Finite Group Databasebeta

← #22598596

Subgroups — #22598596

Order 9088.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986479C211yesmaximal, characteristic, complemented
2#17986332C211yesmaximal, characteristic, complemented
3#17986310C211yesmaximal, characteristic, complemented
4#17986291C211yesmaximal, characteristic, complemented
5#17986276C211yesmaximal, characteristic, complemented
6#17986218C211yesmaximal, characteristic, complemented
7#17986211C211yesmaximal, characteristic, complemented
8#17986159C211yesmaximal, characteristic, complemented
9#17986142C211yesmaximal, characteristic
10#17986099C211yesmaximal, characteristic, complemented
11#17986097C211yesmaximal, characteristic, complemented
12C4×#11765855C211yesmaximal, characteristic, complemented
13C4×#11765850C211yesmaximal, characteristic, complemented
14#17986060C211yesmaximal, characteristic, complemented
15#542×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×#11765855C2211yescharacteristic
18C2×#11765853C2211yescharacteristic
19C2×#11765852C2211yescharacteristic
20C2×#11765850C2211yescharacteristic
21C4×Dic142C2211yescharacteristic
22C4×Dic142C2211yescharacteristic
23C4×D284C2211yescharacteristic
24C4×D284C2211yescharacteristic
25(C22⋊D71)⋊C4—21no—
26(C22⋊D71)⋊C4—21no—
27#14556086—21no—
28C2×C4⋊Dic71C2211yescharacteristic
29C4⋊C4×D71—21no—
30#14556061C2211yescharacteristic
31#14556061C2211yescharacteristic
32#14556061C2211yescharacteristic
33#14556061C2211yescharacteristic
34C4⋊(C71⋊C8)C2211yescharacteristic
35C4⋊(C71⋊C8)C2211yescharacteristic
36#14556052C2211yescharacteristic
37#14556052C2211yescharacteristic
38#14556051C2211yescharacteristic
39#14556051C2211yescharacteristic
40#14556049C2211yescharacteristic
41#14556049C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46#14556039C2211yescharacteristic
47C4×C71⋊C8C2211yescharacteristic
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
59#11765865—22no—
60#11765865—22no—
61C2×Dic142C2311yescharacteristic
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C22×Dic71—21no—
65C2×C4×D71—21no—
66C2×C4×D71—21no—
67C2×C4×D71—21no—
68#11765855—22no—
69#11765853—22no—
70#11765852—22no—
71#11765850—22no—
72C2×C71⋊C8C2311yescharacteristic
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C4⋊Dic71—21no—
77C4⋊Dic71C2311yescharacteristic
78C4⋊Dic71C2311yescharacteristic
79Dic71⋊C4—21no—
80Dic71⋊C4—21no—
81(C2×D71)⋊C4—21no—
82(C2×D71)⋊C4—21no—
83C4×Dic71—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—24no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—81no—
134D284—21no—
135D284#4112yes—
136C4×D71—24no—
137C4×D71—81no—
138C4×D71—81no—
139Dic142—21no—
140Dic142#4112yes—
141C71⋊C8—21no—
142C71⋊C8—21no—
143C71⋊C8—21no—
144C71⋊C8—21no—
145C22×C71—21no—
146C22×C71—21no—
147C22×C71—21no—
148C22×C71—41no—
149C22×C71—41no—
150C22×C71—41no—
151C22×C71C22×D411yescharacteristic
152C2×D71—22no—
153C2×D71—41no—
154C2×D71—41no—
155C4×C71—21no—
156C4×C71—21no—
157C4×C71—21no—
158C4×C71—21no—
159C4×C71—21no—
160C4×C71—41no—
161C4×C71—41no—
162C4×C71—41no—
163C4×C71C2×#4111yescharacteristic
164C4×C71C2×#4111yescharacteristic
165Dic71—22no—
166Dic71—41no—
167Dic71—41no—
168C2×C71—41no—
169C2×C71—81no—
170C2×C71#52511yescharacteristic
171C2×C71#57611yescharacteristic
172C2×C71#57811yescharacteristic
173D71—42no—
174#3124—711nomaximal, Sylow
175C71#312411yescharacteristic, complemented, Sylow
176#542D7111yescharacteristic, complemented
177#520—711no—
178#484—711no—
179#480—711no—
180#477—711no—
181#474—711no—
