Finite Group Databasebeta

← #36447550

Subgroups — #36447550

Order 22784.

482 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#10623494C211yesmaximal, characteristic
2#26020423C211yesmaximal, characteristic, complemented
3#26018998C211yesmaximal, characteristic, complemented
4#26018677C211yesmaximal, characteristic
5#26018148C211yesmaximal, characteristic, complemented
6#26018147C211yesmaximal, characteristic, complemented
7C89×#1486C211yesmaximal, characteristic
8C23×#10623494—21no—
9D4×#10623494—21no—
10D4×#10623494—21no—
11D4×#10623494C412yes—
12D4×#10623494C412yes—
13#19151651C2211yescharacteristic
14C2×#15667947—21no—
15C2×#15667947—21no—
16#19151622C2211yescharacteristic
17C2×C4⋊#10623494C2211yescharacteristic
18C2×C22⋊#10623494—21no—
19C2×C4×#10623494C2211yescharacteristic
20#19151350—21no—
21#19151348—21no—
22D4⋊#10623494—22no—
23C2×C4×D4×C89C2211yescharacteristic
24#431×C89C2211yescharacteristic
25#423×C89C2211yescharacteristic
26D4⋊C8×C89—22no—
27C2×#13083558—21no—
28C22×#10623494—22no—
29C22×#10623494—22no—
30C22×#10623494—21no—
31C22×#10623494—42no—
32C22×#10623494—42no—
33C22×#10623494D411yescharacteristic
34C22×#10623494D411yescharacteristic
35#15667947—42no—
36#15667947—42no—
37C4⋊#10623494—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40C4⋊#10623494—21no—
41C4⋊#10623494C2×C412yes—
42C22⋊#10623494—22no—
43C22⋊#10623494—22no—
44C22⋊#10623494—21no—
45C4×#10623494—21no—
46C4×#10623494C2×C411yescharacteristic
47C4×#10623494C2×C411yescharacteristic
48C4×#10623494D411yescharacteristic
49C4×#10623494D411yescharacteristic
50C22×D4×C89Q811yescharacteristic
51C23×C4×C89—21no—
52C2×M16×C89—21no—
53C4×D4×C89—21no—
54C4×D4×C89—21no—
55C4×D4×C89C2×C412yes—
56C4×D4×C89D412yes—
57C2×C4⋊C4×C89Q811yescharacteristic
58C2×C22⋊C4×C89—21no—
59C2×C42×C89C2311yescharacteristic
60C4⋊C8×C89—21no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89—21no—
63C22⋊C8×C89—21no—
64C4×C8×C89—21no—
65#13083558—41no—
66#13083558—41no—
67C2×#10623494—21no—
68C2×#10623494—21no—
69C2×#10623494—22no—
70C2×#10623494—41no—
71C2×#10623494—41no—
72C2×#10623494—44no—
73C2×#10623494—44no—
74C2×#10623494—41no—
75C2×#10623494—41no—
76C2×#10623494C22⋊C411yescharacteristic
77C2×#10623494C22⋊C411yescharacteristic
78C2×#10623494C22⋊C411yescharacteristic
79C2×#10623494C22⋊C411yescharacteristic
80C2×#10623494D812yes—
81C2×#10623494SD1612yes—
82C24×C89—21no—
83C2×D4×C89—24no—
84C2×D4×C89—21no—
85C2×D4×C89C4⋊C412yes—
86C22×C4×C89—21no—
87C22×C4×C89—22no—
88C22×C4×C89—22no—
89C22×C4×C89—41no—
90C22×C4×C89—41no—
91C22×C4×C89—41no—
92C22×C4×C89—41no—
93C22×C4×C89C2×D411yescharacteristic
94C22×C4×C89C2×Q811yescharacteristic
95C22×C4×C89#4111yescharacteristic
96M16×C89—41no—
97M16×C89—41no—
98C2×C8×C89—41no—
99C2×C8×C89—41no—
100C4⋊C4×C89—21no—
101C4⋊C4×C89C4⋊C412yes—
