Finite Group Databasebeta

← #49131492

Subgroups — #49131492

Order 36224.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827086C211yesmaximal, characteristic
2#31826942C211yesmaximal, characteristic, complemented
3#31826807C211yesmaximal, characteristic, complemented
4#31826790C211yesmaximal, characteristic
5#31826761C211yesmaximal, characteristic, complemented
6#31826751C211yesmaximal, characteristic, complemented
7#31826688C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826623C211yesmaximal, characteristic, complemented
10#31826606C211yesmaximal, characteristic
11#31826573C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13C4×Dic1132C211yesmaximal, characteristic, complemented
14C4×#17985381C211yesmaximal, characteristic, complemented
15#433×C283C211yesmaximal, characteristic, complemented
16C22×Dic566C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583605—21no—
23#22583598C2211yescharacteristic
24#22583596—21no—
25#22583592—21no—
26#22583589C2211yescharacteristic
27#22583588—21no—
28#22583584C2211yescharacteristic
29C4×Dic566C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31C4×Dic566C2211yescharacteristic
32C4×Dic566C2211yescharacteristic
33C4×Dic566C2211yescharacteristic
34#22583575—21no—
35#22583575—21no—
36C4×D1132C2211yescharacteristic
37#22583569C2211yescharacteristic
38#22583566—21no—
39#22583566—21no—
40#22583544C2211yescharacteristic
41#22583544C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583542C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583535C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52#117×C283C2211yescharacteristic
53C4⋊C8×C283C2211yescharacteristic
54C4⋊C8×C283C2211yescharacteristic
55C22⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57#97×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566—22no—
60C2×Dic566—22no—
61C2×Dic566—21no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
69C2×C4×D283—21no—
70Dic1132—22no—
71Dic1132—22no—
72#17985381—22no—
73#17985381—22no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—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×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C22×C4×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283D411yescharacteristic
103C4⋊C4×C283D411yescharacteristic
104C22⋊C4×C283D411yescharacteristic
105C22⋊C4×C283D411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—24no—
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—81no—
115Dic566#4112yes—
116Dic566#4112yes—
117D1132—21no—
118D1132—21no—
119C22⋊D283—81no—
120C2×Dic283—24no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C4×D283—81no—
129C23×C283C2×D411yescharacteristic
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283C2×D411yescharacteristic
133C2×C4×C283C2×D411yescharacteristic
134C2×C4×C283C2×D411yescharacteristic
135C2×C4×C283C2×D411yescharacteristic
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2411yescharacteristic
138C8×C283—21no—
139C8×C283—21no—
140C8×C283—21no—
141C8×C283—21no—
142C22×C283—21no—
143C22×C283—21no—
144C22×C283—21no—
145C22×C283C22×D411yescharacteristic
146C2×D283—41no—
147C2×D283—41no—
148C2×D283—41no—
149C4×C283—21no—
150C4×C283—21no—
151C4×C283—21no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283C2×#4111yescharacteristic
155C4×C283C2×#4111yescharacteristic
156Dic283—22no—
157Dic283—22no—
158Dic283—41no—
159Dic283—41no—
160Dic283—41no—
161Dic283—41no—
162Dic283—41no—
163C2×C283—41no—
164C2×C283#52511yescharacteristic
165C2×C283#57711yescharacteristic
166C2×C283#57811yescharacteristic
167D283—81no—
168C283#312111yescharacteristic, complemented, Sylow
169#3121—2831nomaximal, Sylow
170#542—2831no—
171#519—2831no—
172#485—2831no—
173#482—2831no—
