Finite Group Databasebeta

← C89×#9326 #36387174

Subgroups — C89×#9326 #36387174

Order 22784.

574 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3112C211yesmaximal, characteristic
2C89×#2276C211yesmaximal, characteristic, complemented
3C89×#1980C211yesmaximal, characteristic
4C89×#1505C211yesmaximal, characteristic
5C89×#1491C211yesmaximal, characteristic, complemented
6C89×#1300C211yesmaximal, characteristic, complemented
7C89×#1285C211yesmaximal, characteristic, complemented
8#532×C89C2211yescharacteristic
9C2×C4×Q8×C89—21no—
10C2×C4×Q8×C89C2211yescharacteristic
11#480×C89—21no—
12#477×C89C412yescomplemented
13#460×C89C412yescomplemented
14#448×C89—21no—
15#440×C89—22no—
16#432×C89C2211yescharacteristic
17#432×C89C2211yescharacteristic
18C2×#104×C89—22no—
19C4×M16×C89C2211yescharacteristic
20C4×C4⋊C4×C89—21no—
21C4×C4⋊C4×C89—22no—
22C4×C4⋊C4×C89—21no—
23C4×C4⋊C4×C89C2211yescharacteristic
24#376×C89—21no—
25#376×C89C2211yescharacteristic
26#327×C89—21no—
27#327×C89—21no—
28Q8⋊C8×C89—22no—
29C2×#41×C89—21no—
30C22×Q8×C89D411yescharacteristic
31C2×SD16×C89—22no—
32C2×M16×C89—21no—
33C4⋊Q8×C89C2×C411yescharacteristic
34#127×C89C2×C411yescharacteristic
35#124×C89—21no—
36#121×C89—21no—
37#121×C89—21no—
38C4×Q8×C89—28no—
39C4×Q8×C89—21no—
40C4×Q8×C89—21no—
41C4×Q8×C89C2×C412yes—
42C4×Q8×C89D412yes—
43C4×D4×C89—21no—
44C4×D4×C89—21no—
45C2×C4⋊C4×C89—22no—
46C2×C4⋊C4×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89D411yescharacteristic
49C2×C42×C89—22no—
50C2×C42×C89—21no—
51C2×C42×C89—21no—
52C2×C42×C89—22no—
53C2×C42×C89D412yes—
54C2×C42×C89C2311yescharacteristic
55#107×C89—22no—
56C4⋊C8×C89—21no—
57C4⋊C8×C89C2×C412yes—
58#104×C89—44no—
59#103×C89—22no—
60#102×C89—22no—
61C22⋊C8×C89—21no—
62C22⋊C8×C89—21no—
63#97×C89—21no—
64#97×C89—21no—
65#97×C89—21no—
66C4×C8×C89—21no—
67#95×C89—22no—
68#95×C89—21no—
69#95×C89—21no—
70#95×C89D411yescharacteristic
71#95×C89D411yescharacteristic
72#41×C89—42no—
73#41×C89—42no—
74C2×Q8×C89—24no—
75C2×Q8×C89—21no—
76C2×Q8×C89—21no—
77C2×Q8×C89C22⋊C412yes—
78C2×D4×C89—21no—
79C2×D4×C89—21no—
80C2×D4×C89—21no—
81C2×D4×C89—41no—
82C22×C4×C89—21no—
83C22×C4×C89—21no—
84C22×C4×C89—21no—
85C22×C4×C89—22no—
86C22×C4×C89—21no—
87C22×C4×C89—41no—
88C22×C4×C89C2×D411yescharacteristic
89C22×C4×C89C2×D411yescharacteristic
90C22×C4×C89C2×D411yescharacteristic
91SD16×C89—44no—
92M16×C89—22no—
93M16×C89—41no—
94C2×C8×C89—22no—
95C2×C8×C89—41no—
96C2×C8×C89—41no—
97C4⋊C4×C89—28no—
98C4⋊C4×C89—24no—
99C4⋊C4×C89—22no—
100C4⋊C4×C89—22no—
101C4⋊C4×C89—21no—
102C4⋊C4×C89—21no—
103C4⋊C4×C89—21no—
104C4⋊C4×C89C22⋊C412yes—
105C22⋊C4×C89—41no—
106C22⋊C4×C89—41no—
107C42×C89—28no—
108C42×C89—24no—
109C42×C89—22no—
110C42×C89—22no—
111C42×C89—42no—
112C42×C89—82no—
113C42×C89C22×C411yescharacteristic
