Finite Group Databasebeta

← #22599846

Subgroups — #22599846

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×#14556158C211yesmaximal, characteristic, complemented
2C22×#11765853C211yesmaximal, characteristic, complemented
3D4×Dic142C211yesmaximal, characteristic, complemented
4#17986394C211yesmaximal, characteristic, complemented
5#17986243C211yesmaximal, characteristic, complemented
6#17986238C211yesmaximal, characteristic, complemented
7#17986218C211yesmaximal, characteristic, complemented
8#17986204C211yesmaximal, characteristic, complemented
9#17986161C211yesmaximal, characteristic, complemented
10#17986154C211yesmaximal, characteristic, complemented
11#17986150C211yesmaximal, characteristic, complemented
12#17986137C211yesmaximal, characteristic, complemented
13#17986099C211yesmaximal, characteristic, complemented
14#17986071C211yesmaximal, characteristic, complemented
15#546×C71C211yesmaximal, characteristic
16C22×Dic142C2211yescharacteristic
17C22×Dic142C2211yescharacteristic, complemented
18#14556158—24no—
19C2×#11765855C2211yescharacteristic, complemented
20C2×#11765855C2211yescharacteristic, complemented
21C2×#11765855C2211yescharacteristic, complemented
22C2×#11765853—24no—
23C2×#11765853C2211yescharacteristic
24C2×#11765853C2211yescharacteristic
25C2×#11765853C2211yescharacteristic
26C2×#11765853C2211yescharacteristic
27C2×#11765853C2211yescharacteristic
28C2×#11765853C2211yescharacteristic
29C2×#11765849C2211yescharacteristic, complemented
30C22×C71⋊C8C2211yescharacteristic
31#14556128C2211yescharacteristic, complemented
32#14556127—21no—
33#14556107C2211yescharacteristic
34#14556107C2211yescharacteristic, complemented
35#14556105—21no—
36#14556105—21no—
37C4×Dic142C2211yescharacteristic, complemented
38D4×Dic71—21no—
39#14556061C2211yescharacteristic, complemented
40C4⋊(C71⋊C8)C2211yescharacteristic, complemented
41#14556052C2211yescharacteristic, complemented
42#14556051C2211yescharacteristic, complemented
43#14556051C2211yescharacteristic, complemented
44#14556051C2211yescharacteristic, complemented
45#14556049C2211yescharacteristic
46#14556049C2211yescharacteristic
47C22⋊(C71⋊C8)C2211yescharacteristic
48C22⋊(C71⋊C8)C2211yescharacteristic, complemented
49#14556039C2211yescharacteristic, complemented
50C2×#41×C71C2211yescharacteristic
51C22×D4×C71C2211yescharacteristic
52#124×C71C2211yescharacteristic
53#123×C71—21no—
54C22⋊Q8×C71C2211yescharacteristic
55#121×C71—21no—
56#121×C71C2211yescharacteristic
57#120×C71—21no—
58C4×D4×C71C2211yescharacteristic
59C4×D4×C71C2211yescharacteristic
60C2×C22⋊C4×C71—21no—
61C2×Dic142—22no—
62C2×Dic142—22no—
63C2×Dic142—21no—
64C2×Dic142—21no—
65C2×Dic142—41no—
66C2×Dic142—41no—
67C2×Dic142C2311yescharacteristic
68C2×Dic142C2311yescharacteristic
69C2×Dic142C2311yescharacteristic
70C22×Dic71—21no—
71C22×Dic71—21no—
72#11765855—22no—
73#11765855—22no—
74#11765855—41no—
75#11765853—22no—
76#11765853—22no—
77#11765853—22no—
78#11765853—22no—
79#11765853—41no—
80#11765853D414yescomplemented
81#11765849—22no—
82C2×C71⋊C8—22no—
83C2×C71⋊C8C2311yescharacteristic
84C2×C71⋊C8C2311yescharacteristic
85C2×C71⋊C8C2311yescharacteristic
86C2×C71⋊C8C2311yescharacteristic
87C4⋊Dic71—21no—
88C4⋊Dic71—21no—
89C4⋊Dic71C2311yescharacteristic
90Dic71⋊C4—21no—
91Dic71⋊C4—21no—
92Dic71⋊C4—21no—
