Finite Group Databasebeta

← C89×#10504 #36388352

Subgroups — C89×#10504 #36388352

Order 22784.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3208C211yesmaximal, characteristic
2C89×#1986C211yesmaximal, characteristic, complemented
3C89×#1982C211yesmaximal, characteristic
4C89×#1965C211yesmaximal, characteristic
5C89×#1565C211yesmaximal, characteristic, complemented
6C89×#1550C211yesmaximal, characteristic, complemented
7C89×#1303C211yesmaximal, characteristic, complemented
8#533×C89C2211yescharacteristic
9C2×#127×C89C2211yescharacteristic
10#492×C89—21no—
11#486×C89—21no—
12#460×C89—21no—
13#460×C89—21no—
14#450×C89—22no—
15#431×C89C2211yescharacteristic
16#423×C89C2211yescharacteristic
17C2×C4⋊C8×C89C2211yescharacteristic
18C2×#102×C89—22no—
19C2×#100×C89—21no—
20C2×#100×C89—21no—
21C4×M16×C89C2211yescharacteristic
22C4×C4⋊C4×C89C2211yescharacteristic
23#339×C89—21no—
24#339×C89—21no—
25#335×C89—21no—
26#334×C89—21no—
27#333×C89—21no—
28#332×C89—21no—
29C22×D4×C89—21no—
30C22×D4×C89—21no—
31C22×D4×C89D412yes—
32C2×SD16×C89—22no—
33C2×SD16×C89—22no—
34C2×M16×C89—21no—
35C2×M16×C89D411yescharacteristic
36C2×M16×C89D411yescharacteristic
37C22×C8×C89—21no—
38C4⋊Q8×C89D411yescharacteristic
39C4⋊Q8×C89D411yescharacteristic
40#127×C89—21no—
41#127×C89—21no—
42#127×C89—21no—
43#127×C89—21no—
44#125×C89—21no—
45C22⋊Q8×C89—21no—
46C22⋊Q8×C89—21no—
47C4×Q8×C89—21no—
48C4×Q8×C89—21no—
49#117×C89—21no—
50C2×C4⋊C4×C89—21no—
51C2×C42×C89—21no—
52C2×C42×C89C2311yescharacteristic
53C4⋊C8×C89—21no—
54C4⋊C8×C89—21no—
55C4⋊C8×C89—21no—
56C4⋊C8×C89—21no—
57C4⋊C8×C89D411yescharacteristic
58C4⋊C8×C89D411yescharacteristic
59#102×C89—22no—
60#102×C89—22no—
61#102×C89—44no—
62#100×C89—42no—
63#100×C89—42no—
64C22⋊C8×C89—21no—
65#97×C89—21no—
66C4×C8×C89—21no—
67C4×C8×C89—21no—
68#95×C89—21no—
69C24×C89—22no—
70C2×Q8×C89—21no—
71C2×Q8×C89—21no—
72C2×D4×C89—22no—
73C2×D4×C89—22no—
74C2×D4×C89—42no—
75C2×D4×C89—42no—
76C2×D4×C89—41no—
77C2×D4×C89—41no—
78C2×D4×C89—41no—
79C2×D4×C89—41no—
80C2×D4×C89—41no—
81C2×D4×C89—41no—
82C2×D4×C89—41no—
83C2×D4×C89—41no—
84C2×D4×C89—82no—
85C22×C4×C89—41no—
86C22×C4×C89C2×D411yescharacteristic
87C22×C4×C89C2×D411yescharacteristic
88C22×C4×C89#4111yescharacteristic
89SD16×C89—82no—
90SD16×C89—82no—
91M16×C89—21no—
92M16×C89—21no—
93M16×C89—21no—
94M16×C89—41no—
95M16×C89—41no—
96M16×C89SD1612yescomplemented
97C2×C8×C89—21no—
98C2×C8×C89—21no—
99C2×C8×C89—21no—
100C2×C8×C89—21no—
101C2×C8×C89—42no—
102C2×C8×C89—41no—
103C2×C8×C89—41no—
104C4⋊C4×C89—22no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89—21no—
107C4⋊C4×C89—21no—
108C4⋊C4×C89—21no—
109C4⋊C4×C89—41no—
110C4⋊C4×C89—41no—
111C4⋊C4×C89—41no—
112C22⋊C4×C89—41no—
113C42×C89—41no—
114C42×C89—41no—
115C42×C89—41no—
116C42×C89C2×D411yescharacteristic
117C42×C89C2×D411yescharacteristic
