Finite Group Databasebeta

← #49124157

Subgroups — #49124157

Order 36224.

776 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
1C2×C4×C22⋊D283C211yesmaximal, characteristic
2C2×(C22⋊D283)⋊C4C212yesmaximal
3C22×C4⋊Dic283C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
5#31826362C212yesmaximal, complemented
6#31826339C212yesmaximal, complemented
7#31826337C212yesmaximal, complemented
8#31826334C211yesmaximal, characteristic, complemented
9#31826322C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic283C211yesmaximal, characteristic, complemented
11#380×C283C211yesmaximal, characteristic, complemented
12C22×C22⋊D283C2211yescharacteristic
13C23×Dic283C2212yes—
14C22×C4×D283C2212yes—
15C22×C4×D283C2211yescharacteristic
16C4×C22⋊D283C418yescomplemented
17(C22⋊D283)⋊C4—28no—
18C2×C4⋊Dic283—24no—
19C2×C4⋊Dic283C2211yescharacteristic
20C2×C4⋊Dic283C2212yes—
21C2×C4⋊Dic283C2211yescharacteristic
22C2×Dic283⋊C4C2212yes—
23C2×Dic283⋊C4C2212yes—
24C2×Dic283⋊C4C2212yes—
25C2×Dic283⋊C4C2211yescharacteristic
26C4⋊C4×D283—24no—
27C2×C22⋊Dic283C2211yescharacteristic
28C2×(C2×D283)⋊C4C2212yes—
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×C4×Dic283C2212yes—
31C2×C4×Dic283C2211yescharacteristic
32C283⋊#95C2212yes—
33C283⋊#95C2212yes—
34C23×C4×C283C2211yescharacteristic
35C2×C4⋊C4×C283C2211yescharacteristic
36C2×C4⋊C4×C283C2211yescharacteristic
37C2×C22⋊C4×C283C2212yes—
38#95×C283C2212yes—
39C23×D283C2311yescharacteristic
40C2×C22⋊D283C2×C414yes—
41C2×C22⋊D283D414yes—
42C2×C22⋊D283Q814yes—
43C22×Dic283—24no—
44C22×Dic283—24no—
45C22×Dic283—42no—
46C22×Dic283C2312yes—
47C22×Dic283C2311yescharacteristic
48C22×Dic283C2311yescharacteristic
49C22×Dic283C2312yes—
50C22×Dic283C2311yescharacteristic
51C2×C4×D283—24no—
52C2×C4×D283—24no—
53C2×C4×D283—22no—
54C2×C4×D283—22no—
55C2×C4×D283—42no—
56C2×C4×D283C2×C414yescomplemented
57C4⋊Dic283—24no—
58C4⋊Dic283—22no—
59C4⋊Dic283D414yescomplemented
60Dic283⋊C4—24no—
61Dic283⋊C4—24no—
62Dic283⋊C4—42no—
63Dic283⋊C4C2×C414yescomplemented
64C22⋊Dic283C2×C414yescomplemented
65(C2×D283)⋊C4—24no—
66(C2×D283)⋊C4C2×C414yescomplemented
67C4×Dic283—24no—
68C4×Dic283C2×C414yescomplemented
69C24×C283C2311yescharacteristic
70C22×C4×C283—22no—
71C22×C4×C283—22no—
72C22×C4×C283C2×C414yescomplemented
73C22×C4×C283C2312yes—
74C22×C4×C283C2312yes—
75C22×C4×C283C2311yescharacteristic
76C22×C4×C283C2311yescharacteristic
77C4⋊C4×C283—22no—
78C4⋊C4×C283—22no—
79C22⋊C4×C283—24no—
80C22×D283—21no—
81C22×D283—21no—
82C22×D283—21no—
83C22×D283—21no—
84C22×D283C22×C412yes—
85C22×D283C2×D412yes—
86C22×D283C2×Q812yes—
87C22⋊D283C4⋊C4116yescomplemented
88C2×Dic283—22no—
89C2×Dic283—21no—
90C2×Dic283—21no—
91C2×Dic283—21no—
92C2×Dic283—22no—
93C2×Dic283—21no—
94C2×Dic283—22no—
95C2×Dic283—22no—
96C2×Dic283—22no—
97C2×Dic283—48no—
98C2×Dic283C22×C412yes—
99C2×Dic283C22×C412yes—
100C2×Dic283C22×C412yes—
101C2×Dic283C2×D414yes—
102C2×Dic283C2×D412yes—
103C2×Dic283C2×Q812yes—
104C4×D283—28no—
105C4×D283—48no—
