Finite Group Databasebeta

← #49131479

Subgroups — #49131479

Order 36224.

372 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#31827073C211yesmaximal, characteristic, complemented
2#31826944C211yesmaximal, characteristic
3#31826802C211yesmaximal, characteristic, complemented
4#31826794C211yesmaximal, characteristic, complemented
5#31826771C211yesmaximal, characteristic, complemented
6#31826767C211yesmaximal, characteristic, complemented
7#31826674C211yesmaximal, characteristic, complemented
8#31826668C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic
10#31826624C211yesmaximal, characteristic
11#31826573C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985380C211yesmaximal, characteristic, complemented
14#31826527C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20#22583608C2211yescharacteristic
21#22583605—21no—
22#22583604—21no—
23#22583602—21no—
24#22583601C2211yescharacteristic
25#22583600—21no—
26#22583590C2211yescharacteristic
27#22583586C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×Dic566C2211yescharacteristic
30#22583575C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583567C2211yescharacteristic
35#22583566—21no—
36C2×Dic283⋊C4—21no—
37C4⋊C4×D283C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583531C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—22no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×C22⋊D283—21no—
64C22×Dic283—21no—
65C22×Dic283—21no—
66C2×C4×D283—21no—
67C2×C4×D283C2311yescharacteristic
68Dic1132—22no—
69#17985382—22no—
70#17985380—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86Dic283⋊C4D411yescharacteristic
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4D411yescharacteristic
91(C2×D283)⋊C4D411yescharacteristic
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99SD16×C283—22no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283C2×D411yescharacteristic
109Dic566—21no—
110Dic566—21no—
111Dic566—21no—
112Dic566#4112yes—
113C22⋊D283—24no—
114C2×Dic283—24no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—81no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—21no—
124C4×D283—21no—
125C4×D283—81no—
126C283⋊C8—21no—
127C283⋊C8—21no—
128C23×C283—21no—
129Q8×C283—21no—
130Q8×C283—21no—
131D4×C283—21no—
132D4×C283#4112yes—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—81no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2411yescharacteristic
140C8×C283—21no—
141C8×C283—21no—
142C22×C283—22no—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283C22×D411yescharacteristic
146C2×D283—21no—
147C2×D283—21no—
148C2×D283—21no—
149C4×C283—21no—
150C4×C283—21no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283C2×#4111yescharacteristic
155C4×C283C2×#4111yescharacteristic
156Dic283—21no—
157Dic283—22no—
158Dic283—21no—
159Dic283—21no—
160Dic283—41no—
161Dic283—41no—
162Dic283—41no—
163C2×C283—42no—
164C2×C283#52511yescharacteristic
165C2×C283#57711yescharacteristic
166C2×C283#57811yescharacteristic
167D283—41no—
168C283#312011yescharacteristic, complemented, Sylow
169#3120—2831nomaximal, Sylow
170#541—2831no—
171#520—2831no—
172#484—2831no—
173#483—2831no—
174#479—2831no—
175#478—2831no—
176#462—2831no—
177#461—2831no—
178#452—2831no—
179#452—2831no—
180#441—2831no—
181#440D28311yescharacteristic, complemented
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433—2831no—
185C2×#41—2831no—
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×SD16—2831no—
189C2×SD16C2×D28311yescharacteristic
190C4⋊Q8—2831no—
191#126—5661no—
192#126—5661no—
193#125—2831no—
194#125—5661no—
195#125—5661no—
196C22⋊Q8—2831no—
197C22⋊Q8—2831no—
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8C2×D28311yescharacteristic
202C4×D4—2831no—
203C4×D4—5661no—
204C4×D4—5661no—
205C4×D4C2×D28311yescharacteristic
206#117—2831no—
207#117—5661no—
208C2×C4⋊C4—2831no—
209C2×C4⋊C4—5661no—
210#107—2831no—
211#107C2×D28311yescharacteristic
212#106—2831no—
213#106—2831no—
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#103C2×D28311yescharacteristic
222#102—2831no—
223#102C2×D28311yescharacteristic
224C22⋊C8—2831no—
225C22⋊C8—2831no—
226#97C2×D28311yescharacteristic
227C4×C8—2831no—
228#41—5662no—
229#41—5662no—
230C2×Q8—2831no—
231C2×Q8—2831no—
232C2×Q8C22×D28311yescharacteristic
233C2×D4—5661no—
234C2×D4C22×D28311yescharacteristic
235C22×C4—21no—
236C22×C4—2831no—
237C22×C4—5661no—
238C22×C4—5661no—
239C22×C4—5661no—
240Q16—5662no—
241Q16—5662no—
242SD16—22no—
243SD16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—2831no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
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—21no—
266C22⋊C4—2831no—
267C22⋊C4—2831no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C42—21no—
272C42—2831no—
273C42—5661no—
274C42—5661no—
275C42—5661no—
276C42C22×D28311yescharacteristic
277C23—21no—
278C23—2831no—
279Q8—21no—
280Q8—21no—
281Q8—2832no—
282Q8—5661no—
283Q8—5661no—
284Q8—5661no—
285D4—21no—
286D4—5664no—
287D4#1798539212yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—2831no—
293C2×C4—2831no—
294C2×C4—2831no—
295C2×C4—5664no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—22641no—
303C2×C4—22641no—
304C2×C4D4×D28311yescharacteristic
305C2×C4D4×D28311yescharacteristic
306C2×C4C23×D28311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5661no—
310C8—5661no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—5661no—
315C22—5661no—
316C22—5661no—
317C22C2×D4×D28311yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—5661no—
324C4—5662no—
325C4—5661no—
326C4—5661no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4#41×D28311yescharacteristic
331C4C2×#1798539211yescharacteristic
332C2—42no—
333C2—11321no—
334C2#3182697411yescharacteristic
335C2#3182727511yescharacteristic
336C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985391C22
hypercenter#440D283
hypocenterC283#3120
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31827073C2semidirect
3. #31826802C2semidirect
4. #31826794C2semidirect
5. #31826771C2semidirect
6. #31826767C2semidirect
7. #31826674C2semidirect
8. #31826668C2semidirect
11. #31826573C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985380C2semidirect
14. #31826527C2semidirect
15. #440×C283C2semidirect
168. C283#3120semidirect
181. #440D283semidirect

Maximal subgroups

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

subgroupindex
#318270732
#318269442
#318268022
#318267942
#318267712
#318267672
#318266742
#318266682
#318266282
#318266242
#318265732
C4×#179853822
C4×#179853802
#318265272
#440×C2832
#3120283