Finite Group Databasebeta

← (C2×D283)⋊#95 #49119482

Subgroups — (C2×D283)⋊#95 #49119482

Order 36224.

1088 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D283C211yesmaximal, characteristic
2C22×(C2×D283)⋊C4C212yesmaximal
3C2×C283⋊#95C211yesmaximal, characteristic, complemented
4C2×C283⋊#95C212yesmaximal, complemented
5C2×#95×C283C211yesmaximal, characteristic, complemented
6C24×D283C2211yescharacteristic
7C23×Dic283C2212yes—
8C23×Dic283C2211yescharacteristic
9C22×C4×D283—24no—
10C22×C4×D283—24no—
11C22×C4×D283—22no—
12C22×C4×D283—22no—
13C22×C4×D283C414yescomplemented
14C2×(C2×D283)⋊C4—24no—
15C2×(C2×D283)⋊C4—24no—
16C2×(C2×D283)⋊C4C418yescomplemented
17C283⋊#95—24no—
18C283⋊#95—22no—
19C23×C4×C283C2212yes—
20C23×C4×C283C2211yescharacteristic
21#95×C283—22no—
22C23×D283—22no—
23C23×D283—21no—
24C23×D283—21no—
25C23×D283—21no—
26C23×D283—22no—
27C23×D283—21no—
28C23×D283C2×C414yes—
29C23×D283C2×C412yes—
30C23×D283D412yes—
31C23×D283D414yes—
32C23×D283Q812yes—
33C22×Dic283—22no—
34C22×Dic283—21no—
35C22×Dic283—21no—
36C22×Dic283—22no—
37C22×Dic283—22no—
38C22×Dic283—22no—
39C22×Dic283—22no—
40C22×Dic283—22no—
41C22×Dic283—22no—
42C22×Dic283C2×C412yes—
43C22×Dic283C2×C414yescomplemented
44C22×Dic283D414yes—
45C2×C4×D283—216no—
46C2×C4×D283—216no—
47C2×C4×D283—28no—
48C2×C4×D283—28no—
49C2×C4×D283—28no—
50(C2×D283)⋊C4—216no—
51C24×C283C2311yescharacteristic
52C22×C4×C283—22no—
53C22×C4×C283—22no—
54C22×C4×C283—22no—
55C22×C4×C283—22no—
56C22×C4×C283—22no—
57C22×C4×C283—22no—
58C22×C4×C283—22no—
59C22×C4×C283—22no—
60C22×C4×C283C2×C412yes—
61C22×C4×C283C2×C414yescomplemented
62C22×C4×C283D412yes—
63C22×C4×C283D412yes—
64C22×D283—22no—
65C22×D283—22no—
66C22×D283—22no—
67C22×D283—22no—
68C22×D283—24no—
69C22×D283—24no—
70C22×D283—24no—
71C22×D283—24no—
72C22×D283—24no—
73C22×D283—24no—
74C22×D283—22no—
75C22×D283—24no—
76C22×D283—22no—
77C22×D283—22no—
78C22×D283—24no—
79C22×D283—22no—
80C22×D283—24no—
81C22×D283—24no—
82C22×D283C4214yes—
83C22×D283C22⋊C418yes—
84C22×D283C22⋊C414yes—
85C22×D283C4⋊C414yes—
86C22×D283C4⋊C418yes—
87C2×Dic283—22no—
88C2×Dic283—22no—
89C2×Dic283—24no—
90C2×Dic283—24no—
91C2×Dic283—24no—
92C2×Dic283—24no—
93C2×Dic283—24no—
94C2×Dic283—42no—
95C2×Dic283—42no—
96C2×Dic283—42no—
97C2×Dic283—42no—
98C2×Dic283C22⋊C414yescomplemented
99C4×D283—232no—
100C23×C283C22×C411yescharacteristic
101C23×C283C22×C412yes—
102C23×C283C2×D412yes—
103C23×C283C2×D411yescharacteristic
104C23×C283C2×D412yes—
105C23×C283C2×D411yescharacteristic
106C23×C283C2×D411yescharacteristic
107C23×C283C2×Q811yescharacteristic
108C23×C283#4111yescharacteristic
109C23×C283#4112yes—
110C23×C283#4111yescharacteristic
111C2×C4×C283—22no—
112C2×C4×C283—22no—
113C2×C4×C283—24no—
114C2×C4×C283—24no—
115C2×C4×C283—24no—
116C2×C4×C283—24no—
