Finite Group Databasebeta

← #26023349

Subgroups — #26023349

Order 11392.

464 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×#15668002C211yesmaximal, characteristic
2#19151496C211yesmaximal, characteristic
3#19151495C211yesmaximal, characteristic
4#19151493C211yesmaximal, characteristic
5#19151493C211yesmaximal, characteristic
6#19151484C211yesmaximal, characteristic
7#19151483C211yesmaximal, characteristic
8#19151482C211yesmaximal, characteristic
9#19151482C211yesmaximal, characteristic
10C4×#13083553C211yesmaximal, characteristic
11C4×#13083553C211yesmaximal, characteristic
12C4×#13083553C211yesmaximal, characteristic
13#19151449C211yesmaximal, characteristic
14#19151449C211yesmaximal, characteristic
15C4×C4⋊C4×C89C211yesmaximal, characteristic
16#15668002C418yescomplemented
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2211yescharacteristic
24C2×#13083553C2211yescharacteristic
25C2×#13083553C2211yescharacteristic
26C2×#13083553C2211yescharacteristic
27C2×#13083553C2211yescharacteristic
28C2×#13083553C2211yescharacteristic
29C2×C4×Dic89C2211yescharacteristic
30C2×C4×Dic89C2211yescharacteristic
31C2×C4×Dic89C2211yescharacteristic
32C2×C4×Dic89C2211yescharacteristic
33C2×C4×Dic89C2211yescharacteristic
34C2×C4×Dic89C2211yescharacteristic
35#15667919C2211yescharacteristic
36#15667919C2211yescharacteristic
37#15667919C2211yescharacteristic
38#15667919C2211yescharacteristic
39#15667919C2211yescharacteristic
40#15667919C2211yescharacteristic
41#15667919C2211yescharacteristic
42#15667919C2211yescharacteristic
43#15667919C2211yescharacteristic
44#15667919C2211yescharacteristic
45C2×C4⋊C4×C89C2211yescharacteristic
46C2×C4⋊C4×C89C2211yescharacteristic
47C2×C42×C89C2211yescharacteristic
48C2×C42×C89C2211yescharacteristic
49C2×C42×C89C2211yescharacteristic
50#95×C89C2211yescharacteristic
51#95×C89C2211yescharacteristic
52C22×Dic89C2311yescharacteristic
53C22×Dic89C2311yescharacteristic
54C22×Dic89C2311yescharacteristic
55C22×Dic89C2311yescharacteristic
56C22×Dic89C2311yescharacteristic
57C22×Dic89C2311yescharacteristic
58C22×Dic89C2311yescharacteristic
59C22×Dic89C2311yescharacteristic
60C4⋊Dic89—41no—
61C4⋊Dic89C2×C414yes—
62#13083553—22no—
63#13083553—22no—
64#13083553—22no—
65#13083553—22no—
66#13083553—41no—
67#13083553C2×C414yes—
68#13083553C2×C414yes—
69#13083553C2×C414yes—
70#13083553C2×C414yes—
71#13083553Q814yes—
72C4×Dic89—22no—
73C4×Dic89—22no—
74C4×Dic89—22no—
75C4×Dic89—41no—
76C4×Dic89—41no—
77C4×Dic89C2×C414yes—
78C22×C4×C89C2311yescharacteristic
79C22×C4×C89C2311yescharacteristic
80C22×C4×C89C2311yescharacteristic
81C22×C4×C89C2311yescharacteristic
82C22×C4×C89C2311yescharacteristic
