Finite Group Databasebeta

← #49124277

Subgroups — #49124277

Order 36224.

788 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583584C211yesmaximal, characteristic
2C2×#22583572C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D283C212yesmaximal, complemented
4#31826366C211yesmaximal, characteristic, complemented
5#31826361C211yesmaximal, characteristic, complemented
6#31826355C212yesmaximal, complemented
7#31826344C212yesmaximal, complemented
8#31826336C212yesmaximal, complemented
9C4⋊C4×Dic283C211yesmaximal, characteristic, complemented
10C4×C22⋊Dic283C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C283C211yesmaximal, characteristic, complemented
12C22×D1132C2211yescharacteristic
13C22×C22⋊D283C2212yes—
14C22×C4×D283C2212yes—
15#22583584C418yescomplemented
16#22583572—24no—
17C4×C22⋊D283—28no—
18C2×C4⋊Dic283C2211yescharacteristic
19C2×Dic283⋊C4C2212yes—
20C2×C22⋊Dic283C2211yescharacteristic
21C2×C22⋊Dic283C2211yescharacteristic
22C2×(C2×D283)⋊C4C2212yes—
23C2×(C2×D283)⋊C4C2212yes—
24C2×(C2×D283)⋊C4C2212yes—
25C2×(C2×D283)⋊C4C2212yes—
26C2×C4×Dic283C2211yescharacteristic
27C2×C4×Dic283C2211yescharacteristic
28C2×C4×Dic283C2212yes—
29C283⋊#95C2211yescharacteristic
30C283⋊#95C2211yescharacteristic
31C283⋊#95C2212yes—
32C283⋊#95C2212yes—
33C23×C4×C283C2212yes—
34C23×C4×C283C2211yescharacteristic
35C2×C4⋊C4×C283—24no—
36C2×C4⋊C4×C283C2212yes—
37C2×C4⋊C4×C283C2211yescharacteristic
38C2×C4⋊C4×C283C2211yescharacteristic
39C23×D283C2312yes—
40C2×D1132—22no—
41C2×D1132—22no—
42C2×D1132C2×C414yescomplemented
43C2×C22⋊D283—24no—
44C2×C22⋊D283—24no—
45C2×C22⋊D283C2×C418yescomplemented
46C22×Dic283C2311yescharacteristic
47C22×Dic283C2311yescharacteristic
48C22×Dic283C2312yes—
49C22×Dic283C2311yescharacteristic
50C22×Dic283C2311yescharacteristic
51C2×C4×D283—24no—
52C2×C4×D283—24no—
53C2×C4×D283—42no—
54C4⋊Dic283C2×C414yescomplemented
55Dic283⋊C4—24no—
56C22⋊Dic283—22no—
57C22⋊Dic283D414yescomplemented
58(C2×D283)⋊C4—24no—
59(C2×D283)⋊C4—24no—
60(C2×D283)⋊C4—42no—
61(C2×D283)⋊C4C2×C418yescomplemented
62C4×Dic283—24no—
63C4×Dic283—22no—
64C4×Dic283—22no—
65C24×C283C2311yescharacteristic
66C22×C4×C283—22no—
67C22×C4×C283—22no—
68C22×C4×C283—24no—
69C22×C4×C283—24no—
70C22×C4×C283—42no—
71C22×C4×C283C2×C414yescomplemented
72C22×C4×C283C2312yes—
73C22×C4×C283C2311yescharacteristic
74C22×C4×C283C2312yes—
75C22×C4×C283C2311yescharacteristic
76C4⋊C4×C283—24no—
77C4⋊C4×C283—22no—
78C4⋊C4×C283D414yescomplemented
79C22×D283—22no—
80C22×D283—22no—
81C22×D283—22no—
82C22×D283—22no—
83C22×D283—22no—
84C22×D283—22no—
85C22×D283C22×C414yes—
86D1132—28no—
87C22⋊D283—216no—
88C2×Dic283—22no—
89C2×Dic283—21no—
90C2×Dic283—21no—
91C2×Dic283—22no—
92C2×Dic283—21no—
93C2×Dic283—21no—
94C2×Dic283—21no—
95C2×Dic283—21no—
96C2×Dic283—21no—
97C2×Dic283—21no—
98C2×Dic283—21no—
99C2×Dic283—21no—
100C2×Dic283C22×C414yes—
101C2×Dic283C2×D412yes—
102C2×Dic283C2×D412yes—
