Finite Group Databasebeta

← #36552201

Subgroups — #36552201

Order 22784.

1630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#13083574C211yesmaximal, characteristic
2C2×#19151592C212yesmaximal
3C22×#15667923C211yesmaximal, characteristic, complemented
4#26020085C214yesmaximal, complemented
5#26020080C214yesmaximal, complemented
6#26019968C212yesmaximal, complemented
7C4×#117×C89C211yesmaximal, characteristic, complemented
8C22×#13083574C2211yescharacteristic
9C23×#10623494C2212yes—
10C4×#13083574—24no—
11C4×#13083574C418yescomplemented
12C2×C4×Dic178C2212yes—
13C2×C4×D356C2212yes—
14C2×C4×C22⋊D89—22no—
15C2×#15667971C2211yescharacteristic
16C2×#15667969—21no—
17C2×C42×D89—21no—
18#19151592C4116yescomplemented
19C2×#15667935C2214yes—
20C2×#15667932C2214yes—
21C2×#15667923—24no—
22C2×#15667923C2214yes—
23#19151360C2218yes—
24C2×#117×C89C2212yes—
25C22×C42×C89C2211yescharacteristic
26C4×C4⋊C4×C89C2214yes—
27C4×C22⋊C4×C89—22no—
28#376×C89—21no—
29C43×C89—21no—
30C2×#13083574—22no—
31C2×#13083574—24no—
32C2×#13083574C2×C414yes—
33C2×#13083574C2×C418yes—
34C22×Dic178C2311yescharacteristic
35C22×D356C2311yescharacteristic
36C22×C22⋊D89—21no—
37C22×C4×D89—21no—
38C22×C4×D89—22no—
39C22×#10623494—24no—
40C22×#10623494—24no—
41C22×#10623494C2×C418yescomplemented
42C22×#10623494C2314yes—
43C4×Dic178—24no—
44C4×Dic178C2×C418yes—
45C4×D356—24no—
46C4×D356C2×C418yes—
47C4×C22⋊D89—216no—
48#15667971—22no—
49#15667971C2×C414yes—
50#15667969—28no—
51C2×C4⋊Dic89C2312yes—
52C2×#13083553—22no—
53C2×C22⋊Dic89—21no—
54C2×#13083551—22no—
55C2×C4×Dic89—21no—
56C2×C4×Dic89—22no—
57C42×D89—28no—
58#15667935C2×C4116yescomplemented
59#15667932C2×C4116yescomplemented
60#15667923—28no—
61C23×C4×C89D412yes—
62C23×C4×C89C2311yescharacteristic
63#117×C89—24no—
64#117×C89C2×C418yescomplemented
65C2×C4⋊C4×C89C2314yes—
66C2×C22⋊C4×C89—22no—
67C2×C42×C89—22no—
68C2×C42×C89—24no—
69C2×C42×C89C2×C414yes—
70C2×C42×C89D414yes—
71C2×C42×C89D411yescharacteristic
72C2×C42×C89D411yescharacteristic
73C2×C42×C89C2312yes—
74#95×C89—24no—
75C23×D89—21no—
76#13083574—28no—
77#13083574—216no—
78#13083574C42116yescomplemented
79C2×Dic178—21no—
80C2×Dic178—22no—
81C2×Dic178C22×C412yes—
82C2×Dic178C22×C414yes—
83C2×D356—21no—
84C2×D356—22no—
85C2×D356C22×C412yes—
86C2×D356C22×C414yes—
87C2×C22⋊D89—24no—
88C2×C22⋊D89—28no—
89C22×Dic89—21no—
90C22×Dic89—22no—
91C2×C4×D89—24no—
92C2×C4×D89—28no—
93C2×C4×D89—28no—
94C2×C4×D89—48no—
95C2×#10623494—216no—
96C2×#10623494—24no—
97C2×#10623494—24no—
98C2×#10623494C22×C418yes—
99C4⋊Dic89—22no—
100C4⋊Dic89C22×C414yes—
101#13083553—28no—
102C22⋊Dic89—24no—
103#13083551—28no—
104C4×Dic89—24no—
105C4×Dic89—28no—
106C24×C89C2×D411yescharacteristic
107C22×C4×C89—24no—
108C22×C4×C89—44no—
109C22×C4×C89C22⋊C418yes—
110C22×C4×C89C22×C412yes—
111C22×C4×C89C22×C414yes—
112C22×C4×C89C2×D412yes—
113C22×C4×C89C2×D412yes—
114C22×C4×C89C2×D411yescharacteristic
115C22×C4×C89C2×D412yes—
116C22×C4×C89#4114yes—
117C22×C4×C89C2411yescharacteristic
118C4⋊C4×C89—24no—
119C4⋊C4×C89C22×C418yes—