114C42×C89C2×D411yescharacteristic
115C42×C89#4111yescharacteristic
116C42×C89#4111yescharacteristic
117C23×C89—41no—
118C23×C89#12011yescharacteristic
119Q8×C89—24no—
120Q8×C89—22no—
121Q8×C89—42no—
122Q8×C89#10414yescomplemented
123D4×C89—42no—
124D4×C89—42no—
125D4×C89—81no—
126D4×C89—81no—
127D4×C89—81no—
128C2×C4×C89—24no—
129C2×C4×C89—22no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—22no—
133C2×C4×C89—22no—
134C2×C4×C89—24no—
135C2×C4×C89—22no—
136C2×C4×C89—22no—
137C2×C4×C89—41no—
138C2×C4×C89—41no—
139C2×C4×C89—42no—
140C2×C4×C89—41no—
141C2×C4×C89—42no—
142C2×C4×C89—41no—
143C2×C4×C89—41no—
144C2×C4×C89—41no—
145C2×C4×C89—41no—
146C2×C4×C89—41no—
147C2×C4×C89—82no—
148C2×C4×C89C2×C22⋊C411yescharacteristic
149C2×C4×C89C4×D411yescharacteristic
150C2×C4×C89C4×D411yescharacteristic
151C2×C4×C89#12111yescharacteristic
152C2×C4×C89#12111yescharacteristic
153C2×C4×C89#12311yescharacteristic
154C8×C89—42no—
155C8×C89—42no—
156C8×C89—81no—
157C22×C89—21no—
158C22×C89—21no—
159C22×C89—81no—
160C22×C89—81no—
161C22×C89—81no—
162C22×C89#38611yescharacteristic
163C22×C89#45311yescharacteristic
164C22×C89#45411yescharacteristic
165C4×C89—21no—
166C4×C89—21no—
167C4×C89—24no—
168C4×C89—21no—
169C4×C89—21no—
170C4×C89—21no—
171C4×C89—44no—
172C4×C89—42no—
173C4×C89—42no—
174C4×C89—42no—
175C4×C89—81no—
176C4×C89C2×#10412yes—
177#9326C8911yesmaximal, characteristic, direct product factor, Sylow
178C2×C89—21no—
179C2×C89—21no—
180C2×C89—161no—
181C2×C89#188311yescharacteristic
182C2×C89#189611yescharacteristic
183C2×C89#190511yescharacteristic
184#3112C2×C8911yescharacteristic
185#2276C2×C8911yescharacteristic, complemented
186#1980C2×C8911yescharacteristic
187#1505C2×C8911yescharacteristic
188#1491C2×C8911yescharacteristic, complemented
189#1300C2×C8911yescharacteristic, complemented
190#1285C2×C8911yescharacteristic, complemented
191C89#932611yescharacteristic, direct product factor, Sylow
192#532C22×C8911yescharacteristic
193C2×C4×Q8—21no—
194C2×C4×Q8C22×C8911yescharacteristic
195#480—21no—
196#477C4×C8912yescomplemented
197#460C4×C8912yescomplemented
198#448—21no—
199#440—22no—
200#432C22×C8911yescharacteristic
201#432C22×C8911yescharacteristic
202C2×#104—22no—
203C4×M16C22×C8911yescharacteristic
204C4×C4⋊C4—21no—
205C4×C4⋊C4—22no—
206C4×C4⋊C4—21no—
207C4×C4⋊C4C22×C8911yescharacteristic
208#376—21no—
209#376C22×C8911yescharacteristic
210#327—21no—
211#327—21no—
212Q8⋊C8—22no—
213C2×#41—21no—
214C22×Q8D4×C8911yescharacteristic
215C2×SD16—22no—
216C2×M16—21no—
217C4⋊Q8C2×C4×C8911yescharacteristic
218#127C2×C4×C8911yescharacteristic
219#124—21no—
220#121—21no—
221#121—21no—
222C4×Q8—28no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8C2×C4×C8912yes—
226C4×Q8D4×C8912yes—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C8911yescharacteristic
