Finite Group Databasebeta

← #36453033

Subgroups — #36453033

Order 22784.

368 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
1#26020368C211yesmaximal, characteristic
2#26020107C211yesmaximal, characteristic
3C4×#15667941C211yesmaximal, characteristic
4C2×#19151350C211yesmaximal, characteristic
5#26018087C211yesmaximal, characteristic
6#26018086C211yesmaximal, characteristic
7C2×#334×C89C211yesmaximal, characteristic
8C2×C4⋊#10623494C2211yescharacteristic
9C2×C4⋊#10623494C2211yescharacteristic
10C2×#15667941C411yescharacteristic
11C2×#15667941C411yescharacteristic
12C2×#15667922—21no—
13C2×C4×#10623494C2211yescharacteristic
14C42×Dic89C2211yescharacteristic
15#19151352—21no—
16#19151352—21no—
17#19151352—21no—
18#19151352C411yescharacteristic
19#19151352C411yescharacteristic
20#19151350—22no—
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×C4⋊C8×C89C2211yescharacteristic
23C2×C4×C8×C89C2211yescharacteristic
24#334×C89—22no—
25C22×#10623494—21no—
26C22×#10623494—21no—
27C22×#10623494C2×C411yescharacteristic
28C22×#10623494C2×C411yescharacteristic
29C2×C4×Dic89C2×C411yescharacteristic
30C2×C4×Dic89C2×C411yescharacteristic
31C2×C4×Dic89D411yescharacteristic
32C2×C4×Dic89D411yescharacteristic
33C2×C4×Dic89Q811yescharacteristic
34C2×C4×Dic89Q811yescharacteristic
35C4⋊#10623494—21no—
36C4⋊#10623494—21no—
37C4⋊#10623494—21no—
38C4⋊#10623494Q812yes—
39#15667941—22no—
40#15667941—22no—
41#15667922—42no—
42C4×#10623494—21no—
43C4×#10623494—21no—
44C22×C8×C89—21no—
45C22×C8×C89—21no—
46C22×C8×C89C2×C411yescharacteristic
47C22×C8×C89C2×C411yescharacteristic
48C2×C42×C89C2311yescharacteristic
49C4⋊C8×C89—21no—
50C4⋊C8×C89—21no—
51C4⋊C8×C89—21no—
52C4⋊C8×C89D412yes—
53C4×C8×C89—21no—
54C4×C8×C89—21no—
55C22×Dic89C4⋊C411yescharacteristic
56C22×Dic89C4⋊C411yescharacteristic
57C22×Dic89C4⋊C411yescharacteristic
58C22×Dic89C4⋊C411yescharacteristic
59C2×#10623494—21no—
60C2×#10623494—21no—
61C2×#10623494—21no—
62C2×#10623494—22no—
63C2×#10623494—21no—
64C2×#10623494—21no—
65C2×#10623494—41no—
66C2×#10623494—41no—
67C2×#10623494—41no—
68C2×#10623494—41no—
69C2×#10623494—41no—
70C2×#10623494M1612yes—
71C4×Dic89—21no—
72C4×Dic89—21no—
73C4×Dic89—21no—
74C4×Dic89—21no—
75C4×Dic89—21no—
76C4×Dic89—21no—
77C4×Dic89—21no—
78C4×Dic89—21no—
79C4×Dic89—22no—
80C4×Dic89—41no—
81C22×C4×C89C22×C411yescharacteristic
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89C2×Q811yescharacteristic
84C2×C8×C89—21no—
85C2×C8×C89—21no—
86C2×C8×C89—21no—
87C2×C8×C89—22no—
88C2×C8×C89—21no—
89C2×C8×C89—21no—
90C2×C8×C89—41no—
91C2×C8×C89—41no—
92C2×C8×C89—41no—
93C2×C8×C89—41no—
94C2×C8×C89—41no—
95C2×C8×C89M1612yes—
96C42×C89C2×D411yescharacteristic
97C42×C89C2×Q811yescharacteristic
98C42×C89#4111yescharacteristic
99C42×C89#4111yescharacteristic
100C23×C89C2×C4⋊C411yescharacteristic
