Finite Group Databasebeta

← #36453666

Subgroups — #36453666

Order 22784.

518 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151977C211yesmaximal, characteristic
2#26021205C211yesmaximal, characteristic
3#26021203C211yesmaximal, characteristic
4#26020117C211yesmaximal, characteristic
5C2×#19151350C211yesmaximal, characteristic
6C2×#19151345C211yesmaximal, characteristic
7C2×#332×C89C211yesmaximal, characteristic
8C22×#13083564—21no—
9C22×#13083564—21no—
10C2×#15668012C2211yescharacteristic
11#19151977—22no—
12#19151977C414yescomplemented
13C2×C4⋊#10623494C2211yescharacteristic
14C2×C4×#10623494C2211yescharacteristic
15C2×C8×Dic89—21no—
16C4×C4⋊Dic89C2211yescharacteristic
17#19151361—22no—
18#19151360—22no—
19#19151352—21no—
20#19151350—22no—
21#19151345—22no—
22C2×C4⋊Q8×C89C2211yescharacteristic
23C2×C4⋊C8×C89C2211yescharacteristic
24C2×C4⋊C8×C89C2211yescharacteristic
25#332×C89—22no—
26C22×Dic178—21no—
27C2×#13083564—24no—
28C2×#13083564—24no—
29C2×#13083564—42no—
30C2×#13083564—42no—
31C2×#13083564—42no—
32C2×#13083564—42no—
33C22×#10623494—21no—
34C22×#10623494D411yescharacteristic
35C22×#10623494D411yescharacteristic
36#15668012—21no—
37#15668012—21no—
38#15668012—21no—
39#15668012C2×C412yes—
40C2×C4⋊Dic89—21no—
41C2×C4⋊Dic89—21no—
42C2×C4⋊Dic89D412yes—
43C2×C4×Dic89—21no—
44C4⋊#10623494—21no—
45C4⋊#10623494—21no—
46C4×#10623494C2×C412yes—
47C4×#10623494D412yes—
48C8×Dic89—42no—
49#15667919—21no—
50C22×Q8×C89—21no—
51C22×C8×C89—21no—
52C22×C8×C89—21no—
53C4⋊Q8×C89—21no—
54C4⋊Q8×C89—21no—
55C4⋊Q8×C89—21no—
56C4⋊Q8×C89C2×C412yes—
57C2×C4⋊C4×C89—21no—
58C2×C4⋊C4×C89—21no—
59C2×C42×C89C2311yescharacteristic
60C4⋊C8×C89—21no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89—21no—
63C4⋊C8×C89D412yes—
64C2×Dic178—22no—
65C2×Dic178—41no—
66C2×Dic178—41no—
67C2×Dic178—41no—
68C2×Dic178—41no—
69C2×Dic178—41no—
70C22×Dic89—22no—
71C22×Dic89—41no—
72#13083564—48no—
73#13083564—48no—
74C2×#10623494—21no—
75C2×#10623494—21no—
76C2×#10623494—41no—
77C2×#10623494—42no—
78C2×#10623494C22⋊C412yes—
79C2×#10623494C22⋊C412yes—
80C2×#10623494D812yes—
81C2×#10623494SD1612yes—
82C4⋊Dic89—22no—
83C4⋊Dic89—22no—
84C4⋊Dic89—22no—
85C4⋊Dic89—41no—
86C4⋊Dic89—41no—
87C4⋊Dic89Q1614yescomplemented
88C4×Dic89—41no—
89C4×Dic89—41no—
90C2×Q8×C89—22no—
91C2×Q8×C89—41no—
92C2×Q8×C89—41no—
93C2×Q8×C89—41no—
94C2×Q8×C89—41no—
95C2×Q8×C89—41no—
96C22×C4×C89—41no—
97C22×C4×C89C2×D411yescharacteristic
98C22×C4×C89C2×D411yescharacteristic
99C22×C4×C89#4111yescharacteristic
100C2×C8×C89—22no—
101C2×C8×C89—41no—
102C2×C8×C89—41no—
103C2×C8×C89—41no—
104C2×C8×C89—42no—
105C4⋊C4×C89—22no—
106C4⋊C4×C89—22no—
107C4⋊C4×C89—41no—
108C4⋊C4×C89—41no—
109C42×C89C22×C411yescharacteristic
110C42×C89C2×D411yescharacteristic
