Finite Group Databasebeta

← #36520595

Subgroups — #36520595

Order 22784.

1012 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26029281C212yesmaximal, complemented
2#26018612C214yesmaximal, complemented
3#26018600C214yesmaximal, complemented
4#26018593C212yesmaximal, complemented
5#26018586C212yesmaximal, complemented
6C2×#540×C89C211yesmaximal, characteristic
7#19151670—28no—
8#19151655C2214yes—
9#19151562C2214yes—
10C2×C22⋊#10623494C2214yes—
11#19151324C2214yes—
12#19151322C2214yes—
13#19151322C2218yes—
14#540×C89—28no—
15C2×#127×C89C411yescharacteristic
16C2×#125×C89C411yescharacteristic
17C2×#123×C89C412yes—
18C2×#123×C89C2212yes—
19C2×#121×C89C412yes—
20C2×#121×C89C411yescharacteristic
21C2×#121×C89C411yescharacteristic
22C2×#121×C89C2212yes—
23C2×C4×D4×C89C2211yescharacteristic
24C2×C4×D4×C89C2211yescharacteristic
25C2×#117×C89C2211yescharacteristic
26C2×#13083558—24no—
27C22×#10623494—24no—
28C4⋊#10623494—24no—
29C22⋊#10623494—24no—
30C22⋊#10623494—24no—
31C22⋊#10623494C2318yes—
32#15667923—24no—
33C22×D4×C89C2×C411yescharacteristic
34C22×D4×C89C2×C412yes—
35C22×D4×C89C2×C412yes—
36C22×D4×C89C2×C412yes—
37C22×D4×C89C2×C412yes—
38C22×D4×C89C2×C411yescharacteristic
39C23×C4×C89C2×C411yescharacteristic
40C23×C4×C89C2×C412yes—
41C23×C4×C89C2312yes—
42#127×C89—24no—
43#125×C89—24no—
44#123×C89—24no—
45#123×C89—24no—
46#123×C89—28no—
47#121×C89—24no—
48#121×C89—24no—
49#121×C89—24no—
50#121×C89—24no—
51#121×C89—28no—
52C4×D4×C89—24no—
53C4×D4×C89D418yes—
54#117×C89—24no—
55C2×C4⋊C4×C89C2×C411yescharacteristic
56C2×C4⋊C4×C89C2×C411yescharacteristic
57C2×C4⋊C4×C89C2×C412yes—
58C2×C4⋊C4×C89C2×C412yes—
59C2×C4⋊C4×C89C2×C411yescharacteristic
60C2×C4⋊C4×C89C2311yescharacteristic
61C2×C22⋊C4×C89C2×C411yescharacteristic
62C2×C22⋊C4×C89C2×C412yes—
63C2×C22⋊C4×C89C2×C412yes—
64C2×C22⋊C4×C89C2×C412yes—
65C2×C22⋊C4×C89C2311yescharacteristic
66C2×C22⋊C4×C89C2312yes—
67C2×C42×C89C2×C411yescharacteristic
68C2×C42×C89C2311yescharacteristic
69#13083558—84no—
70C2×#10623494—28no—
71C2×#10623494—84no—
72C24×C89C22×C411yescharacteristic
73C24×C89C22×C412yes—
74C24×C89C22×C412yes—
75C2×D4×C89—24no—
76C2×D4×C89—24no—
77C2×D4×C89—24no—
78C2×D4×C89—22no—
79C2×D4×C89—24no—
80C2×D4×C89—42no—
81C2×D4×C89—42no—
82C2×D4×C89—82no—
83C2×D4×C89—82no—
84C2×D4×C89—82no—
85C2×D4×C89—82no—
86C2×D4×C89C22⋊C414yes—
87C22×C4×C89—22no—
88C22×C4×C89—24no—
89C22×C4×C89—42no—
90C22×C4×C89—82no—
91C22×C4×C89—82no—
92C22×C4×C89C22×C411yescharacteristic
93C22×C4×C89C22×C411yescharacteristic
94C22×C4×C89C22×C411yescharacteristic
95C22×C4×C89C22×C411yescharacteristic
96C22×C4×C89C22×C412yes—
97C22×C4×C89C22×C411yescharacteristic
98C22×C4×C89C22×C412yes—
99C22×C4×C89C2×D414yes—
100C22×C4×C89C2×D414yes—
101C22×C4×C89C2411yescharacteristic
102C4⋊C4×C89—22no—
103C4⋊C4×C89—22no—
104C4⋊C4×C89—24no—
105C4⋊C4×C89—24no—
106C4⋊C4×C89—22no—
107C4⋊C4×C89C22⋊C414yes—