101C2×C4×C89—21no—
102C2×C4×C89—21no—
103C2×C4×C89C4×D411yescharacteristic
104C2×C4×C89C4×Q811yescharacteristic
105C2×C4×C89#12111yescharacteristic
106C2×C4×C89C22⋊Q811yescharacteristic
107C2×C4×C89#12511yescharacteristic
108C2×C4×C89C4⋊Q811yescharacteristic
109C2×C4×C89C2×M1611yescharacteristic
110C2×C4×C89C2×M1611yescharacteristic
111C2×C4×C89#13111yescharacteristic
112C2×C4×C89#13111yescharacteristic
113C2×C4×C89#13511yescharacteristic
114C2×C4×C89#13511yescharacteristic
115C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C89#13711yescharacteristic
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#10812yes—
129C8×C89—22no—
130C8×C89—41no—
131C8×C89—42no—
132C8×C89—81no—
133#10623494—22no—
134#10623494—41no—
135#10623494—42no—
136#10623494—81no—
137C22×C89#38911yescharacteristic
138C22×C89#42311yescharacteristic
139C22×C89#42411yescharacteristic
140C22×C89#42711yescharacteristic
141C22×C89#42811yescharacteristic
142C22×C89C2×#10811yescharacteristic
143C22×C89#43011yescharacteristic
144C4×C89—21no—
145C4×C89—21no—
146C4×C89#43511yescharacteristic
147C4×C89#43511yescharacteristic
148C4×C89#44611yescharacteristic
149C4×C89#44611yescharacteristic
150C4×C89#46311yescharacteristic
151C4×C89#46411yescharacteristic
152C4×C89#47811yescharacteristic
153C4×C89#47911yescharacteristic
154Dic89—22no—
155Dic89—41no—
156Dic89—41no—
157Dic89—41no—
158#9606—891nomaximal, Sylow
159C2×C89#156811yescharacteristic
160C2×C89#156911yescharacteristic
161C2×C89#157211yescharacteristic
162C2×C89#157411yescharacteristic
163C2×C89#194011yescharacteristic
164C2×C89#194911yescharacteristic
165C2×C89#195011yescharacteristic
166#1831—891no—
167#1767—891no—
168C4×C4⋊C8—891no—
169C2×#335—891no—
170C2×#334D8911yescharacteristic
171#1277—891no—
172#1277—891no—
173C89#960611yescharacteristic, complemented, Sylow
174C2×C4⋊C8—891no—
175C2×C4⋊C8—891no—
176C2×C4⋊C8—891no—
177C2×C4⋊C8—891no—
178C2×C4⋊C8C2×D8911yescharacteristic
179C2×C4⋊C8C2×D8911yescharacteristic
180C2×#97—1781no—
181C2×C4×C8—891no—
182C2×C4×C8C2×D8911yescharacteristic
183C43—891no—
184#336—891no—
185#336—891no—
186#336—1781no—
187#336—1781no—
188#336—1781no—
189#335—1782no—
190#334—22no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—891no—
194C22×C8—891no—
195C22×C8—1781no—
196C22×C8—1781no—
197C22×C8C4×D8911yescharacteristic
198C22×C8C4×D8911yescharacteristic
199C2×C42—891no—
200C2×C42—891no—
201C2×C42—891no—
202C2×C42—891no—
203C2×C42—891no—
204C2×C42—891no—
205C2×C42C22×D8911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—892no—
210C4⋊C8—1782no—
211C4⋊C8—1782no—
212C4⋊C8—1781no—
213C4⋊C8—1781no—
214C4⋊C8—1781no—
215C4⋊C8C22⋊D8912yes—
216#97—3562no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—1781no—
220C4×C8—1781no—
221C22×C4—891no—
222C22×C4—891no—
223C22×C4—891no—
224C22×C4—891no—
225C22×C4C2×C4×D8911yescharacteristic
