Finite Group Databasebeta

← #22600810

Subgroups — #22600810

Order 9088.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 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#17986320C211yesmaximal, characteristic, complemented
4#17986317C211yesmaximal, characteristic, complemented
5#17986315C211yesmaximal, characteristic, complemented
6#17986312C211yesmaximal, characteristic, complemented
7#17986299C211yesmaximal, characteristic, complemented
8#17986286C211yesmaximal, characteristic, complemented
9#17986250C211yesmaximal, characteristic, complemented
10#17986233C211yesmaximal, characteristic, complemented
11#17986109C211yesmaximal, characteristic, complemented
12#17986071C211yesmaximal, characteristic, complemented
13#17986039C211yesmaximal, characteristic, complemented
14C2×#14556059C211yesmaximal, characteristic, complemented
15#547×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#14556059C2211yescharacteristic
33#14556059C2211yescharacteristic
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
48C2×#41×C71—21no—
49C4⋊Q8×C71C2211yescharacteristic
50#123×C71—21no—
51#123×C71—21no—
52C22⋊Q8×C71—21no—
53#121×C71C2211yescharacteristic
54#121×C71C2211yescharacteristic
55C4×D4×C71C2211yescharacteristic
56C4×D4×C71C2211yescharacteristic
57C2×C4⋊C4×C71C2211yescharacteristic
58C2×C4⋊C4×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—
82#41×C71—44no—
83C2×Q8×C71—21no—
84C2×D4×C71—21no—
85C2×D4×C71—21no—
86C2×D4×C71D411yescharacteristic
87C2×D4×C71C2311yescharacteristic
88C22×C4×C71—21no—
89C22×C4×C71—21no—
90C22×C4×C71—21no—
91C22×C4×C71C2311yescharacteristic
92C22×C4×C71C2311yescharacteristic
93C4⋊C4×C71—21no—
94C4⋊C4×C71—21no—
95C4⋊C4×C71—21no—
96C4⋊C4×C71D411yescharacteristic
97C4⋊C4×C71C2311yescharacteristic
98C4⋊C4×C71C2311yescharacteristic
99C4⋊C4×C71C2311yescharacteristic
100C22⋊C4×C71—21no—
101C22⋊C4×C71—21no—
102C22⋊C4×C71—21no—
103C22⋊C4×C71D411yescharacteristic
104C22⋊C4×C71D411yescharacteristic
105C42×C71C2311yescharacteristic
106C23×C71—21no—
107C23×C71C2×D411yescharacteristic
108C23×C71C2×D411yescharacteristic
109C22×D71—21no—
110Q8×C71—42no—
111D4×C71—22no—
112D4×C71—21no—
113D4×C71—21no—
114D4×C71—42no—
115D4×C71—42no—
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—21no—
123C2×C4×C71—42no—
124C2×C4×C71—42no—
125C2×C4×C71—42no—
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2×D411yescharacteristic
130C2×C4×C71C2411yescharacteristic
131C22⋊D71—42no—
132C22⋊D71—81no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136C2×Dic71—81no—
137D284—21no—
138D284—21no—
139C4×D71—81no—
140C71⋊C8—21no—
141C71⋊C8—21no—
142C71⋊C8—21no—
143C71⋊C8#4112yescomplemented
144C22×C71—21no—
145C22×C71—21no—
146C22×C71—21no—
147C22×C71—21no—
148C22×C71—21no—
149C22×C71—41no—
150C22×C71—41no—
151C22×C71—41no—
152C22×C71AGL(1,ℤ/8)12yes—
153C22×C71C22×D411yescharacteristic
154C2×D71—41no—
155C2×D71—41no—
156C2×D71—41no—
157C4×C71—21no—
158C4×C71—21no—
159C4×C71—21no—
160C4×C71—21no—
161C4×C71—41no—
162C4×C71—41no—
163C4×C71—41no—
164C4×C71C2×#4111yescharacteristic
165C4×C712−1+411yescharacteristic
166Dic71—41no—
167Dic71—41no—
168Dic71—41no—
169C2×C71—22no—
170C2×C71—41no—
171C2×C71—81no—
172C2×C71#54711yescharacteristic
173C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C71#57711yescharacteristic
175D71—81no—
176#3345—711nomaximal, Sylow
177C71#334511yescharacteristic, complemented, Sylow
178#553—711no—
179#547D7111yescharacteristic, complemented
180#501—711no—
181#482—711no—
182#481—711no—
