Finite Group Databasebeta

← #22598295

Subgroups — #22598295

Order 9088.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986565C211yesmaximal, characteristic
2#17986479C211yesmaximal, characteristic, complemented
3#17986326C211yesmaximal, characteristic, complemented
4#17986323C211yesmaximal, characteristic, complemented
5#17986321C211yesmaximal, characteristic, complemented
6#17986319C211yesmaximal, characteristic, complemented
7#17986315C211yesmaximal, characteristic, complemented
8#17986313C211yesmaximal, characteristic, complemented
9#17986311C211yesmaximal, characteristic, complemented
10#17986038C211yesmaximal, characteristic, complemented
11#17986036C211yesmaximal, characteristic, complemented
12#17986002C211yesmaximal, characteristic, complemented
13#102×D71C211yesmaximal, characteristic, complemented
14#17985964C211yesmaximal, characteristic, complemented
15#482×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×D4×D71C2211yescharacteristic
18C2×#11765848C2211yescharacteristic
19C2×C8×D71C2211yescharacteristic
20#14556124—21no—
21#14556114—21no—
22#14556103C2211yescharacteristic
23#14556102C2211yescharacteristic
24#14556099C2211yescharacteristic
25#14556098—21no—
26#14556096—21no—
27C4×Dic142—21no—
28C4×D284—21no—
29(C22⋊D71)⋊C4—21no—
30(C22⋊D71)⋊C4—21no—
31#14556086C2211yescharacteristic
32#14556086C2211yescharacteristic
33#14556086C2211yescharacteristic, complemented
34C2×C4⋊Dic71C2211yescharacteristic, complemented
35C4⋊C4×D71C2211yescharacteristic
36C4⋊C4×D71C2211yescharacteristic, complemented
37#14556062C2211yescharacteristic, complemented
38#14556062C2211yescharacteristic, complemented
39#14556061C2211yescharacteristic, complemented
40#14556059C2211yescharacteristic, complemented
41#14556059C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic
44#14556050C2211yescharacteristic
45#14556049C2211yescharacteristic
46#14556049C2211yescharacteristic
47#14556048C2211yescharacteristic
48#14556048C2211yescharacteristic
49C22⋊(C71⋊C8)C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52#121×C71C2211yescharacteristic
53#117×C71C2211yescharacteristic, complemented
54#107×C71C2211yescharacteristic, complemented
55#106×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic
57#102×C71C2211yescharacteristic
58C22⋊C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60#11765865—22no—
61#11765865—22no—
62C2×Dic142D411yescharacteristic
63C2×D284—21no—
64C2×D284D411yescharacteristic
65C2×D284C2311yescharacteristic
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68C2×C22⋊D71—21no—
69C2×C22⋊D71D411yescharacteristic
70C2×C22⋊D71D411yescharacteristic
71D4×D71—22no—
72D4×D71—22no—
73C22×Dic71—21no—
74C2×C4×D71—21no—
75C2×C4×D71—21no—
76C2×C4×D71C2311yescharacteristic
77C2×C4×D71C2311yescharacteristic
78#11765848—22no—
79C2×C71⋊C8C2311yescharacteristic
80C2×C71⋊C8C2311yescharacteristic
81C8×D71—22no—
82C4⋊Dic71—21no—
83C4⋊Dic71C2311yescharacteristic
84C4⋊Dic71C2311yescharacteristic
85C4⋊Dic71C2311yescharacteristic
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88C22⋊Dic71—21no—
89(C2×D71)⋊C4—21no—
90(C2×D71)⋊C4—21no—
91(C2×D71)⋊C4—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94C4×Dic71—21no—
