Finite Group Databasebeta

← #22598539

Subgroups — #22598539

Order 9088.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986604C211yesmaximal, characteristic, complemented
2#17986317C211yesmaximal, characteristic, complemented
3#17986312C211yesmaximal, characteristic, complemented
4#17986306C211yesmaximal, characteristic, complemented
5#17986299C211yesmaximal, characteristic, complemented
6#17986199C211yesmaximal, characteristic, complemented
7#17986194C211yesmaximal, characteristic, complemented
8#17986144C211yesmaximal, characteristic, complemented
9#17986144C211yesmaximal, characteristic, complemented
10#17986109C211yesmaximal, characteristic, complemented
11#17986097C211yesmaximal, characteristic, complemented
12C4×#11765852C211yesmaximal, characteristic, complemented
13C4×#11765850C211yesmaximal, characteristic, complemented
14#17986060C211yesmaximal, characteristic, complemented
15#520×C71C211yesmaximal, characteristic, complemented
16C2×#11765852C2211yescharacteristic
17C2×#11765852C2211yescharacteristic
18C2×#11765850C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20#14556125C2211yescharacteristic
21#14556120C2211yescharacteristic
22#14556113—21no—
23#14556113—21no—
24#14556102C2211yescharacteristic
25#14556102C2211yescharacteristic
26#14556101—21no—
27#14556101—21no—
28C4×D284C2211yescharacteristic
29C4×D284C2211yescharacteristic
30#14556061C2211yescharacteristic
31#14556061C2211yescharacteristic
32#14556059C2211yescharacteristic
33#14556059C2211yescharacteristic
34C4⋊(C71⋊C8)C2211yescharacteristic
35C4⋊(C71⋊C8)C2211yescharacteristic
36#14556052C2211yescharacteristic
37#14556052C2211yescharacteristic
38#14556049C2211yescharacteristic
39#14556049C2211yescharacteristic
40#14556048C2211yescharacteristic
41#14556048C2211yescharacteristic
42#14556048C2211yescharacteristic
43#14556048C2211yescharacteristic
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46#14556039C2211yescharacteristic
47C4×C71⋊C8C2211yescharacteristic
48C2×#41×C71C2211yescharacteristic
49C4×Q8×C71C2211yescharacteristic
50C4×Q8×C71C2211yescharacteristic
51C4×D4×C71—21no—
52C4×D4×C71—21no—
53C4×D4×C71C2211yescharacteristic
54C4×D4×C71C2211yescharacteristic
55#117×C71—21no—
56#117×C71C2211yescharacteristic
57C2×C4⋊C4×C71—21no—
58C2×C4⋊C4×C71C2211yescharacteristic
59C2×D284—21no—
60C2×D284—21no—
61C2×D284C2311yescharacteristic
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C2×C22⋊D71—21no—
65C2×C4×D71—21no—
66C2×C4×D71—21no—
67#11765852—22no—
68#11765852—22no—
69#11765850—22no—
70#11765850—22no—
71C2×C71⋊C8C2311yescharacteristic
72C2×C71⋊C8C2311yescharacteristic
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C4⋊Dic71C2311yescharacteristic
76C4⋊Dic71C2311yescharacteristic
77Dic71⋊C4—21no—
78Dic71⋊C4—21no—
79(C2×D71)⋊C4—21no—
80(C2×D71)⋊C4—21no—
81(C2×D71)⋊C4—21no—
82(C2×D71)⋊C4—21no—
83#41×C71—22no—
84#41×C71—22no—
85C2×Q8×C71C2311yescharacteristic
86C2×D4×C71—21no—
87C2×D4×C71C2311yescharacteristic
88C22×C4×C71—21no—
89C22×C4×C71—21no—
90C22×C4×C71—21no—
91C22×C4×C71—21no—
92C22×C4×C71C2311yescharacteristic
93C4⋊C4×C71—21no—
94C4⋊C4×C71—21no—
95C4⋊C4×C71—21no—
96C4⋊C4×C71D411yescharacteristic
97C4⋊C4×C71D411yescharacteristic
98C4⋊C4×C71C2311yescharacteristic
99C4⋊C4×C71C2311yescharacteristic
100C22⋊C4×C71—21no—
101C22⋊C4×C71—21no—
102C22⋊C4×C71D411yescharacteristic
103C22⋊C4×C71D411yescharacteristic
104C42×C71—21no—
105C42×C71—21no—
106C42×C71C2311yescharacteristic
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111C22×D71—21no—
112Q8×C71—21no—
113Q8×C71#4112yes—
114D4×C71—24no—
115D4×C71—21no—
116D4×C71#4112yes—
117C2×C4×C71—24no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—81no—
124C2×C4×C71—81no—
125C2×C4×C71—81no—
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2×D411yescharacteristic
130C2×C4×C71C2×D411yescharacteristic
131C2×C4×C71C2411yescharacteristic
132C22⋊D71—81no—
133C22⋊D71—81no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136D284—21no—
137D284—21no—
138D284—21no—
139D284—21no—
140D284—81no—
141D284—81no—
142C4×D71—81no—
143C4×D71—81no—
144C71⋊C8—21no—
145C71⋊C8—21no—
146C71⋊C8—21no—
147C71⋊C8—21no—
148C22×C71—21no—
149C22×C71—22no—
150C22×C71—21no—
151C22×C71—21no—
152C22×C71—41no—
153C22×C71—41no—
154C22×C71C22×D411yescharacteristic
155C2×D71—41no—
