Finite Group Databasebeta

← #22600840

Subgroups — #22600840

Order 9088.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986695C211yesmaximal, characteristic, complemented
2#17986405C211yesmaximal, characteristic, complemented
3#17986323C211yesmaximal, characteristic, complemented
4#17986323C211yesmaximal, characteristic, complemented
5#17986320C211yesmaximal, characteristic, complemented
6#17986310C211yesmaximal, characteristic, complemented
7#17986299C211yesmaximal, characteristic, complemented
8#17986276C211yesmaximal, characteristic, complemented
9#17986250C211yesmaximal, characteristic, complemented
10#17986233C211yesmaximal, characteristic, complemented
11#17986109C211yesmaximal, characteristic, complemented
12#17986071C211yesmaximal, characteristic, complemented
13#17986042C211yesmaximal, characteristic, complemented
14#17986035C211yesmaximal, characteristic, complemented
15#555×C71C211yesmaximal, characteristic, complemented
16C2×#11765850C2211yescharacteristic
17C2×#11765849C2211yescharacteristic
18C22×C71⋊C8C2211yescharacteristic
19#14556123—21no—
20#14556120C2211yescharacteristic
21#14556110—21no—
22#14556102C2211yescharacteristic
23#14556102C2211yescharacteristic
24#14556100—21no—
25C4×D284C2211yescharacteristic
26(C22⋊D71)⋊C4—21no—
27#14556087C2211yescharacteristic
28C2×C4⋊Dic71C2211yescharacteristic
29#14556061C2211yescharacteristic
30#14556061C2211yescharacteristic
31#14556061C2211yescharacteristic
32#14556061C2211yescharacteristic
33#14556061C2211yescharacteristic
34#14556059C2211yescharacteristic
35#14556059C2211yescharacteristic
36#14556059C2211yescharacteristic
37#14556059C2211yescharacteristic
38C4⋊(C71⋊C8)C2211yescharacteristic
39#14556049C2211yescharacteristic
40#14556049C2211yescharacteristic
41#14556049C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44#14556048C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46C22⋊(C71⋊C8)C2211yescharacteristic
47#14556039C2211yescharacteristic
48C4⋊Q8×C71C2211yescharacteristic
49#124×C71—21no—
50#124×C71—21no—
51#121×C71—21no—
52#121×C71C2211yescharacteristic
53#121×C71C2211yescharacteristic
54C4×D4×C71C2211yescharacteristic
55C4×D4×C71C2211yescharacteristic
56#117×C71—21no—
57#117×C71C2211yescharacteristic
58#117×C71C2211yescharacteristic
59C2×D284C2311yescharacteristic
60C2×C22⋊D71—21no—
61C2×C22⋊D71—21no—
62C22×Dic71—21no—
63C2×C4×D71—21no—
64#11765850—22no—
65#11765849—22no—
66C2×C71⋊C8—22no—
67C2×C71⋊C8C2311yescharacteristic
68C2×C71⋊C8C2311yescharacteristic
69C2×C71⋊C8C2311yescharacteristic
70C2×C71⋊C8C2311yescharacteristic
71C4⋊Dic71—21no—
72C4⋊Dic71C2311yescharacteristic
73C4⋊Dic71C2311yescharacteristic
74C4⋊Dic71C2311yescharacteristic
75Dic71⋊C4—21no—
76Dic71⋊C4—21no—
77C22⋊Dic71—21no—
78(C2×D71)⋊C4—21no—
79(C2×D71)⋊C4—21no—
80(C2×D71)⋊C4—21no—
81C4×Dic71—21no—
82C2×Q8×C71—21no—
83C2×D4×C71—21no—
84C2×D4×C71—21no—
85C2×D4×C71D411yescharacteristic
86C2×D4×C71C2311yescharacteristic
87C22×C4×C71—21no—
88C22×C4×C71C2311yescharacteristic
89C22×C4×C71C2311yescharacteristic
90C4⋊C4×C71—21no—
91C4⋊C4×C71D411yescharacteristic
92C4⋊C4×C71C2311yescharacteristic
93C4⋊C4×C71C2311yescharacteristic
94C4⋊C4×C71C2311yescharacteristic
95C22⋊C4×C71—21no—
96C22⋊C4×C71—21no—
97C22⋊C4×C71—21no—
98C22⋊C4×C71—21no—
99C22⋊C4×C71—21no—
100C22⋊C4×C71D411yescharacteristic
101C22⋊C4×C71D411yescharacteristic
102C42×C71—21no—
103C42×C71—21no—
104C42×C71C2311yescharacteristic
105C23×C71—21no—
106C23×C71C2×D411yescharacteristic
107C23×C71C2×D411yescharacteristic
108C22×D71—21no—
109Q8×C71—81no—
110D4×C71—21no—
111D4×C71—21no—
112D4×C71—41no—
113D4×C71—81no—
114D4×C71—81no—
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—42no—
123C2×C4×C71C2×D411yescharacteristic
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2×D411yescharacteristic
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2411yescharacteristic
128C22⋊D71—42no—
129C22⋊D71—81no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—81no—
134D284—21no—
135D284—21no—
136C4×D71—81no—
137C71⋊C8—21no—
138C71⋊C8—21no—
139C71⋊C8—21no—
140C71⋊C8#4112yes—