95C4×Dic71—21no—
96C4×Dic71—21no—
97C2×D4×C71—21no—
98C2×D4×C71C2311yescharacteristic
99C22×C4×C71C2311yescharacteristic
100C2×C8×C71C2311yescharacteristic
101C2×C8×C71C2311yescharacteristic
102C4⋊C4×C71C2311yescharacteristic
103C4⋊C4×C71C2311yescharacteristic
104C4⋊C4×C71C2311yescharacteristic
105C22⋊C4×C71—21no—
106C22⋊C4×C71—21no—
107C42×C71—21no—
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111C22×D71—42no—
112C22×D71—81no—
113C22×D71—81no—
114C22×D71C2×D411yescharacteristic
115C22×D71C2×D411yescharacteristic
116D4×C71—21no—
117D4×C71—21no—
118D4×C71—81no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2411yescharacteristic
126C22⋊D71—22no—
127C22⋊D71—22no—
128C22⋊D71—42no—
129C22⋊D71—81no—
130C22⋊D71—81no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71—81no—
135C2×Dic71C2×D411yescharacteristic
136C2×Dic71C2×D411yescharacteristic
137D284—22no—
138D284—21no—
139D284—21no—
140D284—81no—
141C4×D71—21no—
142C4×D71—21no—
143C4×D71—81no—
144C4×D71—81no—
145C4×D71#4112yes—
146C4×D71#4112yes—
147Dic142—22no—
148C8×C71—21no—
149C8×C71—21no—
150C71⋊C8—21no—
151C71⋊C8—21no—
152C22×C71—21no—
153C22×C71—21no—
154C22×C71—21no—
155C22×C71—41no—
156C22×C71—41no—
157C22×C71—41no—
158C22×C71C22×D411yescharacteristic
159C2×D71—21no—
160C2×D71—21no—
161C2×D71—21no—
162C2×D71—21no—
163C2×D71—21no—
164C2×D71—41no—
165C2×D71—41no—
166C2×D71—41no—
167C2×D71—84no—
168C2×D71#12312yes—
169C4×C71—21no—
170C4×C71—41no—
171C4×C71—41no—
172C4×C71—41no—
173C4×C71C2×#4111yescharacteristic
174C4×C71C2×#4111yescharacteristic
175Dic71—21no—
176Dic71—41no—
177Dic71—41no—
178Dic71—41no—
179Dic71#12312yes—
180C2×C71—41no—
181C2×C71—81no—
182C2×C71C2×#12311yescharacteristic
183C2×C71#57611yescharacteristic
184C2×C71#57711yescharacteristic
185D71—22no—
186D71—41no—
187D71—81no—
188#3096—711nomaximal, Sylow
189C71#309611yescharacteristic, complemented, Sylow
190#535—711no—
191#520—711no—
192#482—711no—
193#482—711no—
194#482—711no—
195#482D7111yescharacteristic, complemented
196#481—711no—
197#481—711no—
198#480—711no—
199#480—711no—
200#428—711no—
201#427—711no—
202#418—711no—
203C2×#102—711no—
204#408—711no—
205C2×#41—711no—
206C22×D4—711no—
207C2×M16—711no—
208C22×C8—711no—
209#127—1421no—
210#124—1421no—
211#121—711no—
212#121—711no—
213#121—711no—
214#121C2×D7111yescharacteristic
215#120—1421no—
216#120—1421no—
217C4×Q8—1421no—
218C4×D4—1421no—
219C4×D4—1421no—
220C4×D4—1421no—
221#117—711no—
222#117—711no—
223#117—711no—
224#117C2×D7111yescharacteristic, complemented
225C2×C4⋊C4—711no—
226C2×C4⋊C4—711no—
227C2×C4⋊C4—711no—
228#107—711no—
229#107—711no—
230#107—711no—
231#107C2×D7111yescharacteristic, complemented
232#106—711no—
233#106—711no—
234#106—711no—
235#106C2×D7111yescharacteristic, complemented
236#102—711no—
237#102—711no—
238#102—711no—
239#102—711no—
240#102—711no—
241#102—711no—
242#102C2×D7111yescharacteristic
243#102C2×D7111yescharacteristic
244C22⋊C8—711no—
245C22⋊C8—711no—
246C22⋊C8—711no—
247C22⋊C8C2×D7111yescharacteristic, complemented
248C24—1421no—
249#41—1422no—
250#41—1422no—
251C2×Q8—711no—
252C2×D4—21no—
253C2×D4—711no—
254C2×D4—711no—
255C2×D4—711no—
