Finite Group Databasebeta

← #22599850

Subgroups — #22599850

Order 9088.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556157C211yesmaximal, characteristic, complemented
2Q8×C22⋊D71C211yesmaximal, characteristic, complemented
3#17986643C211yesmaximal, characteristic
4#17986390C211yesmaximal, characteristic, complemented
5#17986242C211yesmaximal, characteristic, complemented
6#17986240C211yesmaximal, characteristic, complemented
7#17986219C211yesmaximal, characteristic, complemented
8#17986202C211yesmaximal, characteristic, complemented
9#17986158C211yesmaximal, characteristic, complemented
10#17986155C211yesmaximal, characteristic, complemented
11#17986150C211yesmaximal, characteristic, complemented
12#17986136C211yesmaximal, characteristic, complemented
13#17986100C211yesmaximal, characteristic, complemented
14#17986070C211yesmaximal, characteristic, complemented
15C22×SD16×C71C211yesmaximal, characteristic, complemented
16C2×#11765864C2211yescharacteristic
17C2×Q8×D71C2211yescharacteristic, complemented
18#14556157—24no—
19C2×Dic284C2211yescharacteristic, complemented
20C2×#11765855C2211yescharacteristic, complemented
21C2×#11765855C2211yescharacteristic, complemented
22C2×#11765853C2211yescharacteristic
23C2×#11765853C2211yescharacteristic
24C2×#11765848C2211yescharacteristic, complemented
25#14556126—21no—
26#14556126C2211yescharacteristic, complemented
27#14556115C2211yescharacteristic
28#14556109—21no—
29#14556107—21no—
30#14556107C2211yescharacteristic
31#14556107C2211yescharacteristic
32#14556104—21no—
33#14556104C2211yescharacteristic, complemented
34#14556100—21no—
35#14556099C2211yescharacteristic
36#14556097—21no—
37Q8×Dic71C2211yescharacteristic, complemented
38D4×Dic71C2211yescharacteristic
39C4×C22⋊D71—21no—
40C4×C22⋊D71C2211yescharacteristic
41C2×C22⋊Dic71—21no—
42#14556062C2211yescharacteristic, complemented
43Dic71⋊C8C2211yescharacteristic, complemented
44#14556053C2211yescharacteristic, complemented
45#14556053C2211yescharacteristic, complemented
46#14556052C2211yescharacteristic, complemented
47#14556052C2211yescharacteristic, complemented
48#14556049C2211yescharacteristic
49#14556049C2211yescharacteristic
50C22⋊(C71⋊C8)C2211yescharacteristic
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52#14556038C2211yescharacteristic, complemented
53C22×Q8×C71C2211yescharacteristic
54C22×D4×C71C2211yescharacteristic
55C2×SD16×C71—24no—
56C2×SD16×C71C2211yescharacteristic
57C2×SD16×C71C2211yescharacteristic
58C2×SD16×C71C2211yescharacteristic
59C2×SD16×C71C2211yescharacteristic
60C22×C8×C71C2211yescharacteristic
61#11765864—22no—
62#11765864—41no—
63C2×Dic142—21no—
64C2×Dic142C2311yescharacteristic
65C2×Dic142C2311yescharacteristic
66Q8×D71—22no—
67Q8×D71—41no—
68C2×C22⋊D71—21no—
69C2×C22⋊D71—21no—
70C2×C22⋊D71D411yescharacteristic
71C22×Dic71—21no—
72C22×Dic71—21no—
73C2×C4×D71—21no—
74C2×C4×D71C2311yescharacteristic
75Dic284—22no—
76#11765855—22no—
77#11765855—41no—
78#11765853—22no—
79#11765853—41no—
80#11765848—22no—
81C2×C71⋊C8C2311yescharacteristic
82C2×C71⋊C8C2311yescharacteristic
83C4⋊Dic71—21no—
84C4⋊Dic71C2311yescharacteristic
85C4⋊Dic71C2311yescharacteristic
86Dic71⋊C4—21no—
87Dic71⋊C4—21no—
88Dic71⋊C4—21no—
89Dic71⋊C4—21no—
90Dic71⋊C4—21no—
91Dic71⋊C4D411yescharacteristic
92C22⋊Dic71—21no—
93C22⋊Dic71—21no—
94C22⋊Dic71—21no—
95C22⋊Dic71—21no—
96C22⋊Dic71—21no—
97C22⋊Dic71—21no—
98C22⋊Dic71D411yescharacteristic
99(C2×D71)⋊C4—21no—
