Finite Group Databasebeta

← #49131473

Subgroups — #49131473

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#31826947C211yesmaximal, characteristic
3#31826799C211yesmaximal, characteristic, complemented
4#31826797C211yesmaximal, characteristic, complemented
5#31826774C211yesmaximal, characteristic, complemented
6#31826764C211yesmaximal, characteristic, complemented
7#31826673C211yesmaximal, characteristic, complemented
8#31826669C211yesmaximal, characteristic, complemented
9#31826630C211yesmaximal, characteristic
10#31826626C211yesmaximal, characteristic
11#31826567C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985379C211yesmaximal, characteristic, complemented
14#31826527C211yesmaximal, characteristic, complemented
15#441×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20#22583608C2211yescharacteristic
21#22583605—21no—
22#22583604—21no—
23#22583602—21no—
24#22583601C2211yescharacteristic
25#22583600—21no—
26#22583590C2211yescharacteristic
27#22583586C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29C4×Dic566C2211yescharacteristic
30C4×D1132—21no—
31C4×D1132C2211yescharacteristic
32#22583572—21no—
33#22583572C2211yescharacteristic
34#22583567—21no—
35#22583567C2211yescharacteristic
36C4⋊C4×D283—21no—
37C4⋊C4×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
51C4×C283⋊C8C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—22no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×C4×D283—21no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283—21no—
68C2×C4×D283C2311yescharacteristic
69#17985382—22no—
70#17985381—22no—
71#17985379—22no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
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⋊C4D411yescharacteristic
86Dic283⋊C4D411yescharacteristic
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
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—21no—
111Dic566—21no—
112D1132—24no—
113D1132—21no—
114D1132#4112yes—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283C2×D411yescharacteristic
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C4×D283—24no—
122C4×D283—21no—
123C4×D283—21no—
124C4×D283—81no—
125C4×D283—81no—
126C4×D283—81no—
127C283⋊C8—21no—
128C283⋊C8—21no—
129Q8×C283—21no—
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283#4112yes—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2411yescharacteristic
140C8×C283—21no—
141C8×C283—21no—
142C22×C283C22×D411yescharacteristic
143C2×D283—21no—
144C2×D283—22no—
145C2×D283—21no—
146C2×D283—21no—
147C2×D283—41no—
148C2×D283—41no—
149C4×C283—22no—
150C4×C283—21no—
151C4×C283—21no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283—41no—
155C4×C283C2×#4111yescharacteristic
156C4×C283C2×#4111yescharacteristic
157Dic283—21no—
158Dic283—21no—
159Dic283—21no—
160Dic283—41no—
161Dic283—41no—
162Dic283—41no—
163C2×C283#52511yescharacteristic
164C2×C283#57711yescharacteristic
165C2×C283#57811yescharacteristic
166D283—41no—
167D283—42no—
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#441D28311yescharacteristic, complemented
181#440—2831no—
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433—2831no—
185C2×#41—2831no—
186C2×Q16—2831no—
187C2×Q16C2×D28311yescharacteristic
188C2×SD16—2831no—
189C2×SD16—2831no—
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×Q8C2×D28311yescharacteristic
201C4×Q8C2×D28311yescharacteristic
202C4×D4—2831no—
203C4×D4—2831no—
204C4×D4—5661no—
205C4×D4—5661no—
206#117—2831no—
207#117—5661no—
208C2×C4⋊C4—2831no—
209C2×C4⋊C4—5661no—
210#107—2831no—
211#107—2831no—
212#106—2831no—
213#106C2×D28311yescharacteristic
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103C2×D28311yescharacteristic
221#103C2×D28311yescharacteristic
222#102—2831no—
223#102—2831no—
224C22⋊C8—2831no—
225C22⋊C8—2831no—
226#97C2×D28311yescharacteristic
227C4×C8—2831no—
228#41—5662no—
229#41—5662no—
230C2×Q8—2831no—
231C2×Q8C22×D28311yescharacteristic
232C2×Q8C22×D28311yescharacteristic
233C2×D4—2831no—
234C2×D4—5661no—
235C22×C4—2831no—
236C22×C4—5661no—
237C22×C4—5661no—
238C22×C4—5661no—
239C22×C4—5661no—
240Q16—22no—
241Q16—5662no—
242SD16—5662no—
243SD16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2831no—
251C4⋊C4—2831no—
252C4⋊C4—2831no—
253C4⋊C4—2831no—
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—2831no—
266C22⋊C4—2831no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C42—21no—
272C42—21no—
273C42—2831no—
274C42—5661no—
275C42—5661no—
276C42C22×D28311yescharacteristic
277C23—2831no—
278C23—5661no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—5661no—
283Q8—5661no—
284Q8#1798539212yes—
285D4—2832no—
286D4—5664no—
287D4—5661no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
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—22641no—
302C2×C4—22641no—
303C2×C4—22641no—
304C2×C4D4×D28311yescharacteristic
305C2×C4D4×D28311yescharacteristic
306C2×C4C23×D28311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5661no—
310C8—5661no—
311C22—5662no—
312C22—5661no—
313C22—5661no—
314C22—5661no—
315C22—11321no—
316C22—11321no—
317C22C2×D4×D28311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—5661no—
325C4—5661no—
326C4—5661no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4#41×D28311yescharacteristic
331C4C2×#1798539211yescharacteristic
332C2—11321no—
333C2—11322no—
334C2#3182697411yescharacteristic
335C2#3182727411yescharacteristic
336C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985393C22
hypercenter#441D283
hypocenterC283#3120
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
1. #31827073C2semidirect
3. #31826799C2semidirect
4. #31826797C2semidirect
5. #31826774C2semidirect
6. #31826764C2semidirect
7. #31826673C2semidirect
8. #31826669C2semidirect
11. #31826567C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985379C2semidirect
14. #31826527C2semidirect
15. #441×C283C2semidirect
168. C283#3120semidirect
180. #441D283semidirect

Maximal subgroups

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

subgroupindex
#318270732
#318269472
#318267992
#318267972
#318267742
#318267642
#318266732
#318266692
#318266302
#318266262
#318265672
C4×#179853822
C4×#179853792
#318265272
#441×C2832
#3120283