103C4×D283—48no—
104C23×C283—21no—
105C23×C283—21no—
106C23×C283—21no—
107C23×C283—21no—
108C23×C283C22×C412yes—
109C23×C283C2×D412yes—
110C23×C283#4112yes—
111C23×C283C2411yescharacteristic
112C2×C4×C283—21no—
113C2×C4×C283—22no—
114C2×C4×C283—21no—
115C2×C4×C283—22no—
116C2×C4×C283—28no—
117C2×C4×C283—22no—
118C2×C4×C283—22no—
119C2×C4×C283—22no—
120C2×C4×C283—48no—
121C2×C4×C283C22×C412yes—
122C2×C4×C283C22×C412yes—
123C2×C4×C283C2×D414yes—
124C2×C4×C283C2×D412yes—
125C2×C4×C283#4112yes—
126C22×C283—22no—
127C22×C283—22no—
128C22×C283—22no—
129C22×C283—22no—
130C22×C283—22no—
131C22×C283—22no—
132C22×C283C4×D414yescomplemented
133C22×C283C23×C411yescharacteristic
134C22×C283C22×D411yescharacteristic
135C22×C283C22×D411yescharacteristic
136C22×C283C2×#4111yescharacteristic
137C22×C283C2×#4111yescharacteristic
138C22×C283H(5,𝔽2)11yescharacteristic
139C22×C2832−1+411yescharacteristic
140C2×D283—24no—
141C2×D283—24no—
142C2×D283—24no—
143C2×D283—42no—
144C2×D283—42no—
145C2×D283—42no—
146C2×D283—42no—
147C4×C283—22no—
148C4×C283—24no—
149C4×C283—42no—
150C4×C283C4×D414yescomplemented
151Dic283—24no—
152Dic283—22no—
153Dic283—22no—
154Dic283—41no—
155Dic283—41no—
156C2×C283—24no—
157C2×C283C2×C4×D411yescharacteristic
158C2×C283C2×C4×D411yescharacteristic
159C2×C283#52011yescharacteristic
160C2×C283D4211yescharacteristic
161C2×C283#54711yescharacteristic
162C2×C283#54811yescharacteristic
163C2×C283#55311yescharacteristic
164D283—44no—
165C283#236111yescharacteristic, complemented, Sylow
166#2361—2831nomaximal, Sylow
167C2×#121—2831no—
168C2×C4×D4—2832no—
169C2×C4×D4—2831no—
170C22×C4⋊C4D28311yescharacteristic, complemented
171#390—2831no—
172#389—2831no—
173#388—2832no—
174#386—2832no—
175#385—2832no—
176C4×C4⋊C4—2831no—
177C4×C22⋊C4—2831no—
178C22×D4—2832no—
179C22×D4—2831no—
180C23×C4—2832no—
181C23×C4C2×D28312yes—
182C23×C4C2×D28311yescharacteristic
183#121—2838no—
184C4×D4—5668no—
185C4×D4—5664no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—2831no—
188C2×C4⋊C4—2832no—
189C2×C4⋊C4C2×D28312yes—
190C2×C4⋊C4C2×D28311yescharacteristic
191C2×C4⋊C4C2×D28311yescharacteristic
192C2×C22⋊C4—2831no—
193C2×C22⋊C4—2832no—
194C2×C22⋊C4—2831no—
195C2×C22⋊C4—2832no—
196C2×C22⋊C4—2832no—
197C2×C22⋊C4—2832no—
198C2×C42—2831no—
199C2×C42—2832no—
200C2×C42—2831no—
201#95—2831no—
202#95—2831no—
203#95—2832no—
204#95—2832no—
205C24—2832no—
206C24C22×D28311yescharacteristic
207C2×D4—2838no—
208C2×D4—2834no—
209C2×D4—5664no—
210C2×D4—5664no—
211C2×D4—5662no—
212C2×D4—5662no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—42no—
218C22×C4—2832no—
219C22×C4—2831no—
220C22×C4—2831no—
221C22×C4—2831no—
222C22×C4—2831no—
223C22×C4—5664no—
224C22×C4—5664no—
225C22×C4—11322no—
226C22×C4C4×D28314yescomplemented
227C22×C4C22×D28312yes—
228C22×C4C22×D28311yescharacteristic
229C22×C4C22×D28312yes—
230C22×C4C22×D28311yescharacteristic
231C4⋊C4—24no—
232C4⋊C4—22no—
233C4⋊C4—2834no—