226C22×C4D4×D8911yescharacteristic
227C22×C4Q8×D8911yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—892no—
240C2×C8—3561no—
241C2×C8—3561no—
242C2×C8—3561no—
243C2×C8—3561no—
244C2×C8—3561no—
245C2×C8—1781no—
246C2×C8—1782no—
247C2×C8—1781no—
248C2×C8—1781no—
249C2×C8—1781no—
250C2×C8—1781no—
251C2×C8#1308355712yes—
252C42—3561no—
253C42—1782no—
254C42—1781no—
255C42—1781no—
256C42—1781no—
257C42—1781no—
258C42—1781no—
259C42—1781no—
260C42—1781no—
261C42—1781no—
262C42C2×C22⋊D8911yescharacteristic
263C42Q8×D8911yescharacteristic
264C42#1308357311yescharacteristic
265C42#1308357411yescharacteristic
266C23C4⋊C4×D8911yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—892no—
270C2×C4—1781no—
271C2×C4—1781no—
272C2×C4—1781no—
273C2×C4—1781no—
274C2×C4—1781no—
275C2×C4—1781no—
276C2×C4—1781no—
277C2×C4—1781no—
278C2×C4—1781no—
279C2×C4—1781no—
280C2×C4—1781no—
281C2×C4C4×C22⋊D8911yescharacteristic
282C2×C4#1566797711yescharacteristic
283C2×C4#1566798411yescharacteristic
284C2×C4#1566799011yescharacteristic
285C2×C4#1566800211yescharacteristic
286C2×C4#1566801011yescharacteristic
287C2×C4M16×D8911yescharacteristic
288C2×C4C2×#1308355711yescharacteristic
289C2×C4#1566801811yescharacteristic
290C2×C4#1566802011yescharacteristic
291C2×C4#1566803311yescharacteristic
292C2×C4#1566803311yescharacteristic
293C2×C4#1566803911yescharacteristic
294C2×C4#1566804111yescharacteristic
295C8—22no—
296C8—41no—
297C8—42no—
298C8—81no—
299C8—3562no—
300C8—3561no—
301C8—1782no—
302C8—7121no—
303C22#1915149311yescharacteristic
304C22#1915162011yescharacteristic
305C22#1915162311yescharacteristic
306C22#1915163311yescharacteristic
307C22#1915163711yescharacteristic
308C22#108×D8911yescharacteristic
309C22#1915164511yescharacteristic
310C4—21no—
311C4—21no—
312C4—3561no—
313C4—3561no—
314C4—3561no—
315C4—1782no—
316C4#1915166711yescharacteristic
317C4#1915166911yescharacteristic
318C4#1915172511yescharacteristic
319C4#1915172711yescharacteristic
320C4#1915181511yescharacteristic
321C4#1915181811yescharacteristic
322C4#1915189711yescharacteristic
323C4#1915190811yescharacteristic
324C2#2601901211yescharacteristic
325C2#2601901611yescharacteristic
326C2#2601902911yescharacteristic
327C2#2601903911yescharacteristic
328C2#2602097211yescharacteristic
329C2#2602102111yescharacteristic
330C2#2602102411yescharacteristic
subgroupG/H
centerC22×C4D4×D89
commutatorC22×C4×C89C22×C4
FrattiniC2×C42C22×D89
FittingC2×#334×C89C2
socle, prime radicalC23×C89C2×C4⋊C4
cosocleC2×C42×C89C23
hypercenterC2×#334D89
hypocenterC89#9606
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
173. C89#9606semidirect

Maximal subgroups

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

subgroupindex
#260203682
#260201072
C4×#156679412
C2×#191513502
#260180872
#260180862
C2×#334×C892
#960689