Finite Group Databasebeta

← #49133248

Subgroups — #49133248

Order 36224.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827126C211yesmaximal, characteristic, complemented
2#31827116C211yesmaximal, characteristic, complemented
3#31826826C211yesmaximal, characteristic, complemented
4#31826799C211yesmaximal, characteristic, complemented
5#31826778C211yesmaximal, characteristic, complemented
6#31826758C211yesmaximal, characteristic, complemented
7#31826714C211yesmaximal, characteristic, complemented
8#31826701C211yesmaximal, characteristic, complemented
9#31826683C211yesmaximal, characteristic, complemented
10#31826613C211yesmaximal, characteristic, complemented
11#31826604C211yesmaximal, characteristic, complemented
12#31826568C211yesmaximal, characteristic, complemented
13#31826536C211yesmaximal, characteristic, complemented
14#31826465C211yesmaximal, characteristic, complemented
15C2×#103×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985392—21no—
18C2×#17985379C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22#22583609C2211yescharacteristic
23#22583599—21no—
24#22583599C2211yescharacteristic
25#22583595—21no—
26#22583593—21no—
27#22583588—21no—
28#22583586—21no—
29#22583586C2211yescharacteristic
30#22583585C2211yescharacteristic
31#22583584—21no—
32#22583584C2211yescharacteristic
33#22583584C2211yescharacteristic
34Q8×Dic283C2211yescharacteristic
35#22583572C2211yescharacteristic
36C4×C22⋊D283—21no—
37C4×C22⋊D283C2211yescharacteristic
38C4⋊C4×D283C2211yescharacteristic
39#22583544C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583543C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C22×Q8×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C2×C4⋊C4×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61#17985392—44no—
62C2×Dic566—21no—
63C2×D1132—21no—
64C2×D1132—21no—
65C2×D1132C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283D411yescharacteristic
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74#17985379—22no—
75#17985379—41no—
76D2264—41no—
77#17985375—41no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4D411yescharacteristic
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)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283—21no—
97C4×Dic283C2311yescharacteristic
98C2×Q8×C283—21no—
99C2×Q8×C283—22no—
100C2×Q8×C283—41no—
101C2×Q8×C283C2311yescharacteristic
102C2×Q8×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283—21no—
105C22×C4×C283C2311yescharacteristic
106C2×C8×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283—21no—
110C4⋊C4×C283C2311yescharacteristic
111C4⋊C4×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—21no—
114C22×D283C2×D411yescharacteristic
115Dic566—42no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132—42no—
121D1132—42no—
122C22⋊D283—22no—
123C22⋊D283—42no—
124C22⋊D283—42no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—42no—
134C4×D283—42no—
135C283⋊C8—21no—
136C283⋊C8—21no—
137C23×C283C2×D411yescharacteristic
138Q8×C283—21no—
139Q8×C283—21no—
140Q8×C283—21no—
141Q8×C283—42no—
142Q8×C283#4112yescomplemented
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—42no—
150C2×C4×C283—42no—
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2411yescharacteristic
153C8×C283—21no—
154C8×C283—21no—
155C22×C283—21no—
156C22×C283—21no—
157C22×C283AGL(1,ℤ/8)12yes—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C2×D283—41no—
166C2×D283—41no—
167C2×D283—41no—
168C4×C283—21no—
169C4×C283—22no—
170C4×C283—41no—
171C4×C283—41no—
172C4×C283—41no—
173C4×C283C2×#4111yescharacteristic
174C4×C283H(5,𝔽2)11yescharacteristic
175Dic283—21no—
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179Dic283—41no—
180C2×C283—22no—
181C2×C283#54611yescharacteristic
182C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C283#57811yescharacteristic
184D283—41no—
185D283—81no—
186D283—81no—
187C283#330811yescharacteristic, complemented, Sylow
188#3308—2831nomaximal, Sylow
189#548—2831no—
190#547—2831no—
191#489—2831no—
192#484—2831no—
193#480—2831no—
194#477—2831no—
195#468—2831no—
196#466—2831no—
