Finite Group Databasebeta

← #49133947

Subgroups — #49133947

Order 36224.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827191C211yesmaximal, characteristic, complemented
2#31827187C211yesmaximal, characteristic
3#31826821C211yesmaximal, characteristic
4#31826820C211yesmaximal, characteristic
5#31826814C211yesmaximal, characteristic, complemented
6#31826772C211yesmaximal, characteristic, complemented
7#31826771C211yesmaximal, characteristic, complemented
8#31826744C211yesmaximal, characteristic
9#31826689C211yesmaximal, characteristic
10#31826687C211yesmaximal, characteristic
11#31826673C211yesmaximal, characteristic, complemented
12C8×Dic566C211yesmaximal, characteristic, complemented
13#31826557C211yesmaximal, characteristic, complemented
14#31826550C211yesmaximal, characteristic
15C4×Q16×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985379C2211yescharacteristic
18#22583609—21no—
19#22583609C2211yescharacteristic
20#22583608C2211yescharacteristic
21#22583605—21no—
22#22583604—21no—
23#22583602—21no—
24#22583602C2211yescharacteristic
25#22583601—21no—
26#22583601C2211yescharacteristic
27#22583599C2211yescharacteristic
28#22583598C2211yescharacteristic
29#22583588—21no—
30Q8×Dic283C2211yescharacteristic
31Q8×Dic283C2211yescharacteristic
32C4×Dic566—21no—
33C4×Dic566C2211yescharacteristic
34#22583575C2211yescharacteristic
35#22583572C2211yescharacteristic
36#22583567—21no—
37#22583543C2211yescharacteristic
38#22583541C2211yescharacteristic
39C4⋊(C283⋊C8)C2211yescharacteristic
40Dic283⋊C8C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583530C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566D411yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C4×D283—21no—
64#17985382—22no—
65#17985379—22no—
66C2×C283⋊C8C2311yescharacteristic
67C2×C283⋊C8C2311yescharacteristic
68C4⋊Dic283—21no—
69C4⋊Dic283—21no—
70C4⋊Dic283—21no—
71C4⋊Dic283D411yescharacteristic
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74Dic283⋊C4—21no—
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C4×Dic283C2311yescharacteristic
93C2×Q8×C283C2311yescharacteristic
94C2×Q8×C283C2311yescharacteristic
95Q16×C283—22no—
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283—21no—
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C42×C283—21no—
103C42×C283—21no—
104C42×C283C2311yescharacteristic
105C22×D283—21no—
106Dic566—22no—
107Dic566—21no—
108Dic566—21no—
109Dic566—42no—
110D1132—21no—
111D1132—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283C2×D411yescharacteristic
116C2×Dic283C2×D411yescharacteristic
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C4×D283—42no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122Q8×C283—21no—
123Q8×C283—21no—
124Q8×C283—21no—
125Q8×C283#4112yes—
126C2×C4×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283C2×D411yescharacteristic
131C2×C4×C283C2×D411yescharacteristic
132C2×C4×C283C2411yescharacteristic
133C8×C283—21no—
134C8×C283—21no—
135C22×C283C22×D411yescharacteristic
136C2×D283—41no—
137C2×D283—41no—
138C2×D283—41no—
139C4×C283—22no—
140C4×C283—21no—
141C4×C283—21no—
142C4×C283—41no—
143C4×C283—41no—
144C4×C283—41no—
145C4×C283C2×#4111yescharacteristic
146C4×C2832−1+411yescharacteristic
147Dic283—21no—
148Dic283—21no—
149Dic283—21no—
150Dic283—41no—
151Dic283—41no—
152Dic283—41no—
153Dic283#13512yes—
154C2×C283#54811yescharacteristic
155C2×C283C2×#13511yescharacteristic
156C2×C283#57811yescharacteristic
157D283—81no—
158C283#336411yescharacteristic, complemented, Sylow
159#3364—2831nomaximal, Sylow
160#557—2831no—
161#556—2831no—
162#488—2831no—