111C42×C89C2×D411yescharacteristic
112C42×C89#4111yescharacteristic
113C23×C89#12111yescharacteristic
114Q8×C89—42no—
115Q8×C89—42no—
116Q8×C89—81no—
117Q8×C89—81no—
118C2×C4×C89—22no—
119C2×C4×C89—42no—
120C2×C4×C89—81no—
121C2×C4×C89—81no—
122C2×C4×C89C2×C22⋊C411yescharacteristic
123C2×C4×C89C4×D411yescharacteristic
124C2×C4×C89C4×D411yescharacteristic
125C2×C4×C89#12111yescharacteristic
126C2×C4×C89#12411yescharacteristic
127C2×C4×C89#12711yescharacteristic
128C2×C4×C89C2×D811yescharacteristic
129C2×C4×C89C2×SD1611yescharacteristic
130C2×C4×C89C2×Q1612yes—
131C2×C4×C89#13512yes—
132C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
134C2×Dic89—24no—
135C2×Dic89—42no—
136C2×Dic89—42no—
137C2×Dic89—42no—
138C2×Dic89—81no—
139C2×Dic89—81no—
140Dic178—42no—
141Dic178—42no—
142Dic178—81no—
143Dic178—81no—
144C8×C89—42no—
145C8×C89—81no—
146#10623494—22no—
147#10623494—81no—
148#10623494#10214yes—
149C22×C89#39011yescharacteristic
150C22×C89#45911yescharacteristic
151C22×C89#46011yescharacteristic
152C22×C89#46712yes—
153C22×C89#47312yes—
154C4×C89—21no—
155C4×C89—21no—
156C4×C89—82no—
157C4×C89C2×#10211yescharacteristic
158C4×C89#41811yescharacteristic
159C4×C89C4×Q1612yes—
160C4×C89#45911yescharacteristic
161C4×C89#46011yescharacteristic
162C4×C89#49411yescharacteristic
163C4×C89#49511yescharacteristic
164Dic89—44no—
165Dic89—82no—
166#9733—891nomaximal, Sylow
167C2×C89#166912yes—
168C2×C89#167012yes—
169C2×C89#196911yescharacteristic
170C2×C89#197911yescharacteristic
171C2×C89#198211yescharacteristic
172C2×#494—891no—
173#1988—891no—
174#1988—891no—
175C8×C4⋊C4—891no—
176C2×#335—891no—
177C2×#332—891no—
178C2×#332D8911yescharacteristic
179C89#973311yescharacteristic, complemented, Sylow
180C22×Q16—1781no—
181C22×Q16—1781no—
182C2×C4⋊Q8—891no—
183C2×C4⋊Q8C2×D8911yescharacteristic
184#494—894no—
185#494—1782no—
186C2×C4⋊C8—891no—
187C2×C4⋊C8C2×D8911yescharacteristic
188C2×C4⋊C8C2×D8911yescharacteristic
189C2×C4×C8—891no—
190C2×C4×C8—1781no—
191C4×C4⋊C4—891no—
192#340—1782no—
193#340—1782no—
194#336—1781no—
195#335—1782no—
196#332—22no—
197#332—1782no—
198C22×Q8—21no—
199C22×Q8—1781no—
200C2×Q16—3562no—
201C2×Q16—3562no—
202C2×Q16—3562no—
203C2×Q16—3562no—
204C2×Q16—1784no—
205C2×Q16—1784no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—891no—
209C22×C8—891no—
210C22×C8—1781no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—892no—
215C4⋊Q8—1781no—
216C4⋊Q8—1781no—
217C4⋊Q8—1781no—
218C4⋊Q8C4×D8912yes—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—892no—
222C2×C4⋊C4—1781no—
223C2×C4⋊C4—1781no—
224C2×C42—1781no—
225C2×C42C22×D8911yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—1781no—
230C4⋊C8—1781no—
231C4⋊C8C22⋊D8912yes—
232C4×C8—892no—
233C4×C8—892no—
234C4×C8—3562no—