120C22⋊C4×C89—28no—
121C42×C89—28no—
122C42×C89—48no—
123C42×C89C22⋊C414yes—
124C42×C89C22⋊C414yes—
125C42×C89C22×C414yes—
126C42×C89C2×D414yes—
127C23×C89—24no—
128C23×C89C2×C22⋊C412yes—
129C23×C89C4×D414yes—
130C23×C89C22×D411yescharacteristic
131C22×D89—22no—
132C22×D89—24no—
133C22×D89—44no—
134C2×C4×C89—24no—
135C2×C4×C89—24no—
136C2×C4×C89—28no—
137C2×C4×C89—48no—
138C2×C4×C89—48no—
139C2×C4×C89C2×C4214yes—
140C2×C4×C89C2×C22⋊C414yes—
141C2×C4×C89C2×C22⋊C414yes—
142C2×C4×C89C2×C22⋊C412yes—
143C2×C4×C89#11714yes—
144C2×C4×C89C4×D414yes—
145C2×C4×C89C4×D418yes—
146C2×C4×C89C23×C411yescharacteristic
147C2×C4×C89C23×C412yes—
148C2×C4×C89C22×D411yescharacteristic
149C2×C4×C89C2×#4112yes—
150C22⋊D89—216no—
151C2×Dic89—22no—
152C2×Dic89—24no—
153C2×Dic89—24no—
154C2×Dic89—44no—
155D356—22no—
156D356—24no—
157D356C2×C4214yes—
158C4×D89—216no—
159C4×D89—416no—
160Dic178—22no—
161Dic178—24no—
162Dic178C2×C4214yes—
163#10623494—28no—
164C22×C89—24no—
165C22×C89—28no—
166C22×C89C4×C22⋊C414yes—
167C22×C89C22×C22⋊C411yescharacteristic
168C22×C89C2×C4×D412yes—
169C22×C89#57514yes—
170C2×D89—24no—
171C2×D89—44no—
172C2×D89—48no—
173C4×C89—24no—
174C4×C89—24no—
175C4×C89—48no—
176C4×C89C4×C22⋊C414yes—
177C4×C89C22×C4211yescharacteristic
178C4×C89C2×#11711yescharacteristic
179C4×C89C2×C4×D412yes—
180Dic89—24no—
181Dic89—44no—
182#20411—891nomaximal, Sylow
183C2×C89—24no—
184C2×C89C2×C4×C22⋊C411yescharacteristic
185C2×C89#289612yes—
186C2×C89#294314yes—
187D89—44no—
188C2×C4×#41—891no—
189C2×#416—892no—
190C22×#97—891no—
191C4×#117D8911yescharacteristic, complemented
192#1763—894no—
193#1762—894no—
194#1735—892no—
195C89#2041111yescharacteristic, complemented, Sylow
196C22×#41—891no—
197C23×C8—892no—
198C4×#41—898no—
199C4×#41—1784no—
200C2×C4×Q8—892no—
201C2×C4×D4—892no—
202C2×C4×D4—1782no—
203C2×#117—891no—
204C2×#117—1781no—
205C2×#117C2×D8912yes—
206C22×C42—1781no—
207C22×C42C2×D8911yescharacteristic
208#416—8916no—
209C2×#103—894no—
210C2×#102—894no—
211C2×#97—894no—
212C2×#97—1784no—
213C4×C4⋊C4C2×D8914yes—
214C4×C22⋊C4—22no—
215#376—21no—
216C43—21no—
217#340—898no—
218C2×#41—894no—
219C2×#41—898no—
220C2×#41—1782no—
221C2×#41—1784no—
222C22×Q8—891no—
223C22×D4—891no—
224C22×D4—1781no—
225C23×C4—1782no—
226C23×C4—1781no—
227C23×C4C22⋊D8912yes—
228C23×C4C22×D8911yescharacteristic
229C22×C8—898no—
230C22×C8—894no—
231C22×C8—1784no—
232C22×C8—1784no—
233C4×Q8—898no—
234C4×Q8—1784no—
235C4×D4—898no—
236C4×D4—17816no—
237C4×D4—1784no—
238#117—24no—
239#117—894no—
240#117—1782no—
241#117—1788no—
242#117C4×D8918yescomplemented
243C2×C4⋊C4—892no—
244C2×C4⋊C4—1782no—
245C2×C4⋊C4C22×D8914yes—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—1781no—
248C2×C22⋊C4—1782no—
249C2×C42—22no—
250C2×C42—24no—
251C2×C42—1782no—
252C2×C42—1781no—
253C2×C42—1788no—
254C2×C42C4×D8914yes—
255C2×C42D35614yes—
256C2×C42C22⋊D8911yescharacteristic
257C2×C42C22⋊D8911yescharacteristic
258C2×C42C22×D8912yes—
259#103—8916no—
260#102—8916no—
261#97—1788no—
262#95—24no—
