Finite Group Databasebeta

← #36452741

Subgroups — #36452741

Order 22784.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26021204C211yesmaximal, characteristic
2#26021054C211yesmaximal, characteristic
3#26021010C211yesmaximal, characteristic
4C2×#19151345C211yesmaximal, characteristic
5#26018136C211yesmaximal, characteristic
6#26018087C211yesmaximal, characteristic
7C8×C4⋊C4×C89C211yesmaximal, characteristic
8C2×#15668012C2211yescharacteristic
9C2×#15667945—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667937—21no—
13C2×#15667937—21no—
14#19151468C2211yescharacteristic
15#19151360—21no—
16#19151360—21no—
17#19151360—21no—
18#19151345C414yescomplemented
19C2×C4⋊C8×C89C2211yescharacteristic
20C2×C4×C8×C89—21no—
21C2×C4×C8×C89C2211yescharacteristic
22C4×C4⋊C4×C89C2211yescharacteristic
23#336×C89—21no—
24C22×Dic178—21no—
25C22×#10623494—21no—
26C22×#10623494—21no—
27#15668012—21no—
28#15668012—21no—
29#15668012—21no—
30#15668012C2×C412yes—
31C2×C4⋊Dic89—21no—
32C2×C4⋊Dic89—21no—
33C2×C4⋊Dic89—21no—
34C2×C4⋊Dic89—21no—
35C2×C4⋊Dic89—21no—
36#15667945—42no—
37C4⋊#10623494—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40C4⋊#10623494C2×C412yes—
41#15667937—42no—
42#15667937—42no—
43C22×C8×C89—21no—
44C22×C8×C89D411yescharacteristic
45C22×C8×C89D411yescharacteristic
46C2×C4⋊C4×C89D411yescharacteristic
47C2×C4⋊C4×C89D411yescharacteristic
48C2×C42×C89—21no—
49C2×C42×C89C2311yescharacteristic
50C4⋊C8×C89—21no—
51C4⋊C8×C89C2×C412yes—
52C4×C8×C89—21no—
53C4×C8×C89—21no—
54C4×C8×C89—42no—
55#95×C89—21no—
56C2×Dic178—22no—
57C2×Dic178—41no—
58C2×Dic178—41no—
59C2×Dic178—41no—
60C2×Dic178—41no—
61C2×Dic178—41no—
62C22×Dic89—41no—
63C22×Dic89—41no—
64C2×#10623494—22no—
65C2×#10623494—41no—
66C2×#10623494—41no—
67C2×#10623494—41no—
68C2×#10623494—41no—
69C2×#10623494—41no—
70C4⋊Dic89—22no—
71C4⋊Dic89—22no—
72C4⋊Dic89—41no—
73C4⋊Dic89—41no—
74C4⋊Dic89—41no—
75C4⋊Dic89—41no—
76C4⋊Dic89—41no—
77C4⋊Dic89—41no—
78C4⋊Dic89—81no—
79C22×C4×C89—21no—
80C22×C4×C89—21no—
81C22×C4×C89C2×D411yescharacteristic
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89#4111yescharacteristic
84C2×C8×C89—21no—
85C2×C8×C89—21no—
86C2×C8×C89—22no—
87C2×C8×C89—21no—
88C2×C8×C89—21no—
89C2×C8×C89—21no—
90C2×C8×C89—41no—
91C2×C8×C89—41no—
92C2×C8×C89D812yes—
93C4⋊C4×C89—21no—
94C4⋊C4×C89—21no—
95C4⋊C4×C89SD1612yes—
96C4⋊C4×C89Q1612yes—
97C42×C89—41no—
98C42×C89—41no—
99C42×C89C22×C411yescharacteristic
100C42×C89#4111yescharacteristic
101C42×C89#4111yescharacteristic
102C42×C89#4111yescharacteristic
103C23×C89#12111yescharacteristic
104C2×C4×C89—21no—
105C2×C4×C89—21no—
106C2×C4×C89—22no—
107C2×C4×C89—22no—
108C2×C4×C89—41no—
109C2×C4×C89—41no—
110C2×C4×C89—41no—
111C2×C4×C89—41no—
112C2×C4×C89#11711yescharacteristic
113C2×C4×C89C4×D411yescharacteristic
114C2×C4×C89C4×D411yescharacteristic
115C2×C4×C89#12311yescharacteristic
