Finite Group Databasebeta

← #36477129

Subgroups — #36477129

Order 22784.

2078 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667971C211yesmaximal, characteristic
2C2×#19151461C211yesmaximal, characteristic
3#26018521C212yesmaximal, complemented
4#26018519C212yesmaximal, complemented
5#26018476C214yesmaximal, complemented
6#26018475C214yesmaximal
7C22×#95×C89C211yesmaximal, characteristic
8C2×#15667971—24no—
9C2×#15667971—24no—
10C2×#15667971C418yescomplemented
11C22×C4⋊Dic89C2211yescharacteristic
12C22×C4⋊Dic89C2211yescharacteristic
13C22×C22⋊Dic89C2212yes—
14C22×C22⋊Dic89C2212yes—
15C22×C4×Dic89C2212yes—
16#19151461—24no—
17C2×#15667919C2218yes—
18C2×#15667919C2212yes—
19C2×#15667919C2212yes—
20C2×#15667919C2218yes—
21C24×C4×C89C2212yes—
22C24×C4×C89C2211yescharacteristic
23C2×#95×C89—24no—
24C2×#95×C89C2212yes—
25C2×#95×C89C2212yes—
26C23×Dic89C2314yes—
27C23×Dic89C2312yes—
28C23×Dic89C2312yes—
29#15667971—232no—
30C2×C4⋊Dic89—22no—
31C2×C4⋊Dic89—22no—
32C2×C4⋊Dic89—22no—
33C2×C4⋊Dic89—22no—
34C2×C4⋊Dic89C2×C414yescomplemented
35C2×C4⋊Dic89C2×C414yescomplemented
36C2×C22⋊Dic89—24no—
37C2×C22⋊Dic89—24no—
38C2×C22⋊Dic89—24no—
39C2×C22⋊Dic89—28no—
40C2×C22⋊Dic89C2×C418yes—
41C2×C4×Dic89—24no—
42C2×C4×Dic89—24no—
43C2×C4×Dic89C2×C418yescomplemented
44#15667919—24no—
45#15667919—24no—
46#15667919—216no—
47#15667919—48no—
48C25×C89C2311yescharacteristic
49C23×C4×C89—28no—
50C23×C4×C89—24no—
51C23×C4×C89—28no—
52C23×C4×C89—28no—
53C23×C4×C89—44no—
54C23×C4×C89C2×C414yes—
55C23×C4×C89D414yes—
56C23×C4×C89D414yes—
57C23×C4×C89C2314yes—
58C23×C4×C89C2311yescharacteristic
59C23×C4×C89C2311yescharacteristic
60#95×C89—24no—
61#95×C89—24no—
62C22×Dic89—22no—
63C22×Dic89—22no—
64C22×Dic89—22no—
65C22×Dic89—22no—
66C22×Dic89—28no—
67C22×Dic89—24no—
68C22×Dic89—24no—
69C22×Dic89—24no—
70C22×Dic89—28no—
71C22×Dic89—28no—
72C22×Dic89—24no—
73C22×Dic89—24no—
74C22×Dic89C22×C414yes—
75C22×Dic89C22×C414yes—
76C4⋊Dic89—28no—
77C4⋊Dic89—28no—
78C22⋊Dic89—216no—
79C22⋊Dic89—48no—
80C4×Dic89—216no—
81C24×C89—24no—
82C24×C89—22no—
83C24×C89—22no—
84C24×C89C22×C412yes—
85C24×C89C2×D412yes—
86C24×C89C2×D412yes—
87C24×C89#4118yes—
88C24×C89C2411yescharacteristic
89C22×C4×C89—216no—
90C22×C4×C89—216no—
91C22×C4×C89—216no—
92C22×C4×C89—24no—
93C22×C4×C89—24no—
94C22×C4×C89—216no—
95C22×C4×C89—24no—
96C22×C4×C89—24no—
97C22×C4×C89—28no—
98C22×C4×C89—28no—
99C22×C4×C89—432no—
100C22×C4×C89—48no—
101C22×C4×C89—48no—
102C22×C4×C89C22⋊C4116yes—
103C22×C4×C89C22×C412yes—
104C22×C4×C89C22×C412yes—
105C22×C4×C89C2×D412yes—
106C22×C4×C89C2×D412yes—
107C22×C4×C89C2×D412yes—
108C22×C4×C89C2×D412yes—
109C22×C4×C89#4118yes—
110C23×C89—24no—
111C23×C89—24no—
112C23×C89—24no—
113C23×C89—24no—
114C23×C89—22no—
115C23×C89—22no—
116C23×C89—24no—
117C23×C89—216no—
118C23×C89—216no—
119C23×C89C2×C22⋊C414yes—
120C23×C89#11718yes—
121C23×C89#12318yes—
122C23×C89#12318yes—
123C23×C89C23×C411yescharacteristic
