Finite Group Databasebeta

← #36447479

Subgroups — #36447479

Order 22784.

542 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
1C2×C8×D356C211yesmaximal, characteristic
2#26020249C212yesmaximal
3C2×#19151351C211yesmaximal, characteristic, complemented
4#26018135C212yesmaximal, complemented
5C89×#1845C211yesmaximal, characteristic, complemented
6C22×C8×D89—21no—
7C2×C4×D356C2211yescharacteristic
8C8×D356—22no—
9C8×D356C414yescomplemented
10C2×C4⋊#10623494C2212yes—
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667932—22no—
13C2×#15667924—21no—
14#19151360—22no—
15#19151351—22no—
16C2×#107×C89—21no—
17C2×#107×C89—21no—
18C2×C4×C8×C89C2211yescharacteristic
19#384×C89C2212yes—
20C22×D356D411yescharacteristic
21C22×C4×D89—21no—
22C22×#10623494—21no—
23C22×#10623494—22no—
24C2×C8×D89—24no—
25C2×C8×D89—42no—
26C2×C8×D89—42no—
27C4×D356—21no—
28C4×D356—21no—
29C4×D356C2×C412yes—
30C4×D356Q812yes—
31C2×C4⋊Dic89D411yescharacteristic
32C2×#13083551—21no—
33C4⋊#10623494—21no—
34C4⋊#10623494—22no—
35C4⋊#10623494—22no—
36C4⋊#10623494C2×C412yes—
37#15667932—44no—
38#15667924—24no—
39C22×C8×C89D411yescharacteristic
40C22×C8×C89D411yescharacteristic
41C2×C4⋊C4×C89—22no—
42C2×C4⋊C4×C89—22no—
43C2×C4⋊C4×C89—22no—
44C2×C42×C89C2311yescharacteristic
45#107×C89—42no—
46#107×C89—42no—
47C4×C8×C89C2×C412yes—
48C4×C8×C89D412yes—
49C23×D89—21no—
50C2×D356—21no—
51C2×D356—21no—
52C2×D356—21no—
53C2×D356C4⋊C412yes—
54C2×D356D812yes—
55C2×D356Q1612yes—
56C22×Dic89—21no—
57C2×C4×D89—22no—
58C2×C4×D89—22no—
59C2×C4×D89—41no—
60C2×C4×D89—41no—
61C2×C4×D89—41no—
62C2×C4×D89—41no—
63C2×#10623494—22no—
64C2×#10623494—41no—
65C2×#10623494—41no—
66C2×#10623494—42no—
67C2×#10623494—42no—
68C2×#10623494—42no—
69C8×D89—48no—
70C4⋊Dic89—21no—
71C4⋊Dic89C4⋊C412yes—
72#13083551—22no—
73#13083551—22no—
74C22×C4×C89—42no—
75C22×C4×C89C2×D411yescharacteristic
76C22×C4×C89C2×D411yescharacteristic
77C22×C4×C89#4111yescharacteristic
78C2×C8×C89—21no—
79C2×C8×C89—21no—
80C2×C8×C89C22⋊C412yes—
81C2×C8×C89C22⋊C412yes—
82C2×C8×C89D812yes—
83C2×C8×C89SD1612yes—
84C4⋊C4×C89—42no—
85C4⋊C4×C89—42no—
86C4⋊C4×C89—42no—
87C4⋊C4×C89—42no—
88C4⋊C4×C89—82no—
89C42×C89C22×C411yescharacteristic
90C42×C89C2×D411yescharacteristic
91C42×C89C2×Q811yescharacteristic
92C42×C89#4111yescharacteristic
93C23×C89#12111yescharacteristic
94C22×D89—22no—
95C22×D89—22no—
96C22×D89—22no—
97C22×D89—41no—
98C22×D89—41no—
99C22×D89—41no—
100C22×D89—41no—
101C2×C4×C89—21no—
102C2×C4×C89—21no—
103C2×C4×C89—82no—
104C2×C4×C89—82no—
105C2×C4×C89—82no—
106C2×C4×C89C2×C22⋊C411yescharacteristic
107C2×C4×C89C2×C4⋊C411yescharacteristic
108C2×C4×C89#11711yescharacteristic
109C2×C4×C89#12111yescharacteristic
110C2×C4×C89C22⋊Q811yescharacteristic
111C2×C4×C89C22⋊Q811yescharacteristic
112C2×C4×C89C2×D811yescharacteristic
113C2×C4×C89C2×D811yescharacteristic
114C2×C4×C89C2×SD1611yescharacteristic