235#95—1781no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—3561no—
243C2×Q8—3561no—
244C2×Q8—3561no—
245C2×Q8—3561no—
246C2×Q8—3561no—
247C2×Q8—1782no—
248C22×C4—41no—
249C22×C4—3561no—
250C22×C4—1782no—
251C22×C4D4×D8911yescharacteristic
252C22×C4D4×D8911yescharacteristic
253C22×C4#1308357411yescharacteristic
254Q16—3568no—
255Q16—3568no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—42no—
261C2×C8—892no—
262C2×C8—892no—
263C2×C8—892no—
264C2×C8—892no—
265C2×C8—3561no—
266C2×C8—3562no—
267C2×C8—1781no—
268C2×C8—1781no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—894no—
274C4⋊C4—3561no—
275C4⋊C4—3561no—
276C4⋊C4—1782no—
277C4⋊C4—1782no—
278C4⋊C4—1782no—
279C42—3561no—
280C42—3561no—
281C42C2×C4×D8911yescharacteristic
282C42D4×D8911yescharacteristic
283C42C2×C22⋊D8911yescharacteristic
284C42#1308357311yescharacteristic
285C23#1566798511yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—81no—
289Q8—81no—
290Q8—3562no—
291Q8—3562no—
292Q8—7121no—
293Q8—7121no—
294C2×C4—22no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—3562no—
299C2×C4—3562no—
300C2×C4—3562no—
301C2×C4—1784no—
302C2×C4—7121no—
303C2×C4—7121no—
304C2×C4C22⋊C4×D8911yescharacteristic
305C2×C4#1566797211yescharacteristic
306C2×C4C4×C22⋊D8911yescharacteristic
307C2×C4#1566798411yescharacteristic
308C2×C4#1566799811yescharacteristic
309C2×C4#1566800811yescharacteristic
310C2×C4D8×D8911yescharacteristic
311C2×C4SD16×D8911yescharacteristic
312C2×C4Q16×D8912yes—
313C2×C4#1566803312yes—
314C2×C4#1566803611yescharacteristic
315C2×C4#1566803911yescharacteristic
316C8—42no—
317C8—81no—
318C8—894no—
319C8—1782no—
320C8—7121no—
321C22#1915149811yescharacteristic
322C22#1915179211yescharacteristic
323C22#1915179711yescharacteristic
324C22#1915183812yes—
325C22#1915187212yes—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—3564no—
330C4—7122no—
331C4#102×D8911yescharacteristic
332C4#1915160111yescharacteristic
333C4#1915169012yes—
334C4#1915179111yescharacteristic
335C4#1915179611yescharacteristic
336C4#1915197611yescharacteristic
337C4#1915197911yescharacteristic
338C2#2601961612yes—
339C2#2601962112yes—
340C2#2602111011yescharacteristic
341C2#2602116411yescharacteristic
342C2#2602117711yescharacteristic
subgroupG/H
centerC23#15667985
commutatorC42×C89C22×C4
FrattiniC2×C42C22×D89
FittingC2×#332×C89C2
socle, prime radicalC23×C89#121
cosocleC2×C42×C89C23
hypercenterC2×#332D89
hypocenterC89#9733
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
12. #19151977C4semidirect
87. C4⋊Dic89Q16semidirect
179. C89#9733semidirect

Maximal subgroups

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

subgroupindex
C2×#191519772
#260212052
#260212032
#260201172
C2×#191513502
C2×#191513452
C2×#332×C892
#973389