Finite Group Databasebeta

← #49132799

Subgroups — #49132799

Order 36224.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583636C211yesmaximal, characteristic, complemented
2C2×#22583629C211yesmaximal, characteristic, complemented
3#31827133C211yesmaximal, characteristic, complemented
4#31827109C211yesmaximal, characteristic, complemented
5#31826853C211yesmaximal, characteristic, complemented
6#31826709C211yesmaximal, characteristic, complemented
7#31826700C211yesmaximal, characteristic, complemented
8#31826686C211yesmaximal, characteristic, complemented
9#31826658C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826611C211yesmaximal, characteristic, complemented
12#31826607C211yesmaximal, characteristic, complemented
13#31826562C211yesmaximal, characteristic, complemented
14#31826539C211yesmaximal, characteristic, complemented
15#447×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×#17985391C2211yescharacteristic, complemented
19#22583636—24no—
20#22583629—24no—
21C2×Dic1132C2211yescharacteristic, complemented
22C2×#17985381C2211yescharacteristic, complemented
23C2×#17985380C2211yescharacteristic
24C2×#17985380C2211yescharacteristic
25C2×#17985380C2211yescharacteristic, complemented
26C2×#17985377C2211yescharacteristic
27C2×#17985377C2211yescharacteristic
28C2×#17985376C2211yescharacteristic
29C2×C8×D283C2211yescharacteristic, complemented
30#22583606—21no—
31#22583606C2211yescharacteristic, complemented
32#22583597C2211yescharacteristic
33#22583591—21no—
34#22583589C2211yescharacteristic
35#22583585C2211yescharacteristic, complemented
36#22583583—21no—
37#22583582—21no—
38#22583582—21no—
39#22583581C2211yescharacteristic
40#22583579—21no—
41#22583575C2211yescharacteristic, complemented
42D4×Dic283C2211yescharacteristic
43C4×C22⋊D283C2211yescharacteristic
44(C22⋊D283)⋊C4—21no—
45C2×C22⋊Dic283—21no—
46#22583543C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583533C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic, complemented
52(C2×D283)⋊C8C2211yescharacteristic, complemented
53#22583520C2211yescharacteristic, complemented
54C22×D4×C283C2211yescharacteristic
55C2×D8×C283C2211yescharacteristic
56C2×D8×C283C2211yescharacteristic
57#121×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#102×C283C2211yescharacteristic
60C22⋊C8×C283C2211yescharacteristic
61#17985392—22no—
62#17985392—41no—
63#17985391—22no—
64#17985391—22no—
65#17985391—41no—
66#17985391—41no—
67C2×Dic566C2311yescharacteristic
68C2×Dic566C2311yescharacteristic
69C2×D1132—21no—
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75C2×C22⋊D283—21no—
76C2×C22⋊D283—21no—
77C2×C22⋊D283D411yescharacteristic
78C22×Dic283—21no—
79C22×Dic283—21no—
80C22×Dic283—21no—
81C2×C4×D283—21no—
82C2×C4×D283C2311yescharacteristic
83Dic1132—22no—
84#17985381—41no—
85#17985380—22no—
86#17985380—22no—
87#17985380D414yescomplemented
88#17985377—22no—
89#17985377—22no—
90#17985376—22no—
91C2×C283⋊C8C2311yescharacteristic
92C2×C283⋊C8C2311yescharacteristic
93C8×D283—22no—
94C4⋊Dic283C2311yescharacteristic
95Dic283⋊C4—21no—
96Dic283⋊C4—21no—
97Dic283⋊C4D411yescharacteristic
98C22⋊Dic283—21no—
99C22⋊Dic283—21no—
100C22⋊Dic283—21no—
101C22⋊Dic283—21no—
102C22⋊Dic283—21no—
103C22⋊Dic283D411yescharacteristic
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4D411yescharacteristic
106C4×Dic283—21no—
107C4×Dic283C2311yescharacteristic
108C24×C283—21no—
109C2×D4×C283—22no—
110C2×D4×C283—21no—
111C2×D4×C283—21no—
112C2×D4×C283—41no—
113C2×D4×C283C2311yescharacteristic
114C2×D4×C283C2311yescharacteristic