124C23×C89C22×D411yescharacteristic
125C23×C89C22×D411yescharacteristic
126C23×C89C2×#4114yes—
127C23×C89C2×#4114yes—
128C23×C89H(5,𝔽2)12yes—
129C23×C892−1+412yes—
130C2×C4×C89—24no—
131C2×C4×C89—24no—
132C2×C4×C89—24no—
133C2×C4×C89—24no—
134C2×C4×C89—24no—
135C2×C4×C89—24no—
136C2×C4×C89—232no—
137C2×C4×C89—28no—
138C2×C4×C89—216no—
139C2×C4×C89—432no—
140C2×C4×C89—44no—
141C2×C4×C89—44no—
142C2×C4×C89—48no—
143C2×C4×C89C2×C22⋊C414yes—
144C2×C4×C89C2×C22⋊C414yes—
145C2×Dic89—24no—
146C2×Dic89—24no—
147C2×Dic89—28no—
148C2×Dic89—28no—
149C2×Dic89—44no—
150C2×Dic89—44no—
151C2×Dic89—42no—
152C2×Dic89—42no—
153C2×Dic89—44no—
154C2×Dic89—44no—
155C2×Dic89—44no—
156C2×Dic89—44no—
157C2×Dic89—48no—
158C2×Dic89—48no—
159C22×C89—24no—
160C22×C89—216no—
161C22×C89—28no—
162C22×C89—28no—
163C22×C89—216no—
164C22×C89—24no—
165C22×C89#38118yes—
166C22×C89C22×C22⋊C411yescharacteristic
167C22×C89C2×#11712yes—
168C22×C89C4×#4112yes—
169C22×C89#52012yes—
170C22×C89C2×#12312yes—
171C22×C89C2×#12312yes—
172C22×C89#52512yes—
173C22×C89#53212yes—
174C22×C89#53511yescharacteristic
175C22×C89#53611yescharacteristic
176C22×C89#53712yes—
177C22×C89#55118yes—
178C22×C89#55218yes—
179C4×C89—24no—
180C4×C89—24no—
181C4×C89—48no—
182Dic89—44no—
183Dic89—44no—
184Dic89—84no—
185#13958—891nomaximal, Sylow
186C2×C89—28no—
187C2×C89C2×#38111yescharacteristic
188C2×C89#229711yescharacteristic
189C2×C89#231111yescharacteristic
190C2×C89#234314yes—
191C2×C89#248212yes—
192C2×C89#248412yes—
193C2×C89#249814yes—
194C22×#117—891no—
195C2×#381—891no—
196C22×#95D8911yescharacteristic
197#1445—892no—
198#1445—892no—
199#1434—894no—
200C22⋊#95—894no—
201C89#1395811yescharacteristic, complemented, Sylow
202C24×C4C2×D8912yes—
203C24×C4C2×D8911yescharacteristic
204C2×#117—898no—
205C2×#117—1784no—
206C2×#117—1784no—
207C22×C4⋊C4—891no—
208C22×C4⋊C4—891no—
209C22×C22⋊C4—892no—
210C22×C22⋊C4—892no—
211C22×C42—892no—
212#381—1784no—
213C2×#95—24no—
214C2×#95—898no—
215C2×#95—898no—
216C2×#95—892no—
217C2×#95—892no—
218C2×#95C2×D8912yes—
219C2×#95C2×D8912yes—
220C25C22×D8911yescharacteristic
221C23×C4—28no—
222C23×C4—24no—
223C23×C4—28no—
224C23×C4—28no—
225C23×C4—44no—
226C23×C4—892no—
227C23×C4—892no—
228C23×C4—894no—
229C23×C4C4×D8914yes—
230C23×C4D35614yes—
231C23×C4C22⋊D8914yes—
232C23×C4C22×D8914yes—
233C23×C4C22×D8911yescharacteristic
234C23×C4C22×D8911yescharacteristic
235#117—17832no—
236C2×C4⋊C4—894no—
237C2×C4⋊C4—894no—
238C2×C4⋊C4—1782no—
239C2×C4⋊C4—1782no—
240C2×C4⋊C4—1782no—
241C2×C4⋊C4—1782no—
242C2×C22⋊C4—898no—
243C2×C22⋊C4—1784no—
244C2×C22⋊C4—1788no—
245C2×C22⋊C4—1784no—
246C2×C22⋊C4—1784no—
247C2×C42—898no—
248C2×C42—1784no—
249C2×C42—1784no—
250#95—24no—
251#95—24no—
252#95—3568no—
253#95—1784no—
254#95—1784no—
255#95—17816no—
256C24—24no—
257C24—22no—
258C24—22no—
259C24C2×C4×D8912yes—
260C24C2×C22⋊D8912yes—
261C24C2×D35612yes—
262C24#1308357318yes—
263C24C23×D8911yescharacteristic
264C22×C4—216no—
265C22×C4—216no—