117C2×C4×C283—24no—
118C2×C4×C283—42no—
119C2×C4×C283—42no—
120C2×C4×C283—42no—
121C2×C4×C283—42no—
122C2×C4×C283C22⋊C414yescomplemented
123C22×C283C2×C4211yescharacteristic
124C22×C283C2×C22⋊C411yescharacteristic
125C22×C283C2×C22⋊C412yes—
126C22×C283C2×C22⋊C411yescharacteristic
127C22×C283C2×C22⋊C411yescharacteristic
128C22×C283C2×C4⋊C411yescharacteristic
129C22×C283C2×C4⋊C412yes—
130C22×C283#11711yescharacteristic
131C22×C283#11711yescharacteristic
132C22×C283C4×D412yes—
133C22×C283C4×D412yes—
134C22×C283C4×D412yes—
135C22×C283C4×D412yes—
136C22×C283#12012yes—
137C22×C283#12012yes—
138C22×C283#12111yescharacteristic
139C22×C283#12112yes—
140C22×C283#12111yescharacteristic
141C22×C283C22⋊Q811yescharacteristic
142C22×C283C22⋊Q812yes—
143C22×C283C22⋊Q811yescharacteristic
144C22×C283#12312yes—
145C22×C283#12312yes—
146C2×D283—24no—
147C2×D283—24no—
148C2×D283—24no—
149C2×D283—24no—
150C2×D283—24no—
151C2×D283—24no—
152C2×D283—28no—
153C2×D283—28no—
154C2×D283—28no—
155C2×D283—28no—
156C2×D283#9518yescomplemented
157C4×C283—24no—
158C4×C283—44no—
159Dic283—24no—
160Dic283—44no—
161C2×C283C2×#9511yescharacteristic
162C2×C283C4×C22⋊C411yescharacteristic
163C2×C283C4×C22⋊C411yescharacteristic
164C2×C283#37911yescharacteristic
165C2×C283#38011yescharacteristic
166C2×C283#38011yescharacteristic
167C2×C283#38111yescharacteristic
168C2×C283#38512yes—
169C2×C283#38512yes—
170C2×C283#38612yes—
171C2×C283#38612yes—
172D283—28no—
173C283C22⋊#9511yescharacteristic, complemented, Sylow
174C22⋊#95—2831nomaximal, Sylow
175C24×C4—2831no—
176C22×C22⋊C4—2832no—
177C2×#95—2832no—
178C2×#95—2831no—
179C2×#95D28311yescharacteristic, complemented
180C25—2831no—
181C23×C4—2831no—
182C23×C4—2832no—
183C23×C4—2834no—
184C23×C4—5664no—
185C23×C4—5664no—
186C23×C4—5662no—
187C23×C4—5662no—
188C23×C4C2×D28312yes—
189C23×C4C2×D28311yescharacteristic
190C2×C22⋊C4—2838no—
191C2×C22⋊C4—5664no—
192C2×C22⋊C4—5664no—
193#95—22no—
194#95—5664no—
195#95—5662no—
196C24—2834no—
197C24—2832no—
198C24—2832no—
199C24—2834no—
200C24—2832no—
201C24—5662no—
202C24—5661no—
203C24—5661no—
204C24—5661no—
205C24—5662no—
206C24—5661no—
207C24C22×D28311yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—2832no—
217C22×C4—2834no—
218C22×C4—2834no—
219C22×C4—5668no—
220C22×C4—5668no—
221C22×C4—56616no—
222C22×C4—56616no—
223C22×C4—5662no—
224C22×C4—5661no—
225C22×C4—5661no—
226C22×C4—5668no—
227C22×C4—5662no—
228C22×C4—5662no—
229C22×C4—5662no—
230C22×C4—5662no—
231C22×C4—5662no—
232C22×C4—5662no—
233C22×C4C4×D28312yes—
234C22×C4C4×D28314yescomplemented
235C22×C4C22⋊D28312yes—
236C22×C4D113212yes—
237C22⋊C4—56616no—
238C23—2834no—
239C23—2838no—
240C23—2834no—
241C23—2834no—
242C23—2838no—
243C23—5662no—
244C23—5662no—
245C23—5662no—
246C23—5662no—
247C23—5664no—