93C22⋊Dic71—21no—
94C22⋊Dic71—21no—
95C4×Dic71—21no—
96C24×C71—21no—
97#41×C71—22no—
98#41×C71—41no—
99C2×Q8×C71C2311yescharacteristic
100C2×D4×C71—22no—
101C2×D4×C71—21no—
102C2×D4×C71—21no—
103C2×D4×C71—21no—
104C2×D4×C71—41no—
105C2×D4×C71D411yescharacteristic
106C2×D4×C71C2311yescharacteristic
107C2×D4×C71C2311yescharacteristic
108C22×C4×C71—21no—
109C22×C4×C71—21no—
110C22×C4×C71C2311yescharacteristic
111C22×C4×C71C2311yescharacteristic
112C4⋊C4×C71—21no—
113C4⋊C4×C71D411yescharacteristic
114C4⋊C4×C71C2311yescharacteristic
115C22⋊C4×C71—21no—
116C22⋊C4×C71—21no—
117C22⋊C4×C71—21no—
118C22⋊C4×C71—21no—
119C22⋊C4×C71—21no—
120C22⋊C4×C71D411yescharacteristic
121C22⋊C4×C71D411yescharacteristic
122C42×C71C2311yescharacteristic
123C23×C71—21no—
124C23×C71—21no—
125C23×C71—42no—
126C23×C71—42no—
127C23×C71—81no—
128C23×C71C2×D411yescharacteristic
129C23×C71C2×D411yescharacteristic
130Q8×C71—21no—
131Q8×C71—21no—
132D4×C71—22no—
133D4×C71—21no—
134D4×C71—21no—
135D4×C71—21no—
136D4×C71—42no—
137D4×C71—42no—
138D4×C71—81no—
139D4×C71C2×D412yes—
140C2×C4×C71—21no—
141C2×C4×C71—21no—
142C2×C4×C71—21no—
143C2×C4×C71—21no—
144C2×C4×C71—21no—
145C2×C4×C71—21no—
146C2×C4×C71—42no—
147C2×C4×C71—81no—
148C2×C4×C71C2×D411yescharacteristic
149C2×C4×C71C2×D411yescharacteristic
150C2×C4×C71C2×D411yescharacteristic
151C2×C4×C71C2×D411yescharacteristic
152C2×C4×C71C2411yescharacteristic
153C2×Dic71—21no—
154C2×Dic71—21no—
155C2×Dic71—21no—
156C2×Dic71—21no—
157C2×Dic71—42no—
158C2×Dic71—42no—
159Dic142—21no—
160Dic142—21no—
161Dic142—21no—
162Dic142—21no—
163Dic142—21no—
164Dic142—42no—
165Dic142—42no—
166Dic142C2×D412yes—
167C71⋊C8—21no—
168C71⋊C8—21no—
169C71⋊C8—21no—
170C71⋊C8C2×D412yes—
171C22×C71—21no—
172C22×C71—21no—
173C22×C71—21no—
174C22×C71—22no—
175C22×C71—21no—
176C22×C71—21no—
177C22×C71—41no—
178C22×C71—41no—
179C22×C71—41no—
180C22×C71—41no—
181C22×C71—41no—
182C22×C71—84no—
183C22×C71#13712yescomplemented
184C22×C71C22×D411yescharacteristic
185C4×C71—21no—
186C4×C71—21no—
187C4×C71—21no—
188C4×C71—21no—
189C4×C71—41no—
190C4×C71—41no—
191C4×C71C22×D411yescharacteristic
192C4×C71H(5,𝔽2)11yescharacteristic
193Dic71—22no—
194Dic71—41no—
195Dic71—41no—
196Dic71—41no—
197C2×C71—22no—
198C2×C71—41no—
199C2×C71—42no—
200C2×C71—81no—
201C2×C71D4211yescharacteristic
202C2×C71C2×#13711yescharacteristic
203C2×C71#57711yescharacteristic
204#3266—711nomaximal, Sylow
205C71#326611yescharacteristic, complemented, Sylow
206C2×#137—711no—
207C22×SD16—711no—
208D4×Q8—711no—
209#546D7111yescharacteristic
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×#41C2×D7111yescharacteristic
222C22×Q8—711no—
223C22×Q8—711no—
224C22×D4C2×D7111yescharacteristic
225#137—1424no—
226C2×Q16—711no—
227C2×Q16—711no—
228C2×Q16—711no—
229C2×SD16—711no—
230C2×SD16—711no—
231C2×SD16—711no—
232C2×SD16—711no—
233C2×SD16—711no—
234C2×SD16—711no—
235C2×SD16—1424no—
236C2×M16—711no—
237C22×C8—711no—
238C4⋊Q8—711no—
239C4⋊Q8—1421no—
240#124C2×D7111yescharacteristic
241#123—21no—
242C22⋊Q8—711no—
243C22⋊Q8—711no—
244C22⋊Q8—1421no—
245C22⋊Q8—1421no—
246C22⋊Q8C2×D7111yescharacteristic
247#121—21no—
248#121C2×D7111yescharacteristic
249#120—21no—
250C4×Q8—711no—
251C4×D4—1421no—
252C4×D4C2×D7111yescharacteristic
253C4×D4C2×D7111yescharacteristic
254C2×C22⋊C4—21no—