108C22⋊C4×C89—24no—
109C22⋊C4×C89—22no—
110C22⋊C4×C89—24no—
111C22⋊C4×C89—22no—
112C22⋊C4×C89—22no—
113C22⋊C4×C89—22no—
114C22⋊C4×C89C22⋊C418yes—
115C42×C89—22no—
116C42×C89C2×D414yes—
117C23×C89—24no—
118C23×C89—21no—
119C23×C89—22no—
120C23×C89—22no—
121C23×C89—24no—
122C23×C89—42no—
123C23×C89—42no—
124C23×C89—42no—
125C23×C89—41no—
126C23×C89—42no—
127C23×C89—41no—
128C23×C89C2×C22⋊C414yes—
129C23×C89C23×C411yescharacteristic
130D4×C89—44no—
131D4×C89—44no—
132D4×C89—84no—
133D4×C89—84no—
134D4×C89—84no—
135D4×C89—84no—
136C2×C4×C89—22no—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—22no—
141C2×C4×C89—22no—
142C2×C4×C89—41no—
143C2×C4×C89—41no—
144C2×C4×C89—42no—
145C2×C4×C89—44no—
146C2×C4×C89—44no—
147C2×C4×C89—44no—
148C2×C4×C89—42no—
149C2×C4×C89—41no—
150C2×C4×C89—41no—
151C2×C4×C89—84no—
152C2×C4×C89C2×C22⋊C412yes—
153C2×C4×C89C2×C22⋊C412yes—
154C2×C4×C89C2×C22⋊C414yes—
155C2×C4×C89C22×D412yes—
156#10623494—48no—
157C22×C89—21no—
158C22×C89—21no—
159C22×C89—24no—
160C22×C89—24no—
161C22×C89—24no—
162C22×C89—41no—
163C22×C89—42no—
164C22×C89—41no—
165C22×C89—42no—
166C22×C89—42no—
167C22×C89—41no—
168C22×C89—84no—
169C22×C89—82no—
170C22×C89—84no—
171C22×C89C22×C22⋊C411yescharacteristic
172C22×C89#56812yes—
173C4×C89—22no—
174C4×C89—22no—
175C4×C89—24no—
176C4×C89—22no—
177C4×C89—41no—
178C4×C89—41no—
179C4×C89—42no—
180C4×C89—41no—
181#17408—891nomaximal, Sylow
182C2×C89—22no—
183C2×C89—44no—
184C2×C89—81no—
185C2×C89—82no—
186C2×C89#287911yescharacteristic
187C2×C89#288311yescharacteristic
188C2×C89#288811yescharacteristic
189C2×#540D8911yescharacteristic
190#2973—892no—
191#1471—894no—
192#1468—894no—
193#1466—892no—
194#1464—892no—
195C89#1740811yescharacteristic, complemented, Sylow
196#540—28no—
197C2×#127Dic8911yescharacteristic
198C2×#125Dic8911yescharacteristic
199C2×#123Dic8912yes—
200C2×#123C2×D8912yes—
201C2×#121Dic8912yes—
202C2×#121Dic8911yescharacteristic
203C2×#121Dic8911yescharacteristic
204C2×#121C2×D8912yes—
205C2×C4×D4C2×D8911yescharacteristic
206C2×C4×D4C2×D8911yescharacteristic
207C2×#117C2×D8911yescharacteristic
208#435—1788no—
209#432—894no—
210#407—894no—
211C2×C22⋊C8—894no—
212#324—894no—
213#323—894no—
214#323—898no—
215C22×D4C2×Dic8911yescharacteristic
216C22×D4C2×Dic8912yes—
217C22×D4C2×Dic8912yes—
218C22×D4C2×Dic8912yes—
219C22×D4C2×Dic8912yes—
220C22×D4C2×Dic8911yescharacteristic
221C23×C4C2×Dic8911yescharacteristic
222C23×C4C2×Dic8912yes—
223C23×C4C22×D8912yes—
224C2×M16—1784no—
225C22×C8—1784no—
226#127—24no—
227#125—24no—
228#123—24no—
229#123—24no—
230#123—28no—
231#121—24no—
232#121—24no—
233#121—24no—
234#121—24no—
235#121—28no—
236C4×D4—24no—
237C4×D4C22⋊D8918yes—
238#117—24no—
239C2×C4⋊C4C2×Dic8911yescharacteristic
240C2×C4⋊C4C2×Dic8911yescharacteristic
241C2×C4⋊C4C2×Dic8912yes—
242C2×C4⋊C4C2×Dic8912yes—
243C2×C4⋊C4C2×Dic8911yescharacteristic
