Finite Group Databasebeta

← C89×#8911 #36386759

Subgroups — C89×#8911 #36386759

Order 22784.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2379C211yesmaximal, characteristic
2C89×#1959C211yesmaximal, characteristic
3C89×#1847C211yesmaximal, characteristic, complemented
4C89×#1836C211yesmaximal, characteristic, complemented
5C2×#329×C89C211yesmaximal, characteristic
6C89×#1295C211yesmaximal, characteristic, complemented
7C89×#1295C211yesmaximal, characteristic, complemented
8C2×#124×C89C2211yescharacteristic
9C2×#107×C89—21no—
10C2×#106×C89—21no—
11C2×#103×C89—21no—
12C2×#102×C89—21no—
13C2×#97×C89C2211yescharacteristic
14C2×#97×C89C2211yescharacteristic
15C2×#97×C89C2211yescharacteristic
16#391×C89—21no—
17#388×C89—21no—
18#388×C89—21no—
19#386×C89—21no—
20#385×C89—21no—
21#385×C89—21no—
22#384×C89C2211yescharacteristic
23#382×C89C2211yescharacteristic
24#382×C89C2211yescharacteristic
25#340×C89—21no—
26#340×C89—21no—
27#329×C89C414yescomplemented
28C22×Q8×C89D411yescharacteristic
29C22×D4×C89D411yescharacteristic
30C23×C4×C89—21no—
31C22×C8×C89—21no—
32C22×C8×C89—21no—
33C22×C8×C89—21no—
34#124×C89—21no—
35#124×C89—21no—
36#124×C89C2×C412yes—
37#124×C89Q812yes—
38C2×C4⋊C4×C89—21no—
39C2×C4⋊C4×C89—21no—
40C2×C4⋊C4×C89—21no—
41C2×C4⋊C4×C89—21no—
42C2×C4⋊C4×C89D411yescharacteristic
43C2×C4⋊C4×C89D411yescharacteristic
44C2×C4⋊C4×C89D411yescharacteristic
45C2×C4⋊C4×C89D411yescharacteristic
46C2×C22⋊C4×C89—21no—
47C2×C22⋊C4×C89—21no—
48C2×C22⋊C4×C89—21no—
49C2×C22⋊C4×C89—21no—
50C2×C22⋊C4×C89—21no—
51C2×C42×C89—21no—
52C2×C42×C89C2311yescharacteristic
53#107×C89—42no—
54#106×C89—42no—
55#103×C89—42no—
56#102×C89—42no—
57#97×C89—21no—
58#97×C89—21no—
59#97×C89—21no—
60#97×C89—21no—
61#97×C89C2×C412yescomplemented
62#97×C89C2×C412yescomplemented
63#95×C89—21no—
64#95×C89—21no—
65#95×C89—21no—
66#95×C89—21no—
67#95×C89—21no—
68#95×C89—21no—
69C24×C89—21no—
70C2×Q8×C89—21no—
71C2×Q8×C89—41no—
72C2×Q8×C89—41no—
73C2×Q8×C89C4⋊C412yes—
74C2×D4×C89—21no—
75C2×D4×C89—41no—
76C2×D4×C89—41no—
77C2×D4×C89C4⋊C412yes—
78C22×C4×C89—21no—
79C22×C4×C89—21no—
80C22×C4×C89—21no—
81C22×C4×C89—21no—
82C22×C4×C89—21no—
83C22×C4×C89—41no—
84C22×C4×C89—81no—
85C22×C4×C89—81no—
86C22×C4×C89—81no—
87C22×C4×C89C2×D411yescharacteristic
88C22×C4×C89C2×D411yescharacteristic
89C22×C4×C89C2×D411yescharacteristic
90C2×C8×C89—22no—
91C2×C8×C89—22no—
92C2×C8×C89—22no—
93C2×C8×C89—22no—
94C2×C8×C89—22no—
95C2×C8×C89—41no—
96C2×C8×C89—41no—
97C2×C8×C89—41no—
98C2×C8×C89—41no—
99C4⋊C4×C89—41no—
100C4⋊C4×C89—41no—
101C4⋊C4×C89—41no—
102C4⋊C4×C89—41no—
103C4⋊C4×C89—41no—
104C4⋊C4×C89—41no—
105C4⋊C4×C89—41no—
106C4⋊C4×C89—41no—
107C4⋊C4×C89—42no—
108C4⋊C4×C89—81no—
109C22⋊C4×C89—22no—
110C22⋊C4×C89—22no—
111C22⋊C4×C89—22no—
112C22⋊C4×C89—22no—
113C22⋊C4×C89—81no—
114C22⋊C4×C89—81no—
115C22⋊C4×C89—81no—
116C42×C89—81no—
117C42×C89C22×C411yescharacteristic