248C23—5664no—
249C23—5664no—
250C23—5664no—
251C23—5664no—
252C23—5664no—
253C23—5662no—
254C23—5664no—
255C23—5662no—
256C23—5662no—
257C23—5664no—
258C23—5662no—
259C23—5664no—
260C23—5664no—
261C23C2×C4×D28311yescharacteristic
262C23C2×C4×D28312yes—
263C23D4×D28312yes—
264C23D4×D28311yescharacteristic
265C23D4×D28312yes—
266C23C2×C22⋊D28311yescharacteristic
267C23C2×D113211yescharacteristic
268C23Q8×D28311yescharacteristic
269C23#1798539111yescharacteristic
270C23#1798539212yes—
271C23#1798539311yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—2834no—
284C2×C4—56632no—
285C2×C4—5662no—
286C2×C4—5662no—
287C2×C4—5664no—
288C2×C4—5664no—
289C2×C4—5664no—
290C2×C4—5664no—
291C2×C4—5664no—
292C2×C4—11322no—
293C2×C4—11322no—
294C2×C4—11322no—
295C2×C4—11322no—
296C2×C4(C2×D283)⋊C414yescomplemented
297C22—2838no—
298C22—5664no—
299C22—5664no—
300C22—5664no—
301C22—5664no—
302C22—5664no—
303C22—5664no—
304C22—5668no—
305C22—5668no—
306C22—5668no—
307C22—5668no—
308C22C42×D28311yescharacteristic
309C22C22⋊C4×D28311yescharacteristic
310C22C22⋊C4×D28312yes—
311C22C22⋊C4×D28311yescharacteristic
312C22C2×(C2×D283)⋊C411yescharacteristic
313C22C4⋊C4×D28311yescharacteristic
314C22C4⋊C4×D28312yes—
315C22#2258356711yescharacteristic
316C22#2258356811yescharacteristic
317C22(C22⋊D283)⋊C412yes—
318C22C4×C22⋊D28312yes—
319C22#2258357212yes—
320C22C4×D113212yes—
321C22#2258357812yes—
322C22#2258358012yes—
323C22#2258358111yescharacteristic
324C22#2258358312yes—
325C22#2258358511yescharacteristic
326C22#2258358611yescharacteristic
327C22#2258358812yes—
328C22#2258359011yescharacteristic
329C22#2258359212yes—
330C22#2258359512yes—
331C4—24no—
332C4—44no—
333C4—5664no—
334C4—11324no—
335C2—5668no—
336C2#95×D28311yescharacteristic
337C2#3182631211yescharacteristic
338C2C4×(C2×D283)⋊C411yescharacteristic
339C2#3182632011yescharacteristic
340C2#3182632211yescharacteristic
341C2#3182632411yescharacteristic
342C2#3182632711yescharacteristic
343C2#3182633612yes—
344C2#3182633912yes—
345C2#3182634112yes—
346C2#3182634312yes—
subgroupG/H
center, FrattiniC24C22×D283
commutatorC22×C283C2×C42
FittingC2×#95×C283C2
socle, cosocleC24×C283C23
prime radicalC24×D283C22
hypercenterC2×#95D283
hypocenterC283C22⋊#95
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×C283⋊#95C2semidirect
4. C2×C283⋊#95C2semidirect
5. C2×#95×C283C2semidirect
13. C22×C4×D283C4semidirect
16. C2×(C2×D283)⋊C4C4semidirect
43. C22×Dic283C2×C4semidirect
61. C22×C4×C283C2×C4semidirect
98. C2×Dic283C22⋊C4semidirect
122. C2×C4×C283C22⋊C4semidirect
156. C2×D283#95semidirect
173. C283C22⋊#95semidirect
179. C2×#95D283semidirect
234. C22×C4C4×D283semidirect
296. C2×C4(C2×D283)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D2832
C22×(C2×D283)⋊C42
C2×C283⋊#952
C2×#95×C2832
C22⋊#95283