Finite Group Databasebeta

← #22599796

Subgroups — #22599796

Order 9088.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986620C211yesmaximal, characteristic, complemented
2#17986294C211yesmaximal, characteristic, complemented
3#17986291C211yesmaximal, characteristic, complemented
4#17986279C211yesmaximal, characteristic, complemented
5#17986276C211yesmaximal, characteristic, complemented
6#17986247C211yesmaximal, characteristic, complemented
7#17986243C211yesmaximal, characteristic, complemented
8#17986238C211yesmaximal, characteristic, complemented
9#17986233C211yesmaximal, characteristic
10#17986221C211yesmaximal, characteristic, complemented
11#17986218C211yesmaximal, characteristic, complemented
12#17986214C211yesmaximal, characteristic, complemented
13#17986211C211yesmaximal, characteristic, complemented
14#17986026C211yesmaximal, characteristic, complemented
15#542×C71C211yesmaximal, characteristic, complemented
16C2×#11765855C2211yescharacteristic
17C2×#11765853C2211yescharacteristic
18C2×#11765852C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765849C2211yescharacteristic
21C22×C71⋊C8C2211yescharacteristic
22#14556128C2211yescharacteristic
23#14556123—21no—
24#14556116C2211yescharacteristic
25#14556114—21no—
26#14556110—21no—
27#14556107C2211yescharacteristic
28#14556106—21no—
29#14556102C2211yescharacteristic
30C4×Dic142C2211yescharacteristic
31C4×D284C2211yescharacteristic
32#14556061C2211yescharacteristic
33#14556061C2211yescharacteristic
34#14556061C2211yescharacteristic
35#14556061C2211yescharacteristic
36C4⋊(C71⋊C8)C2211yescharacteristic
37C4⋊(C71⋊C8)C2211yescharacteristic
38C4⋊(C71⋊C8)C2211yescharacteristic
39C4⋊(C71⋊C8)C2211yescharacteristic
40#14556052C2211yescharacteristic
41#14556052C2211yescharacteristic
42#14556051C2211yescharacteristic
43#14556051C2211yescharacteristic
44#14556049C2211yescharacteristic
45#14556049C2211yescharacteristic
46#14556048C2211yescharacteristic
47#14556048C2211yescharacteristic
48C4⋊Q8×C71C2211yescharacteristic
49#126×C71—21no—
50#124×C71—21no—
51#124×C71C2211yescharacteristic
52#123×C71—21no—
53C22⋊Q8×C71—21no—
54C22⋊Q8×C71C2211yescharacteristic
55#121×C71C2211yescharacteristic
56C4×Q8×C71C2211yescharacteristic
57C4×D4×C71C2211yescharacteristic
58#117×C71C2211yescharacteristic
59C2×Dic142—21no—
60C2×Dic142C2311yescharacteristic
61C2×D284C2311yescharacteristic
62C2×C22⋊D71—21no—
63C2×C4×D71—21no—
64#11765855—41no—
65#11765853—41no—
66#11765852—41no—
67#11765850—41no—
68#11765849—41no—
69C2×C71⋊C8—41no—
70C2×C71⋊C8C2311yescharacteristic
71C2×C71⋊C8C2311yescharacteristic
72C2×C71⋊C8C2311yescharacteristic
73C2×C71⋊C8C2311yescharacteristic
74C4⋊Dic71—21no—
75C4⋊Dic71C2311yescharacteristic
76C4⋊Dic71C2311yescharacteristic
77Dic71⋊C4—21no—
78Dic71⋊C4—21no—
79C22⋊Dic71—21no—
80(C2×D71)⋊C4—21no—
81(C2×D71)⋊C4—21no—
82(C2×D71)⋊C4—21no—
83(C2×D71)⋊C4—21no—
84C4×Dic71—21no—
85C2×Q8×C71—21no—
86C2×Q8×C71C2311yescharacteristic
87C2×D4×C71—21no—
88C2×D4×C71C2311yescharacteristic
89C22×C4×C71—21no—
90C22×C4×C71C2311yescharacteristic
91C4⋊C4×C71—21no—
92C4⋊C4×C71—21no—
93C4⋊C4×C71—21no—
94C4⋊C4×C71D411yescharacteristic
95C4⋊C4×C71D411yescharacteristic
96C4⋊C4×C71C2311yescharacteristic
97C4⋊C4×C71C2311yescharacteristic
98C22⋊C4×C71—21no—
99C22⋊C4×C71—21no—
100C22⋊C4×C71—21no—
101C22⋊C4×C71—21no—
102C22⋊C4×C71—21no—
103C22⋊C4×C71D411yescharacteristic
104C22⋊C4×C71D411yescharacteristic
105C42×C71—21no—
106C42×C71C2311yescharacteristic
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111Q8×C71—21no—
112Q8×C71—21no—
113Q8×C71—81no—
114D4×C71—21no—
115D4×C71—21no—
116D4×C71—81no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—81no—
123C2×C4×C71C2×D411yescharacteristic
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2×D411yescharacteristic
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2411yescharacteristic
129C22⋊D71—81no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133D284—21no—
134D284—21no—
135C4×D71—81no—
136Dic142—21no—
137Dic142—21no—
138Dic142—81no—
139C71⋊C8—21no—
140C71⋊C8—21no—
141C71⋊C8—21no—
142C71⋊C8—21no—
143C22×C71—21no—
144C22×C71—21no—
145C22×C71—21no—
146C22×C71—41no—
147C22×C71—41no—
