Finite Group Databasebeta

← C89×#9166 #36387014

Subgroups — C89×#9166 #36387014

Order 22784.

436 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3113C211yesmaximal, characteristic
2C89×#2984C211yesmaximal, characteristic
3C89×#1763C211yesmaximal, characteristic
4C89×#1531C211yesmaximal, characteristic
5C89×#1503C211yesmaximal, characteristic
6C89×#1302C211yesmaximal, characteristic
7C89×#1285C211yesmaximal, characteristic
8#533×C89C2211yescharacteristic
9C2×C4×Q8×C89C2211yescharacteristic
10#483×C89—21no—
11#475×C89C411yescharacteristic, complemented
12#475×C89C411yescharacteristic, complemented
13#462×C89C411yescharacteristic, complemented
14#462×C89C411yescharacteristic, complemented
15#451×C89—21no—
16#446×C89—21no—
17#446×C89—22no—
18C8×Q8×C89—21no—
19#441×C89—21no—
20#441×C89—21no—
21#432×C89—21no—
22#432×C89C2211yescharacteristic
23#432×C89C2211yescharacteristic
24#431×C89—21no—
25#431×C89C2211yescharacteristic
26C2×#103×C89—21no—
27C2×#97×C89C2211yescharacteristic
28C4×C4⋊C4×C89C2211yescharacteristic
29#340×C89—21no—
30#330×C89—22no—
31#328×C89—21no—
32#328×C89—21no—
33C22×Q8×C89D411yescharacteristic
34C2×Q16×C89—21no—
35C2×Q16×C89—21no—
36C22×C8×C89—21no—
37C4⋊Q8×C89C2×C411yescharacteristic
38C4⋊Q8×C89C2×C411yescharacteristic
39#125×C89—21no—
40C22⋊Q8×C89—21no—
41C22⋊Q8×C89—21no—
42C4×Q8×C89—21no—
43C4×Q8×C89—21no—
44C4×Q8×C89—21no—
45C4×Q8×C89—21no—
46C4×Q8×C89C2×C411yescharacteristic
47C4×Q8×C89C2×C411yescharacteristic
48C4×Q8×C89D411yescharacteristic
49C4×Q8×C89D411yescharacteristic
50#117×C89—21no—
51C2×C4⋊C4×C89—21no—
52C2×C4⋊C4×C89—21no—
53C2×C4⋊C4×C89D411yescharacteristic
54C2×C42×C89—21no—
55C2×C42×C89—21no—
56C2×C42×C89C2311yescharacteristic
57#106×C89—21no—
58#106×C89—21no—
59C4⋊C8×C89—22no—
60C4⋊C8×C89—22no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89—21no—
63C4⋊C8×C89C2×C411yescharacteristic
64C4⋊C8×C89C2×C411yescharacteristic
65#103×C89—24no—
66#103×C89—21no—
67#103×C89—21no—
68#103×C89—21no—
69#103×C89—21no—
70C22⋊C8×C89—21no—
71C22⋊C8×C89—21no—
72C22⋊C8×C89D411yescharacteristic
73C22⋊C8×C89D411yescharacteristic
74#97×C89—22no—
75#97×C89—21no—
76#97×C89—21no—
77#97×C89—21no—
78#97×C89D412yes—
79C4×C8×C89—22no—
80C4×C8×C89—21no—
81#95×C89—21no—
82C2×Q8×C89—21no—
83C2×Q8×C89—22no—
84C2×Q8×C89—21no—
85C2×Q8×C89—21no—
86C2×Q8×C89—41no—
87C2×Q8×C89C22⋊C411yescharacteristic
88C2×Q8×C89C22⋊C411yescharacteristic
89C22×C4×C89—21no—
90C22×C4×C89—21no—
91C22×C4×C89—41no—
92C22×C4×C89C2×D411yescharacteristic
93C22×C4×C89C2×D411yescharacteristic
94C22×C4×C89#4111yescharacteristic
95Q16×C89—42no—
96Q16×C89—42no—
97C2×C8×C89—22no—
98C2×C8×C89—21no—
99C2×C8×C89—21no—
100C2×C8×C89—21no—
101C2×C8×C89—21no—
102C2×C8×C89—22no—
103C2×C8×C89—41no—
104C2×C8×C89—41no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89—21no—
107C4⋊C4×C89—21no—
108C4⋊C4×C89—21no—
109C4⋊C4×C89—21no—
110C4⋊C4×C89—22no—
111C4⋊C4×C89—21no—