83C22×C4×C89C2311yescharacteristic
84C22×C4×C89C2311yescharacteristic
85C4⋊C4×C89—22no—
86C4⋊C4×C89C2×C414yes—
87C42×C89—22no—
88C42×C89—41no—
89C42×C89—41no—
90C23×C89C2411yescharacteristic
91C2×C4×C89—21no—
92C2×C4×C89—21no—
93C2×C4×C89—21no—
94C2×C4×C89—21no—
95C2×C4×C89—21no—
96C2×C4×C89—21no—
97C2×C4×C89—21no—
98C2×C4×C89—21no—
99C2×C4×C89—21no—
100C2×C4×C89—21no—
101C2×C4×C89—21no—
102C2×C4×C89—21no—
103C2×C4×C89—21no—
104C2×C4×C89—21no—
105C2×C4×C89—21no—
106C2×C4×C89C22×C412yes—
107C2×C4×C89C22×C412yes—
108C2×C4×C89C22×C412yes—
109C2×C4×C89C2×Q812yes—
110C2×C4×C89#4112yes—
111C2×C4×C89#4112yes—
112C2×Dic89—21no—
113C2×Dic89—21no—
114C2×Dic89—21no—
115C2×Dic89—21no—
116C2×Dic89—21no—
117C2×Dic89—21no—
118C2×Dic89—21no—
119C2×Dic89—21no—
120C2×Dic89—21no—
121C2×Dic89—21no—
122C2×Dic89—21no—
123C2×Dic89—21no—
124C2×Dic89—21no—
125C2×Dic89—21no—
126C2×Dic89—21no—
127C2×Dic89—21no—
128C2×Dic89—21no—
129C2×Dic89C22×C412yes—
130C2×Dic89C22×C412yes—
131C2×Dic89C22×C412yes—
132C2×Dic89C22×C412yes—
133C2×Dic89C2×Q812yes—
134C2×Dic89C2×Q812yes—
135C2×Dic89#4112yes—
136C22×C89C23×C411yescharacteristic
137C22×C89C22×Q811yescharacteristic
138C22×C89C2×#4111yescharacteristic
139C22×C89C2×#4111yescharacteristic
140C22×C89C2×#4111yescharacteristic
141C22×C89H(5,𝔽2)11yescharacteristic
142C22×C892−1+411yescharacteristic
143C4×C89—22no—
144C4×C89—22no—
145C4×C89—22no—
146C4×C89—22no—
147C4×C89—22no—
148C4×C89—22no—
149C4×C89—41no—
150Dic89—22no—
151Dic89—22no—
152Dic89—22no—
153Dic89—22no—
154Dic89—41no—
155Dic89—41no—
156Dic89—41no—
157Dic89C4×Q814yes—
158C2×C89C2×C4×Q811yescharacteristic
159C2×C89C4×#4111yescharacteristic
160C2×C89#52011yescharacteristic
161C2×C89#55211yescharacteristic
162C2×C89#55311yescharacteristic
163C2×C89#55411yescharacteristic
164C2×C89#55711yescharacteristic
165#2370—891nomaximal, Sylow
166C89#237011yescharacteristic, complemented, Sylow
167C2×#125—891no—
168#389—891no—
169#389—891no—
170#389—891no—
171#389—891no—
172#387—891no—
173#387—891no—
174#387—891no—
175#387—891no—
176C4×C4⋊C4—891no—
177C4×C4⋊C4—891no—
178C4×C4⋊C4—891no—
179C4×C4⋊C4—891no—
180C4×C4⋊C4—891no—
181C4×C4⋊C4D8911yescharacteristic
182#125—898no—
183C2×C4⋊C4—891no—
184C2×C4⋊C4—891no—
185C2×C4⋊C4—891no—
186C2×C4⋊C4—891no—
187C2×C4⋊C4—891no—
188C2×C4⋊C4—891no—
189C2×C4⋊C4—891no—
190C2×C4⋊C4—891no—
191C2×C4⋊C4—891no—
192C2×C4⋊C4—891no—
193C2×C4⋊C4—891no—
194C2×C4⋊C4—891no—
195C2×C4⋊C4C2×D8911yescharacteristic
196C2×C4⋊C4C2×D8911yescharacteristic
197C2×C42—891no—
198C2×C42—891no—
199C2×C42—891no—
200C2×C42—891no—
201C2×C42—891no—
202C2×C42—891no—
203C2×C42C2×D8911yescharacteristic
204C2×C42C2×D8911yescharacteristic
205C2×C42C2×D8911yescharacteristic
206#95—891no—