266C22×C4—216no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—216no—
270C22×C4—24no—
271C22×C4—28no—
272C22×C4—24no—
273C22×C4—28no—
274C22×C4—432no—
275C22×C4—48no—
276C22×C4—48no—
277C22×C4—894no—
278C22×C4—894no—
279C22×C4—1784no—
280C22×C4—1788no—
281C22×C4—1788no—
282C22×C4—1784no—
283C22×C4—1784no—
284C22×C4—1782no—
285C22×C4—1782no—
286C22×C4—1782no—
287C22×C4—1782no—
288C22×C4—1788no—
289C22×C4—1784no—
290C22×C4—1784no—
291C22×C4#13083551116yes—
292C22×C4C2×C4×D8912yes—
293C22×C4C2×C4×D8912yes—
294C22×C4C2×C22⋊D8912yes—
295C22×C4C2×C22⋊D8912yes—
296C22×C4C2×D35612yes—
297C22×C4C2×D35612yes—
298C22×C4#1308357418yes—
299C4⋊C4—1788no—
300C4⋊C4—1788no—
301C22⋊C4—3568no—
302C22⋊C4—17816no—
303C42—17816no—
304C23—24no—
305C23—22no—
306C23—22no—
307C23—24no—
308C23—216no—
309C23—216no—
310C23—24no—
311C23—24no—
312C23—24no—
313C23C2×#1308355114yes—
314C23#1566796818yes—
315C23#1566799318yes—
316C23#1566799618yes—
317C23C22×C4×D8911yescharacteristic
318C23C22×C22⋊D8911yescharacteristic
319C23C22×D35611yescharacteristic
320C23C2×#1308357314yes—
321C23C2×#1308357414yes—
322C23#1566805712yes—
323C23#1566806012yes—
324C2×C4—232no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—216no—
332C2×C4—28no—
333C2×C4—432no—
334C2×C4—44no—
335C2×C4—48no—
336C2×C4—44no—
337C2×C4—3564no—
338C2×C4—3562no—
339C2×C4—3562no—
340C2×C4—3564no—
341C2×C4—3564no—
342C2×C4—3564no—
343C2×C4—3564no—
344C2×C4—3568no—
345C2×C4—3568no—
346C2×C4—3564no—
347C2×C4—1784no—
348C2×C4—1784no—
349C2×C4—1788no—
350C2×C4—1788no—
351C2×C4C2×#1308355114yes—
352C2×C4C2×#1308355114yes—
353C22—28no—
354C22—24no—
355C22—28no—
356C22—24no—
357C22—216no—
358C22—216no—
359C22#1915145918yes—
360C22C22×#1308355111yescharacteristic
361C22C2×#1566796812yes—
362C22C4×#1308357412yes—
363C22#1915207912yes—
364C22C2×#1566799312yes—
365C22C2×#1566799612yes—
366C22#1915210912yes—
367C22#1915214812yes—
368C22#1915216511yescharacteristic
369C22#1915217211yescharacteristic
370C22#1915217912yes—
371C22#1915227418yes—
372C22#1915228318yes—
373C4—24no—
374C4—24no—
375C4—48no—
376C4—3564no—
377C4—3564no—
378C4—7124no—
379C2—28no—
380C2C2×#1915145911yescharacteristic
381C2#2602274211yescharacteristic
382C2#2602284511yescharacteristic
383C2#2602310814yes—
384C2#2602452612yes—
385C2#2602453912yes—
386C2#2602469614yes—
subgroupG/H
center, FrattiniC24C23×D89
commutatorC23×C89C23×C4
FittingC22×#95×C89C2
socle, cosocleC24×C89C24
prime radicalC25×C89C23
hypercenterC22×#95D89
hypocenterC89#13958
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. #26018521C2semidirect
4. #26018519C2semidirect
5. #26018476C2semidirect
10. C2×#15667971C4semidirect
34. C2×C4⋊Dic89C2×C4semidirect
35. C2×C4⋊Dic89C2×C4semidirect
43. C2×C4×Dic89C2×C4semidirect
201. C89#13958semidirect

Maximal subgroups

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

subgroupindex
C22×#156679712
C2×#191514612
#260185212
#260185192
#260184762
#260184752
C22×#95×C892
#1395889