Finite Group Databasebeta

← #49131389

Subgroups — #49131389

Order 36224.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827019C211yesmaximal, characteristic
2C4×Q8×D283C211yesmaximal, characteristic
3#31826797C211yesmaximal, characteristic
4#31826794C211yesmaximal, characteristic
5#31826749C211yesmaximal, characteristic, complemented
6#31826748C211yesmaximal, characteristic, complemented
7#31826674C211yesmaximal, characteristic, complemented
8#31826673C211yesmaximal, characteristic, complemented
9#31826622C211yesmaximal, characteristic
10#31826619C211yesmaximal, characteristic
11#31826573C211yesmaximal, characteristic, complemented
12#31826570C211yesmaximal, characteristic, complemented
13#31826570C211yesmaximal, characteristic, complemented
14#31826520C211yesmaximal, characteristic
15#441×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583608C2211yescharacteristic
22#22583600—21no—
23#22583590C2211yescharacteristic
24#22583588—21no—
25#22583586C2211yescharacteristic
26Q8×Dic283C2211yescharacteristic
27C4×Dic566—21no—
28C4×Dic566—21no—
29C4×Dic566C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31#22583575—21no—
32#22583575C2211yescharacteristic
33#22583567—21no—
34C4⋊C4×D283—21no—
35C4⋊C4×D283C2211yescharacteristic
36C42×D283—21no—
37C42×D283C2211yescharacteristic
38#22583542C2211yescharacteristic
39#22583541C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
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×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283—22no—
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283D411yescharacteristic
68C2×C4×D283D411yescharacteristic
69C2×C4×D283C2311yescharacteristic
70Dic1132—22no—
71#17985382—22no—
72#17985382—22no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
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⋊C4—21no—
86Dic283⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89C4×Dic283—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×D283C2×D411yescharacteristic
109Dic566—24no—
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—42no—
114Dic566#4112yes—
115C2×Dic283—21no—
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—22no—
127C4×D283—42no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130Q8×C283—21no—
131Q8×C283—21no—
132Q8×C283—21no—
133Q8×C283#4112yes—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2411yescharacteristic
141C8×C283—21no—
142C8×C283—21no—
143C22×C283C22×D411yescharacteristic
144C2×D283—21no—
145C2×D283—21no—
146C2×D283#13712yes—
147C4×C283—22no—
148C4×C283—21no—
149C4×C283—21no—
150C4×C283—41no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283C2×#4111yescharacteristic
154C4×C283C2×#4111yescharacteristic
155Dic283—22no—
156Dic283—21no—
157Dic283—21no—
158Dic283—41no—
159Dic283—41no—
160Dic283—41no—
161Dic283#13712yes—
162C2×C283#52511yescharacteristic
163C2×C283C2×#13711yescharacteristic
164C2×C283C2×#13711yescharacteristic
165D283—22no—
166C283#311311yescharacteristic, complemented, Sylow
167#3113—2831nomaximal, Sylow
168#533—2831no—
169C2×C4×Q8—2831no—
170#483—2831no—
171#483—2831no—
172#475—2831no—
173#475—2831no—
174#462—2831no—
175#462—2831no—
176#451—2831no—
177#451—2831no—
178#441—2831no—
179#441—2831no—
180#441—2831no—
181#441D28311yescharacteristic, complemented
182#432—2831no—
183C22×Q8—2831no—
184C2×Q16—2831no—
185C2×Q16—2831no—
186C2×Q16—2831no—
187C2×Q16C2×D28311yescharacteristic
188C4⋊Q8—2831no—
189C4⋊Q8—2831no—
190#125—5661no—
191C22⋊Q8—2831no—
192C22⋊Q8—2831no—
193C22⋊Q8—5661no—
194C4×Q8—2831no—
195C4×Q8—2831no—
196C4×Q8—2831no—
197C4×Q8—2831no—
198C4×Q8—5661no—
199C4×Q8—5661no—
200C4×Q8—5661no—
201C4×Q8C2×D28311yescharacteristic
202C4×Q8C2×D28311yescharacteristic
203#117—5661no—
204C2×C4⋊C4—2831no—
205C2×C4⋊C4—5661no—
206C2×C42—2831no—
207C2×C42—5661no—
208#106—2831no—
209#106—2831no—
210#106—2831no—
211#106C2×D28311yescharacteristic
212C4⋊C8—2831no—
213C4⋊C8—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103C2×D28311yescharacteristic
221#103C2×D28311yescharacteristic
222C22⋊C8—2831no—
223C22⋊C8—2831no—
224#97—2831no—
225#97C2×D28311yescharacteristic
226C2×Q8—2831no—
227C2×Q8—2831no—
228C2×Q8—5661no—
229C2×Q8—5661no—
230C2×Q8—5662no—
231C2×Q8—5662no—
232C2×Q8C22×D28311yescharacteristic
233C2×Q8C22×D28311yescharacteristic
234C22×C4—2831no—
235C22×C4—2831no—
236C22×C4—2831no—
237C22×C4—5661no—
238C22×C4—5661no—
239Q16—22no—
240Q16—5662no—
241Q16—5662no—
242Q16—5662no—
243C2×C8—2831no—
244C2×C8—2831no—
245C2×C8C22×D28311yescharacteristic
246C2×C8C22×D28311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
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⋊C4C22×D28311yescharacteristic
262C4⋊C4C22×D28311yescharacteristic
263C22⋊C4—5661no—
264C22⋊C4—5661no—
265C42—21no—
266C42—21no—
267C42—2831no—
268C42—2831no—
269C42—2831no—
270C42—5661no—
271C42—5661no—
272C42—5661no—
273C42—5661no—
274C42C22×D28311yescharacteristic
275C23—2831no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—2832no—
280Q8—5664no—
281Q8—5661no—
282Q8—5661no—
283Q8—5661no—
284Q8—11322no—
285Q8#1798539212yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2831no—
291C2×C4—2831no—
292C2×C4—2831no—
293C2×C4—5662no—
294C2×C4—5662no—
295C2×C4—5664no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—11322no—
303C2×C4D4×D28311yescharacteristic
304C2×C4D4×D28311yescharacteristic
305C2×C4C23×D28311yescharacteristic
306C8—21no—
307C8—21no—
308C8—5661no—
309C8—5661no—
310C22—2832no—
311C22—5661no—
312C22—5661no—
313C22C2×D4×D28311yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2832no—
321C4—5661no—
322C4—5662no—
323C4—5661no—
324C4—11321no—
325C4—11321no—
326C4—11321no—
327C4#41×D28311yescharacteristic
328C4C2×#1798539211yescharacteristic
329C2—5662no—
330C2#3182697411yescharacteristic
331C2#137×D28311yescharacteristic
332C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#441×C283C2
socleC22×C283C22×D4
prime radicalC22×D283C2×D4
hypercenter#441D283
hypocenterC283#3113
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
5. #31826749C2semidirect
6. #31826748C2semidirect
7. #31826674C2semidirect
8. #31826673C2semidirect
11. #31826573C2semidirect
12. #31826570C2semidirect
13. #31826570C2semidirect
15. #441×C283C2semidirect
166. C283#3113semidirect
181. #441D283semidirect

Maximal subgroups

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

subgroupindex
#318270192
C4×Q8×D2832
#318267972
#318267942
#318267492
#318267482
#318266742
#318266732
#318266222
#318266192
#318265732
#318265702
#318265202
#441×C2832
#3113283