118C42×C89#4111yescharacteristic
119C42×C89#4111yescharacteristic
120C23×C89—42no—
121C23×C89—42no—
122C23×C89—42no—
123C23×C89—82no—
124C23×C89—82no—
125C23×C89#12111yescharacteristic
126Q8×C89—41no—
127Q8×C89—41no—
128Q8×C89—81no—
129D4×C89—44no—
130D4×C89—42no—
131D4×C89—42no—
132D4×C89—82no—
133D4×C89—82no—
134D4×C89—81no—
135D4×C89—81no—
136D4×C89—81no—
137D4×C89—81no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—41no—
141C2×C4×C89—42no—
142C2×C4×C89—41no—
143C2×C4×C89—41no—
144C2×C4×C89—81no—
145C2×C4×C89—81no—
146C2×C4×C89#12011yescharacteristic
147C2×C4×C89#12111yescharacteristic
148C2×C4×C89#12111yescharacteristic
149C2×C4×C89#12311yescharacteristic
150C2×C4×C89#12311yescharacteristic
151C2×C4×C89#12411yescharacteristic
152C2×C4×C89C2×SD1611yescharacteristic
153C2×C4×C89#13511yescharacteristic
154C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C89#13711yescharacteristic
156C8×C89—22no—
157C8×C89—41no—
158C8×C89—41no—
159C8×C89—41no—
160C8×C89—81no—
161C8×C89—81no—
162C22×C89—21no—
163C22×C89—21no—
164C22×C89—82no—
165C22×C89—82no—
166C22×C89—82no—
167C22×C89—162no—
168C22×C89—162no—
169C22×C89#39411yescharacteristic
170C22×C89#46111yescharacteristic
171C22×C89#46311yescharacteristic
172C4×C89—21no—
173C4×C89—21no—
174C4×C89—21no—
175C4×C89—82no—
176C4×C89—81no—
177C4×C89—81no—
178C4×C89#45311yescharacteristic
179C4×C89#45511yescharacteristic
180C4×C89#46011yescharacteristic
181C4×C89#46411yescharacteristic
182C4×C89#46511yescharacteristic
183C4×C89#46811yescharacteristic
184#10504C8911yesmaximal, characteristic, direct product factor, Sylow
185C2×C89—21no—
186C2×C89—21no—
187C2×C89—162no—
188C2×C89#203711yescharacteristic
189C2×C89#204811yescharacteristic
190C2×C89#205511yescharacteristic
191#3208C2×C8911yescharacteristic
192#1986C2×C8911yescharacteristic, complemented
193#1982C2×C8911yescharacteristic
194#1965C2×C8911yescharacteristic
195#1565C2×C8911yescharacteristic, complemented
196#1550C2×C8911yescharacteristic, complemented
197#1303C2×C8911yescharacteristic, complemented
198C89#1050411yescharacteristic, direct product factor, Sylow
199#533C22×C8911yescharacteristic
200C2×#127C22×C8911yescharacteristic
201#492—21no—
202#486—21no—
203#460—21no—
204#460—21no—
205#450—22no—
206#431C22×C8911yescharacteristic
207#423C22×C8911yescharacteristic
208C2×C4⋊C8C22×C8911yescharacteristic
209C2×#102—22no—
210C2×#100—21no—
211C2×#100—21no—
212C4×M16C22×C8911yescharacteristic
213C4×C4⋊C4C22×C8911yescharacteristic
214#339—21no—
215#339—21no—
216#335—21no—
217#334—21no—
218#333—21no—
219#332—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4D4×C8912yes—
223C2×SD16—22no—
224C2×SD16—22no—
225C2×M16—21no—
226C2×M16D4×C8911yescharacteristic
227C2×M16D4×C8911yescharacteristic
228C22×C8—21no—
229C4⋊Q8D4×C8911yescharacteristic
230C4⋊Q8D4×C8911yescharacteristic
231#127—21no—