118C42×C89C2×Q811yescharacteristic
119C42×C89#4111yescharacteristic
120C42×C89#4111yescharacteristic
121C23×C89—22no—
122C23×C89—41no—
123C23×C89—41no—
124C23×C89—41no—
125C23×C89—41no—
126C23×C89—41no—
127C23×C89—41no—
128C23×C89#12011yescharacteristic
129Q8×C89—42no—
130Q8×C89—81no—
131D4×C89—42no—
132D4×C89—81no—
133C2×C4×C89—21no—
134C2×C4×C89—21no—
135C2×C4×C89—21no—
136C2×C4×C89—21no—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—22no—
140C2×C4×C89—41no—
141C2×C4×C89—41no—
142C2×C4×C89—41no—
143C2×C4×C89—41no—
144C2×C4×C89—41no—
145C2×C4×C89—41no—
146C2×C4×C89—41no—
147C2×C4×C89—41no—
148C2×C4×C89—41no—
149C2×C4×C89—41no—
150C2×C4×C89—41no—
151C2×C4×C89—41no—
152C2×C4×C89—41no—
153C2×C4×C89—41no—
154C2×C4×C89—84no—
155C2×C4×C89—81no—
156C2×C4×C89—81no—
157C2×C4×C89—81no—
158C2×C4×C89C2×C4⋊C411yescharacteristic
159C2×C4×C89C4×D411yescharacteristic
160C2×C4×C89C4×D411yescharacteristic
161C2×C4×C89C22⋊Q811yescharacteristic
162C2×C4×C89C22⋊Q811yescharacteristic
163C2×C4×C89#12311yescharacteristic
164C8×C89—24no—
165C8×C89—42no—
166C8×C89—42no—
167C22×C89—42no—
168C22×C89—42no—
169C22×C89—42no—
170C22×C89—81no—
171C22×C89—81no—
172C22×C89—81no—
173C22×C89—81no—
174C22×C89#38511yescharacteristic
175C22×C89#45311yescharacteristic
176C22×C89#45311yescharacteristic
177C22×C89#45411yescharacteristic
178C22×C89#45511yescharacteristic
179C22×C89#45511yescharacteristic
180C22×C89#45611yescharacteristic
181C4×C89—21no—
182C4×C89—21no—
183C4×C89—21no—
184C4×C89—21no—
185C4×C89—21no—
186C4×C89—21no—
187C4×C89—42no—
188C4×C89—81no—
189C4×C89—81no—
190C4×C89—81no—
191C4×C89—81no—
192C4×C89—161no—
193#8911C8911yesmaximal, characteristic, direct product factor, Sylow
194C2×C89—82no—
195C2×C89#165611yescharacteristic
196C2×C89#165911yescharacteristic
197C2×C89#166111yescharacteristic
198C2×C89#166411yescharacteristic
199C2×C89#185611yescharacteristic
200C2×C89#185911yescharacteristic
201C2×C89#186011yescharacteristic
202#2379C2×C8911yescharacteristic
203#1959C2×C8911yescharacteristic
204#1847C2×C8911yescharacteristic, complemented
205#1836C2×C8911yescharacteristic, complemented
206C2×#329C2×C8911yescharacteristic
207#1295C2×C8911yescharacteristic, complemented
208#1295C2×C8911yescharacteristic, complemented
209C89#891111yescharacteristic, direct product factor, Sylow
210C2×#124C22×C8911yescharacteristic
211C2×#107—21no—
212C2×#106—21no—
213C2×#103—21no—
214C2×#102—21no—
215C2×#97C22×C8911yescharacteristic
216C2×#97C22×C8911yescharacteristic
217C2×#97C22×C8911yescharacteristic
218#391—21no—
219#388—21no—
220#388—21no—
221#386—21no—
222#385—21no—
223#385—21no—
224#384C22×C8911yescharacteristic
225#382C22×C8911yescharacteristic
226#382C22×C8911yescharacteristic
227#340—21no—
228#340—21no—
229#329C4×C8914yescomplemented
230C22×Q8D4×C8911yescharacteristic
231C22×D4D4×C8911yescharacteristic
232C23×C4—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236#124—21no—