244C2×C4⋊C4C22×D8911yescharacteristic
245C2×C22⋊C4C2×Dic8911yescharacteristic
246C2×C22⋊C4C2×Dic8912yes—
247C2×C22⋊C4C2×Dic8912yes—
248C2×C22⋊C4C2×Dic8912yes—
249C2×C22⋊C4C22×D8911yescharacteristic
250C2×C22⋊C4C22×D8912yes—
251C2×C42C2×Dic8911yescharacteristic
252C2×C42C22×D8911yescharacteristic
253C4⋊C8—1784no—
254C22⋊C8—898no—
255C22⋊C8—1784no—
256C22⋊C8—1784no—
257#97—1784no—
258C24C22×Dic8911yescharacteristic
259C24C22×Dic8912yes—
260C24C22×Dic8912yes—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4—24no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—82no—
269C2×D4—82no—
270C2×D4—82no—
271C2×D4—82no—
272C2×D4C22⋊Dic8914yes—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—42no—
276C22×C4—82no—
277C22×C4—82no—
278C22×C4C22×Dic8911yescharacteristic
279C22×C4C22×Dic8911yescharacteristic
280C22×C4C22×Dic8911yescharacteristic
281C22×C4C22×Dic8911yescharacteristic
282C22×C4C22×Dic8912yes—
283C22×C4C22×Dic8911yescharacteristic
284C22×C4C22×Dic8912yes—
285C22×C4C2×C22⋊D8914yes—
286C22×C4C2×C22⋊D8914yes—
287C22×C4C23×D8911yescharacteristic
288M16—7124no—
289C2×C8—1788no—
290C2×C8—7124no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4C22⋊Dic8914yes—
297C22⋊C4—24no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—24no—
303C22⋊C4C22⋊Dic8918yes—
304C42—22no—
305C42C2×C22⋊D8914yes—
306C23—24no—
307C23—21no—
308C23—22no—
309C23—22no—
310C23—24no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—41no—
315C23—42no—
316C23—41no—
317C23C2×C22⋊Dic8914yes—
318C23C23×Dic8911yescharacteristic
319D4—44no—
320D4—44no—
321D4—84no—
322D4—84no—
323D4—84no—
324D4—84no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4C2×C22⋊Dic8912yes—
342C2×C4C2×C22⋊Dic8912yes—
343C2×C4C2×C22⋊Dic8914yes—
344C2×C4C22×C22⋊D8912yes—
345C8—3568no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—24no—
350C22—24no—
351C22—41no—
352C22—42no—
353C22—41no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22—84no—
358C22—82no—
359C22—84no—
360C22C22×C22⋊Dic8911yescharacteristic
361C22#1915236512yes—
362C4—22no—
363C4—22no—
364C4—24no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—42no—
369C4—41no—
370C2—22no—
371C2—44no—
372C2—81no—
373C2—82no—
374C2#2602869711yescharacteristic
375C2#2602871311yescharacteristic
376C2#2602873111yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic89
commutatorC23×C89C23×C4
FrattiniC22×C4C23×D89
Fitting, prime radicalC2×#540×C89C2
socleC22×C89C22×C22⋊C4
cosocleC22×C4×C89C24
hypercenterC2×#540D89
hypocenterC89#17408
LCSG ▷ C23×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #26029281C2semidirect
2. #26018612C2semidirect
3. #26018600C2semidirect
4. #26018593C2semidirect
5. #26018586C2semidirect
195. C89#17408semidirect

Maximal subgroups

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

subgroupindex
#260292812
#260186122
#260186002
#260185932
#260185862
C2×#540×C892
#1740889