182#464—711no—
183#463—711no—
184#452—711no—
185#449—711no—
186#440—711no—
187#440—711no—
188C4×Q16—711no—
189C4×D8—711no—
190#433—711no—
191C2×#41—711no—
192C2×Q16—711no—
193C2×SD16—711no—
194C2×SD16—711no—
195C2×D8—711no—
196C4⋊Q8C2×D7111yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D7111yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D7111yescharacteristic
203#121C2×D7111yescharacteristic
204C4×Q8—711no—
205C4×Q8—711no—
206C4×Q8C2×D7111yescharacteristic
207C4×D4—711no—
208C4×D4—711no—
209C4×D4—1421no—
210C4×D4—1421no—
211C4×D4C2×D7111yescharacteristic
212#117—1421no—
213#117C2×D7111yescharacteristic
214C2×C4⋊C4—711no—
215C2×C4⋊C4—1421no—
216#107—711no—
217#107—711no—
218#107—711no—
219#107—711no—
220C4⋊C8—711no—
221C4⋊C8—711no—
222#103—711no—
223#103—711no—
224#103—711no—
225#103—711no—
226#102—711no—
227#102—711no—
228#102—711no—
229#102—711no—
230C22⋊C8—711no—
231C22⋊C8—711no—
232#97—711no—
233C4×C8—711no—
234#41—1422no—
235#41—1422no—
236C2×Q8—21no—
237C2×Q8—711no—
238C2×Q8C22×D7111yescharacteristic
239C2×D4—21no—
240C2×D4—711no—
241C2×D4—1421no—
242C2×D4C22×D7111yescharacteristic
243C22×C4—21no—
244C22×C4—1421no—
245C22×C4—1421no—
246C22×C4—1421no—
247C22×C4—1421no—
248C22×C4C22×D7111yescharacteristic
249Q16—1422no—
250SD16—1422no—
251SD16—1422no—
252D8—1422no—
253C2×C8—711no—
254C2×C8—711no—
255C2×C8—711no—
256C2×C8—711no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—711no—
261C4⋊C4—711no—
262C4⋊C4—1421no—
263C4⋊C4—1421no—
264C4⋊C4—1421no—
265C4⋊C4C22⋊D7111yescharacteristic
266C4⋊C4C22⋊D7111yescharacteristic
267C4⋊C4C22×D7111yescharacteristic
268C4⋊C4C22×D7111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1421no—
275C22⋊C4—1421no—
276C22⋊C4C22⋊D7111yescharacteristic
277C22⋊C4C22⋊D7111yescharacteristic
278C42—21no—
279C42—1421no—
280C42—1421no—
281C42C22×D7111yescharacteristic
282C42C22×D7111yescharacteristic
283C23—21no—
284C23—1421no—
285C23C2×C22⋊D7111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—712no—
290Q8—1421no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—712no—
295D4—1424no—
296D4—1421no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—5681no—
304C2×C4—5681no—
305C2×C4—5681no—
306C2×C4—1424no—
307C2×C4—1421no—
308C2×C4—1421no—
309C2×C4—1421no—
310C2×C4C2×C22⋊D7111yescharacteristic
311C2×C4C2×C22⋊D7111yescharacteristic
312C2×C4C2×C22⋊D7111yescharacteristic
313C2×C4C2×C22⋊D7111yescharacteristic
314C2×C4C2×C22⋊D7111yescharacteristic
315C2×C4C23×D7111yescharacteristic
316C8—1421no—
317C8—1421no—
318C8—1421no—
319C8—1421no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2841no—
327C22—2841no—
328C22—1422no—
329C22C22×C22⋊D7111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2841no—
339C4—2841no—
340C4—1422no—
341C4#41×D7111yescharacteristic
342C4#41×D7111yescharacteristic
343C2—41no—
344C2—81no—
345C2—2842no—
346C2#1798650611yescharacteristic
347C2#1798680211yescharacteristic
348C2#1798681411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#542×C71C2
socleC22×C71C22×D4
hypercenter#542D71
hypocenterC71#3124
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. #17986479C2semidirect
2. #17986332C2semidirect
3. #17986310C2semidirect
4. #17986291C2semidirect
5. #17986276C2semidirect
6. #17986218C2semidirect
7. #17986211C2semidirect
8. #17986159C2semidirect
10. #17986099C2semidirect
11. #17986097C2semidirect
12. C4×#11765855C2semidirect
13. C4×#11765850C2semidirect
14. #17986060C2semidirect
15. #542×C71C2semidirect
175. C71#3124semidirect
176. #542D71semidirect