112C4⋊C4×C89—21no—
113C4⋊C4×C89—21no—
114C4⋊C4×C89—21no—
115C4⋊C4×C89—41no—
116C4⋊C4×C89—41no—
117C4⋊C4×C89—41no—
118C4⋊C4×C89C22⋊C411yescharacteristic
119C4⋊C4×C89C22⋊C411yescharacteristic
120C22⋊C4×C89—41no—
121C42×C89—21no—
122C42×C89—21no—
123C42×C89—21no—
124C42×C89—21no—
125C42×C89—41no—
126C42×C89—81no—
127C42×C89C22×C411yescharacteristic
128C42×C89C2×D411yescharacteristic
129C42×C89C2×D411yescharacteristic
130C42×C89#4111yescharacteristic
131C23×C89#12111yescharacteristic
132Q8×C89—21no—
133Q8×C89—21no—
134Q8×C89—21no—
135Q8×C89—42no—
136Q8×C89—41no—
137Q8×C89—41no—
138Q8×C89—81no—
139Q8×C89#10412yes—
140C2×C4×C89—21no—
141C2×C4×C89—21no—
142C2×C4×C89—21no—
143C2×C4×C89—21no—
144C2×C4×C89—21no—
145C2×C4×C89—21no—
146C2×C4×C89—21no—
147C2×C4×C89—21no—
148C2×C4×C89—41no—
149C2×C4×C89—42no—
150C2×C4×C89—41no—
151C2×C4×C89—41no—
152C2×C4×C89—42no—
153C2×C4×C89—41no—
154C2×C4×C89—41no—
155C2×C4×C89—81no—
156C2×C4×C89—81no—
157C2×C4×C89C2×C22⋊C411yescharacteristic
158C2×C4×C89C4×D411yescharacteristic
159C2×C4×C89C4×D411yescharacteristic
160C2×C4×C89#12011yescharacteristic
161C2×C4×C89#12111yescharacteristic
162C2×C4×C89#12311yescharacteristic
163C8×C89—41no—
164C8×C89—41no—
165C8×C89—42no—
166C8×C89—42no—
167C8×C89—41no—
168C8×C89—41no—
169C22×C89—21no—
170C22×C89—21no—
171C22×C89#38611yescharacteristic
172C22×C89#47111yescharacteristic
173C22×C89#47311yescharacteristic
174C4×C89—21no—
175C4×C89—22no—
176C4×C89—21no—
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—41no—
181C4×C89—41no—
182C4×C89—41no—
183C4×C89—82no—
184C4×C89—81no—
185C4×C89—81no—
186C4×C89C2×#10411yescharacteristic
187C4×C89#42111yescharacteristic
188#9166C8911yesmaximal, characteristic, direct product factor, Sylow
189C2×C89—21no—
190C2×C89—21no—
191C2×C89#187111yescharacteristic
192C2×C89#190511yescharacteristic
193C2×C89#190811yescharacteristic
194#3113C2×C8911yescharacteristic
195#2984C2×C8911yescharacteristic
196#1763C2×C8911yescharacteristic
197#1531C2×C8911yescharacteristic
198#1503C2×C8911yescharacteristic
199#1302C2×C8911yescharacteristic
200#1285C2×C8911yescharacteristic
201C89#916611yescharacteristic, direct product factor, Sylow
202#533C22×C8911yescharacteristic
203C2×C4×Q8C22×C8911yescharacteristic
204#483—21no—
205#475C4×C8911yescharacteristic, complemented
206#475C4×C8911yescharacteristic, complemented
207#462C4×C8911yescharacteristic, complemented
208#462C4×C8911yescharacteristic, complemented
209#451—21no—
210#446—21no—
211#446—22no—
212C8×Q8—21no—
213#441—21no—
214#441—21no—
215#432—21no—
216#432C22×C8911yescharacteristic
217#432C22×C8911yescharacteristic
218#431—21no—
219#431C22×C8911yescharacteristic
220C2×#103—21no—
221C2×#97C22×C8911yescharacteristic
222C4×C4⋊C4C22×C8911yescharacteristic
223#340—21no—
224#330—22no—
225#328—21no—
226#328—21no—
227C22×Q8D4×C8911yescharacteristic
228C2×Q16—21no—
229C2×Q16—21no—
230C22×C8—21no—
