Finite Group Databasebeta

← #49131408

Subgroups — #49131408

Order 36224.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827012C211yesmaximal, characteristic, complemented
2C4×#17985391C211yesmaximal, characteristic, complemented
3#31826791C211yesmaximal, characteristic, complemented
4#31826787C211yesmaximal, characteristic, complemented
5#31826749C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826664C211yesmaximal, characteristic, complemented
8#31826658C211yesmaximal, characteristic, complemented
9#31826611C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826575C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13#31826565C211yesmaximal, characteristic, complemented
14#31826520C211yesmaximal, characteristic, complemented
15#442×C283C211yesmaximal, characteristic, complemented
16C2×#17985392—21no—
17C2×#17985391C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583606C2211yescharacteristic
23#22583596—21no—
24#22583585C2211yescharacteristic
25#22583583—21no—
26#22583581C2211yescharacteristic
27C4×Dic566C2211yescharacteristic
28#22583575C2211yescharacteristic
29C4×D1132C2211yescharacteristic
30D4×Dic283C2211yescharacteristic
31C4×C22⋊D283—21no—
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583568C2211yescharacteristic
35#22583566—21no—
36C2×C4×Dic283—21no—
37C42×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985392—44no—
60#17985391—22no—
61#17985391—22no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×D1132—21no—
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C22×Dic283—21no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283D411yescharacteristic
74C2×C4×D283D411yescharacteristic
75C2×C4×D283C2311yescharacteristic
76#17985381—22no—
77#17985380—22no—
78#17985377—22no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283D411yescharacteristic
95C4×Dic283D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283—21no—
101D8×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C42×C283C2311yescharacteristic
109C22×D283—21no—
110C22×D283C2×D411yescharacteristic
111Dic566—21no—
112Dic566—42no—
113Dic566#4112yescomplemented
114D1132—21no—
115D1132—21no—
116D1132—42no—
117C22⋊D283—24no—
118C22⋊D283—42no—
119C22⋊D283—42no—
120C22⋊D283—42no—
121C2×Dic283—24no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—42no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—22no—
132C4×D283—41no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137C23×C283—21no—
138D4×C283—21no—
139D4×C283—21no—
140D4×C283—21no—
141D4×C283#4112yescomplemented
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—42no—
145C2×C4×C283—42no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—22no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283C22×D411yescharacteristic
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283C2×#4111yescharacteristic
169C4×C283C2×#4111yescharacteristic
170Dic283—21no—
171Dic283—22no—
172Dic283—21no—
173Dic283—41no—
174Dic283—41no—
175Dic283AGL(1,ℤ/8)12yes—
176C2×C283—42no—
177C2×C283—81no—
178C2×C283#52511yescharacteristic
179C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C283#57511yescharacteristic
181D283—41no—
182D283—81no—
183C283#311511yescharacteristic, complemented, Sylow
184#3115—2831nomaximal, Sylow
185#532—2831no—
186C4×#41—2831no—
187#482—2831no—
188#482—2831no—
189#475—2831no—
190#474—2831no—
191#460—2831no—
192#459—2831no—
193#449—2831no—
194#449—2831no—
195#442—2831no—
196#442D28311yescharacteristic, complemented
197#440—2831no—
198#440—2831no—
199#432—2831no—
200C2×#41—2831no—
201C2×#41—5661no—
202C2×SD16—2831no—
203C2×SD16—2831no—
204C2×D8—2831no—
205C2×D8C2×D28311yescharacteristic
206C4⋊Q8—2831no—
207#127—2831no—
208#124—5661no—
209#121—2831no—
210#121—2831no—
211#121—5661no—
212C4×Q8—2831no—
213C4×Q8—2831no—
214C4×D4—2831no—
215C4×D4—2831no—
216C4×D4—5661no—
217C4×D4—5661no—
218C4×D4—5661no—
219C4×D4C2×D28311yescharacteristic
220C4×D4C2×D28311yescharacteristic
221#117—2831no—
222#117—5661no—
223C2×C42—2831no—
224C2×C42—5661no—
225#107—2831no—
226#107—2831no—
227#106—2831no—
228#106C2×D28311yescharacteristic
229C4⋊C8—2831no—
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102C2×D28311yescharacteristic
238#102C2×D28311yescharacteristic
239C22⋊C8—2831no—
240C22⋊C8—2831no—
241#97—2831no—
242#97C2×D28311yescharacteristic
243#41—5662no—
244#41—5662no—
245#41—11324no—
246C2×Q8—2831no—
247C2×Q8—5661no—
248C2×D4—2831no—
249C2×D4—5661no—
250C2×D4—5661no—
251C2×D4—5661no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4C22×D28311yescharacteristic
255C2×D4C22×D28311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—2831no—
259C22×C4—2831no—
260C22×C4—2831no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4—5661no—
264SD16—5662no—
265SD16—5662no—
266D8—22no—
267D8—5662no—
268C2×C8—2831no—
269C2×C8—2831no—
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—2831no—
273C4⋊C4—2831no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4C22×D28311yescharacteristic
278C4⋊C4C22×D28311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—2831no—
287C42—2831no—
288C42—2831no—
289C42—5661no—
290C42—5661no—
291C42—5661no—
292C42C22×D28311yescharacteristic
293C23—21no—
294C23—21no—
295C23—2831no—
296C23—5661no—
297Q8—2832no—
298Q8—5661no—
299Q8—11322no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—5664no—
304D4—5661no—
305D4—5661no—
306D4—11322no—
307D4—11322no—
308D4—11322no—
309D4—11322no—
310D4#1798539212yescomplemented
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2831no—
316C2×C4—2831no—
317C2×C4—2831no—
318C2×C4—5662no—
319C2×C4—5664no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—11321no—
326C2×C4—11322no—
327C2×C4—11322no—
328C2×C4D4×D28311yescharacteristic
329C2×C4D4×D28311yescharacteristic
330C2×C4C23×D28311yescharacteristic
331C8—21no—
332C8—21no—
333C8—5661no—
334C8—5661no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—5661no—
342C22—5661no—
343C22—5661no—
344C22—11321no—
345C22—11321no—
346C22—11321no—
347C22C2×D4×D28311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—2832no—
353C4—5661no—
354C4—5662no—
355C4—5661no—
356C4—11321no—
357C4—11321no—
358C4#41×D28311yescharacteristic
359C4C2×#1798539211yescharacteristic
360C2—42no—
361C2—81no—
362C2—11321no—
363C2—22641no—
364C2#3182697411yescharacteristic
365C2AGL(1,ℤ/8)×D28311yescharacteristic
366C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
hypercenter#442D283
hypocenterC283#3115
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31827012C2semidirect
2. C4×#17985391C2semidirect
3. #31826791C2semidirect
4. #31826787C2semidirect
5. #31826749C2semidirect
6. #31826743C2semidirect
7. #31826664C2semidirect
8. #31826658C2semidirect
9. #31826611C2semidirect
10. #31826607C2semidirect
11. #31826575C2semidirect
12. #31826567C2semidirect
13. #31826565C2semidirect
14. #31826520C2semidirect
15. #442×C283C2semidirect
113. Dic566#41semidirect
141. D4×C283#41semidirect
183. C283#3115semidirect
196. #442D283semidirect
310. D4#17985392semidirect

Maximal subgroups

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

subgroupindex
#318270122
C4×#179853912
#318267912
#318267872
#318267492
#318267432
#318266642
#318266582
#318266112
#318266072
#318265752
#318265672
#318265652
#318265202
#442×C2832
#3115283