263C24—1781no—
264C24C2×C22⋊D8911yescharacteristic
265#41—8916no—
266#41—1788no—
267#41—17816no—
268C2×Q8—894no—
269C2×Q8—892no—
270C2×Q8—1781no—
271C2×Q8—1782no—
272C2×D4—894no—
273C2×D4—892no—
274C2×D4—1788no—
275C2×D4—1784no—
276C2×D4—1781no—
277C2×D4—1782no—
278C22×C4—24no—
279C22×C4—44no—
280C22×C4—3568no—
281C22×C4—1782no—
282C22×C4—1788no—
283C22×C4—1781no—
284C22×C4—1788no—
285C22×C4—1784no—
286C22×C4#1308355118yes—
287C22×C4C2×C4×D8912yes—
288C22×C4C2×C4×D8914yes—
289C22×C4C2×C22⋊D8912yes—
290C22×C4C2×C22⋊D8912yes—
291C22×C4C2×C22⋊D8911yescharacteristic
292C22×C4C2×D35612yes—
293C22×C4#1308357414yes—
294C22×C4C23×D8911yescharacteristic
295C2×C8—898no—
296C2×C8—17816no—
297C2×C8—1784no—
298C2×C8—1784no—
299C4⋊C4—24no—
300C4⋊C4—894no—
301C4⋊C4—1782no—
302C4⋊C4—1788no—
303C4⋊C4C2×C4×D8918yes—
304C22⋊C4—28no—
305C22⋊C4—1784no—
306C22⋊C4—1788no—
307C42—28no—
308C42—48no—
309C42—1784no—
310C42—1788no—
311C42#1308355114yes—
312C42#1308355114yes—
313C42C2×C4×D8914yes—
314C42C2×D35614yes—
315C23—24no—
316C23—3564no—
317C23—1782no—
318C23—1784no—
319C23C2×#1308355112yes—
320C23C4×C22⋊D8914yes—
321C23C22×C22⋊D8911yescharacteristic
322Q8—894no—
323Q8—1782no—
324Q8—1784no—
325D4—894no—
326D4—17816no—
327D4—1782no—
328D4—1784no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—48no—
333C2×C4—48no—
334C2×C4—35616no—
335C2×C4—3564no—
336C2×C4—1784no—
337C2×C4—1782no—
338C2×C4—1784no—
339C2×C4—17816no—
340C2×C4C42×D8914yes—
341C2×C4C2×#1308355114yes—
342C2×C4C2×#1308355114yes—
343C2×C4C2×#1308355112yes—
344C2×C4#1566796914yes—
345C2×C4C4×C22⋊D8914yes—
346C2×C4C4×D35618yes—
347C2×C4C22×C4×D8911yescharacteristic
348C2×C4C22×C4×D8912yes—
349C2×C4C22×D35611yescharacteristic
350C2×C4C2×#1308357412yes—
351C8—1788no—
352C22—24no—
353C22—28no—
354C22—3564no—
355C22—3568no—
356C22—1784no—
357C22C4×#1308355114yes—
358C22C22×#1308355111yescharacteristic
359C22C2×C4×C22⋊D8912yes—
360C22#1915239614yes—
361C4—24no—
362C4—24no—
363C4—48no—
364C4—3564no—
365C4—1784no—
366C4C4×#1308355114yes—
367C4C2×C42×D8911yescharacteristic
368C4C2×#1566796911yescharacteristic
369C4C2×C4×D35612yes—
370C2—24no—
371C2—3564no—
372C2C2×C4×#1308355111yescharacteristic
373C2#2602876912yes—
374C2#2602905014yes—
subgroupG/H
centerC22×C4C2×C22⋊D89
commutatorC4×C89C22×C42
FrattiniC22×C4C23×D89
FittingC4×#117×C89C2
socleC23×C89C22×D4
prime radicalC22×#13083574C22
cosocleC22×C4×C89C24
hypercenterC4×#117D89
hypocenterC89#20411
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
3. C22×#15667923C2semidirect
4. #26020085C2semidirect
5. #26020080C2semidirect
6. #26019968C2semidirect
7. C4×#117×C89C2semidirect
11. C4×#13083574C4semidirect
18. #19151592C4semidirect
41. C22×#10623494C2×C4semidirect
58. #15667935C2×C4semidirect
59. #15667932C2×C4semidirect
64. #117×C89C2×C4semidirect
78. #13083574C42semidirect
191. C4×#117D89semidirect
195. C89#20411semidirect
242. #117C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#130835742
C2×#191515922
C22×#156679232
#260200852
#260200802
#260199682
C4×#117×C892
#2041189