102C22⋊C4×C89—22no—
103C22⋊C4×C89—22no—
104C42×C89C22×C411yescharacteristic
105C42×C89C2×D411yescharacteristic
106C42×C89C2×D411yescharacteristic
107C42×C89#4111yescharacteristic
108C23×C89—24no—
109C23×C89—22no—
110C23×C89—42no—
111C23×C89—41no—
112C23×C89—41no—
113C23×C89C22⋊Q811yescharacteristic
114D4×C89—24no—
115D4×C89—22no—
116D4×C89#10814yescomplemented
117C2×C4×C89—22no—
118C2×C4×C89—22no—
119C2×C4×C89—41no—
120C2×C4×C89—41no—
121C2×C4×C89—41no—
122C2×C4×C89—42no—
123C2×C4×C89—42no—
124C2×C4×C89—42no—
125C2×C4×C89—42no—
126C2×C4×C89C2×C22⋊C411yescharacteristic
127C2×C4×C89C2×C4⋊C411yescharacteristic
128C2×C4×C89#11711yescharacteristic
129C2×C4×C89#12111yescharacteristic
130C2×C4×C89#12111yescharacteristic
131C2×C4×C89C22⋊Q811yescharacteristic
132C2×C4×C89C2×D811yescharacteristic
133C2×C4×C89C2×SD1611yescharacteristic
134C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C89#13711yescharacteristic
136C8×C89—81no—
137C8×C89—81no—
138#10623494—21no—
139#10623494—21no—
140#10623494—42no—
141#10623494—81no—
142#10623494—81no—
143#10623494#10212yes—
144#10623494#10212yes—
145C22×C89—21no—
146C22×C89—21no—
147C22×C89—24no—
148C22×C89—44no—
149C22×C89—44no—
150C22×C89—42no—
151C22×C89—42no—
152C22×C89#38011yescharacteristic
153C22×C89#47411yescharacteristic
154C22×C89#47611yescharacteristic
155C4×C89—21no—
156C4×C89—21no—
157C4×C89—21no—
158C4×C89—42no—
159C4×C89C2×#10211yescharacteristic
160C4×C89#41711yescharacteristic
161C4×C89C2×#10812yes—
162C4×C89#45911yescharacteristic
163C4×C89#46111yescharacteristic
164#8658—891nomaximal, Sylow
165C2×C89—21no—
166C2×C89—21no—
167C2×C89—44no—
168C2×C89#180211yescharacteristic
169C2×C89#181011yescharacteristic
170C2×C89#181411yescharacteristic
171C2×C8×D4—891no—
172#1848—891no—
173#1564—891no—
174#1486—891no—
175#1486D8911yescharacteristic
176#1301—891no—
177#1301—891no—
178C89#865811yescharacteristic, complemented, Sylow
179C23×C8—1781no—
180C2×C4×D4C2×D8911yescharacteristic
181C8×D4—892no—
182C8×D4—892no—
183C8×D4—1781no—
184C8×D4—1781no—
185#431—891no—
186#431C2×D8911yescharacteristic
187C2×#108—1781no—
188C2×#108—1781no—
189#423—891no—
190#423C2×D8911yescharacteristic
191C2×C4⋊C8—891no—
192C2×C22⋊C8—1781no—
193C2×C4×C8—891no—
194#335—1781no—
195#334—1781no—
196D4⋊C8—22no—
197D4⋊C8—1782no—
198C22×D4Dic17811yescharacteristic
199C23×C4—21no—
200C2×M16—21no—
201C2×M16—1781no—
202C22×C8—891no—
203C22×C8—891no—
204C22×C8—3562no—
205C22×C8—3562no—
206C22×C8—1782no—
207C22×C8—1782no—
208C22×C8—1781no—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4C4×D8912yes—
212C4×D4C22⋊D8912yes—
213C2×C4⋊C4Dic17811yescharacteristic
214C2×C22⋊C4—21no—
215C2×C42C22×D8911yescharacteristic
216#108—3562no—
217#108—3562no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—892no—
222C4⋊C8—1781no—
