Finite Group Databasebeta

← C89×#10197 #36388045

Subgroups — C89×#10197 #36388045

Order 22784.

524 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3246C211yesmaximal, characteristic
2C89×#3206C211yesmaximal, characteristic
3C89×#3165C211yesmaximal, characteristic, complemented
4C89×#1987C211yesmaximal, characteristic, complemented
5C89×#1980C211yesmaximal, characteristic
6C89×#1503C211yesmaximal, characteristic, complemented
7C89×#1283C211yesmaximal, characteristic, complemented
8#533×C89C2211yescharacteristic
9#532×C89C2211yescharacteristic
10C2×C4⋊Q8×C89C2211yescharacteristic
11#501×C89—22no—
12#500×C89—21no—
13#498×C89—21no—
14#492×C89—21no—
15#487×C89—21no—
16#476×C89—21no—
17#475×C89—21no—
18#465×C89—22no—
19#461×C89—22no—
20#461×C89—21no—
21#460×C89—21no—
22#448×C89—22no—
23#431×C89C2211yescharacteristic
24#428×C89—22no—
25C2×C4⋊C8×C89C2211yescharacteristic
26C2×#104×C89—22no—
27C4×M16×C89C2211yescharacteristic
28C4×C4⋊C4×C89C2211yescharacteristic
29#340×C89—22no—
30#328×C89—22no—
31C2×#41×C89—21no—
32C22×Q8×C89—21no—
33C2×SD16×C89—24no—
34C2×SD16×C89—22no—
35C2×M16×C89D412yes—
36C22×C8×C89D412yes—
37C4⋊Q8×C89—21no—
38C4⋊Q8×C89—21no—
39C4⋊Q8×C89—21no—
40C4⋊Q8×C89D411yescharacteristic
41C4⋊Q8×C89D412yes—
42C4⋊Q8×C89D411yescharacteristic
43C4⋊Q8×C89D411yescharacteristic
44#127×C89D411yescharacteristic
45#125×C89—21no—
46#124×C89—21no—
47C22⋊Q8×C89—21no—
48C22⋊Q8×C89—21no—
49#121×C89—21no—
50#121×C89—21no—
51C4×Q8×C89—21no—
52C4×Q8×C89—21no—
53C4×D4×C89—21no—
54C4×D4×C89—21no—
55#117×C89—21no—
56C2×C4⋊C4×C89—21no—
57C2×C4⋊C4×C89—21no—
58C2×C4⋊C4×C89—21no—
59C2×C42×C89—21no—
60C2×C42×C89C2311yescharacteristic
61#107×C89—24no—
62#106×C89—24no—
63#106×C89—22no—
64C4⋊C8×C89—21no—
65C4⋊C8×C89—21no—
66C4⋊C8×C89—21no—
67#104×C89—44no—
68#103×C89—24no—
69#103×C89—22no—
70#102×C89—22no—
71C22⋊C8×C89D412yes—
72#97×C89—21no—
73C4×C8×C89—21no—
74C4×C8×C89—21no—
75#95×C89—21no—
76#41×C89—42no—
77#41×C89—42no—
78C2×Q8×C89—21no—
79C2×Q8×C89—22no—
80C2×Q8×C89—21no—
81C2×Q8×C89—21no—
82C2×Q8×C89—41no—
83C2×Q8×C89—82no—
84C2×D4×C89—21no—
85C2×D4×C89—21no—
86C2×D4×C89—21no—
87C2×D4×C89—41no—
88C22×C4×C89—41no—
89C22×C4×C89—41no—
90C22×C4×C89—41no—
91C22×C4×C89C2×D411yescharacteristic
92C22×C4×C89C2×D411yescharacteristic
93C22×C4×C89C2×D411yescharacteristic
94SD16×C89—84no—
95SD16×C89—82no—
96M16×C89—22no—
97M16×C89SD1614yescomplemented
98C2×C8×C89—22no—
99C2×C8×C89—22no—
100C2×C8×C89—22no—
101C2×C8×C89—42no—
102C4⋊C4×C89—22no—
103C4⋊C4×C89—21no—
104C4⋊C4×C89—21no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89—21no—
107C4⋊C4×C89—22no—
108C4⋊C4×C89—21no—
109C4⋊C4×C89—22no—
110C4⋊C4×C89—21no—
111C4⋊C4×C89—41no—
112C4⋊C4×C89—41no—
113C4⋊C4×C89—41no—
114C4⋊C4×C89—41no—
115C4⋊C4×C89—41no—
116C22⋊C4×C89—41no—
117C22⋊C4×C89—41no—
118C22⋊C4×C89—41no—
119C42×C89—41no—
120C42×C89—42no—
121C42×C89C2×D411yescharacteristic
122C42×C89C2×D411yescharacteristic
123C42×C89C2×D411yescharacteristic
124C42×C89#4111yescharacteristic
125C23×C89—41no—
126C23×C89#12711yescharacteristic
127Q8×C89—44no—
128Q8×C89—41no—
129Q8×C89—41no—
130Q8×C89—42no—
131Q8×C89—81no—
132Q8×C89—82no—
133D4×C89—42no—
134D4×C89—41no—
135D4×C89—41no—
136D4×C89—42no—
137D4×C89—81no—
138D4×C89—81no—
139C2×C4×C89—21no—
140C2×C4×C89—21no—
141C2×C4×C89—41no—
142C2×C4×C89—42no—
143C2×C4×C89—41no—
144C2×C4×C89—41no—
145C2×C4×C89—41no—
146C2×C4×C89—42no—
147C2×C4×C89—81no—
148C2×C4×C89—82no—
149C2×C4×C89—81no—
150C2×C4×C89—82no—
151C2×C4×C89#12011yescharacteristic
152C2×C4×C89#12011yescharacteristic
153C2×C4×C89#12011yescharacteristic
154C2×C4×C89#12111yescharacteristic
155C2×C4×C89#12111yescharacteristic
156C2×C4×C89#12111yescharacteristic
157C2×C4×C89C2×SD1612yes—
158C2×C4×C89#13712yes—
159C8×C89—24no—
160C8×C89—42no—
161C8×C89—42no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—81no—
165C22×C89—81no—
166C22×C89—81no—
167C22×C89#39211yescharacteristic
168C22×C89#49211yescharacteristic
169C22×C89#49711yescharacteristic
170C4×C89—21no—
171C4×C89—21no—
172C4×C89—21no—
