Finite Group Databasebeta

← C89×#9761 #36387609

Subgroups — C89×#9761 #36387609

Order 22784.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3167C211yesmaximal, characteristic
2C89×#1726C211yesmaximal, characteristic, complemented
3C89×#1568C211yesmaximal, characteristic, complemented
4C89×#1531C211yesmaximal, characteristic, complemented
5C89×#1530C211yesmaximal, characteristic
6C89×#1506C211yesmaximal, characteristic, complemented
7C89×#1505C211yesmaximal, characteristic
8#533×C89C2211yescharacteristic
9#532×C89C2211yescharacteristic
10#498×C89C411yescharacteristic, complemented
11#492×C89C411yescharacteristic, complemented
12#487×C89C411yescharacteristic, complemented
13#486×C89C411yescharacteristic, complemented
14#465×C89—21no—
15#465×C89—21no—
16C4×SD16×C89—21no—
17C4×SD16×C89—21no—
18#432×C89C2211yescharacteristic
19#432×C89C2211yescharacteristic
20C2×#97×C89—21no—
21C2×#97×C89C2211yescharacteristic
22C2×C4×C8×C89—21no—
23C2×C4×C8×C89C2211yescharacteristic
24#376×C89C2211yescharacteristic
25#335×C89—21no—
26#334×C89—21no—
27#330×C89—22no—
28#329×C89—22no—
29#328×C89—22no—
30#327×C89—22no—
31C2×#41×C89—21no—
32C2×SD16×C89—21no—
33C2×SD16×C89—21no—
34C22×C8×C89—21no—
35C22×C8×C89D411yescharacteristic
36C22×C8×C89D411yescharacteristic
37C4⋊Q8×C89C2×C411yescharacteristic
38C4⋊Q8×C89C2×C411yescharacteristic
39C4⋊Q8×C89C2×C411yescharacteristic
40#127×C89C2×C411yescharacteristic
41#125×C89—21no—
42#124×C89—21no—
43C22⋊Q8×C89—21no—
44C22⋊Q8×C89—21no—
45#121×C89—21no—
46#121×C89—21no—
47C4×Q8×C89—21no—
48C4×Q8×C89—21no—
49C4×D4×C89—21no—
50C4×D4×C89—21no—
51#117×C89—21no—
52C2×C42×C89—21no—
53C2×C42×C89C2311yescharacteristic
54#106×C89—21no—
55#106×C89—21no—
56C4⋊C8×C89—21no—
57C4⋊C8×C89—21no—
58#103×C89—21no—
59#103×C89—21no—
60#102×C89—21no—
61#102×C89—21no—
62C22⋊C8×C89—21no—
63C22⋊C8×C89—21no—
64#97×C89—24no—
65#97×C89—21no—
66#97×C89—21no—
67#97×C89—21no—
68#97×C89D412yes—
69C4×C8×C89—24no—
70C4×C8×C89C2×C411yescharacteristic
71C4×C8×C89C2×C411yescharacteristic
72C4×C8×C89D411yescharacteristic
73C4×C8×C89D411yescharacteristic
74#95×C89—21no—
75#95×C89D412yes—
76#41×C89—82no—
77C2×Q8×C89—21no—
78C2×Q8×C89—21no—
79C2×Q8×C89—21no—
80C2×D4×C89—21no—
81C2×D4×C89—21no—
82C2×D4×C89—21no—
83C2×D4×C89—41no—
84C22×C4×C89—22no—
85C22×C4×C89—41no—
86C22×C4×C89C2×D411yescharacteristic
87C22×C4×C89C2×D411yescharacteristic
88C22×C4×C89#4111yescharacteristic
89SD16×C89—42no—
90SD16×C89—42no—
91C2×C8×C89—22no—
92C2×C8×C89—22no—
93C2×C8×C89—22no—
94C2×C8×C89—22no—
95C2×C8×C89—22no—
96C2×C8×C89—41no—
97C2×C8×C89—41no—
98C2×C8×C89C22⋊C411yescharacteristic
99C2×C8×C89C22⋊C411yescharacteristic
100C2×C8×C89C22⋊C411yescharacteristic
101C2×C8×C89C22⋊C411yescharacteristic
102C4⋊C4×C89—21no—
103C4⋊C4×C89—21no—
104C4⋊C4×C89—21no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89—21no—
107C4⋊C4×C89—21no—