234C4⋊C4—5664no—
235C4⋊C4C22⋊D28314yescomplemented
236C22⋊C4—2834no—
237C22⋊C4—2838no—
238C22⋊C4—5664no—
239C22⋊C4—5662no—
240C22⋊C4—5664no—
241C22⋊C4—11322no—
242C42—5664no—
243C42—5662no—
244C42—5662no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—2834no—
250C23—5662no—
251C23—5662no—
252C23—5662no—
253C23—5662no—
254C23—5662no—
255C23—5662no—
256C23C2×C4×D28312yes—
257C23D4×D28312yes—
258C23#1798539312yes—
259C23C23×D28311yescharacteristic
260D4—56616no—
261D4—5668no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—2834no—
272C2×C4—2832no—
273C2×C4—2832no—
274C2×C4—5662no—
275C2×C4—5661no—
276C2×C4—5661no—
277C2×C4—5662no—
278C2×C4—5661no—
279C2×C4—5661no—
280C2×C4—5661no—
281C2×C4—5661no—
282C2×C4—5661no—
283C2×C4—5661no—
284C2×C4—5661no—
285C2×C4—5661no—
286C2×C4—11328no—
287C2×C4C2×C4×D28312yes—
288C2×C4C2×C4×D28312yes—
289C2×C4C2×C22⋊D28314yes—
290C2×C4C2×C22⋊D28312yes—
291C2×C4#1798539212yes—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—5664no—
299C22—5664no—
300C22—5664no—
301C22—11322no—
302C22—11322no—
303C22—11322no—
304C22—11322no—
305C22#2258357214yescomplemented
306C22C22×C4×D28311yescharacteristic
307C22C2×D4×D28311yescharacteristic
308C22C22×C22⋊D28311yescharacteristic
309C22C2×#1798539211yescharacteristic
310C22C2×#1798539311yescharacteristic
311C22#2258365511yescharacteristic
312C22#2258365811yescharacteristic
313C4—24no—
314C4—22no—
315C4—42no—
316C4—5662no—
317C4—5662no—
318C4—5664no—
319C4—11321no—
320C4—11321no—
321C4C4×C22⋊D28314yescomplemented
322C2—24no—
323C2—11324no—
324C2C2×C4×C22⋊D28311yescharacteristic
325C2C2×#2258357211yescharacteristic
326C2#3182694611yescharacteristic
327C2D4×C22⋊D28311yescharacteristic
328C2#3182711611yescharacteristic
329C2#3182712611yescharacteristic
330C2#3182716311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC22×C4⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583584C2
hypercenterC22×C4⋊C4D283
hypocenterC283#2361
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#22583572C2semidirect
3. C2×C4×C22⋊D283C2semidirect
4. #31826366C2semidirect
5. #31826361C2semidirect
6. #31826355C2semidirect
7. #31826344C2semidirect
8. #31826336C2semidirect
9. C4⋊C4×Dic283C2semidirect
10. C4×C22⋊Dic283C2semidirect
11. C22×C4⋊C4×C283C2semidirect
15. #22583584C4semidirect
42. C2×D1132C2×C4semidirect
45. C2×C22⋊D283C2×C4semidirect
54. C4⋊Dic283C2×C4semidirect
57. C22⋊Dic283D4semidirect
61. (C2×D283)⋊C4C2×C4semidirect
71. C22×C4×C283C2×C4semidirect
78. C4⋊C4×C283D4semidirect
132. C22×C283C4×D4semidirect
150. C4×C283C4×D4semidirect
165. C283#2361semidirect
170. C22×C4⋊C4D283semidirect
226. C22×C4C4×D283semidirect
235. C4⋊C4C22⋊D283semidirect
305. C22#22583572semidirect
321. C4C4×C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835842
C2×#225835722
C2×C4×C22⋊D2832
#318263662
#318263612
#318263552
#318263442
#318263362
C4⋊C4×Dic2832
C4×C22⋊Dic2832
C22×C4⋊C4×C2832
#2361283