Finite Group Databasebeta

← #36572566

Subgroups — #36572566

Order 22784.

982 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D356C211yesmaximal, characteristic
2C2×#19151633C212yesmaximal, complemented
3#26023199C212yesmaximal
4#26021010C212yesmaximal, complemented
5#26020452C214yesmaximal, complemented
6#26020409C211yesmaximal, characteristic, complemented
7#26020274C212yesmaximal, complemented
8C4×#106×C89C211yesmaximal, characteristic, complemented
9C22×C8×D89C2212yes—
10C2×C4×D356C2211yescharacteristic
11C2×#15667970C2214yes—
12C8×D356C418yescomplemented
13#19151633—28no—
14C2×#15667945C2214yes—
15C2×#15667944C2212yes—
16C2×#15667944C2212yes—
17C2×C4⋊#10623494C2211yescharacteristic
18C2×#15667924C2212yes—
19#19151500—22no—
20#19151490—24no—
21#19151468C2212yes—
22#19151455C2214yes—
23C4×C4⋊Dic89—22no—
24#19151360C2214yes—
25C2×#106×C89C2211yescharacteristic
26C2×#106×C89C2211yescharacteristic
27C2×C4×C8×C89C2211yescharacteristic
28C4×C4⋊C4×C89C2212yes—
29#340×C89C2212yes—
30C22×D356D411yescharacteristic
31C22×C4×D89C2312yes—
32C22×#10623494C2312yes—
33C2×C8×D89—24no—
34C2×C8×D89—24no—
35C2×C8×D89C2×C418yes—
36C4×D356C2×C414yes—
37C4×D356Q814yes—
38#15667970—28no—
39#15667970—44no—
40C2×C4⋊Dic89—22no—
41C2×C4⋊Dic89—22no—
42C2×C4⋊Dic89D411yescharacteristic
43C2×C4⋊Dic89C2314yes—
44C2×#13083551—24no—
45C2×#13083551—24no—
46C2×#13083551D412yes—
47C2×C4×Dic89—24no—
48#15667945—28no—
49#15667944—24no—
50#15667944—42no—
51C4⋊#10623494C2×C414yes—
52#15667924C2×C418yes—
53#15667919—24no—
54C22×C8×C89C2311yescharacteristic
55C22×C8×C89C2311yescharacteristic
56C2×C4⋊C4×C89C2312yes—
57C2×C4⋊C4×C89C2312yes—
58C2×C42×C89—22no—
59C2×C42×C89C2311yescharacteristic
60#106×C89—22no—
61#106×C89D414yescomplemented
62C4×C8×C89C2×C414yes—
63#95×C89—22no—
64C23×D89C2×D412yes—
65C2×D356—24no—
66C2×D356C4⋊C414yes—
67C22×Dic89—24no—
68C22×Dic89C2×D412yes—
69C2×C4×D89—22no—
70C2×C4×D89—22no—
71C2×C4×D89—22no—
72C2×C4×D89—22no—
73C2×C4×D89C22×C414yes—
74C2×C4×D89C2×Q814yes—
75C2×#10623494—22no—
76C2×#10623494—22no—
77C2×#10623494C22×C414yes—
78C8×D89—216no—
79C4⋊Dic89—24no—
80C4⋊Dic89—24no—
81C4⋊Dic89—44no—
82C4⋊Dic89—82no—
83C4⋊Dic89C4⋊C414yes—
84#13083551—48no—
85#13083551—84no—
86#13083551C4⋊C418yes—
87C4×Dic89—48no—
88C22×C4×C89—22no—
89C22×C4×C89—22no—
90C22×C4×C89C2×D411yescharacteristic
91C22×C4×C89C2×D411yescharacteristic
92C22×C4×C89C2411yescharacteristic
93C2×C8×C89—21no—
94C2×C8×C89—21no—
95C2×C8×C89C22×C412yes—
96C2×C8×C89C22×C412yes—
97C2×C8×C89C2×D412yes—
98C2×C8×C89#4112yes—
99C4⋊C4×C89—22no—
100C4⋊C4×C89—22no—
101C4⋊C4×C89—22no—
102C4⋊C4×C89C2×D414yes—
103C42×C89—44no—
104C42×C89C22×C412yes—
105C42×C89C2×Q812yes—
106C23×C89C22×D411yescharacteristic
107C22×D89—22no—
108C22×D89—22no—
109C22×D89—24no—
110C22×D89—24no—
