×D284—21no—
64C2×D284C2311yescharacteristic
65C2×C22⋊D71—21no—
66C2×C22⋊D71—21no—
67C2×C22⋊D71D411yescharacteristic
68C22×Dic71—21no—
69C22×Dic71—21no—
70C2×C4×D71—21no—
71C2×C4×D71—21no—
72C2×C4×D71—21no—
73C2×C4×D71C2311yescharacteristic
74#11765850—22no—
75C2×C71⋊C8—22no—
76C2×C71⋊C8C2311yescharacteristic
77C2×C71⋊C8C2311yescharacteristic
78C8×D71—22no—
79C4⋊Dic71—21no—
80C4⋊Dic71C2311yescharacteristic
81C4⋊Dic71C2311yescharacteristic
82C4⋊Dic71C2311yescharacteristic
83Dic71⋊C4—21no—
84Dic71⋊C4—21no—
85Dic71⋊C4—21no—
86Dic71⋊C4—21no—
87Dic71⋊C4D411yescharacteristic
88C22⋊Dic71—21no—
89C22⋊Dic71—21no—
90C22⋊Dic71D411yescharacteristic
91(C2×D71)⋊C4—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4D411yescharacteristic
95C4×Dic71C2311yescharacteristic
96C2×D4×C71—21no—
97C2×D4×C71C2311yescharacteristic
98C22×C4×C71—21no—
99C22×C4×C71C2311yescharacteristic
100C2×C8×C71C2311yescharacteristic
101C2×C8×C71C2311yescharacteristic
102C4⋊C4×C71—21no—
103C4⋊C4×C71C2311yescharacteristic
104C4⋊C4×C71C2311yescharacteristic
105C4⋊C4×C71C2311yescharacteristic
106C22⋊C4×C71—21no—
107C23×C71—21no—
108C23×C71C2×D411yescharacteristic
109C22×D71—21no—
110C22×D71C2×D411yescharacteristic
111D4×C71—21no—
112D4×C71—21no—
113D4×C71—42no—
114C2×C4×C71—21no—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—42no—
120C2×C4×C71C2×D411yescharacteristic
121C2×C4×C71C2411yescharacteristic
122C22⋊D71—42no—
123C22⋊D71—42no—
124C22⋊D71D814yescomplemented
125C2×Dic71—21no—
126C2×Dic71—21no—
127C2×Dic71—21no—
128C2×Dic71—42no—
129C2×Dic71—42no—
130C2×Dic71C2×D411yescharacteristic
131C2×Dic71C2×D411yescharacteristic
132C2×Dic71C2×D411yescharacteristic
133D284—21no—
134D284—21no—
135D284—42no—
136C4×D71—21no—
137C4×D71—21no—
138C4×D71—42no—
139C4×D71—42no—
140C4×D71—42no—
141Dic142—42no—
142Dic142—42no—
143C8×C71—21no—
144C8×C71—21no—
145C71⋊C8—21no—
146C71⋊C8#4112yescomplemented
147C22×C71—21no—
148C22×C71—21no—
149C22×C71—41no—
150C22×C71—41no—
151C22×C71—41no—
152C22×C71C2×D812yes—
153C22×C71C22×D411yescharacteristic
154C2×D71—21no—
155C2×D71—21no—
156C2×D71—41no—
157C2×D71—41no—
158C2×D71—41no—
159C2×D71C2×D812yes—
160C4×C71—21no—
161C4×C71—41no—
162C4×C71—41no—
163C4×C71—41no—
164C4×C71C2×#4111yescharacteristic
165C4×C712−1+411yescharacteristic
166Dic71—21no—
167Dic71—21no—
168Dic71—41no—
169Dic71—41no—
170Dic71—41no—
171Dic71C2×D812yes—
172C2×C71—22no—
173C2×C71—81no—
174C2×C71#54711yescharacteristic
175C2×C71C22×D811yescharacteristic
176C2×C71#57811yescharacteristic
177D71—22no—
178D71—81no—
179#3334—711nomaximal, Sylow
180C71#333411yescharacteristic, complemented, Sylow
181#547—711no—
182#547—711no—
183#500—711no—
184#480—711no—
185#480—711no—
186#480—711no—
187#480D7111yescharacteristic, complemented
188#474—711no—
189#474—711no—
190#466—711no—
191#466—711no—
192C4×D8—711no—
193C8×D4—711no—
194C2×#107—711no—
195C2×#107—711no—
196C2×#41—1421no—
197C2×#41—1421no—
198C2×D8—711no—
199C22×C8—711no—
200C22×C8—711no—
201C4⋊Q8—711no—
202C4⋊Q8—711no—
203#123—1421no—
204#123—1421no—
205#123—1421no—
206#123—1421no—
207C22⋊Q8—1421no—
208C22⋊Q8—1421no—
209#121—711no—
210#121—711no—
211#121—711no—
212#121C2×D7111yescharacteristic
213C4×D4—711no—
214C4×D4—711no—
215C4×D4—711no—