115C2×C4×C89C2×Q1611yescharacteristic
116C2×C4×C89#13511yescharacteristic
117C2×C4×C89#13511yescharacteristic
118C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C89#13711yescharacteristic
120C2×Dic89—22no—
121C2×Dic89—41no—
122C2×Dic89—41no—
123D356—22no—
124D356—22no—
125D356—22no—
126D356#10714yescomplemented
127C4×D89—42no—
128C4×D89—42no—
129C4×D89—42no—
130C4×D89—42no—
131C8×C89—22no—
132C8×C89#10214yescomplemented
133#10623494—42no—
134#10623494—82no—
135C22×C89#38011yescharacteristic
136C22×C89#45911yescharacteristic
137C22×C89#46111yescharacteristic
138C22×C89#46611yescharacteristic
139C22×C89#46711yescharacteristic
140C22×C89#47211yescharacteristic
141C22×C89#47311yescharacteristic
142C2×D89—24no—
143C2×D89—42no—
144C2×D89—42no—
145C2×D89—42no—
146C2×D89—42no—
147C2×D89—42no—
148C2×D89—42no—
149C4×C89—21no—
150C4×C89—21no—
151C4×C89—162no—
152C4×C89C2×#10211yescharacteristic
153C4×C89#41711yescharacteristic
154C4×C89C2×#10711yescharacteristic
155C4×C89#42711yescharacteristic
156C4×C89#46611yescharacteristic
157C4×C89#46711yescharacteristic
158C4×C89#47411yescharacteristic
159C4×C89#47611yescharacteristic
160Dic89—42no—
161#8644—891nomaximal, Sylow
162C2×C89#166711yescharacteristic
163C2×C89#166911yescharacteristic
164C2×C89#167311yescharacteristic
165C2×C89#167511yescharacteristic
166C2×C89#180211yescharacteristic
167C2×C89#180811yescharacteristic
168C2×C89#181611yescharacteristic
169D89—44no—
170C2×C8×D4—891no—
171#1845D8911yescharacteristic, complemented
172#1802—892no—
173C2×#335—891no—
174#1296—892no—
175C89#864411yescharacteristic, complemented, Sylow
176C23×C8—1781no—
177C2×C4×D4—891no—
178C8×D4—894no—
179C8×D4—1782no—
180C2×#107—21no—
181C2×#107—21no—
182C2×C4⋊C8—891no—
183C2×C4⋊C8—892no—
184C2×#102—1782no—
185C2×C22⋊C8—1781no—
186C2×C4×C8C2×D8911yescharacteristic
187#384C2×D8912yes—
188#340—1782no—
189#335—1782no—
190C22×D4—891no—
191C23×C4—1781no—
192C22×C8—3562no—
193C22×C8—3562no—
194C22×C8—1782no—
195C22×C8—1781no—
196C22×C8—1784no—
197C22×C8C22⋊D8911yescharacteristic
198C22×C8C22⋊D8911yescharacteristic
199C4×D4—892no—
200C4×D4—892no—
201C4×D4—1781no—
202C4×D4—1781no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—891no—
207C2×C22⋊C4—1781no—
208C2×C42C22×D8911yescharacteristic
209#107—42no—
210#107—42no—
211C4⋊C8—892no—
212C4⋊C8—1782no—
213C4⋊C8—1781no—
214C4⋊C8—1782no—
215#102—3564no—
216C22⋊C8—1784no—
217C4×C8C4×D8912yes—
218C4×C8D35612yes—
219C24—1781no—
220C2×D4—892no—
221C2×D4—892no—
222C2×D4—892no—
223C2×D4—1781no—
224C2×D4—1781no—
225C2×D4—1781no—
226C22×C4—42no—
227C22×C4—3561no—
228C22×C4—3561no—
229C22×C4—3561no—
230C22×C4—3561no—
231C22×C4—1781no—
232C22×C4—1782no—
233C22×C4—1782no—
234C22×C4D4×D8911yescharacteristic
235C22×C4C2×C22⋊D8911yescharacteristic
236C22×C4#1308357311yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—3561no—
240C2×C8—3561no—
241C2×C8—3568no—
242C2×C8—3562no—