115C2×D4×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117D8×C283—22no—
118D8×C283—41no—
119C2×C8×C283C2311yescharacteristic
120C2×C8×C283C2311yescharacteristic
121C4⋊C4×C283C2311yescharacteristic
122C22⋊C4×C283—21no—
123C22×D283—21no—
124C22×D283C2×D411yescharacteristic
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566C2×D412yes—
129D1132—21no—
130D1132—21no—
131D1132—81no—
132C22⋊D283—41no—
133C22⋊D283—42no—
134C22⋊D283—42no—
135C22⋊D283—42no—
136C22⋊D283—42no—
137C22⋊D283—81no—
138C22⋊D283—81no—
139C2×Dic283—21no—
140C2×Dic283—21no—
141C2×Dic283—21no—
142C2×Dic283—42no—
143C2×Dic283—42no—
144C2×Dic283—81no—
145C2×Dic283C2×D411yescharacteristic
146C2×Dic283C2×D411yescharacteristic
147C2×Dic283C2×D411yescharacteristic
148C4×D283—21no—
149C4×D283—21no—
150C4×D283—42no—
151C283⋊C8—21no—
152C283⋊C8C2×D412yes—
153C23×C283—21no—
154C23×C283—21no—
155C23×C283—21no—
156C23×C283—42no—
157C23×C283—42no—
158C23×C283—81no—
159C23×C283C2×D411yescharacteristic
160D4×C283—21no—
161D4×C283—21no—
162D4×C283—21no—
163D4×C283—21no—
164D4×C283—21no—
165D4×C283—42no—
166D4×C283—81no—
167D4×C283C2×D412yes—
168C2×C4×C283—21no—
169C2×C4×C283—21no—
170C2×C4×C283—21no—
171C2×C4×C283C2×D411yescharacteristic
172C2×C4×C283C2411yescharacteristic
173C8×C283—21no—
174C8×C283—21no—
175C22×C283—21no—
176C22×C283—22no—
177C22×C283—21no—
178C22×C283—21no—
179C22×C283—41no—
180C22×C283—41no—
181C22×C283—41no—
182C22×C283—41no—
183C22×C283—41no—
184C22×C283—41no—
185C22×C283—41no—
186C22×C283—41no—
187C22×C283—84no—
188C22×C283C22×D411yescharacteristic
189C2×D283—21no—
190C2×D283—21no—
191C2×D283—21no—
192C2×D283—41no—
193C2×D283—41no—
194C2×D283—41no—
195C4×C283—21no—
196C4×C283—41no—
197C4×C283C22×D411yescharacteristic
198C4×C283H(5,𝔽2)11yescharacteristic
199Dic283—21no—
200Dic283—22no—
201Dic283—21no—
202Dic283—21no—
203Dic283—41no—
204Dic283—41no—
205C2×C283—41no—
206C2×C283—42no—
207C2×C283—81no—
208C2×C283—81no—
209C2×C283D4211yescharacteristic
210C2×C283#57511yescharacteristic
211C2×C283#57611yescharacteristic
212D283—41no—
213D283—81no—
214C283#326811yescharacteristic, complemented, Sylow
215#3268—2831nomaximal, Sylow
216C2×AGL(1,ℤ/8)—2831no—
217C2×#135—2831no—
218#550—2831no—
219#546—2831no—
220#496—2831no—
221#468—2831no—
222#466—2831no—
223#464—2831no—
224#459—2831no—
225#452—2831no—
226#449—2831no—
227#449—2831no—
228#447D28311yescharacteristic, complemented
229#440—2831no—
230#435—2831no—
231C2×#41—2831no—
232C2×#41—2831no—
233C2×#41—2831no—
234C22×D4C2×D28311yescharacteristic
235AGL(1,ℤ/8)—5664no—
236#135—5664no—
237C2×Q16—2831no—
238C2×SD16—2831no—
239C2×SD16—2831no—
240C2×SD16—2831no—
241C2×SD16—2831no—
242C2×D8—2831no—
243C2×D8—2831no—
244C2×D8C2×D28311yescharacteristic
245C2×D8C2×D28311yescharacteristic
246C2×M16—2831no—
247C22×C8—2831no—
248#127—2831no—
249#127—5661no—
250#124—2831no—
251#123—5661no—
252C22⋊Q8—2831no—
253#121—2831no—
254#121—2831no—
255#121—5661no—
256#121—5661no—
257#121—5661no—
258#121C2×D28311yescharacteristic
259#120—5661no—
260C4×Q8—2831no—
261C4×D4—2831no—
262C4×D4—2831no—
263C4×D4—5661no—
264C2×C22⋊C4—5661no—
265#107—2831no—
266C4⋊C8—2831no—
267#103—2831no—
268#103—2831no—
269#102—2831no—
270#102—2831no—
271#102C2×D28311yescharacteristic
272#102C2×D28311yescharacteristic
273C22⋊C8—2831no—
274C22⋊C8C2×D28311yescharacteristic
275#97—2831no—
276C24—21no—
277#41—5662no—
278#41—5662no—
279#41—5662no—
280#41—11321no—
281#41—11321no—
282#41—11321no—
283C2×Q8—2831no—
284C2×Q8—2831no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—2831no—