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—22no—
268#41—41no—
269C2×Q8—2841no—
270C2×Q8—2841no—
271C2×Q8—711no—
272C2×Q8—711no—
273C2×Q8—711no—
274C2×Q8—1422no—
275C2×Q8—1422no—
276C2×Q8—1421no—
277C2×Q8—1421no—
278C2×Q8C22×D7111yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D7111yescharacteristic
285C2×D4C22×D7111yescharacteristic
286C2×D4C22×D7111yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—1421no—
290C22×C4—1421no—
291C22×C4C22×D7111yescharacteristic
292C22×C4C22×D7111yescharacteristic
293Q16—2841no—
294Q16—1422no—
295Q16—1422no—
296SD16—2841no—
297SD16—714no—
298SD16—1422no—
299SD16—1422no—
300SD16—1422no—
301SD16—1422no—
302M16—1422no—
303C2×C8—711no—
304C2×C8—711no—
305C2×C8—711no—
306C2×C8—711no—
307C2×C8—1422no—
308C4⋊C4—21no—
309C4⋊C4—711no—
310C4⋊C4—1421no—
311C4⋊C4—1421no—
312C4⋊C4—1421no—
313C4⋊C4—1421no—
314C4⋊C4—1421no—
315C4⋊C4C22⋊D7111yescharacteristic
316C4⋊C4C22×D7111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1421no—
323C22⋊C4—1421no—
324C22⋊C4C22⋊D7111yescharacteristic
325C22⋊C4C22⋊D7111yescharacteristic
326C42—1421no—
327C42C22×D7111yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D7111yescharacteristic
334C23C2×C22⋊D7111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—2842no—
338Q8—2842no—
339Q8—712no—
340Q8—1421no—
341Q8—1421no—
342Q8—1421no—
343Q8—1421no—
344Q8—1421no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D7112yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—2842no—
362C2×C4—2842no—
363C2×C4—1421no—
364C2×C4—1421no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4C2×C22⋊D7111yescharacteristic
368C2×C4C2×C22⋊D7111yescharacteristic
369C2×C4C2×C22⋊D7111yescharacteristic
370C2×C4C2×C22⋊D7111yescharacteristic
371C2×C4C23×D7111yescharacteristic
372C8—712no—
373C8—1421no—
374C8—1421no—
375C8—1421no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#1455615812yescomplemented
389C22C22×C22⋊D7111yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—2841no—
397C4—2841no—
398C4—2841no—
399C4—1422no—
400C4C2×D4×D7111yescharacteristic
401C4#1455617311yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D7111yescharacteristic
407C2C2×#1455615811yescharacteristic
408C2#1798681011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#546×C71C2
socleC22×C71C22×D4
hypercenter#546D71
hypocenterC71#3266
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14556158C2semidirect
2. C22×#11765853C2semidirect
3. D4×Dic142C2semidirect
4. #17986394C2semidirect
5. #17986243C2semidirect
6. #17986238C2semidirect
7. #17986218C2semidirect
8. #17986204C2semidirect
9. #17986161C2semidirect
10. #17986154C2semidirect
11. #17986150C2semidirect
12. #17986137C2semidirect
13. #17986099C2semidirect
14. #17986071C2semidirect
17. C22×Dic142C22semidirect
19. C2×#11765855C22semidirect
20. C2×#11765855C22semidirect
21. C2×#11765855C22semidirect
29. C2×#11765849C22semidirect
31. #14556128C22semidirect
34. #14556107C22semidirect
37. C4×Dic142C22semidirect
39. #14556061C22semidirect
40. C4⋊(C71⋊C8)C22semidirect
41. #14556052C22semidirect
42. #14556051C22semidirect
43. #14556051C22semidirect
44. #14556051C22semidirect
48. C22⋊(C71⋊C8)C22semidirect
49. #14556039C22semidirect
80. #11765853D4semidirect
183. C22×C71#137semidirect
205. C71#3266semidirect
388. C22#14556158semidirect