243C2×C8—3562no—
244C2×C8—3562no—
245C2×C8—1782no—
246C2×C8#1308355112yes—
247C2×C8#1308355112yes—
248C2×C8#1308355912yes—
249C2×C8#1308356112yes—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—82no—
255C4⋊C4—892no—
256C4⋊C4—1781no—
257C22⋊C4—1782no—
258C22⋊C4—1782no—
259C42C2×C4×D8911yescharacteristic
260C42C2×D35611yescharacteristic
261C42Q8×D8911yescharacteristic
262C42#1308357511yescharacteristic
263C23—3561no—
264C23—3561no—
265C23—3561no—
266C23—3561no—
267C23—1782no—
268C23—1782no—
269C23—1782no—
270C23#1566798311yescharacteristic
271D4—894no—
272D4—1782no—
273D4—1782no—
274D4—1782no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—3561no—
281C2×C4—3561no—
282C2×C4—3562no—
283C2×C4—3562no—
284C2×C4—3562no—
285C2×C4—3562no—
286C2×C4—1782no—
287C2×C4C2×#1308355111yescharacteristic
288C2×C4C4⋊C4×D8911yescharacteristic
289C2×C4#1566797011yescharacteristic
290C2×C4#1566798711yescharacteristic
291C2×C4#1566798811yescharacteristic
292C2×C4#1566799211yescharacteristic
293C2×C4D8×D8911yescharacteristic
294C2×C4C2×#1308355911yescharacteristic
295C2×C4C2×#1308356111yescharacteristic
296C2×C4Q16×D8911yescharacteristic
297C2×C4#1566803111yescharacteristic
298C2×C4#1566803511yescharacteristic
299C2×C4#1566803811yescharacteristic
300C2×C4#1566804311yescharacteristic
301C8—22no—
302C8—3562no—
303C8—7122no—
304C8#1566793214yescomplemented
305C22—3562no—
306C22—3562no—
307C22—3562no—
308C22—3562no—
309C22—3562no—
310C22—3562no—
311C22—1784no—
312C22#1915145511yescharacteristic
313C22#1915179011yescharacteristic
314C22#1915180011yescharacteristic
315C22#1915183111yescharacteristic
316C22#1915183611yescharacteristic
317C22#1915186511yescharacteristic
318C22#1915187011yescharacteristic
319C4—21no—
320C4—21no—
321C4—162no—
322C4—3562no—
323C4C2×#1566793211yescharacteristic
324C4#1915159711yescharacteristic
325C4#107×D8911yescharacteristic
326C4#1915163511yescharacteristic
327C4#1915183511yescharacteristic
328C4#1915184011yescharacteristic
329C4#1915187511yescharacteristic
330C4#1915188511yescharacteristic
331C2—3564no—
332C2#2601960411yescharacteristic
333C2#2601961411yescharacteristic
334C2#2601963811yescharacteristic
335C2#2601964811yescharacteristic
336C2#2602024911yescharacteristic
337C2#2602027811yescharacteristic
338C2#2602031711yescharacteristic
subgroupG/H
centerC23#15667983
commutatorC42×C89C22×C4
FrattiniC2×C42C22×D89
FittingC89×#1845C2
socleC23×C89#121
prime radicalC22×D356D4
cosocleC2×C42×C89C23
hypercenter#1845D89
hypocenterC89#8644
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
3. C2×#19151351C2semidirect
4. #26018135C2semidirect
5. C89×#1845C2semidirect
9. C8×D356C4semidirect
126. D356#107semidirect
132. C8×C89#102semidirect
171. #1845D89semidirect
175. C89#8644semidirect
304. C8#15667932semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D3562
#260202492
C2×#191513512
#260181352
C89×#18452
#864489