Finite Group Databasebeta

← #49133207

Subgroups — #49133207

Order 36224.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827178C211yesmaximal, characteristic, complemented
2#31827134C211yesmaximal, characteristic, complemented
3#31826810C211yesmaximal, characteristic, complemented
4#31826789C211yesmaximal, characteristic, complemented
5#31826787C211yesmaximal, characteristic, complemented
6#31826758C211yesmaximal, characteristic, complemented
7#31826701C211yesmaximal, characteristic, complemented
8#31826700C211yesmaximal, characteristic, complemented
9#31826659C211yesmaximal, characteristic, complemented
10#31826613C211yesmaximal, characteristic, complemented
11#31826610C211yesmaximal, characteristic, complemented
12#31826550C211yesmaximal, characteristic, complemented
13C8×C22⋊D283C211yesmaximal, characteristic, complemented
14#31826460C211yesmaximal, characteristic, complemented
15#416×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18C2×D2264C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583606—21no—
23#22583606C2211yescharacteristic
24#22583598—21no—
25#22583596—21no—
26#22583585C2211yescharacteristic
27#22583584—21no—
28#22583584C2211yescharacteristic
29#22583584C2211yescharacteristic
30#22583583—21no—
31#22583581—21no—
32#22583581C2211yescharacteristic
33Q8×Dic283C2211yescharacteristic
34#22583572C2211yescharacteristic
35C4×C22⋊D283—21no—
36C4×C22⋊D283C2211yescharacteristic
37#22583568C2211yescharacteristic
38#22583567—21no—
39#22583544C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583541C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×#41×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×Dic566—21no—
62C2×D1132—21no—
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283D411yescharacteristic
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75#17985379—22no—
76D2264—41no—
77#17985377—41no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—41no—
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97#41×C283—22no—
98#41×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104C2×C8×C283—41no—
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283C2×D411yescharacteristic
114Dic566—81no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—42no—
120D1132—81no—
121C22⋊D283—22no—
122C22⋊D283—42no—
123C22⋊D283—81no—
124C22⋊D283—81no—
125C22⋊D283—81no—
126C22⋊D283—81no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—42no—
135C4×D283—42no—
136C283⋊C8—21no—
137C283⋊C8—21no—
138C23×C283—21no—
139C23×C283C2×D411yescharacteristic
140Q8×C283—21no—
141Q8×C283#4112yes—
142D4×C283—21no—
143D4×C283—21no—
144D4×C283—42no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—42no—
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283—21no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—21no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C4×C283—21no—
172C4×C283—22no—
173C4×C283—41no—
174C4×C283—41no—
175C4×C283C2×#4111yescharacteristic
176C4×C283H(5,𝔽2)11yescharacteristic
177Dic283—21no—
178Dic283—21no—
179Dic283—41no—
180Dic283—41no—
181Dic283#13512yes—
182C2×C283—41no—
183C2×C283—81no—
184C2×C283#54611yescharacteristic
185C2×C283C2×#13511yescharacteristic
186C2×C283#57611yescharacteristic
187D283—41no—
188D283—81no—
189D283—81no—
190C283#330511yescharacteristic, complemented, Sylow
191#3305—2831nomaximal, Sylow
192#555—2831no—
193#550—2831no—
194#486—2831no—
195#482—2831no—
196#482—2831no—
197#477—2831no—
198#466—2831no—
199#466—2831no—
200#459—2831no—
201#449—2831no—
202#449—2831no—
203C4×SD16—2831no—
204C8×D4—2831no—
205#416—2831no—
206#416D28311yescharacteristic, complemented
207C2×#41—2831no—
208C2×#41C2×D28311yescharacteristic
209C2×SD16—2831no—
210C2×D8—2831no—
211C2×D8—2831no—