100(C2×D71)⋊C4D411yescharacteristic
101C4×Dic71—21no—
102C4×Dic71C2311yescharacteristic
103C24×C71—21no—
104C2×Q8×C71—21no—
105C2×Q8×C71—22no—
106C2×Q8×C71—41no—
107C2×Q8×C71C2311yescharacteristic
108C2×Q8×C71C2311yescharacteristic
109C2×D4×C71—22no—
110C2×D4×C71—21no—
111C2×D4×C71—41no—
112C2×D4×C71C2311yescharacteristic
113C2×D4×C71C2311yescharacteristic
114C22×C4×C71—21no—
115C22×C4×C71C2311yescharacteristic
116SD16×C71—22no—
117SD16×C71—22no—
118SD16×C71—22no—
119SD16×C71D414yescomplemented
120C2×C8×C71—22no—
121C2×C8×C71C2311yescharacteristic
122C2×C8×C71C2311yescharacteristic
123C23×C71—21no—
124C23×C71—21no—
125C23×C71—42no—
126C23×C71—42no—
127C23×C71—81no—
128C23×C71C2×D411yescharacteristic
129C22×D71C2×D411yescharacteristic
130Q8×C71—21no—
131Q8×C71—21no—
132Q8×C71—21no—
133Q8×C71—42no—
134Q8×C71C2×D412yes—
135D4×C71—21no—
136D4×C71—21no—
137D4×C71—21no—
138D4×C71—42no—
139D4×C71C2×D412yes—
140C2×C4×C71—21no—
141C2×C4×C71—21no—
142C2×C4×C71—21no—
143C2×C4×C71—21no—
144C2×C4×C71—42no—
145C2×C4×C71C2×D411yescharacteristic
146C2×C4×C71C2411yescharacteristic
147C22⋊D71—22no—
148C22⋊D71—42no—
149C22⋊D71—81no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152C2×Dic71—21no—
153C2×Dic71—21no—
154C2×Dic71—42no—
155C2×Dic71—81no—
156C2×Dic71C2×D411yescharacteristic
157C2×Dic71C2×D411yescharacteristic
158C2×Dic71C2×D411yescharacteristic
159C4×D71—21no—
160C4×D71—21no—
161C4×D71—42no—
162Dic142—21no—
163Dic142—21no—
164Dic142—21no—
165Dic142—21no—
166Dic142—42no—
167C8×C71—21no—
168C8×C71C2×D412yes—
169C71⋊C8—21no—
170C71⋊C8—21no—
171C22×C71—21no—
172C22×C71—21no—
173C22×C71—22no—
174C22×C71—41no—
175C22×C71—41no—
176C22×C71—41no—
177C22×C71—41no—
178C22×C71—41no—
179C22×C71—84no—
180C22×C71#13712yescomplemented
181C22×C71C22×D411yescharacteristic
182C2×D71—21no—
183C2×D71—21no—
184C2×D71—21no—
185C4×C71—22no—
186C4×C71—21no—
187C4×C71—41no—
188C4×C71C22×D411yescharacteristic
189C4×C71H(5,𝔽2)11yescharacteristic
190Dic71—21no—
191Dic71—21no—
192Dic71—21no—
193Dic71—41no—
194Dic71—41no—
195Dic71—41no—
196Dic71—41no—
197C2×C71—22no—
198C2×C71—42no—
199C2×C71—81no—
200C2×C71D4211yescharacteristic
201C2×C71C2×#13711yescharacteristic
202C2×C71#57711yescharacteristic
203D71—41no—
204#3266—711nomaximal, Sylow
205C71#326611yescharacteristic, complemented, Sylow
206C2×#137—711no—
207C22×SD16D7111yescharacteristic, complemented
208D4×Q8—711no—
209#546—711no—
210#497—711no—
211#468—711no—
212#467—711no—
213#464—711no—
214#461—711no—
215#452—711no—
216#451—711no—
217#450—711no—
218#448—711no—
219#440—711no—
220#435—711no—
221C2×#41—711no—
222C22×Q8—711no—
223C22×Q8C2×D7111yescharacteristic
224C22×D4C2×D7111yescharacteristic
225#137—1424no—
226C2×Q16—711no—
227C2×Q16—711no—
228C2×Q16—711no—
229C2×SD16—24no—
230C2×SD16—711no—
231C2×SD16—711no—
232C2×SD16C2×D7111yescharacteristic
233C2×SD16C2×D7111yescharacteristic
234C2×SD16C2×D7111yescharacteristic
235C2×SD16C2×D7111yescharacteristic
236C2×M16—711no—
237C22×C8C2×D7111yescharacteristic
238C4⋊Q8—711no—
239C4⋊Q8—1421no—
240#124—711no—
241#123—1421no—
242C22⋊Q8—711no—
243C22⋊Q8—711no—
244C22⋊Q8—711no—
245C22⋊Q8—1421no—
246C22⋊Q8—1421no—
247#121—711no—
248#121—1421no—
249#120—1421no—
250C4×Q8—711no—
251C4×D4—711no—
252C4×D4—711no—
253C4×D4—1421no—
254C2×C22⋊C4—1421no—
255#107—711no—
256C4⋊C8—711no—
257#103—711no—
258#103—711no—
259#103—711no—
260#103—711no—
261#102—711no—
262#102—711no—
263C22⋊C8—711no—
264C22⋊C8—711no—
265#97—711no—