232#127—21no—
233#127—21no—
234#127—21no—
235#125—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240#117—21no—
241C2×C4⋊C4—21no—
242C2×C42—21no—
243C2×C42C23×C8911yescharacteristic
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C8911yescharacteristic
249C4⋊C8D4×C8911yescharacteristic
250#102—22no—
251#102—22no—
252#102—44no—
253#100—42no—
254#100—42no—
255C22⋊C8—21no—
256#97—21no—
257C4×C8—21no—
258C4×C8—21no—
259#95—21no—
260C24—22no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C22×C4—41no—
277C22×C4C2×D4×C8911yescharacteristic
278C22×C4C2×D4×C8911yescharacteristic
279C22×C4#41×C8911yescharacteristic
280SD16—82no—
281SD16—82no—
282M16—21no—
283M16—21no—
284M16—21no—
285M16—41no—
286M16—41no—
287M16SD16×C8912yescomplemented
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—42no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C42—41no—
305C42—41no—
306C42—41no—
307C42C2×D4×C8911yescharacteristic
308C42C2×D4×C8911yescharacteristic
309C42#41×C8911yescharacteristic
310C42#41×C8911yescharacteristic
311C23—42no—
312C23—42no—
313C23—42no—
314C23—82no—
315C23—82no—
316C23#121×C8911yescharacteristic
317Q8—41no—
318Q8—41no—
319Q8—81no—
320D4—44no—
321D4—42no—
322D4—42no—
323D4—82no—
324D4—82no—
325D4—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#120×C8911yescharacteristic
338C2×C4#121×C8911yescharacteristic
339C2×C4#121×C8911yescharacteristic
340C2×C4#123×C8911yescharacteristic
341C2×C4#123×C8911yescharacteristic
342C2×C4#124×C8911yescharacteristic
343C2×C4C2×SD16×C8911yescharacteristic
344C2×C4#135×C8911yescharacteristic
345C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
346C2×C4#137×C8911yescharacteristic
347C8—22no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—162no—
359C22—162no—
360C22#394×C8911yescharacteristic
361C22#461×C8911yescharacteristic
362C22#463×C8911yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4#453×C8911yescharacteristic
370C4#455×C8911yescharacteristic
371C4#460×C8911yescharacteristic
372C4#464×C8911yescharacteristic
373C4#465×C8911yescharacteristic
374C4#468×C8911yescharacteristic
375C2—21no—
376C2—21no—
377C2—162no—
378C2C89×#203711yescharacteristic
379C2C89×#204811yescharacteristic
380C2C89×#205511yescharacteristic
subgroupG/H
center, socleC22×C89#394
commutator, Frattini, cosocleC2×C42C23×C89
prime radicalC2×#127×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
2. C89×#1986C2semidirect
5. C89×#1565C2semidirect
6. C89×#1550C2semidirect
7. C89×#1303C2semidirect
96. M16×C89SD16semidirect
184. #10504C89direct (N × H)
192. #1986C2×C89semidirect
195. #1565C2×C89semidirect
196. #1550C2×C89semidirect
197. #1303C2×C89semidirect
198. C89#10504direct (N × H)
287. M16SD16×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#32082
C89×#19862
C89×#19822
C89×#19652
C89×#15652
C89×#15502
C89×#13032
#1050489