116C2×C4×C89#12411yescharacteristic
117C2×C4×C89#12611yescharacteristic
118C2×C4×C89C2×D811yescharacteristic
119C2×C4×C89C2×SD1611yescharacteristic
120C2×C4×C89C2×Q1611yescharacteristic
121C2×C4×C89#13511yescharacteristic
122C2×C4×C89#13511yescharacteristic
123C2×C4×C89#13511yescharacteristic
124C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C89#13711yescharacteristic
126C2×Dic89—42no—
127C2×Dic89—81no—
128C2×Dic89—81no—
129C2×Dic89—81no—
130C2×Dic89—81no—
131C2×Dic89—81no—
132Dic178—42no—
133Dic178—42no—
134Dic178—81no—
135Dic178—81no—
136C8×C89—22no—
137C8×C89—42no—
138C8×C89—41no—
139#10623494—42no—
140#10623494—81no—
141C22×C89#38811yescharacteristic
142C22×C89#45911yescharacteristic
143C22×C89#46411yescharacteristic
144C22×C89#46511yescharacteristic
145C22×C89#46711yescharacteristic
146C22×C89#47111yescharacteristic
147C22×C89#47311yescharacteristic
148C4×C89—21no—
149C4×C89—21no—
150C4×C89—42no—
151C4×C89—42no—
152C4×C89C4×D811yescharacteristic
153C4×C89C4×SD1611yescharacteristic
154C4×C89C4×Q1611yescharacteristic
155C4×C89#44011yescharacteristic
156C4×C89#48011yescharacteristic
157C4×C89#48211yescharacteristic
158C4×C89#48711yescharacteristic
159C4×C89#48811yescharacteristic
160Dic89—82no—
161Dic89—161no—
162#9561—891nomaximal, Sylow
163C2×C89#166511yescharacteristic
164C2×C89#166911yescharacteristic
165C2×C89#168011yescharacteristic
166C2×C89#168411yescharacteristic
167C2×C89#192511yescharacteristic
168C2×C89#193011yescharacteristic
169C2×C89#193311yescharacteristic
170#1988—891no—
171#1956—891no—
172#1947—891no—
173C8×C4⋊C4D8911yescharacteristic
174C2×#332—891no—
175#1296—891no—
176#1277—891no—
177C89#956111yescharacteristic, complemented, Sylow
178C2×C4⋊Q8—891no—
179C2×#107—1781no—
180C2×C4⋊C8—891no—
181C2×C4⋊C8—891no—
182C2×C4⋊C8C2×D8911yescharacteristic
183C2×#103—1781no—
184C2×#103—1781no—
185C2×C4×C8—21no—
186C2×C4×C8C2×D8911yescharacteristic
187#384—891no—
188C4×C4⋊C4C2×D8911yescharacteristic
189#340—1781no—
190#340—1781no—
191#340—1781no—
192#336—21no—
193#332—894no—
194C22×Q8—1781no—
195C22×C8—21no—
196C22×C8—1781no—
197C22×C8—1781no—
198C22×C8C22⋊D8911yescharacteristic
199C22×C8C22⋊D8911yescharacteristic
200C4⋊Q8—892no—
201C4⋊Q8—1781no—
202C4⋊Q8—1781no—
203C4⋊Q8—1781no—
204C2×C4⋊C4—1781no—
205C2×C4⋊C4—1781no—
206C2×C4⋊C4—1781no—
207C2×C4⋊C4—1781no—
208C2×C4⋊C4—1781no—
209C2×C4⋊C4D35611yescharacteristic
210C2×C4⋊C4D35611yescharacteristic
211C2×C42—21no—
212C2×C42C22×D8911yescharacteristic
213#107—3562no—
214C4⋊C8—21no—
215C4⋊C8—892no—
216C4⋊C8—1781no—
217C4⋊C8—1781no—
218C4⋊C8—1781no—
219C4⋊C8C4×D8912yes—
220#103—3562no—
221#103—3562no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—42no—
225#95—21no—
226C2×Q8—3561no—
227C2×Q8—3561no—
228C2×Q8—3561no—
229C2×Q8—3561no—
230C2×Q8—3561no—
231C2×Q8—1782no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—3561no—
235C22×C4—3561no—
