Finite Group Databasebeta

← #49131436

Subgroups — #49131436

Order 36224.

386 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#31827002C211yesmaximal, characteristic
2C4×Q8×D283C211yesmaximal, characteristic, complemented
3#31826799C211yesmaximal, characteristic, complemented
4#31826785C211yesmaximal, characteristic
5#31826775C211yesmaximal, characteristic, complemented
6#31826774C211yesmaximal, characteristic, complemented
7#31826690C211yesmaximal, characteristic, complemented
8#31826689C211yesmaximal, characteristic, complemented
9#31826619C211yesmaximal, characteristic, complemented
10#31826605C211yesmaximal, characteristic
11#31826570C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13#31826563C211yesmaximal, characteristic, complemented
14#31826520C211yesmaximal, characteristic, complemented
15#441×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20#22583605—21no—
21#22583601C2211yescharacteristic
22#22583599C2211yescharacteristic
23#22583595—21no—
24#22583586C2211yescharacteristic
25#22583585C2211yescharacteristic
26Q8×Dic283C2211yescharacteristic
27C4×Dic566—21no—
28C4×Dic566C2211yescharacteristic
29#22583575—21no—
30#22583575C2211yescharacteristic
31C4×D1132—21no—
32C4×D1132C2211yescharacteristic
33#22583567—21no—
34C4⋊C4×D283—21no—
35C4⋊C4×D283C2211yescharacteristic
36C42×D283—21no—
37C42×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61Q8×D283—22no—
62Q8×D283—22no—
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283D411yescharacteristic
69C2×C4×D283D411yescharacteristic
70C2×C4×D283C2311yescharacteristic
71#17985382—22no—
72#17985381—22no—
73#17985379—22no—
74C2×C283⋊C8C2311yescharacteristic
75C2×C283⋊C8C2311yescharacteristic
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊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—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283D411yescharacteristic
94C4×Dic283D411yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98Q16×C283—22no—
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C42×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—24no—
111Dic566—21no—
112Dic566#4112yes—
113D1132—21no—
114D1132—21no—
115D1132—42no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—24no—
123C4×D283—22no—
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—41no—
127C4×D283—42no—
128C4×D283—42no—
129C283⋊C8—21no—
130C283⋊C8—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283#4112yes—
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#13712yes—
151C4×C283—22no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283C2×#4111yescharacteristic
158C4×C283C2×#4111yescharacteristic
159Dic283—22no—
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165C2×C283#52511yescharacteristic
166C2×C283C2×#13711yescharacteristic
167C2×C283#57511yescharacteristic
168D283—22no—
169D283—81no—
170C283#311711yescharacteristic, complemented, Sylow
171#3117—2831nomaximal, Sylow
172#529—2831no—
173C2×C4×Q8—2831no—
174#484—2831no—
175#481—2831no—
176#479—2831no—
177#479—2831no—
178#464—2831no—
179#464—2831no—
180#451—2831no—
181#448—2831no—
182#441—2831no—
183#441D28311yescharacteristic, complemented
184#440—2831no—
185#440—2831no—
186#432—2831no—
187C22×Q8—2831no—
188C2×Q16—2831no—
189C2×Q16C2×D28311yescharacteristic
190C2×SD16—2831no—
191C2×SD16—2831no—
192#126—5661no—
193#125—2831no—
194#124—2831no—
195#123—5661no—
196C22⋊Q8—2831no—
197#121—2831no—
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—5661no—
202C4×Q8—5661no—
203C4×Q8C2×D28311yescharacteristic
204C4×Q8C2×D28311yescharacteristic
205C4×D4—2831no—
206C4×D4—5661no—
207#117—5661no—
208C2×C4⋊C4—2831no—
209C2×C4⋊C4—5661no—
210C2×C42—2831no—
211C2×C42—5661no—
212#107—2831no—
213#107—2831no—
214#106—2831no—
215#106C2×D28311yescharacteristic
216C4⋊C8—2831no—
217C4⋊C8—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#103—2831no—
222#103C2×D28311yescharacteristic
223#103C2×D28311yescharacteristic
224#102—2831no—
225#102—2831no—
226C22⋊C8—2831no—
227C22⋊C8—2831no—
228#97—2831no—
229#97C2×D28311yescharacteristic
230C2×Q8—2831no—
231C2×Q8—5661no—
232C2×Q8—5662no—
233C2×Q8—5662no—
234C2×Q8C22×D28311yescharacteristic
235C2×Q8C22×D28311yescharacteristic
236C2×D4—2831no—
237C2×D4—5661no—
238C22×C4—2831no—
239C22×C4—2831no—
240C22×C4—2831no—
241C22×C4—5661no—
242C22×C4—5661no—
243C22×C4—5661no—
244Q16—22no—
245Q16—5662no—
246SD16—5662no—
247SD16—5662no—
248C2×C8—2831no—
249C2×C8—2831no—
250C2×C8C22×D28311yescharacteristic
251C2×C8C22×D28311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4C22×D28311yescharacteristic
264C4⋊C4C22×D28311yescharacteristic
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C42—21no—
271C42—21no—
272C42—2831no—
273C42—2831no—
274C42—2831no—
275C42—5661no—
276C42—5661no—
277C42—5661no—
278C42C22×D28311yescharacteristic
279C23—2831no—
280C23—5661no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—2832no—
285Q8—5664no—
286Q8—5661no—
287Q8#1798539212yes—
288D4—5661no—
289D4—5661no—
290D4—11322no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2831no—
296C2×C4—2831no—
297C2×C4—2831no—
298C2×C4—5662no—
299C2×C4—5664no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—11321no—
306C2×C4—11322no—
307C2×C4—11322no—
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—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—5661no—
329C4—5662no—
330C4—5661no—
331C4—5661no—
332C4—11321no—
333C4—11321no—
334C4#41×D28311yescharacteristic
335C4C2×#1798539211yescharacteristic
336C2—5662no—
337C2—22641no—
338C2#3182697411yescharacteristic
339C2#137×D28311yescharacteristic
340C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radical#22583585C22
hypercenter#441D283
hypocenterC283#3117
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D283C2semidirect
3. #31826799C2semidirect
5. #31826775C2semidirect
6. #31826774C2semidirect
7. #31826690C2semidirect
8. #31826689C2semidirect
9. #31826619C2semidirect
11. #31826570C2semidirect
12. #31826567C2semidirect
13. #31826563C2semidirect
14. #31826520C2semidirect
15. #441×C283C2semidirect
170. C283#3117semidirect
183. #441D283semidirect

Maximal subgroups

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

subgroupindex
#318270022
C4×Q8×D2832
#318267992
#318267852
#318267752
#318267742
#318266902
#318266892
#318266192
#318266052
#318265702
#318265672
#318265632
#318265202
#441×C2832
#3117283