Finite Group Databasebeta

← #49133924

Subgroups — #49133924

Order 36224.

362 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827198C211yesmaximal, characteristic, complemented
2#31827171C211yesmaximal, characteristic, complemented
3#31826822C211yesmaximal, characteristic, complemented
4#31826818C211yesmaximal, characteristic, complemented
5#31826810C211yesmaximal, characteristic, complemented
6#31826764C211yesmaximal, characteristic, complemented
7#31826759C211yesmaximal, characteristic, complemented
8#31826681C211yesmaximal, characteristic, complemented
9#31826679C211yesmaximal, characteristic, complemented
10#31826659C211yesmaximal, characteristic
11#31826589C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826547C211yesmaximal, characteristic, complemented
14C4×#17985377C211yesmaximal, characteristic, complemented
15#478×C283C211yesmaximal, characteristic, complemented
16C2×#17985381C2211yescharacteristic
17C2×D2264C2211yescharacteristic
18C2×#17985377C2211yescharacteristic
19#22583609C2211yescharacteristic
20#22583606C2211yescharacteristic
21#22583601C2211yescharacteristic
22#22583598C2211yescharacteristic
23#22583597C2211yescharacteristic
24#22583596—21no—
25#22583593—21no—
26#22583592—21no—
27#22583590—21no—
28#22583588—21no—
29#22583588—21no—
30C4×Dic566C2211yescharacteristic
31#22583575C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33#22583572C2211yescharacteristic
34#22583572C2211yescharacteristic
35#22583572C2211yescharacteristic
36C4×C22⋊D283—21no—
37C4⋊C4×D283—21no—
38#22583543C2211yescharacteristic
39Dic283⋊C8C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41#22583535C2211yescharacteristic
42#22583533C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49C4×C283⋊C8C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566D411yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70#17985381—22no—
71D2264—22no—
72#17985377—22no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283—21no—
76C4⋊Dic283D411yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83C22⋊Dic283—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×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C2×D4×C283C2311yescharacteristic
95C22×C4×C283—21no—
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283—21no—
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C42×C283C2311yescharacteristic
105C22×D283—21no—
106C22×D283—21no—
107Dic566—22no—
108Dic566—21no—
109Dic566—21no—
110Dic566—81no—
111D1132—21no—
112D1132—21no—
113D1132—21no—
114D1132#4112yes—
115C22⋊D283—42no—
116C22⋊D283—81no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—42no—
124C4×D283—81no—
125C4×D283—81no—
126C4×D283—81no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129C23×C283—21no—
130D4×C283—21no—
131D4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—81no—
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—21no—
141C22×C283—41no—
142C22×C283—41no—
143C22×C283—41no—
144C22×C283C22×D411yescharacteristic
145C2×D283—22no—
146C2×D283—41no—
147C2×D283—41no—
148C2×D283—41no—
149C2×D283—41no—
150C2×D283—41no—
151C4×C283—21no—
152C4×C283—21no—
153C4×C283—41no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283C2×#4111yescharacteristic
157C4×C2832−1+411yescharacteristic
158Dic283—21no—
159Dic283—21no—
160Dic283—21no—
161Dic283—41no—
162Dic283—41no—
163Dic283#13512yes—
164C2×C283—81no—
165C2×C283#54811yescharacteristic
166C2×C283C2×#13511yescharacteristic
167C2×C283#57611yescharacteristic
168D283—42no—
169D283—81no—
170C283#336111yescharacteristic, complemented, Sylow
171#3361—2831nomaximal, Sylow
172#559—2831no—
173#554—2831no—
174#488—2831no—
175#488—2831no—
176#486—2831no—
177#478—2831no—
178#478D28311yescharacteristic, complemented