237#124—21no—
238#124C2×C4×C8912yes—
239#124Q8×C8912yes—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C8911yescharacteristic
245C2×C4⋊C4D4×C8911yescharacteristic
246C2×C4⋊C4D4×C8911yescharacteristic
247C2×C4⋊C4D4×C8911yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42—21no—
254C2×C42C23×C8911yescharacteristic
255#107—42no—
256#106—42no—
257#103—42no—
258#102—42no—
259#97—21no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97C2×C4×C8912yescomplemented
264#97C2×C4×C8912yescomplemented
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271C24—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C4⋊C4×C8912yes—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4C4⋊C4×C8912yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C8911yescharacteristic
290C22×C4C2×D4×C8911yescharacteristic
291C22×C4C2×D4×C8911yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—81no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—81no—
316C22⋊C4—81no—
317C22⋊C4—81no—
318C42—81no—
319C42C22×C4×C8911yescharacteristic
320C42C2×Q8×C8911yescharacteristic
321C42#41×C8911yescharacteristic
322C42#41×C8911yescharacteristic
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23#120×C8911yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—42no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C2×C4⋊C4×C8911yescharacteristic
361C2×C4C4×D4×C8911yescharacteristic
362C2×C4C4×D4×C8911yescharacteristic
363C2×C4C22⋊Q8×C8911yescharacteristic
364C2×C4C22⋊Q8×C8911yescharacteristic
365C2×C4#123×C8911yescharacteristic
366C8—24no—
367C8—42no—
368C8—42no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22#385×C8911yescharacteristic
377C22#453×C8911yescharacteristic
378C22#453×C8911yescharacteristic
379C22#454×C8911yescharacteristic
380C22#455×C8911yescharacteristic
381C22#455×C8911yescharacteristic
382C22#456×C8911yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—161no—
395C2—82no—
396C2C89×#165611yescharacteristic
397C2C89×#165911yescharacteristic
398C2C89×#166111yescharacteristic
399C2C89×#166411yescharacteristic
400C2C89×#185611yescharacteristic
401C2C89×#185911yescharacteristic
402C2C89×#186011yescharacteristic
subgroupG/H
center, socleC23×C89#120
commutatorC42C22×C4×C89
Frattini, cosocleC2×C42C23×C89
prime radicalC22×D4×C89D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C89×#1847C2semidirect
4. C89×#1836C2semidirect
6. C89×#1295C2semidirect
7. C89×#1295C2semidirect
27. #329×C89C4semidirect
61. #97×C89C2×C4semidirect
62. #97×C89C2×C4semidirect
193. #8911C89direct (N × H)
204. #1847C2×C89semidirect
205. #1836C2×C89semidirect
207. #1295C2×C89semidirect
208. #1295C2×C89semidirect
209. C89#8911direct (N × H)
229. #329C4×C89semidirect
263. #97C2×C4×C89semidirect
264. #97C2×C4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#23792
C89×#19592
C89×#18472
C89×#18362
C2×#329×C892
C89×#12952
#891189