231C4⋊Q8C2×C4×C8911yescharacteristic
232C4⋊Q8C2×C4×C8911yescharacteristic
233#125—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8C2×C4×C8911yescharacteristic
241C4×Q8C2×C4×C8911yescharacteristic
242C4×Q8D4×C8911yescharacteristic
243C4×Q8D4×C8911yescharacteristic
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C8911yescharacteristic
248C2×C42—21no—
249C2×C42—21no—
250C2×C42C23×C8911yescharacteristic
251#106—21no—
252#106—21no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8C2×C4×C8911yescharacteristic
258C4⋊C8C2×C4×C8911yescharacteristic
259#103—24no—
260#103—21no—
261#103—21no—
262#103—21no—
263#103—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8D4×C8911yescharacteristic
267C22⋊C8D4×C8911yescharacteristic
268#97—22no—
269#97—21no—
270#97—21no—
271#97—21no—
272#97D4×C8912yes—
273C4×C8—22no—
274C4×C8—21no—
275#95—21no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8C22⋊C4×C8911yescharacteristic
282C2×Q8C22⋊C4×C8911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4C2×D4×C8911yescharacteristic
287C22×C4C2×D4×C8911yescharacteristic
288C22×C4#41×C8911yescharacteristic
289Q16—42no—
290Q16—42no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4C22⋊C4×C8911yescharacteristic
313C4⋊C4C22⋊C4×C8911yescharacteristic
314C22⋊C4—41no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—81no—
321C42C22×C4×C8911yescharacteristic
322C42C2×D4×C8911yescharacteristic
323C42C2×D4×C8911yescharacteristic
324C42#41×C8911yescharacteristic
325C23#121×C8911yescharacteristic
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—81no—
333Q8#104×C8912yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4C2×C22⋊C4×C8911yescharacteristic
352C2×C4C4×D4×C8911yescharacteristic
353C2×C4C4×D4×C8911yescharacteristic
354C2×C4#120×C8911yescharacteristic
355C2×C4#121×C8911yescharacteristic
356C2×C4#123×C8911yescharacteristic
357C8—41no—
358C8—41no—
359C8—42no—
360C8—42no—
361C8—41no—
362C8—41no—
363C22—21no—
364C22—21no—
365C22#386×C8911yescharacteristic
366C22#471×C8911yescharacteristic
367C22#473×C8911yescharacteristic
368C4—21no—
369C4—22no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—82no—
378C4—81no—
379C4—81no—
380C4C2×#104×C8911yescharacteristic
381C4#421×C8911yescharacteristic
382C2—21no—
383C2—21no—
384C2C89×#187111yescharacteristic
385C2C89×#190511yescharacteristic
386C2C89×#190811yescharacteristic
subgroupG/H
center, socleC22×C89#386
commutatorC42C22×C4×C89
Frattini, cosocleC2×C42C23×C89
prime radicalC23×C89#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
11. #475×C89C4semidirect
12. #475×C89C4semidirect
13. #462×C89C4semidirect
14. #462×C89C4semidirect
188. #9166C89direct (N × H)
201. C89#9166direct (N × H)
205. #475C4×C89semidirect
206. #475C4×C89semidirect
207. #462C4×C89semidirect
208. #462C4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#31132
C89×#29842
C89×#17632
C89×#15312
C89×#15032
C89×#13022
C89×#12852
#916689