174#477—2831no—
175#475—2831no—
176#464—2831no—
177#464—2831no—
178#451—2831no—
179#448—2831no—
180#441—2831no—
181#440—2831no—
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433D28311yescharacteristic, complemented
185C22×Q8—2831no—
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×SD16—2831no—
189C2×SD16—2831no—
190C4⋊Q8—2831no—
191#126—5661no—
192#124—2831no—
193#124—5661no—
194#123—5661no—
195C22⋊Q8—2831no—
196C22⋊Q8—5661no—
197#121—2831no—
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—2831no—
202C4×Q8—2831no—
203C4×Q8—5661no—
204C4×Q8—5661no—
205C4×D4—2831no—
206#117—2831no—
207#117—5661no—
208#117—5661no—
209#117C2×D28311yescharacteristic
210#107—2831no—
211#107—2831no—
212#106—2831no—
213#106—2831no—
214C4⋊C8C2×D28311yescharacteristic
215C4⋊C8C2×D28311yescharacteristic
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#103—2831no—
222#102—2831no—
223#102—2831no—
224C22⋊C8C2×D28311yescharacteristic
225C22⋊C8C2×D28311yescharacteristic
226#97C2×D28311yescharacteristic
227C4×C8C2×D28311yescharacteristic
228C2×Q8—2831no—
229C2×Q8—2831no—
230C2×Q8—2831no—
231C2×Q8—5662no—
232C2×Q8—5662no—
233C2×Q8—5661no—
234C2×Q8—5661no—
235C2×D4—2831no—
236C2×D4—5661no—
237C22×C4—5661no—
238C22×C4—5661no—
239C22×C4C22×D28311yescharacteristic
240Q16—5662no—
241Q16—5662no—
242SD16—5662no—
243SD16—5662no—
244C2×C8C22×D28311yescharacteristic
245C2×C8C22×D28311yescharacteristic
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—2831no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4D113211yescharacteristic
260C4⋊C4D113211yescharacteristic
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C22⋊C4—5661no—
264C22⋊C4—5661no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4D113211yescharacteristic
268C22⋊C4D113211yescharacteristic
269C42—5661no—
270C42—5661no—
271C42—5661no—
272C42—5661no—
273C42—5661no—
274C42—5661no—
275C42C22×D28311yescharacteristic
276C42C22×D28311yescharacteristic
277C23—5661no—
278C23C2×D113211yescharacteristic
279Q8—2832no—
280Q8—2832no—
281Q8—5664no—
282Q8—5661no—
283Q8—5661no—
284Q8—5661no—
285Q8—5661no—
286Q8—22641no—
287D4—5661no—
288D4—5661no—
289D4—22641no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—5664no—
293C2×C4—5661no—
294C2×C4—5661no—
295C2×C4—5661no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—22641no—
301C2×C4C2×D113211yescharacteristic
302C2×C4C2×D113211yescharacteristic
303C2×C4C2×D113211yescharacteristic
304C2×C4C2×D113211yescharacteristic
305C2×C4C2×D113211yescharacteristic
306C2×C4C23×D28311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—11321no—
315C22—11321no—
316C22—11321no—
317C22C22×D113211yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—5662no—
324C4—5662no—
325C4—11321no—
326C4—11321no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4#41×D28311yescharacteristic
331C4#41×D28311yescharacteristic
332C2—41no—
333C2—22641no—
334C2#3182697711yescharacteristic
335C2#3182727711yescharacteristic
336C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#433×C283C2
socleC22×C283C22×D4
prime radical#22583584C22
hypercenter#433D283
hypocenterC283#3121
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #31826942C2semidirect
3. #31826807C2semidirect
5. #31826761C2semidirect
6. #31826751C2semidirect
7. #31826688C2semidirect
8. #31826688C2semidirect
9. #31826623C2semidirect
11. #31826573C2semidirect
12. #31826567C2semidirect
13. C4×Dic1132C2semidirect
14. C4×#17985381C2semidirect
15. #433×C283C2semidirect
168. C283#3121semidirect
184. #433D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318269422
#318268072
#318267902
#318267612
#318267512
#318266882
#318266232
#318266062
#318265732
#318265672
C4×Dic11322
C4×#179853812
#433×C2832
#3121283