Finite Group Databasebeta

← #49134335

Subgroups — #49134335

Order 36224.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827189C211yesmaximal, characteristic, complemented
2#31827187C211yesmaximal, characteristic, complemented
3#31826858C211yesmaximal, characteristic, complemented
4#31826857C211yesmaximal, characteristic, complemented
5#31826850C211yesmaximal, characteristic
6#31826690C211yesmaximal, characteristic, complemented
7#31826689C211yesmaximal, characteristic, complemented
8#31826683C211yesmaximal, characteristic
9#31826681C211yesmaximal, characteristic
10#31826673C211yesmaximal, characteristic, complemented
11#31826594C211yesmaximal, characteristic, complemented
12#31826568C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14#31826557C211yesmaximal, characteristic, complemented
15#462×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21C2×#17985379C2211yescharacteristic
22C2×D2264C2211yescharacteristic
23#22583608C2211yescharacteristic
24#22583605—21no—
25#22583605—21no—
26#22583605—21no—
27#22583604—21no—
28#22583599C2211yescharacteristic
29#22583599C2211yescharacteristic
30#22583599C2211yescharacteristic
31#22583598C2211yescharacteristic
32#22583590—21no—
33#22583588—21no—
34Q8×Dic283C2211yescharacteristic
35Q8×Dic283C2211yescharacteristic
36C4×Dic566C2211yescharacteristic
37#22583575C2211yescharacteristic
38C4×D1132C2211yescharacteristic
39#22583572C2211yescharacteristic
40#22583568—21no—
41#22583567—21no—
42#22583543C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583521C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic
54C4⋊Q8×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566D411yescharacteristic
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C4×D283—21no—
64C2×C4×D283—21no—
65#17985382—22no—
66#17985382—41no—
67#17985381—41no—
68#17985379—22no—
69#17985379—22no—
70#17985379—41no—
71D2264—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283D411yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—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—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C4×Dic283C2311yescharacteristic
98C2×Q8×C283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101Q16×C283—41no—
102Q16×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283—21no—
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—41no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—42no—
127C4×D283—42no—
128C283⋊C8—21no—
129C283⋊C8#4112yes—
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135Q8×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283C22×D411yescharacteristic
146C2×D283—41no—
147C2×D283—41no—
148C2×D283—41no—
149C2×D283—41no—
150C2×D283—41no—
151C2×D283—41no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283C2×#4111yescharacteristic
159C4×C283H(5,𝔽2)11yescharacteristic
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—21no—
164Dic283—41no—
165Dic283—41no—
166C2×C283#55011yescharacteristic
167C2×C283#57511yescharacteristic
168C2×C283#57811yescharacteristic
169D283—81no—
170D283—81no—
171C283#340211yescharacteristic, complemented, Sylow
172#3402—2831nomaximal, Sylow
173#556—2831no—
174#556—2831no—
175#497—2831no—
176#497—2831no—
177#495—2831no—
178#464—2831no—
179#464—2831no—
180#463—2831no—
181#463—2831no—
182#462—2831no—
183#462D28311yescharacteristic, complemented
184#446—2831no—
185#440—2831no—
186#440—2831no—
187C4×Q16—2831no—
188C2×Q16—2831no—
189C2×Q16—2831no—
190C2×Q16C2×D28311yescharacteristic
191C2×Q16C2×D28311yescharacteristic
192C2×SD16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×SD16—2831no—
196C2×D8—2831no—
197C4⋊Q8—2831no—
198C4⋊Q8C2×D28311yescharacteristic
199#126—5661no—
200#126—5661no—
201#126—5661no—
202#126—5661no—
203#124—2831no—
204#124—2831no—
205#124—2831no—
206#124—2831no—
207C22⋊Q8—5661no—
208C22⋊Q8—5661no—
209C4×Q8—2831no—
210C4×Q8—2831no—
211C4×Q8—2831no—
212C4×Q8—2831no—
213C4×Q8C2×D28311yescharacteristic
214C4×D4—2831no—
215C4×D4—2831no—
216#117—5661no—
217#117—5661no—
218#107—2831no—
219C4⋊C8—2831no—
220C4⋊C8—2831no—
221C4⋊C8C2×D28311yescharacteristic
222#103—2831no—
223#103—2831no—
224#103C2×D28311yescharacteristic
225#103C2×D28311yescharacteristic
226#102—2831no—
227#102—2831no—
228#97—2831no—
229#97—2831no—
230C4×C8—2831no—
231C2×Q8—2831no—
232C2×Q8—2831no—
233C2×Q8C22×D28311yescharacteristic
234C2×Q8C22×D28311yescharacteristic
235C2×Q8C22×D28311yescharacteristic
236C2×D4—2831no—
237C2×D4—2831no—
238C22×C4—5661no—
239C22×C4—5661no—
240Q16—41no—
241Q16—41no—
242Q16—5662no—
243Q16—11321no—
244SD16—5662no—
245SD16—5662no—
246SD16—11321no—
247SD16—11321no—
248D8—11321no—
249C2×C8—2831no—
250C2×C8—2831no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4C22×D28311yescharacteristic
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—21no—
277C42—2831no—
278C42—2831no—
279C42—5661no—
280C42—5661no—
281C42—5661no—
282C42C22×D28311yescharacteristic
283C23—5661no—
284C23—5661no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—5661no—
292Q8—5661no—
293Q8—11321no—
294D4—5661no—
295D4—5661no—
296D4—5661no—
297D4—5661no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—2831no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—2831no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—11322no—
309C2×C4—11322no—
310C2×C4D4×D28311yescharacteristic
311C2×C4D4×D28311yescharacteristic
312C2×C4C23×D28311yescharacteristic
313C8—21no—
314C8—21no—
315C8—2832no—
316C8—5661no—
317C22—11321no—
318C22—11321no—
319C22—11321no—
320C22—11321no—
321C22—11321no—
322C22—11321no—
323C22C2×D4×D28311yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—5661no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4#41×D28311yescharacteristic
337C4#2258365511yescharacteristic
338C2—22641no—
339C2—22641no—
340C2#3182713311yescharacteristic
341C2#3182726411yescharacteristic
342C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socleC22×C283C22×D4
prime radicalC2×D2264C22
hypercenter#462D283
hypocenterC283#3402
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #31827189C2semidirect
2. #31827187C2semidirect
3. #31826858C2semidirect
4. #31826857C2semidirect
6. #31826690C2semidirect
7. #31826689C2semidirect
10. #31826673C2semidirect
11. #31826594C2semidirect
12. #31826568C2semidirect
13. #31826563C2semidirect
14. #31826557C2semidirect
15. #462×C283C2semidirect
171. C283#3402semidirect
183. #462D283semidirect

Maximal subgroups

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

subgroupindex
#318271892
#318271872
#318268582
#318268572
#318268502
#318266902
#318266892
#318266832
#318266812
#318266732
#318265942
#318265682
#318265632
#318265572
#462×C2832
#3402283