223C4⋊C8—1781no—
224C4⋊C8—1781no—
225C4⋊C8—1781no—
226C22⋊C8—21no—
227C22⋊C8—1782no—
228C22⋊C8—1782no—
229C22⋊C8—1781no—
230C4×C8—21no—
231C4×C8—891no—
232C4×C8—891no—
233C4×C8—891no—
234C4×C8—891no—
235C4×C8—1781no—
236C24—21no—
237C2×D4—24no—
238C2×D4—21no—
239C2×D4#1308355312yes—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4D4×D8911yescharacteristic
248C22×C4C2×Dic17811yescharacteristic
249C22×C4#1308357311yescharacteristic
250M16—41no—
251M16—41no—
252M16—3561no—
253M16—3561no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—892no—
257C2×C8—892no—
258C2×C8—891no—
259C2×C8—891no—
260C2×C8—891no—
261C2×C8—891no—
262C2×C8—3564no—
263C2×C8—3564no—
264C2×C8—3561no—
265C2×C8—3561no—
266C2×C8—3561no—
267C2×C8—3561no—
268C2×C8—1782no—
269C2×C8—1781no—
270C2×C8—1781no—
271C4⋊C4—21no—
272C4⋊C4#1308355312yes—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C42C2×C4×D8911yescharacteristic
276C42D4×D8911yescharacteristic
277C42C2×C22⋊D8911yescharacteristic
278C42#1308357311yescharacteristic
279C23—24no—
280C23—22no—
281C23—42no—
282C23—41no—
283C23—41no—
284C23#1566798911yescharacteristic
285D4—24no—
286D4—22no—
287D4#1566794714yescomplemented
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4C22⋊C4×D8911yescharacteristic
298C2×C4C2×#1308355311yescharacteristic
299C2×C4#1566796811yescharacteristic
300C2×C4#1566798411yescharacteristic
301C2×C4#1566798411yescharacteristic
302C2×C4#1566798911yescharacteristic
303C2×C4D8×D8911yescharacteristic
304C2×C4SD16×D8911yescharacteristic
305C2×C4#1566803611yescharacteristic
306C2×C4#1566804111yescharacteristic
307C8—81no—
308C8—81no—
309C8—892no—
310C8—892no—
311C8—3562no—
312C8—1781no—
313C8—1781no—
314C8—7121no—
315C8—7121no—
316C22—21no—
317C22—21no—
318C22—24no—
319C22—44no—
320C22—44no—
321C22—42no—
322C22—42no—
323C22#1915145611yescharacteristic
324C22#1915187611yescharacteristic
325C22#1915188611yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4#102×D8911yescharacteristic
331C4#1915159611yescharacteristic
332C4C2×#1566794712yes—
333C4#1915179111yescharacteristic
334C4#1915180111yescharacteristic
335C2—21no—
336C2—21no—
337C2—44no—
338C2#2602025011yescharacteristic
339C2#2602028811yescharacteristic
340C2#2602030411yescharacteristic
subgroupG/H
centerC2×C4#15667984
commutatorC42×C89C22×C4
FrattiniC2×C42C22×D89
FittingC89×#1486C2
socleC22×C89#380
prime radicalC22×D4×C89Q8
cosocleC2×C42×C89C23
hypercenter#1486D89
hypocenterC89#8658
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #26020423C2semidirect
3. #26018998C2semidirect
5. #26018148C2semidirect
6. #26018147C2semidirect
116. D4×C89#108semidirect
178. C89#8658semidirect
287. D4#15667947semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#106234942
#260204232
#260189982
#260186772
#260181482
#260181472
C89×#14862
#865889