183#481—711no—
184#480—711no—
185#478—711no—
186#476—711no—
187#469—711no—
188#466—711no—
189#442—711no—
190#435—711no—
191#428—711no—
192C2×#106—711no—
193C2×#41—21no—
194C2×D8—711no—
195C2×M16—711no—
196C22×C8—711no—
197C4⋊Q8C2×D7111yescharacteristic
198#126—1421no—
199#125—711no—
200#123—21no—
201#123—21no—
202#123—1421no—
203C22⋊Q8—21no—
204#121—711no—
205#121—711no—
206#121—1421no—
207#121C2×D7111yescharacteristic
208#121C2×D7111yescharacteristic
209C4×D4—711no—
210C4×D4—1421no—
211C4×D4C2×D7111yescharacteristic
212C4×D4C2×D7111yescharacteristic
213#117—711no—
214C2×C4⋊C4—711no—
215C2×C4⋊C4C2×D7111yescharacteristic
216C2×C4⋊C4C2×D7111yescharacteristic
217#107—711no—
218#107—711no—
219#107—711no—
220#106—711no—
221#106—711no—
222#106—711no—
223#106—711no—
224#106—711no—
225#106—711no—
226C4⋊C8—711no—
227#102—711no—
228#102—711no—
229#102—711no—
230#102—711no—
231#102—711no—
232#102—711no—
233C22⋊C8—711no—
234C22⋊C8—711no—
235#97—711no—
236#41—44no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—711no—
241C2×D4—1421no—
242C2×D4—1421no—
243C2×D4C22⋊D7111yescharacteristic
244C2×D4C22×D7111yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1421no—
249C22×C4—1421no—
250C22×C4C22×D7111yescharacteristic
251C22×C4C22×D7111yescharacteristic
252D8—1422no—
253M16—1422no—
254C2×C8—711no—
255C2×C8—711no—
256C2×C8—711no—
257C2×C8—711no—
258C2×C8—1422no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—711no—
263C4⋊C4—711no—
264C4⋊C4—711no—
265C4⋊C4—1421no—
266C4⋊C4—1421no—
267C4⋊C4—1421no—
268C4⋊C4C22⋊D7111yescharacteristic
269C4⋊C4C22×D7111yescharacteristic
270C4⋊C4C22×D7111yescharacteristic
271C4⋊C4C22×D7111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—1421no—
276C22⋊C4—1421no—
277C22⋊C4—1421no—
278C22⋊C4—1421no—
279C22⋊C4C22⋊D7111yescharacteristic
280C22⋊C4C22⋊D7111yescharacteristic
281C42—1421no—
282C42C22×D7111yescharacteristic
283C23—21no—
284C23—1421no—
285C23C2×C22⋊D7111yescharacteristic
286C23C2×C22⋊D7111yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—42no—
293D4—2842no—
294D4—5681no—
295D4—1421no—
296D4—1421no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—5681no—
308C2×C4—5681no—
309C2×C4—1421no—
310C2×C4—1421no—
311C2×C4—1421no—
312C2×C4C2×C22⋊D7111yescharacteristic
313C2×C4C2×C22⋊D7111yescharacteristic
314C2×C4C2×C22⋊D7111yescharacteristic
315C2×C4C2×C22⋊D7111yescharacteristic
316C2×C4C23×D7111yescharacteristic
317C8—712no—
318C8—1421no—
319C8—1421no—
320C8—1421no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2841no—
330C22—2841no—
331C22—2841no—
332C22#1455615412yes—
333C22C22×C22⋊D7111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2841no—
342C4—2841no—
343C4—2841no—
344C4#41×D7111yescharacteristic
345C4#1455617511yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—5681no—
350C2#1798664811yescharacteristic
351C2C2×#1455615411yescharacteristic
352C2#1798680711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#547×C71C2
socleC22×C71C22×D4
hypercenter#547D71
hypocenterC71#3345
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #17986695C2semidirect
2. #17986405C2semidirect
3. #17986320C2semidirect
4. #17986317C2semidirect
5. #17986315C2semidirect
6. #17986312C2semidirect
7. #17986299C2semidirect
8. #17986286C2semidirect
9. #17986250C2semidirect
10. #17986233C2semidirect
11. #17986109C2semidirect
12. #17986071C2semidirect
13. #17986039C2semidirect
14. C2×#14556059C2semidirect
15. #547×C71C2semidirect
143. C71⋊C8#41semidirect
177. C71#3345semidirect
179. #547D71semidirect