236C22×C4C2×C22⋊D8911yescharacteristic
237C22×C4C2×D35611yescharacteristic
238C22×C4#1308357411yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—22no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—3561no—
248C2×C8—3561no—
249C2×C8—3561no—
250C2×C8—3561no—
251C2×C8—3561no—
252C2×C8—1782no—
253C2×C8#1308355912yes—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—3561no—
257C4⋊C4—3561no—
258C4⋊C4—3561no—
259C4⋊C4—3561no—
260C4⋊C4—3561no—
261C4⋊C4—3561no—
262C4⋊C4—1782no—
263C4⋊C4—1782no—
264C4⋊C4—7121no—
265C4⋊C4#1308356312yes—
266C4⋊C4Dic35612yes—
267C42—41no—
268C42—41no—
269C42C2×C4×D8911yescharacteristic
270C42#1308357411yescharacteristic
271C42#1308357411yescharacteristic
272C42#1308357411yescharacteristic
273C23#1566798611yescharacteristic
274Q8—3562no—
275Q8—3562no—
276Q8—7121no—
277Q8—7121no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—3562no—
287C2×C4—7121no—
288C2×C4—7121no—
289C2×C4—7121no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4#1566796911yescharacteristic
293C2×C4C4×C22⋊D8911yescharacteristic
294C2×C4C4×D35611yescharacteristic
295C2×C4#1566799511yescharacteristic
296C2×C4#1566800011yescharacteristic
297C2×C4#1566800611yescharacteristic
298C2×C4C2×#1308355911yescharacteristic
299C2×C4C2×#1308356311yescharacteristic
300C2×C4C2×Dic35611yescharacteristic
301C2×C4#1566803211yescharacteristic
302C2×C4#1566803411yescharacteristic
303C2×C4#1566803411yescharacteristic
304C2×C4#1566803711yescharacteristic
305C2×C4#1566804311yescharacteristic
306C8—22no—
307C8—41no—
308C8—42no—
309C8—3562no—
310C8—7121no—
311C22#1915148911yescharacteristic
312C22#1915179311yescharacteristic
313C22#1915182011yescharacteristic
314C22#1915182711yescharacteristic
315C22#1915183911yescharacteristic
316C22#1915186111yescharacteristic
317C22#1915187311yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—14241no—
323C4—7122no—
324C4C4×#1308355911yescharacteristic
325C4C4×#1308356311yescharacteristic
326C4C4×Dic35611yescharacteristic
327C4#1915169611yescharacteristic
328C4#1915191111yescharacteristic
329C4#1915192211yescharacteristic
330C4#1915194911yescharacteristic
331C4#1915195311yescharacteristic
332C2#2601959311yescharacteristic
333C2#2601961711yescharacteristic
334C2#2601968211yescharacteristic
335C2#2601971011yescharacteristic
336C2#2602087211yescharacteristic
337C2#2602090711yescharacteristic
338C2#2602092811yescharacteristic
subgroupG/H
centerC23#15667986
commutatorC42×C89C22×C4
FrattiniC2×C42C22×D89
FittingC8×C4⋊C4×C89C2
socle, prime radicalC23×C89#121
cosocleC2×C42×C89C23
hypercenterC8×C4⋊C4D89
hypocenterC89#9561
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
18. #19151345C4semidirect
177. C89#9561semidirect

Maximal subgroups

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

subgroupindex
#260212042
#260210542
#260210102
C2×#191513452
#260181362
#260180872
C8×C4⋊C4×C892
#956189