173C4×C89—82no—
174C4×C89—81no—
175C4×C89—82no—
176C4×C89—81no—
177C4×C89—81no—
178C4×C89#44812yes—
179C4×C89#45511yescharacteristic
180C4×C89#45611yescharacteristic
181C4×C89#46112yes—
182#10197C8911yesmaximal, characteristic, direct product factor, Sylow
183C2×C89—21no—
184C2×C89—21no—
185C2×C89—161no—
186C2×C89#200711yescharacteristic
187C2×C89#200811yescharacteristic
188C2×C89#201311yescharacteristic
189#3246C2×C8911yescharacteristic
190#3206C2×C8911yescharacteristic
191#3165C2×C8911yescharacteristic, complemented
192#1987C2×C8911yescharacteristic, complemented
193#1980C2×C8911yescharacteristic
194#1503C2×C8911yescharacteristic, complemented
195#1283C2×C8911yescharacteristic, complemented
196C89#1019711yescharacteristic, direct product factor, Sylow
197#533C22×C8911yescharacteristic
198#532C22×C8911yescharacteristic
199C2×C4⋊Q8C22×C8911yescharacteristic
200#501—22no—
201#500—21no—
202#498—21no—
203#492—21no—
204#487—21no—
205#476—21no—
206#475—21no—
207#465—22no—
208#461—22no—
209#461—21no—
210#460—21no—
211#448—22no—
212#431C22×C8911yescharacteristic
213#428—22no—
214C2×C4⋊C8C22×C8911yescharacteristic
215C2×#104—22no—
216C4×M16C22×C8911yescharacteristic
217C4×C4⋊C4C22×C8911yescharacteristic
218#340—22no—
219#328—22no—
220C2×#41—21no—
221C22×Q8—21no—
222C2×SD16—24no—
223C2×SD16—22no—
224C2×M16D4×C8912yes—
225C22×C8D4×C8912yes—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C8912yes—
230C4⋊Q8D4×C8911yescharacteristic
231C4⋊Q8D4×C8911yescharacteristic
232C4⋊Q8D4×C8911yescharacteristic
233#127D4×C8911yescharacteristic
234#125—21no—
235#124—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238#121—21no—
239#121—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—21no—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C42—21no—
249C2×C42C23×C8911yescharacteristic
250#107—24no—
251#106—24no—
252#106—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256#104—44no—
257#103—24no—
258#103—22no—
259#102—22no—
260C22⋊C8D4×C8912yes—
261#97—21no—
262C4×C8—21no—
263C4×C8—21no—
264#95—21no—
265#41—42no—
266#41—42no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C2×D4×C8911yescharacteristic
281C22×C4C2×D4×C8911yescharacteristic
282C22×C4C2×D4×C8911yescharacteristic
283SD16—84no—
284SD16—82no—
285M16—22no—
286M16SD16×C8914yescomplemented
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—42no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42—42no—
310C42C2×D4×C8911yescharacteristic
311C42C2×D4×C8911yescharacteristic
312C42C2×D4×C8911yescharacteristic
313C42#41×C8911yescharacteristic
314C23—41no—
315C23#127×C8911yescharacteristic
316Q8—44no—
317Q8—41no—
318Q8—41no—
319Q8—42no—
320Q8—81no—
321Q8—82no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4#120×C8911yescharacteristic
341C2×C4#120×C8911yescharacteristic
342C2×C4#120×C8911yescharacteristic
343C2×C4#121×C8911yescharacteristic
344C2×C4#121×C8911yescharacteristic
345C2×C4#121×C8911yescharacteristic
346C2×C4C2×SD16×C8912yes—
347C2×C4#137×C8912yes—
348C8—24no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#392×C8911yescharacteristic
357C22#492×C8911yescharacteristic
358C22#497×C8911yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4#448×C8912yes—
368C4#455×C8911yescharacteristic
369C4#456×C8911yescharacteristic
370C4#461×C8912yes—
371C2—21no—
372C2—21no—
373C2—161no—
374C2C89×#200711yescharacteristic
375C2C89×#200811yescharacteristic
376C2C89×#201311yescharacteristic
subgroupG/H
center, socleC22×C89#392
commutator, Frattini, cosocleC2×C42C23×C89
prime radical#532×C89C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C89×#3165C2semidirect
4. C89×#1987C2semidirect
6. C89×#1503C2semidirect
7. C89×#1283C2semidirect
97. M16×C89SD16semidirect
182. #10197C89direct (N × H)
191. #3165C2×C89semidirect
192. #1987C2×C89semidirect
194. #1503C2×C89semidirect
195. #1283C2×C89semidirect
196. C89#10197direct (N × H)
286. M16SD16×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#32462
C89×#32062
C89×#31652
C89×#19872
C89×#19802
C89×#15032
C89×#12832
#1019789