163#488—2831no—
164#487—2831no—
165#479—2831no—
166#479—2831no—
167#474—2831no—
168#464—2831no—
169#464—2831no—
170#462—2831no—
171C8×Q8—2831no—
172C4×Q16—2831no—
173C4×Q16D28311yescharacteristic, complemented
174C4×SD16—2831no—
175C2×Q16—2831no—
176C2×Q16C2×D28311yescharacteristic
177C2×SD16—2831no—
178C4⋊Q8—2831no—
179C4⋊Q8—2831no—
180C4⋊Q8—5661no—
181#126—5661no—
182#126—5661no—
183#125—2831no—
184#125—2831no—
185#125—5661no—
186#125—5661no—
187#124—2831no—
188#124—2831no—
189C22⋊Q8—5661no—
190C4×Q8—2831no—
191C4×Q8—2831no—
192C4×Q8—2831no—
193C4×Q8—2831no—
194C4×Q8—5661no—
195C4×Q8C2×D28311yescharacteristic
196C4×Q8C2×D28311yescharacteristic
197C4×D4—2831no—
198#117—5661no—
199#107—2831no—
200#107C2×D28311yescharacteristic
201#106—2831no—
202C4⋊C8—2831no—
203C4⋊C8—2831no—
204C4⋊C8—2831no—
205#103—2831no—
206#103—2831no—
207#103—2831no—
208#103—2831no—
209#103—2831no—
210#103C2×D28311yescharacteristic
211#103C2×D28311yescharacteristic
212#102—2831no—
213#102—2831no—
214#102—2831no—
215C4×C8—2831no—
216C4×C8—2831no—
217C4×C8C2×D28311yescharacteristic
218C2×Q8—2831no—
219C2×Q8—2831no—
220C2×Q8—5661no—
221C2×Q8C22×D28311yescharacteristic
222C2×Q8C22×D28311yescharacteristic
223C2×D4—2831no—
224C22×C4—5661no—
225Q16—22no—
226Q16—5662no—
227SD16—5662no—
228C2×C8—2831no—
229C2×C8—2831no—
230C2×C8C22×D28311yescharacteristic
231C2×C8C22×D28311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—2831no—
235C4⋊C4—2831no—
236C4⋊C4—2831no—
237C4⋊C4—2831no—
238C4⋊C4—2831no—
239C4⋊C4—5661no—
240C4⋊C4—5661no—
241C4⋊C4—5661no—
242C4⋊C4—5661no—
243C4⋊C4—5661no—
244C4⋊C4—5661no—
245C4⋊C4—5661no—
246C4⋊C4—5661no—
247C4⋊C4—5661no—
248C4⋊C4—5661no—
249C4⋊C4C22×D28311yescharacteristic
250C4⋊C4C22×D28311yescharacteristic
251C22⋊C4—5661no—
252C22⋊C4—5661no—
253C22⋊C4—5661no—
254C22⋊C4—5661no—
255C22⋊C4—5661no—
256C42—21no—
257C42—21no—
258C42—2831no—
259C42—2831no—
260C42—5661no—
261C42—5661no—
262C42—5661no—
263C42C22×D28311yescharacteristic
264C23—5661no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—5662no—
269Q8—5661no—
270Q8—5661no—
271Q8—11322no—
272Q8#1798539212yes—
273D4—5661no—
274D4—5661no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—2831no—
280C2×C4—2831no—
281C2×C4—2831no—
282C2×C4—2831no—
283C2×C4—5661no—
284C2×C4—5661no—
285C2×C4—5661no—
286C2×C4—11322no—
287C2×C4D4×D28311yescharacteristic
288C2×C4D4×D28311yescharacteristic
289C2×C4C23×D28311yescharacteristic
290C8—21no—
291C8—21no—
292C8—5661no—
293C8—5661no—
294C22—11321no—
295C22—11321no—
296C22—11321no—
297C22C2×D4×D28311yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—2832no—
305C4—5661no—
306C4—5661no—
307C4—5661no—
308C4—11321no—
309C4—11321no—
310C4—11321no—
311C4C2×#1798539211yescharacteristic
312C4#2258365711yescharacteristic
313C2—22641no—
314C2#3182712411yescharacteristic
315C2#135×D28311yescharacteristic
316C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×Q16×C283C2
socleC22×C283C22×D4
prime radicalC2×D1132C23
hypercenterC4×Q16D283
hypocenterC283#3364
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #31827191C2semidirect
5. #31826814C2semidirect
6. #31826772C2semidirect
7. #31826771C2semidirect
11. #31826673C2semidirect
12. C8×Dic566C2semidirect
13. #31826557C2semidirect
15. C4×Q16×C283C2semidirect
158. C283#3364semidirect
173. C4×Q16D283semidirect

Maximal subgroups

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

subgroupindex
#318271912
#318271872
#318268212
#318268202
#318268142
#318267722
#318267712
#318267442
#318266892
#318266872
#318266732
C8×Dic5662
#318265572
#318265502
C4×Q16×C2832
#3364283