Finite Group Databasebeta

← #49131849

Subgroups — #49131849

Order 36224.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827010C211yesmaximal, characteristic, complemented
2#31827001C211yesmaximal, characteristic, complemented
3#31826873C211yesmaximal, characteristic, complemented
4#31826851C211yesmaximal, characteristic, complemented
5#31826828C211yesmaximal, characteristic, complemented
6#31826826C211yesmaximal, characteristic, complemented
7#31826718C211yesmaximal, characteristic, complemented
8#31826716C211yesmaximal, characteristic, complemented
9#31826713C211yesmaximal, characteristic, complemented
10SD16×Dic283C211yesmaximal, characteristic, complemented
11#31826550C211yesmaximal, characteristic, complemented
12#31826547C211yesmaximal, characteristic, complemented
13#31826545C211yesmaximal, characteristic, complemented
14M16×Dic283C211yesmaximal, characteristic, complemented
15#468×C283C211yesmaximal, characteristic, complemented
16C2×#17985391—21no—
17C2×#17985379C2211yescharacteristic
18C2×D2264C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20C2×#17985376C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583606C2211yescharacteristic
23#22583605—21no—
24#22583601C2211yescharacteristic
25#22583599C2211yescharacteristic
26#22583596—21no—
27#22583594—21no—
28#22583584C2211yescharacteristic
29#22583584C2211yescharacteristic
30#22583582—21no—
31Q8×Dic283C2211yescharacteristic
32D4×Dic283C2211yescharacteristic
33#22583572C2211yescharacteristic
34#22583572C2211yescharacteristic
35(C22⋊D283)⋊C4—21no—
36(C22⋊D283)⋊C4—21no—
37#22583568—21no—
38C2×C4×Dic283C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583520C2211yescharacteristic
49#22583520C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985391—44no—
60C2×Dic566—21no—
61C2×D1132C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C22×Dic283—21no—
68C22×Dic283D411yescharacteristic
69C22×Dic283D411yescharacteristic
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72#17985379—22no—
73D2264—22no—
74#17985377—22no—
75#17985376—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C4⋊Dic283—21no—
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84C22⋊Dic283—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283D411yescharacteristic
93C4×Dic283D411yescharacteristic
94C4×Dic283C2311yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100SD16×C283—22no—
101M16×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C22×D283—21no—
110C22×D283—21no—
111Dic566—42no—
112D1132—21no—
113D1132—21no—
114D1132—21no—
115D1132—21no—
116C22⋊D283—42no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C22⋊D283—42no—
120C2×Dic283—22no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—41no—
124C2×Dic283—42no—
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—42no—
130C4×D283—42no—
131C283⋊C8—21no—
132C283⋊C8#4112yescomplemented
133C23×C283—21no—
134C23×C283C2×D411yescharacteristic
135Q8×C283—21no—
136Q8×C283—21no—
137D4×C283—21no—
138D4×C283—21no—
139D4×C283—42no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283#4112yescomplemented
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—21no—
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283AGL(1,ℤ/8)12yes—
174C2×C283—41no—
175C2×C283—81no—
176C2×C283#53211yescharacteristic
177C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C283#57511yescharacteristic
179D283—81no—
180D283—81no—
181C283#317111yescharacteristic, complemented, Sylow
182#3171—2831nomaximal, Sylow
183#532—2831no—
184#529—2831no—
185#501—2831no—
186#496—2831no—
187#490—2831no—
188#489—2831no—
189#469—2831no—
190#469—2831no—
191#468—2831no—
192#468D28311yescharacteristic, complemented
193C4×SD16—2831no—
194C4×SD16—2831no—
195C4×D8—2831no—
196C4×D8—2831no—
197C4×M16—2831no—
198C2×#41—5661no—
199C2×SD16—2831no—
200C2×SD16C2×D28311yescharacteristic
201C2×D8—2831no—
202C2×D8—2831no—
203C2×M16—2831no—
204C2×M16C2×D28311yescharacteristic
205C4⋊Q8—2831no—
206#127—2831no—
207#126—5661no—
208#125—2831no—
209#124—2831no—
210#124—5661no—
211#123—5661no—
212C22⋊Q8C2×D28311yescharacteristic
213#121—2831no—
214#121—2831no—
215#121—5661no—
216#121C2×D28311yescharacteristic
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4—2831no—
221C4×D4—5661no—
222C4×D4—5661no—
223#117—5661no—
224C2×C42—2831no—
225#107—2831no—
226#107C2×D28311yescharacteristic
227#106—2831no—
228#106—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102C2×D28311yescharacteristic
237#97—2831no—
238#97—2831no—
239C4×C8—2831no—
240C4×C8—2831no—
241#41—11324no—
242C2×Q8—5661no—
243C2×Q8C22×D28311yescharacteristic
244C2×D4—21no—
245C2×D4—2831no—
246C2×D4—2831no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4—5661no—
251C2×D4C22×D28311yescharacteristic
252C22×C4—2831no—
253C22×C4—2831no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4C22×D28311yescharacteristic
258SD16—22no—
259SD16—5662no—
260D8—5662no—
261D8—5662no—
262M16—22no—
263M16—5662no—
264C2×C8—2831no—
265C2×C8—2831no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—2831no—
288C42—2831no—
289C42—2831no—
290C42—5661no—
291C23—21no—
292C23—5661no—
293C23—5661no—
294C23D4×D28311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—11322no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—5661no—
302D4—5661no—
303D4—5661no—
304D4—5661no—
305D4—11322no—
306D4—11322no—
307D4—11322no—
308D4—11322no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—2831no—
315C2×C4—2831no—
316C2×C4—2831no—
317C2×C4—2831no—
318C2×C4—5662no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4—11322no—
323C2×C4—11322no—
324C2×C4—11321no—
325C2×C4D4×D28311yescharacteristic
326C2×C4C23×D28311yescharacteristic
327C8—21no—
328C8—2832no—
329C8—5661no—
330C8#1798539112yescomplemented
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—11321no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22—11321no—
342C22—11321no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2832no—
349C4—5661no—
350C4—5661no—
351C4—5661no—
352C4—11321no—
353C4—11321no—
354C4#41×D28311yescharacteristic
355C4C2×#1798539111yescharacteristic
356C2—41no—
357C2—81no—
358C2—22641no—
359C2—22641no—
360C2#3182701011yescharacteristic
361C2AGL(1,ℤ/8)×D28311yescharacteristic
362C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#468×C283C2
socleC22×C283C22×D4
hypercenter#468D283
hypocenterC283#3171
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #31827010C2semidirect
2. #31827001C2semidirect
3. #31826873C2semidirect
4. #31826851C2semidirect
5. #31826828C2semidirect
6. #31826826C2semidirect
7. #31826718C2semidirect
8. #31826716C2semidirect
9. #31826713C2semidirect
10. SD16×Dic283C2semidirect
11. #31826550C2semidirect
12. #31826547C2semidirect
13. #31826545C2semidirect
14. M16×Dic283C2semidirect
15. #468×C283C2semidirect
132. C283⋊C8#41semidirect
148. C8×C283#41semidirect
181. C283#3171semidirect
192. #468D283semidirect
330. C8#17985391semidirect

Maximal subgroups

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

subgroupindex
#318270102
#318270012
#318268732
#318268512
#318268282
#318268262
#318267182
#318267162
#318267132
SD16×Dic2832
#318265502
#318265472
#318265452
M16×Dic2832
#468×C2832
#3171283