Finite Group Databasebeta

← C89×#9433 #36387281

Subgroups — C89×#9433 #36387281

Order 22784.

440 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3141C211yesmaximal, characteristic
2C89×#2979C211yesmaximal, characteristic
3C89×#1560C211yesmaximal, characteristic
4C89×#1548C211yesmaximal, characteristic, complemented
5C89×#1546C211yesmaximal, characteristic, complemented
6C89×#1299C211yesmaximal, characteristic, complemented
7C89×#1299C211yesmaximal, characteristic, complemented
8#532×C89C2211yescharacteristic
9C2×C4⋊Q8×C89C2211yescharacteristic
10#489×C89C414yes—
11#487×C89—21no—
12#486×C89—21no—
13#436×C89—21no—
14#436×C89—21no—
15C8×D4×C89—21no—
16C8×D4×C89—21no—
17#431×C89C2211yescharacteristic
18#431×C89C2211yescharacteristic
19#423×C89C2211yescharacteristic
20#423×C89C2211yescharacteristic
21#417×C89—22no—
22#408×C89—22no—
23C4×M16×C89C2211yescharacteristic
24#333×C89—21no—
25#333×C89—21no—
26#333×C89—21no—
27#332×C89—21no—
28#332×C89—21no—
29#331×C89—21no—
30C2×#41×C89D412yes—
31C22×Q8×C89—21no—
32C2×M16×C89—21no—
33C2×M16×C89—22no—
34C2×M16×C89—21no—
35C2×M16×C89—21no—
36C22×C8×C89—22no—
37C4⋊Q8×C89—21no—
38C4⋊Q8×C89—21no—
39C4⋊Q8×C89—21no—
40C4⋊Q8×C89C2×C412yes—
41C4⋊Q8×C89D411yescharacteristic
42#127×C89D411yescharacteristic
43#124×C89C2×C412yes—
44#121×C89—21no—
45#121×C89—21no—
46C4×D4×C89—21no—
47C4×D4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89—21no—
50C2×C42×C89C2311yescharacteristic
51C4⋊C8×C89—21no—
52C4⋊C8×C89—21no—
53C4⋊C8×C89—21no—
54C4⋊C8×C89—21no—
55C4⋊C8×C89D411yescharacteristic
56C4⋊C8×C89D411yescharacteristic
57C4⋊C8×C89D411yescharacteristic
58C4⋊C8×C89D411yescharacteristic
59#103×C89—24no—
60#102×C89—24no—
61C22⋊C8×C89—22no—
62C22⋊C8×C89—22no—
63C22⋊C8×C89—21no—
64C22⋊C8×C89—21no—
65#97×C89C2×C412yes—
66C4×C8×C89—21no—
67C4×C8×C89—21no—
68C4×C8×C89—21no—
69#41×C89—42no—
70#41×C89—42no—
71C2×Q8×C89—22no—
72C2×Q8×C89—41no—
73C2×Q8×C89—81no—
74C2×Q8×C89—81no—
75C2×Q8×C89C22⋊C412yes—
76C2×D4×C89—22no—
77C2×D4×C89—21no—
78C2×D4×C89—21no—
79C2×D4×C89C22⋊C412yes—
80C22×C4×C89—22no—
81C22×C4×C89—41no—
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89#4111yescharacteristic
84C22×C4×C89#4111yescharacteristic
85M16×C89—41no—
86M16×C89—41no—
87M16×C89—82no—
88M16×C89—81no—
89M16×C89—81no—
90C2×C8×C89—22no—
91C2×C8×C89—21no—
92C2×C8×C89—21no—
93C2×C8×C89—21no—
94C2×C8×C89—21no—
95C2×C8×C89—41no—
96C2×C8×C89—41no—
97C2×C8×C89—82no—
98C4⋊C4×C89—21no—
99C4⋊C4×C89—21no—
100C4⋊C4×C89—22no—
101C4⋊C4×C89—22no—
102C4⋊C4×C89—41no—
103C4⋊C4×C89—41no—
104C22⋊C4×C89—22no—
105C22⋊C4×C89—22no—
106C42×C89C22×C411yescharacteristic
107C42×C89C2×D411yescharacteristic
108C42×C89C2×D411yescharacteristic
109C42×C89C2×D411yescharacteristic
110C23×C89—22no—
111C23×C89#12311yescharacteristic
112Q8×C89—42no—
113Q8×C89—82no—
114Q8×C89—81no—
115Q8×C89—81no—
116D4×C89—42no—
117D4×C89—41no—
118D4×C89—41no—
119D4×C89—41no—
120D4×C89—41no—
121D4×C89—82no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—22no—
129C2×C4×C89—42no—
130C2×C4×C89—42no—
131C2×C4×C89—42no—
132C2×C4×C89—82no—
133C2×C4×C89C2×C22⋊C411yescharacteristic
134C2×C4×C89C4×D411yescharacteristic
135C2×C4×C89C4×D411yescharacteristic
136C2×C4×C89#12011yescharacteristic
137C2×C4×C89#12111yescharacteristic
138C2×C4×C89#12111yescharacteristic
139C8×C89—42no—
140C8×C89—41no—
141C8×C89—41no—
142C8×C89—41no—
143C8×C89—41no—
144C8×C89—81no—
145C8×C89—81no—
146C22×C89—21no—
147C22×C89—21no—
148C22×C89—21no—
149C22×C89—42no—
150C22×C89—42no—
151C22×C89—42no—
152C22×C89#38611yescharacteristic
153C4×C89—21no—
154C4×C89—21no—
155C4×C89—21no—
156C4×C89—42no—
157C4×C89—82no—
158C4×C89#45511yescharacteristic
159C4×C89#45511yescharacteristic
160C4×C89#47111yescharacteristic
161C4×C89#47111yescharacteristic
162C4×C89#47211yescharacteristic
163C4×C89#47311yescharacteristic