106C23×C283—21no—
107C23×C283—21no—
108C23×C283—21no—
109C23×C283—21no—
110C23×C283C22×C412yes—
111C23×C283C2×D412yes—
112C23×C283C2×Q812yes—
113C23×C283C2411yescharacteristic
114C2×C4×C283—21no—
115C2×C4×C283—21no—
116C2×C4×C283—28no—
117C2×C4×C283—22no—
118C2×C4×C283—22no—
119C2×C4×C283—22no—
120C2×C4×C283—22no—
121C2×C4×C283—22no—
122C2×C4×C283—22no—
123C2×C4×C283C22×C412yes—
124C2×C4×C283C22×C412yes—
125C2×C4×C283C2×D412yes—
126C2×C4×C283#4112yes—
127C22×C283—22no—
128C22×C283—22no—
129C22×C283—22no—
130C22×C283—22no—
131C22×C283—22no—
132C22×C283—22no—
133C22×C283C2×C4⋊C414yescomplemented
134C22×C283C23×C411yescharacteristic
135C22×C283C22×D411yescharacteristic
136C22×C283C22×D411yescharacteristic
137C22×C283C22×Q811yescharacteristic
138C22×C283C2×#4111yescharacteristic
139C22×C283H(5,𝔽2)11yescharacteristic
140C22×C2832−1+411yescharacteristic
141C2×D283—22no—
142C2×D283—22no—
143C2×D283—22no—
144C2×D283—22no—
145C2×D283—22no—
146C2×D283—22no—
147C2×D283C2×C4⋊C414yescomplemented
148C4×C283—22no—
149C4×C283—42no—
150C4×C283—42no—
151C4×C283C4×D414yescomplemented
152Dic283—22no—
153Dic283—22no—
154Dic283—24no—
155Dic283—42no—
156Dic283C2×C4⋊C414yescomplemented
157C2×C283—24no—
158C2×C283C22×C4⋊C411yescharacteristic
159C2×C283C2×C4×D411yescharacteristic
160C2×C283#52011yescharacteristic
161C2×C283D4211yescharacteristic
162C2×C283#54711yescharacteristic
163C2×C283D4×Q811yescharacteristic
164C2×C283#55411yescharacteristic
165D283—24no—
166C283D4×C4⋊C411yescharacteristic, complemented, Sylow
167D4×C4⋊C4—2831nomaximal, Sylow
168C2×C4×D4—2831no—
169C2×C4×D4—2832no—
170C22×C4⋊C4—2831no—
171C22×C4⋊C4—2831no—
172#389—2832no—
173#385—2832no—
174#385—2832no—
175#384—2831no—
176#380—2831no—
177#380D28311yescharacteristic, complemented
178C4×C4⋊C4—2831no—
179C22×D4—2831no—
180C23×C4—2831no—
181C23×C4—2832no—
182C23×C4—2832no—
183C23×C4C2×D28311yescharacteristic
184C4×D4—2838no—
185C4×D4—5668no—
186C2×C4⋊C4—2831no—
187C2×C4⋊C4—2831no—
188C2×C4⋊C4—2832no—
189C2×C4⋊C4—2831no—
190C2×C4⋊C4—2832no—
191C2×C4⋊C4—2832no—
192C2×C4⋊C4—2832no—
193C2×C4⋊C4—5664no—
194C2×C4⋊C4—5664no—
195C2×C4⋊C4C2×D28311yescharacteristic
196C2×C4⋊C4C2×D28311yescharacteristic
197C2×C22⋊C4—2831no—
198C2×C22⋊C4—2831no—
199C2×C22⋊C4—2832no—
200C2×C22⋊C4C2×D28312yes—
201C2×C42—2831no—
202C2×C42—2832no—
203#95—2832no—
204#95—2832no—
205#95C2×D28312yes—
206C24—2831no—
207C24C22×D28311yescharacteristic
208C2×D4—2834no—
209C2×D4—2834no—
210C2×D4—2834no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—2831no—
214C22×C4—2831no—
215C22×C4—2831no—
216C22×C4—2832no—
217C22×C4—2834no—
218C22×C4—2832no—
219C22×C4—5664no—
220C22×C4—5664no—
221C22×C4—5664no—
222C22×C4—5662no—
223C22×C4—5662no—
224C22×C4—5664no—
225C22×C4—11322no—
226C22×C4—11322no—
227C22×C4C4×D28314yescomplemented
228C22×C4C22×D28312yes—
229C22×C4C22×D28312yes—
230C22×C4C22×D28311yescharacteristic
231C22×C4C22×D28311yescharacteristic
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—2834no—