207#95—891no—
208#95—891no—
209#95—891no—
210#95—891no—
211#95—891no—
212#95—891no—
213#95—891no—
214#95—891no—
215#95—891no—
216#95C2×D8911yescharacteristic
217#95C2×D8911yescharacteristic
218C22×C4—891no—
219C22×C4—891no—
220C22×C4—891no—
221C22×C4—891no—
222C22×C4—891no—
223C22×C4—891no—
224C22×C4—891no—
225C22×C4—891no—
226C22×C4C22×D8911yescharacteristic
227C22×C4C22×D8911yescharacteristic
228C22×C4C22×D8911yescharacteristic
229C22×C4C22×D8911yescharacteristic
230C22×C4C22×D8911yescharacteristic
231C22×C4C22×D8911yescharacteristic
232C22×C4C22×D8911yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—894no—
235C4⋊C4—894no—
236C4⋊C4—894no—
237C4⋊C4—894no—
238C4⋊C4—894no—
239C4⋊C4—894no—
240C4⋊C4—3561no—
241C4⋊C4—3561no—
242C4⋊C4—1782no—
243C4⋊C4—1782no—
244C4⋊C4—1782no—
245C4⋊C4—1782no—
246C4⋊C4C4×D8914yes—
247C42—22no—
248C42—41no—
249C42—41no—
250C42—894no—
251C42—3561no—
252C42—3561no—
253C42—1782no—
254C42—1782no—
255C42—1782no—
256C23C23×D8911yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—892no—
273C2×C4—892no—
274C2×C4—892no—
275C2×C4—892no—
276C2×C4—892no—
277C2×C4—892no—
278C2×C4—892no—
279C2×C4—1781no—
280C2×C4—1781no—
281C2×C4—1781no—
282C2×C4—1781no—
283C2×C4—1781no—
284C2×C4—1781no—
285C2×C4—1781no—
286C2×C4—1781no—
287C2×C4—1781no—
288C2×C4—1781no—
289C2×C4—1781no—
290C2×C4—1781no—
291C2×C4—1781no—
292C2×C4—1781no—
293C2×C4—1781no—
294C2×C4—1781no—
295C2×C4—1781no—
296C2×C4C2×C4×D8912yes—
297C2×C4C2×C4×D8912yes—
298C2×C4C2×C4×D8912yes—
299C2×C4Q8×D8912yes—
300C2×C4#1308357412yes—
301C2×C4#1308357412yes—
302C22C22×C4×D8911yescharacteristic
303C22C2×Q8×D8911yescharacteristic
304C22#41×D8911yescharacteristic
305C22C2×#1308357411yescharacteristic
306C22C2×#1308357411yescharacteristic
307C22#1566805711yescharacteristic
308C22#1566805911yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—894no—
317C4—3561no—
318C4—3561no—
319C4—3561no—
320C4—1782no—
321C4—1782no—
322C4—1782no—
323C4—1782no—
324C2C4×Q8×D8911yescharacteristic
325C2C4×#1308357411yescharacteristic
326C2#1915207711yescharacteristic
327C2#1915228111yescharacteristic
328C2#1915229711yescharacteristic
329C2#1915230311yescharacteristic
330C2#1915232611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutatorC22×C89C23×C4
FittingC4×C4⋊C4×C89C2
socle, prime radical, cosocleC23×C89C24
hypercenterC4×C4⋊C4D89
hypocenterC89#2370
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #15668002C4semidirect
166. C89#2370semidirect

Maximal subgroups

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

subgroupindex
C2×#156680022
#191514962
#191514952
#191514932
#191514842
#191514832
#191514822
C4×#130835532
#191514492
C4×C4⋊C4×C892
#237089