256C2×D4—711no—
257C2×D4—1421no—
258C2×D4—1422no—
259C2×D4—1422no—
260C2×D4—1421no—
261C2×D4—1421no—
262C2×D4—1421no—
263C2×D4C22×D7111yescharacteristic
264C22×C4—711no—
265C22×C4—711no—
266C22×C4—1421no—
267C22×C4—1421no—
268C22×C4—1421no—
269C22×C4C22×D7111yescharacteristic
270M16—1422no—
271C2×C8—711no—
272C2×C8—711no—
273C2×C8—1422no—
274C2×C8C22×D7111yescharacteristic
275C2×C8C22×D7111yescharacteristic
276C4⋊C4—711no—
277C4⋊C4—711no—
278C4⋊C4—711no—
279C4⋊C4—1421no—
280C4⋊C4—1421no—
281C4⋊C4—1421no—
282C4⋊C4C22×D7111yescharacteristic
283C4⋊C4C22×D7111yescharacteristic
284C4⋊C4C22×D7111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1421no—
288C22⋊C4—1421no—
289C22⋊C4—1421no—
290C22⋊C4—1421no—
291C22⋊C4—1421no—
292C22⋊C4—1421no—
293C42—21no—
294C42—1421no—
295C42—1421no—
296C42—1421no—
297C23—21no—
298C23—2842no—
299C23—5681no—
300C23—5681no—
301C23—711no—
302C23—711no—
303C23—1421no—
304C23D4×D7111yescharacteristic
305Q8—1422no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—2842no—
310D4—5681no—
311D4—5681no—
312D4—5681no—
313D4—1422no—
314D4—1422no—
315D4—1422no—
316D4—1421no—
317D4—1421no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—5681no—
324C2×C4—5681no—
325C2×C4—5681no—
326C2×C4—711no—
327C2×C4—712no—
328C2×C4—712no—
329C2×C4—711no—
330C2×C4—1421no—
331C2×C4—1421no—
332C2×C4—1421no—
333C2×C4—1421no—
334C2×C4—1421no—
335C2×C4D4×D7111yescharacteristic
336C2×C4C23×D7111yescharacteristic
337C8—21no—
338C8—21no—
339C8—1421no—
340C8—1421no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—2841no—
348C22—2841no—
349C22—2841no—
350C22—5684no—
351C22—712no—
352C22—1421no—
353C22—1421no—
354C22—1421no—
355C22—1421no—
356C22—1421no—
357C22C2×D4×D7111yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—2841no—
363C4—2841no—
364C4—2841no—
365C4—712no—
366C4—1421no—
367C4#41×D7111yescharacteristic
368C4#41×D7111yescharacteristic
369C2—41no—
370C2—81no—
371C2—2841no—
372C2—5681no—
373C2—1422no—
374C2#123×D7111yescharacteristic
375C2#1798680111yescharacteristic
376C2#1798680911yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#482×C71C2
socleC22×C71C22×D4
hypercenter#482D71
hypocenterC71#3096
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #17986479C2semidirect
3. #17986326C2semidirect
4. #17986323C2semidirect
5. #17986321C2semidirect
6. #17986319C2semidirect
7. #17986315C2semidirect
8. #17986313C2semidirect
9. #17986311C2semidirect
10. #17986038C2semidirect
11. #17986036C2semidirect
12. #17986002C2semidirect
13. #102×D71C2semidirect
14. #17985964C2semidirect
15. #482×C71C2semidirect
33. #14556086C22semidirect
34. C2×C4⋊Dic71C22semidirect
36. C4⋊C4×D71C22semidirect
37. #14556062C22semidirect
38. #14556062C22semidirect
39. #14556061C22semidirect
40. #14556059C22semidirect
41. #14556059C22semidirect
42. #14556059C22semidirect
49. C22⋊(C71⋊C8)C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. (C2×D71)⋊C8C22semidirect
53. #117×C71C22semidirect
54. #107×C71C22semidirect
55. #106×C71C22semidirect
58. C22⋊C8×C71C22semidirect
189. C71#3096semidirect
195. #482D71semidirect
224. #117C2×D71semidirect
231. #107C2×D71semidirect
235. #106C2×D71semidirect
247. C22⋊C8C2×D71semidirect