156C2×D71—41no—
157C2×D71—41no—
158C2×D71—41no—
159C2×D71—41no—
160C2×D71—41no—
161C4×C71—21no—
162C4×C71—22no—
163C4×C71—21no—
164C4×C71—21no—
165C4×C71—21no—
166C4×C71—21no—
167C4×C71—41no—
168C4×C71—41no—
169C4×C71C2×#4111yescharacteristic
170C4×C71C2×#4111yescharacteristic
171Dic71—41no—
172Dic71—41no—
173C2×C71—41no—
174C2×C71—42no—
175C2×C71#52511yescharacteristic
176C2×C71#57611yescharacteristic
177C2×C71#57711yescharacteristic
178D71—81no—
179D71—81no—
180#3119—711nomaximal, Sylow
181C71#311911yescharacteristic, complemented, Sylow
182#540—711no—
183#520D7111yescharacteristic, complemented
184#481—711no—
185#480—711no—
186#479—711no—
187#478—711no—
188#460—711no—
189#459—711no—
190#449—711no—
191#449—711no—
192#442—711no—
193#440—711no—
194C4×SD16—711no—
195C4×D8—711no—
196#433—711no—
197C2×#41C2×D7111yescharacteristic
198C2×SD16—711no—
199C2×SD16—711no—
200C2×D8—711no—
201C2×D8—711no—
202#127—711no—
203#125—711no—
204#123—1421no—
205#123—1421no—
206#121—711no—
207#121—711no—
208#121—1421no—
209#121—1421no—
210C4×Q8C2×D7111yescharacteristic
211C4×Q8C2×D7111yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—711no—
215C4×D4—711no—
216C4×D4C2×D7111yescharacteristic
217C4×D4C2×D7111yescharacteristic
218#117—21no—
219#117C2×D7111yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D7111yescharacteristic
222#107—711no—
223#107—711no—
224#106—711no—
225#106—711no—
226C4⋊C8—711no—
227C4⋊C8—711no—
228#103—711no—
229#103—711no—
230#102—711no—
231#102—711no—
232#102—711no—
233#102—711no—
234#102—711no—
235#102—711no—
236C22⋊C8—711no—
237C22⋊C8—711no—
238#97—711no—
239C4×C8—711no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D7111yescharacteristic
243C2×D4—21no—
244C2×D4—711no—
245C2×D4—711no—
246C2×D4—1421no—
247C2×D4—1421no—
248C2×D4—1421no—
249C2×D4—1421no—
250C2×D4C22×D7111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1421no—
256C22×C4—1421no—
257C22×C4C22×D7111yescharacteristic
258SD16—1422no—
259SD16—1422no—
260D8—1422no—
261D8—1422no—
262C2×C8—711no—
263C2×C8—711no—
264C2×C8—711no—
265C2×C8—711no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—711no—
270C4⋊C4—711no—
271C4⋊C4—1421no—
272C4⋊C4—1421no—
273C4⋊C4C22⋊D7111yescharacteristic
274C4⋊C4C22⋊D7111yescharacteristic
275C4⋊C4C22×D7111yescharacteristic
276C4⋊C4C22×D7111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1421no—
280C22⋊C4—1421no—
281C22⋊C4—1421no—
282C22⋊C4—1421no—
283C22⋊C4C22⋊D7111yescharacteristic
284C22⋊C4C22⋊D7111yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D7111yescharacteristic
288C42C22×D7111yescharacteristic
289C23—21no—
290C23—1421no—
291C23—1421no—
292C23C2×C22⋊D7111yescharacteristic
293Q8—21no—
294Q8#1176586512yes—
295D4—24no—
296D4—21no—
297D4—5681no—
298D4—5681no—
299D4—5681no—
300D4—5681no—
301D4—1421no—
302D4—1421no—
303D4—1421no—
304D4—1421no—
305D4#1176586512yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—5681no—
316C2×C4—5681no—
317C2×C4—1421no—
318C2×C4—1421no—
319C2×C4C2×C22⋊D7111yescharacteristic
320C2×C4C2×C22⋊D7111yescharacteristic
321C2×C4C2×C22⋊D7111yescharacteristic
322C2×C4C2×C22⋊D7111yescharacteristic
323C2×C4C2×C22⋊D7111yescharacteristic
324C2×C4C23×D7111yescharacteristic
325C8—1421no—
326C8—1421no—
327C8—1421no—
328C8—1421no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—2841no—
336C22—2841no—
337C22—2841no—
338C22—2841no—
339C22—2841no—
340C22—2841no—
341C22C22×C22⋊D7111yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—2841no—
351C4—2841no—
352C4C2×#1176586511yescharacteristic
353C4C2×#1176586511yescharacteristic
354C2—41no—
355C2—42no—
356C2—5681no—
357C2—5681no—
358C2#1798651011yescharacteristic
359C2#1798680211yescharacteristic
360C2#1798680711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#520×C71C2
socleC22×C71C22×D4
hypercenter#520D71
hypocenterC71#3119
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #17986604C2semidirect
2. #17986317C2semidirect
3. #17986312C2semidirect
4. #17986306C2semidirect
5. #17986299C2semidirect
6. #17986199C2semidirect
7. #17986194C2semidirect
8. #17986144C2semidirect
9. #17986144C2semidirect
10. #17986109C2semidirect
11. #17986097C2semidirect
12. C4×#11765852C2semidirect
13. C4×#11765850C2semidirect
14. #17986060C2semidirect
15. #520×C71C2semidirect
181. C71#3119semidirect
183. #520D71semidirect