108C4⋊C4×C89—41no—
109C4⋊C4×C89—41no—
110C22⋊C4×C89—41no—
111C22⋊C4×C89—41no—
112C22⋊C4×C89—41no—
113C42×C89—22no—
114C42×C89—22no—
115C42×C89—41no—
116C42×C89C22×C411yescharacteristic
117C42×C89C2×D411yescharacteristic
118C42×C89C2×D411yescharacteristic
119C42×C89#4111yescharacteristic
120C23×C89—41no—
121C23×C89#12111yescharacteristic
122Q8×C89—41no—
123Q8×C89—41no—
124Q8×C89—81no—
125Q8×C89—81no—
126D4×C89—41no—
127D4×C89—41no—
128D4×C89—81no—
129D4×C89—81no—
130D4×C89—82no—
131C2×C4×C89—22no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—24no—
135C2×C4×C89—41no—
136C2×C4×C89—42no—
137C2×C4×C89—42no—
138C2×C4×C89—41no—
139C2×C4×C89—41no—
140C2×C4×C89—41no—
141C2×C4×C89—82no—
142C2×C4×C89C2×C22⋊C411yescharacteristic
143C2×C4×C89C4×D411yescharacteristic
144C2×C4×C89C4×D411yescharacteristic
145C2×C4×C89#12111yescharacteristic
146C2×C4×C89#12411yescharacteristic
147C2×C4×C89#12711yescharacteristic
148C8×C89—24no—
149C8×C89—21no—
150C8×C89—21no—
151C8×C89—81no—
152C8×C89—81no—
153C8×C89#10412yes—
154C8×C89#10412yes—
155C22×C89—21no—
156C22×C89—21no—
157C22×C89—81no—
158C22×C89—81no—
159C22×C89—81no—
160C22×C89#39011yescharacteristic
161C22×C89#47112yes—
162C4×C89—21no—
163C4×C89—21no—
164C4×C89—21no—
165C4×C89—21no—
166C4×C89—21no—
167C4×C89—44no—
168C4×C89—81no—
169C4×C89—81no—
170C4×C89—81no—
171C4×C89C2×#10411yescharacteristic
172C4×C89C2×#10411yescharacteristic
173#9761C8911yesmaximal, characteristic, direct product factor, Sylow
174C2×C89—22no—
175C2×C89—161no—
176C2×C89#196211yescharacteristic
177C2×C89#197611yescharacteristic
178C2×C89#197711yescharacteristic
179#3167C2×C8911yescharacteristic
180#1726C2×C8911yescharacteristic, complemented
181#1568C2×C8911yescharacteristic, complemented
182#1531C2×C8911yescharacteristic, complemented
183#1530C2×C8911yescharacteristic
184#1506C2×C8911yescharacteristic, complemented
185#1505C2×C8911yescharacteristic
186C89#976111yescharacteristic, direct product factor, Sylow
187#533C22×C8911yescharacteristic
188#532C22×C8911yescharacteristic
189#498C4×C8911yescharacteristic, complemented
190#492C4×C8911yescharacteristic, complemented
191#487C4×C8911yescharacteristic, complemented
192#486C4×C8911yescharacteristic, complemented
193#465—21no—
194#465—21no—
195C4×SD16—21no—
196C4×SD16—21no—
197#432C22×C8911yescharacteristic
198#432C22×C8911yescharacteristic
199C2×#97—21no—
200C2×#97C22×C8911yescharacteristic
201C2×C4×C8—21no—
202C2×C4×C8C22×C8911yescharacteristic
203#376C22×C8911yescharacteristic
204#335—21no—
205#334—21no—
206#330—22no—
207#329—22no—
208#328—22no—
209#327—22no—
210C2×#41—21no—
211C2×SD16—21no—
212C2×SD16—21no—
213C22×C8—21no—
214C22×C8D4×C8911yescharacteristic
215C22×C8D4×C8911yescharacteristic
216C4⋊Q8C2×C4×C8911yescharacteristic
217C4⋊Q8C2×C4×C8911yescharacteristic
218C4⋊Q8C2×C4×C8911yescharacteristic
219#127C2×C4×C8911yescharacteristic