212C22×C8—2831no—
213C22×C8C2×D28311yescharacteristic
214C4⋊Q8—2831no—
215#127—2831no—
216#127—5661no—
217#124—5661no—
218#124—5661no—
219#121—2831no—
220#121—2831no—
221#121—2831no—
222#121—2831no—
223#121—5661no—
224#121—5661no—
225#121—5661no—
226C4×Q8—2831no—
227C4×D4—2831no—
228C4×D4—2831no—
229C4×D4—5661no—
230#117—2831no—
231#117—5661no—
232#117C2×D28311yescharacteristic
233#107—2831no—
234#107—2831no—
235#106—2831no—
236C4⋊C8—2831no—
237#103—2831no—
238#103C2×D28311yescharacteristic
239#103C2×D28311yescharacteristic
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244#102—2831no—
245#102C2×D28311yescharacteristic
246#102C2×D28311yescharacteristic
247C22⋊C8—2831no—
248C22⋊C8—2831no—
249C4×C8—2831no—
250#41—22no—
251#41—41no—
252#41—5662no—
253#41—11321no—
254C2×Q8—5661no—
255C2×Q8C22×D28311yescharacteristic
256C2×D4—21no—
257C2×D4—2831no—
258C2×D4—2831no—
259C2×D4—2831no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—5661no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4C22×D28311yescharacteristic
268C22×C4—21no—
269C22×C4—2831no—
270C22×C4—5661no—
271C22×C4—5661no—
272C22×C4C22×D28311yescharacteristic
273SD16—5662no—
274D8—11321no—
275D8—11321no—
276C2×C8—41no—
277C2×C8—2831no—
278C2×C8—2831no—
279C2×C8—11321no—
280C2×C8C22×D28311yescharacteristic
281C2×C8C22×D28311yescharacteristic
282C4⋊C4—2831no—
283C4⋊C4—2831no—
284C4⋊C4—2831no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4C22×D28311yescharacteristic
288C4⋊C4C22×D28311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—2831no—
291C22⋊C4—2831no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C42—21no—
299C42—2831no—
300C42—5661no—
301C42—5661no—
302C23—21no—
303C23—2831no—
304C23—5661no—
305C23—5661no—
306C23D4×D28311yescharacteristic
307Q8—21no—
308Q8—22641no—
309Q8#1798539212yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—5662no—
314D4—5661no—
315D4—5661no—
316D4—5661no—
317D4—5661no—
318D4—11322no—
319D4—11322no—
320D4—22641no—
321D4—22641no—
322D4—22641no—
323D4—22641no—
324D4—22641no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—2831no—
332C2×C4—2831no—
333C2×C4—2831no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5661no—
338C2×C4—11322no—
339C2×C4—11322no—
340C2×C4D4×D28311yescharacteristic
341C2×C4C23×D28311yescharacteristic
342C8—21no—
343C8—21no—
344C8—5661no—
345C8—5661no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—5661no—
353C22—5661no—
354C22—5661no—
355C22—11321no—
356C22—11321no—
357C22—11321no—
358C22—11321no—
359C22—11321no—
360C22—11321no—
361C22C2×D4×D28311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—2832no—
367C4—5661no—
368C4—5661no—
369C4—11321no—
370C4—11321no—
371C4C2×#1798539211yescharacteristic
372C4#2258365511yescharacteristic
373C2—41no—
374C2—81no—
375C2—11321no—
376C2—22641no—
377C2—22641no—
378C2#3182710511yescharacteristic
379C2#135×D28311yescharacteristic
380C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
hypercenter#416D283
hypocenterC283#3305
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #31827178C2semidirect
2. #31827134C2semidirect
3. #31826810C2semidirect
4. #31826789C2semidirect
5. #31826787C2semidirect
6. #31826758C2semidirect
7. #31826701C2semidirect
8. #31826700C2semidirect
9. #31826659C2semidirect
10. #31826613C2semidirect
11. #31826610C2semidirect
12. #31826550C2semidirect
13. C8×C22⋊D283C2semidirect
14. #31826460C2semidirect
15. #416×C283C2semidirect
190. C283#3305semidirect
206. #416D283semidirect

Maximal subgroups

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

subgroupindex
#318271782
#318271342
#318268102
#318267892
#318267872
#318267582
#318267012
#318267002
#318266592
#318266132
#318266102
#318265502
C8×C22⋊D2832
#318264602
#416×C2832
#3305283