216C2×C4⋊C4—711no—
217C2×C4⋊C4—711no—
218C2×C4⋊C4—711no—
219C2×C4⋊C4C2×D7111yescharacteristic
220#107—711no—
221#107—711no—
222#107—711no—
223#107—711no—
224#107—711no—
225#107—711no—
226#107—711no—
227#107C2×D7111yescharacteristic
228#107C2×D7111yescharacteristic
229C4⋊C8—711no—
230#102—711no—
231#102—711no—
232#102—711no—
233#102—711no—
234#102C2×D7111yescharacteristic
235#102C2×D7111yescharacteristic
236C22⋊C8—711no—
237C22⋊C8C2×D7111yescharacteristic
238C4×C8—711no—
239#41—2844no—
240#41—2844no—
241C2×Q8—1421no—
242C2×Q8—1421no—
243C2×D4—21no—
244C2×D4—711no—
245C2×D4—711no—
246C2×D4—1421no—
247C2×D4—1421no—
248C2×D4—1421no—
249C2×D4C22×D7111yescharacteristic
250C22×C4—21no—
251C22×C4—711no—
252C22×C4—1421no—
253C22×C4—1421no—
254C22×C4—1421no—
255C22×C4—1421no—
256C22×C4—1421no—
257C22×C4C22×D7111yescharacteristic
258D8—1422no—
259C2×C8—711no—
260C2×C8—711no—
261C2×C8—1422no—
262C2×C8—1422no—
263C2×C8C22×D7111yescharacteristic
264C2×C8C22×D7111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—711no—
267C4⋊C4—711no—
268C4⋊C4—711no—
269C4⋊C4—711no—
270C4⋊C4—1421no—
271C4⋊C4—1421no—
272C4⋊C4—1421no—
273C4⋊C4—1421no—
274C4⋊C4—1421no—
275C4⋊C4C22×D7111yescharacteristic
276C4⋊C4C22×D7111yescharacteristic
277C4⋊C4C22×D7111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—711no—
280C22⋊C4—711no—
281C22⋊C4—1421no—
282C22⋊C4—1421no—
283C22⋊C4—1421no—
284C22⋊C4—1421no—
285C22⋊C4—1421no—
286C42—711no—
287C23—21no—
288C23—711no—
289C23—1421no—
290C23D4×D7111yescharacteristic
291Q8—2842no—
292Q8—2842no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—2842no—
297D4—2842no—
298D4—2842no—
299D4—714no—
300D4—1421no—
301D4—1421no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—2842no—
309C2×C4—2842no—
310C2×C4—2842no—
311C2×C4—2842no—
312C2×C4—2842no—
313C2×C4—711no—
314C2×C4—711no—
315C2×C4—711no—
316C2×C4—1421no—
317C2×C4—1421no—
318C2×C4—1421no—
319C2×C4—1421no—
320C2×C4—1421no—
321C2×C4D4×D7111yescharacteristic
322C2×C4C23×D7111yescharacteristic
323C8—21no—
324C8—21no—
325C8—712no—
326C8—1421no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2841no—
333C22—2841no—
334C22—2841no—
335C22—712no—
336C22—1421no—
337C22—1421no—
338C22D8×D7112yes—
339C22C2×D4×D7111yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—2841no—
345C4—2841no—
346C4—2841no—
347C4—712no—
348C4—1421no—
349C4—1421no—
350C4#41×D7111yescharacteristic
351C4#1455617511yescharacteristic
352C2—22no—
353C2—81no—
354C2—5681no—
355C2—1422no—
356C2#1798664711yescharacteristic
357C2C2×D8×D7111yescharacteristic
358C2#1798681511yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#480×C71C2
socleC22×C71C22×D4
hypercenter#480D71
hypocenterC71#3334
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #17986650C2semidirect
2. #17986649C2semidirect
3. #17986403C2semidirect
4. #17986314C2semidirect
5. #17986313C2semidirect
6. #17986311C2semidirect
7. #17986278C2semidirect
8. #17986277C2semidirect
9. #17986234C2semidirect
10. #17986233C2semidirect
11. #17986079C2semidirect
12. (C22⋊D71)⋊C8C2semidirect
13. C2×#14556061C2semidirect
14. #107×D71C2semidirect
15. #480×C71C2semidirect
124. C22⋊D71D8semidirect
146. C71⋊C8#41semidirect
180. C71#3334semidirect
187. #480D71semidirect