148C22×C71—41no—
149C22×C71C22×D411yescharacteristic
150C2×D71—41no—
151C2×D71—41no—
152C2×D71—41no—
153C4×C71—21no—
154C4×C71—21no—
155C4×C71—21no—
156C4×C71—21no—
157C4×C71—21no—
158C4×C71—41no—
159C4×C71—41no—
160C4×C71—41no—
161C4×C71H(5,𝔽2)11yescharacteristic
162C4×C712−1+411yescharacteristic
163Dic71—41no—
164Dic71—41no—
165Dic71—41no—
166C2×C71—41no—
167C2×C71—81no—
168C2×C71#53711yescharacteristic
169C2×C71#57611yescharacteristic
170C2×C71#57811yescharacteristic
171D71—81no—
172#3262—711nomaximal, Sylow
173C71#326211yescharacteristic, complemented, Sylow
174#542—711no—
175#542D7111yescharacteristic, complemented
176#477—711no—
177#477—711no—
178#474—711no—
179#474—711no—
180#468—711no—
181#468—711no—
182#467—711no—
183#466—711no—
184#464—711no—
185#464—711no—
186#463—711no—
187#463—711no—
188#424—711no—
189C2×Q16—711no—
190C2×SD16—711no—
191C2×SD16—711no—
192C2×D8—711no—
193C2×M16—711no—
194C22×C8—711no—
195C4⋊Q8—711no—
196C4⋊Q8C2×D7111yescharacteristic
197#126—21no—
198#126—1421no—
199#124—21no—
200#124—711no—
201#124—1421no—
202#124C2×D7111yescharacteristic
203#123—21no—
204#123—1421no—
205C22⋊Q8—21no—
206C22⋊Q8—711no—
207C22⋊Q8—1421no—
208C22⋊Q8C2×D7111yescharacteristic
209#121—711no—
210#121C2×D7111yescharacteristic
211C4×Q8—711no—
212C4×Q8C2×D7111yescharacteristic
213C4×D4—711no—
214C4×D4C2×D7111yescharacteristic
215#117C2×D7111yescharacteristic
216#107—711no—
217#107—711no—
218#107—711no—
219#107—711no—
220C4⋊C8—711no—
221C4⋊C8—711no—
222C4⋊C8—711no—
223C4⋊C8—711no—
224#103—711no—
225#103—711no—
226#103—711no—
227#103—711no—
228#102—711no—
229#102—711no—
230#102—711no—
231#102—711no—
232C2×Q8—21no—
233C2×Q8—711no—
234C2×Q8—1421no—
235C2×Q8C22×D7111yescharacteristic
236C2×D4—21no—
237C2×D4—711no—
238C2×D4—1421no—
239C2×D4C22×D7111yescharacteristic
240C22×C4—21no—
241C22×C4—1421no—
242C22×C4C22×D7111yescharacteristic
243Q16—2841no—
244SD16—2841no—
245SD16—2841no—
246D8—2841no—
247M16—2841no—
248C2×C8—2841no—
249C2×C8—711no—
250C2×C8—711no—
251C2×C8—711no—
252C2×C8—711no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—711no—
257C4⋊C4—711no—
258C4⋊C4—1421no—
259C4⋊C4—1421no—
260C4⋊C4—1421no—
261C4⋊C4C22⋊D7111yescharacteristic
262C4⋊C4C22⋊D7111yescharacteristic
263C4⋊C4C22×D7111yescharacteristic
264C4⋊C4C22×D7111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1421no—
271C22⋊C4—1421no—
272C22⋊C4—1421no—
273C22⋊C4—1421no—
274C22⋊C4—1421no—
275C22⋊C4C22⋊D7111yescharacteristic
276C22⋊C4C22⋊D7111yescharacteristic
277C42—21no—
278C42—1421no—
279C42C22×D7111yescharacteristic
280C42C22×D7111yescharacteristic
281C23—21no—
282C23—1421no—
283C23C2×C22⋊D7111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—5681no—
288Q8—1421no—
289Q8—1421no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—5681no—
294D4—1421no—
295D4—1421no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—5681no—
303C2×C4—1421no—
304C2×C4—1421no—
305C2×C4—1421no—
306C2×C4C2×C22⋊D7111yescharacteristic
307C2×C4C2×C22⋊D7111yescharacteristic
308C2×C4C2×C22⋊D7111yescharacteristic
309C2×C4C2×C22⋊D7111yescharacteristic
310C2×C4C2×C22⋊D7111yescharacteristic
311C2×C4C23×D7111yescharacteristic
312C8—1421no—
313C8—1421no—
314C8—1421no—
315C8—1421no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2841no—
323C22—2841no—
324C22—2841no—
325C22C22×C22⋊D7111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2841no—
335C4—2841no—
336C4—2841no—
337C4#1455617411yescharacteristic
338C4#1455617511yescharacteristic
339C2—41no—
340C2—81no—
341C2—5681no—
342C2#1798657711yescharacteristic
343C2#1798680211yescharacteristic
344C2#1798681411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#542×C71C2
socleC22×C71C22×D4
hypercenter#542D71
hypocenterC71#3262
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #17986620C2semidirect
2. #17986294C2semidirect
3. #17986291C2semidirect
4. #17986279C2semidirect
5. #17986276C2semidirect
6. #17986247C2semidirect
7. #17986243C2semidirect
8. #17986238C2semidirect
10. #17986221C2semidirect
11. #17986218C2semidirect
12. #17986214C2semidirect
13. #17986211C2semidirect
14. #17986026C2semidirect
15. #542×C71C2semidirect
173. C71#3262semidirect
175. #542D71semidirect