141C22×C71—21no—
142C22×C71—21no—
143C22×C71—21no—
144C22×C71—21no—
145C22×C71—21no—
146C22×C71—21no—
147C22×C71—41no—
148C22×C71—41no—
149C22×C71—41no—
150C22×C71C22×D411yescharacteristic
151C2×D71—41no—
152C2×D71—41no—
153C2×D71—41no—
154C4×C71—21no—
155C4×C71—21no—
156C4×C71—21no—
157C4×C71—21no—
158C4×C71—41no—
159C4×C71—41no—
160C4×C71—41no—
161C4×C71C2×#4111yescharacteristic
162C4×C712−1+411yescharacteristic
163Dic71—41no—
164Dic71—41no—
165Dic71—41no—
166C2×C71—41no—
167C2×C71—41no—
168C2×C71—81no—
169C2×C71#54711yescharacteristic
170C2×C71#57511yescharacteristic
171C2×C71#57611yescharacteristic
172D71—81no—
173#3347—711nomaximal, Sylow
174C71#334711yescharacteristic, complemented, Sylow
175#555D7111yescharacteristic, complemented
176#553—711no—
177#501—711no—
178#482—711no—
179#482—711no—
180#482—711no—
181#480—711no—
182#478—711no—
183#474—711no—
184#469—711no—
185#466—711no—
186#442—711no—
187#435—711no—
188#428—711no—
189#427—711no—
190C2×D8—711no—
191C2×M16—711no—
192C22×C8—711no—
193C4⋊Q8C2×D7111yescharacteristic
194#126—1421no—
195#125—711no—
196#124—21no—
197#124—21no—
198#123—1421no—
199#121—21no—
200#121—711no—
201#121—711no—
202#121—1421no—
203#121C2×D7111yescharacteristic
204#121C2×D7111yescharacteristic
205C4×D4—711no—
206C4×D4—1421no—
207C4×D4C2×D7111yescharacteristic
208C4×D4C2×D7111yescharacteristic
209#117—21no—
210#117—711no—
211#117C2×D7111yescharacteristic
212#117C2×D7111yescharacteristic
213C2×C4⋊C4—711no—
214#107—711no—
215#107—711no—
216#107—711no—
217#107—711no—
218#107—711no—
219#106—711no—
220#106—711no—
221#106—711no—
222#106—711no—
223C4⋊C8—711no—
224#102—711no—
225#102—711no—
226#102—711no—
227#102—711no—
228#102—711no—
229#102—711no—
230C22⋊C8—711no—
231C22⋊C8—711no—
232#97—711no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—711no—
237C2×D4—1421no—
238C2×D4—1421no—
239C2×D4C22⋊D7111yescharacteristic
240C2×D4C22×D7111yescharacteristic
241C22×C4—21no—
242C22×C4—1421no—
243C22×C4—1421no—
244C22×C4C22×D7111yescharacteristic
245C22×C4C22×D7111yescharacteristic
246D8—1422no—
247M16—1422no—
248C2×C8—711no—
249C2×C8—711no—
250C2×C8—711no—
251C2×C8—711no—
252C2×C8—1422no—
253C4⋊C4—21no—
254C4⋊C4—711no—
255C4⋊C4—711no—
256C4⋊C4—711no—
257C4⋊C4—1421no—
258C4⋊C4—1421no—
259C4⋊C4—1421no—
260C4⋊C4C22⋊D7111yescharacteristic
261C4⋊C4C22×D7111yescharacteristic
262C4⋊C4C22×D7111yescharacteristic
263C4⋊C4C22×D7111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1421no—
270C22⋊C4—1421no—
271C22⋊C4—1421no—
272C22⋊C4—1421no—
273C22⋊C4C22⋊D7111yescharacteristic
274C22⋊C4C22⋊D7111yescharacteristic
275C42—21no—
276C42—21no—
277C42—1421no—
278C42C22×D7111yescharacteristic
279C23—21no—
280C23—1421no—
281C23C2×C22⋊D7111yescharacteristic
282C23C2×C22⋊D7111yescharacteristic
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—81no—
288D4—81no—
289D4—2842no—
290D4—5681no—
291D4—1421no—
292D4—1421no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—5681no—
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×C4C23×D7111yescharacteristic
311C8—712no—
312C8—1421no—
313C8—1421no—
314C8—1421no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—2841no—
325C22—2841no—
326C22—2841no—
327C22C22×C22⋊D7111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2841no—
336C4—2841no—
337C4—2841no—
338C4#41×D7111yescharacteristic
339C4#1455617511yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—5681no—
344C2#1798664811yescharacteristic
345C2#1798679711yescharacteristic
346C2#1798680211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#555×C71C2
socleC22×C71C22×D4
hypercenter#555D71
hypocenterC71#3347
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #17986695C2semidirect
2. #17986405C2semidirect
3. #17986323C2semidirect
4. #17986323C2semidirect
5. #17986320C2semidirect
6. #17986310C2semidirect
7. #17986299C2semidirect
8. #17986276C2semidirect
9. #17986250C2semidirect
10. #17986233C2semidirect
11. #17986109C2semidirect
12. #17986071C2semidirect
13. #17986042C2semidirect
14. #17986035C2semidirect
15. #555×C71C2semidirect
174. C71#3347semidirect
175. #555D71semidirect