164#9433C8911yesmaximal, characteristic, direct product factor, Sylow
165C2×C89—41no—
166C2×C89—82no—
167C2×C89#188511yescharacteristic
168C2×C89#190711yescharacteristic
169C2×C89#190811yescharacteristic
170#3141C2×C8911yescharacteristic
171#2979C2×C8911yescharacteristic
172#1560C2×C8911yescharacteristic
173#1548C2×C8911yescharacteristic, complemented
174#1546C2×C8911yescharacteristic, complemented
175#1299C2×C8911yescharacteristic, complemented
176#1299C2×C8911yescharacteristic, complemented
177C89#943311yescharacteristic, direct product factor, Sylow
178#532C22×C8911yescharacteristic
179C2×C4⋊Q8C22×C8911yescharacteristic
180#489C4×C8914yes—
181#487—21no—
182#486—21no—
183#436—21no—
184#436—21no—
185C8×D4—21no—
186C8×D4—21no—
187#431C22×C8911yescharacteristic
188#431C22×C8911yescharacteristic
189#423C22×C8911yescharacteristic
190#423C22×C8911yescharacteristic
191#417—22no—
192#408—22no—
193C4×M16C22×C8911yescharacteristic
194#333—21no—
195#333—21no—
196#333—21no—
197#332—21no—
198#332—21no—
199#331—21no—
200C2×#41D4×C8912yes—
201C22×Q8—21no—
202C2×M16—21no—
203C2×M16—22no—
204C2×M16—21no—
205C2×M16—21no—
206C22×C8—22no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8C2×C4×C8912yes—
211C4⋊Q8D4×C8911yescharacteristic
212#127D4×C8911yescharacteristic
213#124C2×C4×C8912yes—
214#121—21no—
215#121—21no—
216C4×D4—21no—
217C4×D4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C42C23×C8911yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C8911yescharacteristic
226C4⋊C8D4×C8911yescharacteristic
227C4⋊C8D4×C8911yescharacteristic
228C4⋊C8D4×C8911yescharacteristic
229#103—24no—
230#102—24no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235#97C2×C4×C8912yes—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239#41—42no—
240#41—42no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—81no—
244C2×Q8—81no—
245C2×Q8C22⋊C4×C8912yes—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊C4×C8912yes—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4C2×D4×C8911yescharacteristic
253C22×C4#41×C8911yescharacteristic
254C22×C4#41×C8911yescharacteristic
255M16—41no—
256M16—41no—
257M16—82no—
258M16—81no—
259M16—81no—
260C2×C8—22no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—82no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C42C22×C4×C8911yescharacteristic
277C42C2×D4×C8911yescharacteristic
278C42C2×D4×C8911yescharacteristic
279C42C2×D4×C8911yescharacteristic
280C23—22no—
281C23#123×C8911yescharacteristic
282Q8—42no—
283Q8—82no—
284Q8—81no—
285Q8—81no—
286D4—42no—
287D4—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—82no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4C2×C22⋊C4×C8911yescharacteristic
304C2×C4C4×D4×C8911yescharacteristic
305C2×C4C4×D4×C8911yescharacteristic
306C2×C4#120×C8911yescharacteristic
307C2×C4#121×C8911yescharacteristic
308C2×C4#121×C8911yescharacteristic
309C8—42no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—41no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22#386×C8911yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—82no—
328C4#455×C8911yescharacteristic
329C4#455×C8911yescharacteristic
330C4#471×C8911yescharacteristic
331C4#471×C8911yescharacteristic
332C4#472×C8911yescharacteristic
333C4#473×C8911yescharacteristic
334C2—41no—
335C2—82no—
336C2C89×#188511yescharacteristic
337C2C89×#190711yescharacteristic
338C2C89×#190811yescharacteristic
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
4. C89×#1548C2semidirect
5. C89×#1546C2semidirect
6. C89×#1299C2semidirect
7. C89×#1299C2semidirect
164. #9433C89direct (N × H)
173. #1548C2×C89semidirect
174. #1546C2×C89semidirect
175. #1299C2×C89semidirect
176. #1299C2×C89semidirect
177. C89#9433direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#31412
C89×#29792
C89×#15602
C89×#15482
C89×#15462
C89×#12992
#943389