179#477—2831no—
180#463—2831no—
181#463—2831no—
182#459—2831no—
183C8×Q8—2831no—
184C4×SD16—2831no—
185C4×D8—2831no—
186C4×D8—2831no—
187C2×SD16—2831no—
188C2×D8—2831no—
189C2×D8—2831no—
190C4⋊Q8—2831no—
191#127—2831no—
192#125—2831no—
193#125C2×D28311yescharacteristic
194#124—2831no—
195#124—2831no—
196#124—5661no—
197#123—5661no—
198#123—5661no—
199C22⋊Q8—5661no—
200C22⋊Q8—5661no—
201C22⋊Q8—5661no—
202C4×Q8—2831no—
203C4×Q8—2831no—
204C4×D4—2831no—
205C4×D4—2831no—
206C4×D4—2831no—
207C4×D4—2831no—
208C4×D4—5661no—
209C4×D4C2×D28311yescharacteristic
210C2×C4⋊C4—5661no—
211#107—2831no—
212#107C2×D28311yescharacteristic
213#106C2×D28311yescharacteristic
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216C4⋊C8C2×D28311yescharacteristic
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#102—2831no—
221#102—2831no—
222#102—2831no—
223#102—2831no—
224#102—2831no—
225#102C2×D28311yescharacteristic
226#102C2×D28311yescharacteristic
227C4×C8—2831no—
228C4×C8—2831no—
229C4×C8—2831no—
230C2×Q8—2831no—
231C2×Q8—2831no—
232C2×Q8—5661no—
233C2×D4—2831no—
234C2×D4—2831no—
235C2×D4—5661no—
236C2×D4—5661no—
237C2×D4C22×D28311yescharacteristic
238C22×C4—21no—
239C22×C4—5661no—
240C22×C4—5661no—
241C22×C4—5661no—
242C22×C4—5661no—
243SD16—5662no—
244D8—5662no—
245D8—5662no—
246C2×C8—2831no—
247C2×C8—2831no—
248C2×C8C22×D28311yescharacteristic
249C2×C8C22×D28311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—2831no—
253C4⋊C4—2831no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4C22×D28311yescharacteristic
261C4⋊C4C22×D28311yescharacteristic
262C4⋊C4C22×D28311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—5661no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C42—2831no—
273C42—2831no—
274C42—5661no—
275C42C22×D28311yescharacteristic
276C23—21no—
277C23—5661no—
278C23—5661no—
279Q8—5662no—
280Q8—5661no—
281Q8—5661no—
282Q8—22641no—
283D4—21no—
284D4—21no—
285D4—2832no—
286D4—5661no—
287D4—5661no—
288D4—5661no—
289D4—11322no—
290D4—22641no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—2831no—
296C2×C4—2831no—
297C2×C4—2831no—
298C2×C4—2831no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—11322no—
302C2×C4—22641no—
303C2×C4—22641no—
304C2×C4—22641no—
305C2×C4D4×D28311yescharacteristic
306C2×C4D4×D28311yescharacteristic
307C2×C4C23×D28311yescharacteristic
308C8—21no—
309C8—21no—
310C8—5661no—
311C8—5661no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—5662no—
316C22—11321no—
317C22—11321no—
318C22—11321no—
319C22—11321no—
320C22—11321no—
321C22C2×D4×D28311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2832no—
328C4—5661no—
329C4—5661no—
330C4—5661no—
331C4—11321no—
332C4—11321no—
333C4#41×D28311yescharacteristic
334C4#2258365811yescharacteristic
335C2—81no—
336C2—11322no—
337C2—22641no—
338C2#3182712511yescharacteristic
339C2#135×D28311yescharacteristic
340C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#478×C283C2
socleC22×C283C22×D4
prime radical#31826659C2
hypercenter#478D283
hypocenterC283#3361
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31827198C2semidirect
2. #31827171C2semidirect
3. #31826822C2semidirect
4. #31826818C2semidirect
5. #31826810C2semidirect
6. #31826764C2semidirect
7. #31826759C2semidirect
8. #31826681C2semidirect
9. #31826679C2semidirect
11. #31826589C2semidirect
12. #31826552C2semidirect
13. #31826547C2semidirect
14. C4×#17985377C2semidirect
15. #478×C283C2semidirect
170. C283#3361semidirect
178. #478D283semidirect

Maximal subgroups

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

subgroupindex
#318271982
#318271712
#318268222
#318268182
#318268102
#318267642
#318267592
#318266812
#318266792
#318266592
#318265892
#318265522
#318265472
C4×#179853772
#478×C2832
#3361283