220#125—21no—
221#124—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224#121—21no—
225#121—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×D4—21no—
229C4×D4—21no—
230#117—21no—
231C2×C42—21no—
232C2×C42C23×C8911yescharacteristic
233#106—21no—
234#106—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#103—21no—
238#103—21no—
239#102—21no—
240#102—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#97—24no—
244#97—21no—
245#97—21no—
246#97—21no—
247#97D4×C8912yes—
248C4×C8—24no—
249C4×C8C2×C4×C8911yescharacteristic
250C4×C8C2×C4×C8911yescharacteristic
251C4×C8D4×C8911yescharacteristic
252C4×C8D4×C8911yescharacteristic
253#95—21no—
254#95D4×C8912yes—
255#41—82no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4C2×D4×C8911yescharacteristic
266C22×C4C2×D4×C8911yescharacteristic
267C22×C4#41×C8911yescharacteristic
268SD16—42no—
269SD16—42no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22⋊C4×C8911yescharacteristic
278C2×C8C22⋊C4×C8911yescharacteristic
279C2×C8C22⋊C4×C8911yescharacteristic
280C2×C8C22⋊C4×C8911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—22no—
293C42—22no—
294C42—41no—
295C42C22×C4×C8911yescharacteristic
296C42C2×D4×C8911yescharacteristic
297C42C2×D4×C8911yescharacteristic
298C42#41×C8911yescharacteristic
299C23—41no—
300C23#121×C8911yescharacteristic
301Q8—41no—
302Q8—41no—
303Q8—81no—
304Q8—81no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309D4—82no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4C2×C22⋊C4×C8911yescharacteristic
322C2×C4C4×D4×C8911yescharacteristic
323C2×C4C4×D4×C8911yescharacteristic
324C2×C4#121×C8911yescharacteristic
325C2×C4#124×C8911yescharacteristic
326C2×C4#127×C8911yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—81no—
331C8—81no—
332C8#104×C8912yes—
333C8#104×C8912yes—
334C22—21no—
335C22—21no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#390×C8911yescharacteristic
340C22#471×C8912yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4C2×#104×C8911yescharacteristic
351C4C2×#104×C8911yescharacteristic
352C2—22no—
353C2—161no—
354C2C89×#196211yescharacteristic
355C2C89×#197611yescharacteristic
356C2C89×#197711yescharacteristic
subgroupG/H
center, socleC22×C89#390
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×#1726C2semidirect
3. C89×#1568C2semidirect
4. C89×#1531C2semidirect
6. C89×#1506C2semidirect
10. #498×C89C4semidirect
11. #492×C89C4semidirect
12. #487×C89C4semidirect
13. #486×C89C4semidirect
173. #9761C89direct (N × H)
180. #1726C2×C89semidirect
181. #1568C2×C89semidirect
182. #1531C2×C89semidirect
184. #1506C2×C89semidirect
186. C89#9761direct (N × H)
189. #498C4×C89semidirect
190. #492C4×C89semidirect
191. #487C4×C89semidirect
192. #486C4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#31672
C89×#17262
C89×#15682
C89×#15312
C89×#15302
C89×#15062
C89×#15052
#976189