197#463—2831no—
198#449—2831no—
199#448—2831no—
200#440—2831no—
201#435—2831no—
202#417—2831no—
203C2×#103D28311yescharacteristic, complemented
204C2×#41—2831no—
205C2×#41—5661no—
206C22×Q8C2×D28311yescharacteristic
207C2×SD16—2831no—
208C2×SD16—2831no—
209C2×D8—2831no—
210C2×M16—2831no—
211C22×C8C2×D28311yescharacteristic
212C4⋊Q8—2831no—
213#124—2831no—
214#124—5661no—
215#123—5661no—
216#123—5661no—
217C22⋊Q8—2831no—
218C22⋊Q8—5661no—
219C22⋊Q8—5661no—
220#121—2831no—
221#121—2831no—
222#121—2831no—
223#121—5661no—
224C4×Q8—2831no—
225C4×D4—2831no—
226C4×D4—2831no—
227C4×D4—5661no—
228C2×C4⋊C4—2831no—
229C2×C4⋊C4C2×D28311yescharacteristic
230#107—2831no—
231#107—2831no—
232#107—2831no—
233C4⋊C8—2831no—
234#103—2831no—
235#103—2831no—
236#103C2×D28311yescharacteristic
237#103C2×D28311yescharacteristic
238#103C2×D28311yescharacteristic
239#103C2×D28311yescharacteristic
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102—2831no—
244C22⋊C8—2831no—
245C22⋊C8—2831no—
246#97—2831no—
247#41—5662no—
248#41—11324no—
249#41—11321no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—5661no—
254C2×Q8C22×D28311yescharacteristic
255C2×Q8C22×D28311yescharacteristic
256C2×D4—2831no—
257C2×D4—2831no—
258C2×D4—2831no—
259C2×D4—5661no—
260C2×D4—5661no—
261C2×D4—5661no—
262C2×D4—5661no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—2831no—
266C22×C4—5661no—
267C22×C4—5661no—
268C22×C4—5661no—
269C22×C4C22×D28311yescharacteristic
270SD16—5662no—
271SD16—11321no—
272D8—11321no—
273M16—11321no—
274C2×C8—41no—
275C2×C8—2831no—
276C2×C8—2831no—
277C2×C8C22×D28311yescharacteristic
278C2×C8C22×D28311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—2831no—
281C4⋊C4—2831no—
282C4⋊C4—2831no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4C22×D28311yescharacteristic
288C4⋊C4C22×D28311yescharacteristic
289C22⋊C4—2831no—
290C22⋊C4—2831no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C22⋊C4—5661no—
295C22⋊C4—5661no—
296C22⋊C4—5661no—
297C22⋊C4—5661no—
298C42—2831no—
299C42—5661no—
300C23—2831no—
301C23—5661no—
302C23—5661no—
303C23D4×D28311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—11322no—
309Q8#1798539212yescomplemented
310D4—5662no—
311D4—5661no—
312D4—5661no—
313D4—5661no—
314D4—5661no—
315D4—11322no—
316D4—11322no—
317D4—11322no—
318D4—11322no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—2831no—
328C2×C4—2831no—
329C2×C4—2831no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—5661no—
334C2×C4—11322no—
335C2×C4—11322no—
336C2×C4—11322no—
337C2×C4D4×D28311yescharacteristic
338C2×C4C23×D28311yescharacteristic
339C8—21no—
340C8—21no—
341C8—5661no—
342C8—5661no—
343C22—21no—
344C22—21no—
345C22—5661no—
346C22—5661no—
347C22—5661no—
348C22—11321no—
349C22—11321no—
350C22—11321no—
351C22—11321no—
352C22—11321no—
353C22—11321no—
354C22#2258363712yes—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—5661no—
362C4—5661no—
363C4—5661no—
364C4—11321no—
365C4—11321no—
366C4C2×#1798539211yescharacteristic
367C4#2258365511yescharacteristic
368C2—22no—
369C2—11321no—
370C2—22641no—
371C2—22641no—
372C2#3182710511yescharacteristic
373C2C2×#2258363711yescharacteristic
374C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC22×C283C22×D4
hypercenterC2×#103D283
hypocenterC283#3308
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #31827126C2semidirect
2. #31827116C2semidirect
3. #31826826C2semidirect
4. #31826799C2semidirect
5. #31826778C2semidirect
6. #31826758C2semidirect
7. #31826714C2semidirect
8. #31826701C2semidirect
9. #31826683C2semidirect
10. #31826613C2semidirect
11. #31826604C2semidirect
12. #31826568C2semidirect
13. #31826536C2semidirect
14. #31826465C2semidirect
15. C2×#103×C283C2semidirect
142. Q8×C283#41semidirect
187. C283#3308semidirect
203. C2×#103D283semidirect
309. Q8#17985392semidirect

Maximal subgroups

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

subgroupindex
#318271262
#318271162
#318268262
#318267992
#318267782
#318267582
#318267142
#318267012
#318266832
#318266132
#318266042
#318265682
#318265362
#318264652
C2×#103×C2832
#3308283