235C4⋊C4—2834no—
236C4⋊C4—5664no—
237C4⋊C4—5664no—
238C4⋊C4—5664no—
239C4⋊C4—5662no—
240C4⋊C4—11322no—
241C22⋊C4—24no—
242C22⋊C4—2834no—
243C22⋊C4—2834no—
244C22⋊C4—5664no—
245C42—2834no—
246C42—5664no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—2832no—
252C23—2832no—
253C23—2832no—
254C23—5661no—
255C23—5661no—
256C23—5661no—
257C23—5661no—
258C23C2×C4×D28312yes—
259C23D4×D28312yes—
260C23Q8×D28312yes—
261C23C23×D28311yescharacteristic
262D4—28316no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—28no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—2832no—
273C2×C4—2832no—
274C2×C4—2832no—
275C2×C4—2832no—
276C2×C4—2832no—
277C2×C4—2834no—
278C2×C4—5662no—
279C2×C4—5661no—
280C2×C4—5661no—
281C2×C4—5661no—
282C2×C4—5662no—
283C2×C4—5661no—
284C2×C4—5668no—
285C2×C4—5662no—
286C2×C4—5662no—
287C2×C4—5662no—
288C2×C4—11328no—
289C2×C4—11328no—
290C2×C4C2×C4×D28312yes—
291C2×C4C2×C4×D28312yes—
292C2×C4D4×D28312yes—
293C2×C4#1798539112yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—2834no—
301C22—5662no—
302C22—5662no—
303C22—5662no—
304C22—5662no—
305C22—5662no—
306C22—5662no—
307C22C4⋊C4×D28314yescomplemented
308C22C22×C4×D28311yescharacteristic
309C22C2×D4×D28311yescharacteristic
310C22C2×D4×D28311yescharacteristic
311C22C2×Q8×D28311yescharacteristic
312C22C2×#1798539111yescharacteristic
313C22#2258365611yescharacteristic
314C22#2258365711yescharacteristic
315C4—22no—
316C4—42no—
317C4—42no—
318C4—2834no—
319C4—5662no—
320C4—5664no—
321C4—5662no—
322C4—11322no—
323C4(C22⋊D283)⋊C414yescomplemented
324C2—24no—
325C2—5664no—
326C2C2×C4⋊C4×D28311yescharacteristic
327C2C2×(C22⋊D283)⋊C411yescharacteristic
328C2#3182694511yescharacteristic
329C2#3182709911yescharacteristic
330C2#3182711511yescharacteristic
331C2#3182712811yescharacteristic
332C2#3182717311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#380×C283C2
socle, cosocleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenter#380D283
hypocenterC283D4×C4⋊C4
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic283C2semidirect
4. C2×C4⋊C4×D283C2semidirect
5. #31826362C2semidirect
6. #31826339C2semidirect
7. #31826337C2semidirect
8. #31826334C2semidirect
9. #31826322C2semidirect
10. C4⋊C4×Dic283C2semidirect
11. #380×C283C2semidirect
16. C4×C22⋊D283C4semidirect
56. C2×C4×D283C2×C4semidirect
59. C4⋊Dic283D4semidirect
63. Dic283⋊C4C2×C4semidirect
64. C22⋊Dic283C2×C4semidirect
66. (C2×D283)⋊C4C2×C4semidirect
68. C4×Dic283C2×C4semidirect
72. C22×C4×C283C2×C4semidirect
87. C22⋊D283C4⋊C4semidirect
133. C22×C283C2×C4⋊C4semidirect
147. C2×D283C2×C4⋊C4semidirect
151. C4×C283C4×D4semidirect
156. Dic283C2×C4⋊C4semidirect
166. C283D4×C4⋊C4semidirect
177. #380D283semidirect
227. C22×C4C4×D283semidirect
307. C22C4⋊C4×D283semidirect
323. C4(C22⋊D283)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2832
C2×(C22⋊D283)⋊C42
C22×C4⋊Dic2832
C2×C4⋊C4×D2832
#318263622
#318263392
#318263372
#318263342
#318263222
C4⋊C4×Dic2832
#380×C2832
D4×C4⋊C4283