233C2×C42—22no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42D4×C8912yes—
238C2×C42C23×C8911yescharacteristic
239#107—22no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C8912yes—
242#104—44no—
243#103—22no—
244#102—22no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#97—21no—
248#97—21no—
249#97—21no—
250C4×C8—21no—
251#95—22no—
252#95—21no—
253#95—21no—
254#95D4×C8911yescharacteristic
255#95D4×C8911yescharacteristic
256#41—42no—
257#41—42no—
258C2×Q8—24no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8C22⋊C4×C8912yes—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C8911yescharacteristic
273C22×C4C2×D4×C8911yescharacteristic
274C22×C4C2×D4×C8911yescharacteristic
275SD16—44no—
276M16—22no—
277M16—41no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—28no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4C22⋊C4×C8912yes—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—28no—
292C42—24no—
293C42—22no—
294C42—22no—
295C42—42no—
296C42—82no—
297C42C22×C4×C8911yescharacteristic
298C42C2×D4×C8911yescharacteristic
299C42#41×C8911yescharacteristic
300C42#41×C8911yescharacteristic
301C23—41no—
302C23#120×C8911yescharacteristic
303Q8—24no—
304Q8—22no—
305Q8—42no—
306Q8#104×C8914yescomplemented
307D4—42no—
308D4—42no—
309D4—81no—
310D4—81no—
311D4—81no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4C2×C22⋊C4×C8911yescharacteristic
333C2×C4C4×D4×C8911yescharacteristic
334C2×C4C4×D4×C8911yescharacteristic
335C2×C4#121×C8911yescharacteristic
336C2×C4#121×C8911yescharacteristic
337C2×C4#123×C8911yescharacteristic
338C8—42no—
339C8—42no—
340C8—81no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#386×C8911yescharacteristic
347C22#453×C8911yescharacteristic
348C22#454×C8911yescharacteristic
349C4—21no—
350C4—21no—
351C4—24no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—44no—
356C4—42no—
357C4—42no—
358C4—42no—
359C4—81no—
360C4C2×#104×C8912yes—
361C2—21no—
362C2—21no—
363C2—161no—
364C2C89×#188311yescharacteristic
365C2C89×#189611yescharacteristic
366C2C89×#190511yescharacteristic
subgroupG/H
center, socleC22×C89#386
commutatorC42C22×C4×C89
Frattini, cosocleC2×C42C23×C89
prime radical#532×C89C22
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
2. C89×#2276C2semidirect
5. C89×#1491C2semidirect
6. C89×#1300C2semidirect
7. C89×#1285C2semidirect
12. #477×C89C4semidirect
13. #460×C89C4semidirect
122. Q8×C89#104semidirect
177. #9326C89direct (N × H)
185. #2276C2×C89semidirect
188. #1491C2×C89semidirect
189. #1300C2×C89semidirect
190. #1285C2×C89semidirect
191. C89#9326direct (N × H)
196. #477C4×C89semidirect
197. #460C4×C89semidirect
306. Q8#104×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#31122
C89×#22762
C89×#19802
C89×#15052
C89×#14912
C89×#13002
C89×#12852
#932689