290C2×D4—2831no—
291C2×D4—5661no—
292C2×D4—5661no—
293C2×D4—5661no—
294C2×D4—5661no—
295C2×D4—5661no—
296C2×D4—5661no—
297C2×D4—5661no—
298C2×D4C22×D28311yescharacteristic
299C2×D4C22×D28311yescharacteristic
300C2×D4C22×D28311yescharacteristic
301C22×C4—2831no—
302C22×C4—5661no—
303C22×C4—5661no—
304C22×C4—5661no—
305C22×C4—5661no—
306C22×C4C22×D28311yescharacteristic
307Q16—5662no—
308SD16—2834no—
309SD16—5662no—
310SD16—5662no—
311SD16—11321no—
312D8—22no—
313D8—41no—
314D8—5662no—
315D8—5662no—
316M16—5662no—
317C2×C8—2831no—
318C2×C8—2831no—
319C2×C8—5662no—
320C2×C8C22×D28311yescharacteristic
321C2×C8C22×D28311yescharacteristic
322C4⋊C4—2831no—
323C4⋊C4—2831no—
324C4⋊C4—5661no—
325C4⋊C4—5661no—
326C4⋊C4C22×D28311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—2831no—
329C22⋊C4—2831no—
330C22⋊C4—5661no—
331C22⋊C4—5661no—
332C22⋊C4—5661no—
333C22⋊C4—5661no—
334C22⋊C4—5661no—
335C22⋊C4—5661no—
336C42—2831no—
337C42—5661no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—2831no—
345C23—5661no—
346C23D4×D28311yescharacteristic
347Q8—2832no—
348Q8—5661no—
349Q8—5661no—
350Q8—5661no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—5661no—
359D4—5661no—
360D4—11321no—
361D4—11322no—
362D4—11322no—
363D4—11322no—
364D4—11322no—
365D4—22641no—
366D4—22641no—
367D4—22641no—
368D4D4×D28312yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—2831no—
373C2×C4—2831no—
374C2×C4—2831no—
375C2×C4—5661no—
376C2×C4—5661no—
377C2×C4—5661no—
378C2×C4—5661no—
379C2×C4—5661no—
380C2×C4—11322no—
381C2×C4—11322no—
382C2×C4—11322no—
383C2×C4—22641no—
384C2×C4D4×D28311yescharacteristic
385C2×C4C23×D28311yescharacteristic
386C8—21no—
387C8—21no—
388C8—2832no—
389C8—5661no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—5661no—
404C22—5661no—
405C22—5661no—
406C22—11321no—
407C22—11321no—
408C22—11321no—
409C22C2×D4×D28311yescharacteristic
410C4—21no—
411C4—41no—
412C4—5661no—
413C4—5661no—
414C4—5661no—
415C4—5662no—
416C4—11321no—
417C4—11321no—
418C4C2×D4×D28311yescharacteristic
419C4#2258365511yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—11321no—
425C2—22641no—
426C2#3182709711yescharacteristic
427C2#3182726111yescharacteristic
428C2#3182726611yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#447×C283C2
socleC22×C283C22×D4
hypercenter#447D283
hypocenterC283#3268
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#22583636C2semidirect
2. C2×#22583629C2semidirect
3. #31827133C2semidirect
4. #31827109C2semidirect
5. #31826853C2semidirect
6. #31826709C2semidirect
7. #31826700C2semidirect
8. #31826686C2semidirect
9. #31826658C2semidirect
10. #31826629C2semidirect
11. #31826611C2semidirect
12. #31826607C2semidirect
13. #31826562C2semidirect
14. #31826539C2semidirect
15. #447×C283C2semidirect
18. C2×#17985391C22semidirect
21. C2×Dic1132C22semidirect
22. C2×#17985381C22semidirect
25. C2×#17985380C22semidirect
29. C2×C8×D283C22semidirect
31. #22583606C22semidirect
35. #22583585C22semidirect
41. #22583575C22semidirect
46. #22583543C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583535C22semidirect
49. #22583533C22semidirect
50. #22583532C22semidirect
51. #22583531C22semidirect
52. (C2×D283)⋊C8C22semidirect
53. #22583520C22semidirect
87. #17985380D4semidirect
214. C283#3268semidirect
228. #447D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#225836362
C2×#225836292
#318271332
#318271092
#318268532
#318267092
#318267002
#318266862
#318266582
#318266292
#318266112
#318266072
#318265622
#318265392
#447×C2832
#3268283