Finite Group Databasebeta

← #49131621

Subgroups — #49131621

Order 36224.

372 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#31827092C211yesmaximal, characteristic, complemented
2#31827040C211yesmaximal, characteristic
3#31826833C211yesmaximal, characteristic, complemented
4#31826832C211yesmaximal, characteristic, complemented
5#31826827C211yesmaximal, characteristic, complemented
6#31826826C211yesmaximal, characteristic, complemented
7#31826821C211yesmaximal, characteristic, complemented
8#31826820C211yesmaximal, characteristic, complemented
9#31826814C211yesmaximal, characteristic, complemented
10#31826472C211yesmaximal, characteristic, complemented
11#31826465C211yesmaximal, characteristic
12#31826460C211yesmaximal, characteristic
13#103×D283C211yesmaximal, characteristic, complemented
14#31826419C211yesmaximal, characteristic, complemented
15#487×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583608—21no—
22#22583608C2211yescharacteristic
23#22583602C2211yescharacteristic
24#22583601C2211yescharacteristic
25#22583600—21no—
26#22583599C2211yescharacteristic
27#22583598C2211yescharacteristic
28#22583595—21no—
29#22583595—21no—
30#22583588—21no—
31#22583588—21no—
32#22583588—21no—
33#22583586—21no—
34#22583568C2211yescharacteristic
35#22583567C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37#22583535C2211yescharacteristic
38#22583535C2211yescharacteristic
39#22583534C2211yescharacteristic
40#22583534C2211yescharacteristic
41#22583534C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583521C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C4⋊Q8×C283C2211yescharacteristic
53C4⋊Q8×C283C2211yescharacteristic
54#103×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—22no—
61C2×Dic566—21no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283—22no—
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×C4×D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283C2311yescharacteristic
72#17985375—22no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C8×D283—22no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4D411yescharacteristic
87Dic283⋊C4D411yescharacteristic
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
94(C2×D283)⋊C4D411yescharacteristic
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283—21no—
98C2×Q8×C283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283—21no—
104C4⋊C4×C283—21no—
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566—21no—
112Dic566—42no—
113Dic566—81no—
114D1132—21no—
115D1132—21no—
116D1132—42no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—42no—
124C4×D283—42no—
125C4×D283—81no—
126C4×D283#4112yes—
127C4×D283#4112yes—
128C283⋊C8—21no—
129C283⋊C8—21no—
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—81no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2411yescharacteristic
142C8×C283—21no—
143C8×C283—21no—
144C22×C283C22×D411yescharacteristic
145C2×D283—21no—
146C2×D283—21no—
147C2×D283—41no—
148C2×D283—41no—
149C2×D283—41no—
150C2×D283#12412yes—
151C4×C283—21no—
152C4×C283—21no—
153C4×C283—41no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283C2×#4111yescharacteristic
158C4×C283C2×#4111yescharacteristic
159Dic283—21no—
160Dic283—21no—
161Dic283—41no—
162Dic283—41no—
163Dic283—41no—
164Dic283#12412yes—
165C2×C283C2×#12411yescharacteristic
166C2×C283#57711yescharacteristic
167C2×C283#57811yescharacteristic
168D283—22no—
169D283—81no—
170C283#313711yescharacteristic, complemented, Sylow
171#3137—2831nomaximal, Sylow
172#544—2831no—
173#536—2831no—
174#491—2831no—
175#491—2831no—
176#489—2831no—
177#489—2831no—
178#488—2831no—
179#488—2831no—
180#487—2831no—
181#487D28311yescharacteristic, complemented
182#419—2831no—
183#417—2831no—
184#416—2831no—
185C2×#103—2831no—
186#405—2831no—
187C2×#41—2831no—
188C22×Q8—2831no—
189C2×M16—2831no—
190C22×C8—2831no—
191C4⋊Q8—2831no—
192C4⋊Q8—2831no—
193C4⋊Q8—5661no—
194C4⋊Q8C2×D28311yescharacteristic
195C4⋊Q8C2×D28311yescharacteristic
196#125—2831no—
197#125—2831no—
198#125—5661no—
199#124—2831no—
200#124—2831no—
201#123—5661no—
202#123—5661no—
203C22⋊Q8—5661no—
204C22⋊Q8—5661no—
205C22⋊Q8—5661no—
206C22⋊Q8—5661no—
207#117—2831no—
208#117—2831no—
209C2×C4⋊C4—2831no—
210#103—2831no—
211#103—2831no—
212#103—2831no—
213#103—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103—2831no—
218#103C2×D28311yescharacteristic
219#103C2×D28311yescharacteristic
220#103C2×D28311yescharacteristic
221#103C2×D28311yescharacteristic
222#102—2831no—
223#102—2831no—
224#102—2831no—
225#102—2831no—
226#97—2831no—
227#97—2831no—
228C4×C8—2831no—
229C4×C8C2×D28311yescharacteristic
230#41—5662no—
231#41—5662no—
232C2×Q8—21no—
233C2×Q8—2831no—
234C2×Q8—5661no—
235C2×Q8—5661no—
236C2×Q8—5662no—
237C2×Q8—5662no—
238C2×Q8C22×D28311yescharacteristic
239C2×Q8C22×D28311yescharacteristic
240C2×D4—2831no—
241C2×D4—5661no—
242C22×C4—2831no—
243C22×C4—5661no—
244C22×C4—5661no—
245C22×C4—5661no—
246M16—5662no—
247C2×C8—2831no—
248C2×C8—2831no—
249C2×C8—5662no—
250C2×C8C22×D28311yescharacteristic
251C2×C8C22×D28311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—2831no—
270C22⋊C4—2831no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—2831no—
277C42—5661no—
278C42C22×D28311yescharacteristic
279C23—2831no—
280C23—5661no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—81no—
286Q8—5661no—
287Q8—5661no—
288Q8—11322no—
289Q8—22641no—
290D4—5661no—
291D4—5661no—
292D4—11322no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—2831no—
298C2×C4—2832no—
299C2×C4—2832no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—11322no—
306C2×C4—11322no—
307C2×C4—22641no—
308C2×C4D4×D28311yescharacteristic
309C2×C4D4×D28311yescharacteristic
310C2×C4C23×D28311yescharacteristic
311C8—21no—
312C8—21no—
313C8—5661no—
314C8—5661no—
315C22—2832no—
316C22—5661no—
317C22—5661no—
318C22—11321no—
319C22—11321no—
320C22—11321no—
321C22C2×D4×D28311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—2832no—
329C4—5661no—
330C4—5661no—
331C4—11321no—
332C4—11321no—
333C4—11321no—
334C4#41×D28311yescharacteristic
335C4#41×D28311yescharacteristic
336C2—5662no—
337C2—22641no—
338C2#124×D28311yescharacteristic
339C2#3182727111yescharacteristic
340C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#487×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985393C22
hypercenter#487D283
hypocenterC283#3137
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #31827092C2semidirect
3. #31826833C2semidirect
4. #31826832C2semidirect
5. #31826827C2semidirect
6. #31826826C2semidirect
7. #31826821C2semidirect
8. #31826820C2semidirect
9. #31826814C2semidirect
10. #31826472C2semidirect
13. #103×D283C2semidirect
14. #31826419C2semidirect
15. #487×C283C2semidirect
170. C283#3137semidirect
181. #487D283semidirect

Maximal subgroups

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

subgroupindex
#318270922
#318270402
#318268332
#318268322
#318268272
#318268262
#318268212
#318268202
#318268142
#318264722
#318264652
#318264602
#103×D2832
#318264192
#487×C2832
#3137283