111C22×D89C2×C4⋊C414yes—
112C2×C4×C89—22no—
113C2×C4×C89—24no—
114C2×C4×C89—42no—
115C2×C4×C89—42no—
116C2×C4×C89—42no—
117C2×C4×C89—42no—
118C2×C4×C89—42no—
119C2×C4×C89C2×C4⋊C412yes—
120C2×C4×C89C2×C4⋊C412yes—
121C2×C4×C89#13514yes—
122C2×C4×C89C23×C411yescharacteristic
123C2×C4×C89C22×D411yescharacteristic
124C2×C4×C89C22×Q811yescharacteristic
125C2×C4×C89C2×#4111yescharacteristic
126C2×C4×C89H(5,𝔽2)11yescharacteristic
127C2×C4×C892−1+411yescharacteristic
128C2×Dic89—22no—
129C2×Dic89—22no—
130C2×Dic89—44no—
131C2×Dic89—44no—
132C2×Dic89—44no—
133C2×Dic89C2×C4⋊C414yes—
134D356—28no—
135C4×D89—24no—
136C4×D89—24no—
137C4×D89—24no—
138C4×D89—24no—
139C8×C89—22no—
140C8×C89C4×D414yes—
141#10623494—24no—
142C22×C89C22×C4⋊C411yescharacteristic
143C22×C89D4211yescharacteristic
144C22×C89#54711yescharacteristic
145C22×C89C2×#13512yes—
146C22×C89#57712yes—
147C2×D89—24no—
148C2×D89—24no—
149C2×D89—24no—
150C2×D89—44no—
151C2×D89—44no—
152C4×C89—22no—
153C4×C89—44no—
154C4×C89—82no—
155C4×C89#42714yescomplemented
156C4×C89C2×C4×D411yescharacteristic
157C4×C89#52011yescharacteristic
158C4×C89D4×Q811yescharacteristic
159C4×C89#55411yescharacteristic
160Dic89—24no—
161Dic89—84no—
162#22657—891nomaximal, Sylow
163C2×C89D4×C4⋊C411yescharacteristic
164C2×C89C2×#42711yescharacteristic
165C2×C89#291211yescharacteristic
166C2×C89#328412yes—
167C2×C89#334012yes—
168D89—44no—
169C2×C8×D4—891no—
170C2×#427—892no—
171#2354—892no—
172#1947—892no—
173#1854—894no—
174#1844—891no—
175#1807—892no—
176C4×#106D8911yescharacteristic, complemented
177C89#2265711yescharacteristic, complemented, Sylow
178C23×C8—892no—
179C2×C4×D4—891no—
180C2×#117—894no—
181C8×D4—898no—
182#427—1788no—
183C2×#107—894no—
184C2×#106—892no—
185C2×#106—892no—
186C2×#106C2×D8911yescharacteristic
187C2×#106C2×D8911yescharacteristic
188C2×C4⋊C8—891no—
189C2×C22⋊C8—892no—
190C2×C4×C8C2×D8911yescharacteristic
191#390—1782no—
192#388—1784no—
193#384—892no—
194#380—894no—
195C4×C4⋊C4—1782no—
196C4×C4⋊C4C2×D8912yes—
197#340—894no—
198#340C2×D8912yes—
199C22×D4—891no—
200C23×C4—892no—
201C22×C8—892no—
202C22×C8—898no—
203C22×C8—1784no—
204C22×C8—1784no—
205C22×C8C22×D8911yescharacteristic
206C22×C8C22×D8911yescharacteristic
207C4×D4—894no—
208C4×D4—894no—
209#117—3564no—
210#117—1788no—
211C2×C4⋊C4—891no—
212C2×C4⋊C4—894no—
213C2×C4⋊C4—1782no—
214C2×C4⋊C4—1782no—
215C2×C4⋊C4C22×D8912yes—
216C2×C4⋊C4C22×D8912yes—
217C2×C22⋊C4—892no—
218C2×C22⋊C4—1784no—
219C2×C22⋊C4—1784no—
220C2×C42—22no—
221C2×C42—1784no—
222C2×C42C22×D8911yescharacteristic
223#107—1788no—
224#106—22no—
225#106—3562no—
226#106—1784no—
227#106D35614yescomplemented
228C4⋊C8—894no—
229C22⋊C8—898no—
230C4×C8C4×D8914yes—
231#95—22no—
232#95—1784no—
233C24—892no—
234C2×D4—894no—