266C24—21no—
267#41—2841no—
268#41—1422no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2841no—
273C2×Q8—711no—
274C2×Q8—711no—
275C2×Q8—1421no—
276C2×Q8—1422no—
277C2×Q8C22×D7111yescharacteristic
278C2×Q8C22×D7111yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—711no—
283C2×D4—1421no—
284C2×D4—1421no—
285C2×D4C22×D7111yescharacteristic
286C2×D4C22×D7111yescharacteristic
287C22×C4—21no—
288C22×C4—711no—
289C22×C4—1421no—
290C22×C4—1421no—
291C22×C4—1421no—
292C22×C4C22×D7111yescharacteristic
293Q16—2841no—
294Q16—1422no—
295Q16—1422no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—2841no—
300SD16—1422no—
301SD16C22⋊D7114yescomplemented
302M16—1422no—
303C2×C8—22no—
304C2×C8—711no—
305C2×C8—711no—
306C2×C8C22×D7111yescharacteristic
307C2×C8C22×D7111yescharacteristic
308C4⋊C4—711no—
309C4⋊C4—711no—
310C4⋊C4—711no—
311C4⋊C4—1421no—
312C4⋊C4—1421no—
313C4⋊C4—1421no—
314C4⋊C4—1421no—
315C4⋊C4—1421no—
316C4⋊C4—1421no—
317C22⋊C4—711no—
318C22⋊C4—711no—
319C22⋊C4—1421no—
320C22⋊C4—1421no—
321C22⋊C4—1421no—
322C22⋊C4—1421no—
323C22⋊C4—1421no—
324C22⋊C4—1421no—
325C22⋊C4—1421no—
326C42—711no—
327C42—1421no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—711no—
334C23D4×D7111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—2842no—
340Q8—1421no—
341Q8—1421no—
342Q8—1421no—
343Q8—1421no—
344Q8C2×C22⋊D7112yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—2842no—
350D4—5681no—
351D4—1422no—
352D4C2×C22⋊D7112yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—2842no—
359C2×C4—2842no—
360C2×C4—5681no—
361C2×C4—711no—
362C2×C4—711no—
363C2×C4—711no—
364C2×C4—1421no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4—1421no—
370C2×C4D4×D7111yescharacteristic
371C2×C4C23×D7111yescharacteristic
372C8—21no—
373C8—1421no—
374C8—1421no—
375C8C2×C22⋊D7112yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—1421no—
386C22—1421no—
387C22—1421no—
388C22#1455615712yescomplemented
389C22C2×D4×D7111yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—2841no—
394C4—2841no—
395C4—2841no—
396C4—2841no—
397C4—1421no—
398C4—1421no—
399C4—1421no—
400C4C22×C22⋊D7111yescharacteristic
401C4#1455617311yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—2841no—
406C2D4×C22⋊D7111yescharacteristic
407C2C2×#1455615711yescharacteristic
408C2#1798680511yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC22×SD16×C71C2
socleC22×C71C22×D4
hypercenterC22×SD16D71
hypocenterC71#3266
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14556157C2semidirect
2. Q8×C22⋊D71C2semidirect
4. #17986390C2semidirect
5. #17986242C2semidirect
6. #17986240C2semidirect
7. #17986219C2semidirect
8. #17986202C2semidirect
9. #17986158C2semidirect
10. #17986155C2semidirect
11. #17986150C2semidirect
12. #17986136C2semidirect
13. #17986100C2semidirect
14. #17986070C2semidirect
15. C22×SD16×C71C2semidirect
17. C2×Q8×D71C22semidirect
19. C2×Dic284C22semidirect
20. C2×#11765855C22semidirect
21. C2×#11765855C22semidirect
24. C2×#11765848C22semidirect
26. #14556126C22semidirect
33. #14556104C22semidirect
37. Q8×Dic71C22semidirect
42. #14556062C22semidirect
43. Dic71⋊C8C22semidirect
44. #14556053C22semidirect
45. #14556053C22semidirect
46. #14556052C22semidirect
47. #14556052C22semidirect
51. (C2×D71)⋊C8C22semidirect
52. #14556038C22semidirect
119. SD16×C71D4semidirect
180. C22×C71#137semidirect
205. C71#3266semidirect
207. C22×SD16D71semidirect
301. SD16C22⋊D71semidirect
388. C22#14556157semidirect