235C2×D4—1784no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—892no—
239C22×C4—894no—
240C22×C4—894no—
241C22×C4—1784no—
242C22×C4—1782no—
243C22×C4—1782no—
244C22×C4—1782no—
245C22×C4—1782no—
246C22×C4D4×D8911yescharacteristic
247C22×C4D4×D8911yescharacteristic
248C22×C4C23×D8911yescharacteristic
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—894no—
252C2×C8—1782no—
253C2×C8—1782no—
254C2×C8—17816no—
255C2×C8C2×C4×D8912yes—
256C2×C8C2×C4×D8912yes—
257C2×C8C2×D35612yes—
258C2×C8#1308357412yes—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—894no—
263C4⋊C4—3564no—
264C4⋊C4—1784no—
265C4⋊C4—1784no—
266C4⋊C4—7122no—
267C4⋊C4C2×D35614yes—
268C22⋊C4—898no—
269C22⋊C4—3568no—
270C22⋊C4—7124no—
271C42—44no—
272C42—3568no—
273C42C2×C4×D8912yes—
274C42Q8×D8912yes—
275C23—894no—
276C23—1784no—
277C23—1782no—
278C23—1782no—
279C23—1784no—
280C23C2×D4×D8911yescharacteristic
281D4—1788no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—894no—
290C2×C4—3564no—
291C2×C4—3564no—
292C2×C4—3564no—
293C2×C4—1782no—
294C2×C4—1782no—
295C2×C4—1784no—
296C2×C4—1784no—
297C2×C4—1784no—
298C2×C4—1784no—
299C2×C4C4⋊C4×D8912yes—
300C2×C4C4⋊C4×D8912yes—
301C2×C4#1566803314yes—
302C2×C4C22×C4×D8911yescharacteristic
303C2×C4C22×D35611yescharacteristic
304C2×C4C2×Q8×D8911yescharacteristic
305C2×C4C2×#1308357411yescharacteristic
306C2×C4#1566805811yescharacteristic
307C2×C4#1566805911yescharacteristic
308C8—22no—
309C8—1784no—
310C8C4×D35614yes—
311C22—3564no—
312C22—3564no—
313C22—1784no—
314C22—1784no—
315C22—1784no—
316C22C2×C4⋊C4×D8911yescharacteristic
317C22D4×D35611yescharacteristic
318C22#1915225311yescharacteristic
319C22C2×#1566803312yes—
320C22#1915240512yes—
321C4—22no—
322C4—44no—
323C4—82no—
324C4—1784no—
325C4—7124no—
326C4#1915163314yescomplemented
327C4C2×C4×D35611yescharacteristic
328C4#1915207811yescharacteristic
329C4Q8×D35611yescharacteristic
330C4#1915230811yescharacteristic
331C2—3564no—
332C2C4⋊C4×D35611yescharacteristic
333C2C2×#1915163311yescharacteristic
334C2#2602884411yescharacteristic
335C2#2603198312yes—
336C2#2603266712yes—
subgroupG/H
centerC23C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC4×#106×C89C2
socleC23×C89C22×D4
prime radicalC22×D356D4
cosocleC22×C4×C89C24
hypercenterC4×#106D89
hypocenterC89#22657
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
2. C2×#19151633C2semidirect
4. #26021010C2semidirect
5. #26020452C2semidirect
6. #26020409C2semidirect
7. #26020274C2semidirect
8. C4×#106×C89C2semidirect
12. C8×D356C4semidirect
61. #106×C89D4semidirect
155. C4×C89#427semidirect
176. C4×#106D89semidirect
177. C89#22657semidirect
227. #106D356semidirect
326. C4#19151633semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D3562
C2×#191516332
#260231992
#260210102
#260204522
#260204092
#260202742
C4×#106×C892
#2265789