Finite Group Databasebeta

← C89×#35498 #36413346

Subgroups — C89×#35498 #36413346

Order 22784.

1492 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2590C213yesmaximal
2C89×#2585C213yesmaximal
3C89×#2533C213yesmaximal
4C89×#2528C213yesmaximal
5C89×#2524C213yesmaximal
6C89×#2506C213yesmaximal
7C89×#2462C213yesmaximal
8C89×#2462C213yesmaximal
9C89×#2336C213yesmaximal
10C4×#125×C89C213yesmaximal
11C89×#2276C211yesmaximal, characteristic
12C2×#125×C89C2213yes—
13C2×#125×C89C2213yes—
14C2×C4×Q8×C89C2213yes—
15#401×C89C2211yescharacteristic
16#400×C89C2213yes—
17#400×C89C2213yes—
18#400×C89C2213yes—
19#400×C89C2213yes—
20#398×C89C2213yes—
21#398×C89C2213yes—
22#398×C89C2213yes—
23#398×C89C2213yes—
24#398×C89C2213yes—
25#395×C89C2213yes—
26#395×C89C2211yescharacteristic
27#389×C89C2213yes—
28#389×C89C2213yes—
29#389×C89C2213yes—
30#389×C89C2213yes—
31#389×C89C2213yes—
32#389×C89C2213yes—
33#389×C89C2213yes—
34#387×C89C2213yes—
35#387×C89C2213yes—
36#387×C89C2213yes—
37#387×C89C2213yes—
38#387×C89C2213yes—
39#387×C89C2213yes—
40#387×C89C2213yes—
41#387×C89C2213yes—
42#387×C89C2213yes—
43#387×C89C2213yes—
44#387×C89C2213yes—
45#387×C89C2213yes—
46#387×C89C2213yes—
47#387×C89C2213yes—
48#387×C89C2213yes—
49#387×C89C2213yes—
50#387×C89C2213yes—
51#387×C89C2213yes—
52#387×C89C2213yes—
53#384×C89C2211yescharacteristic
54#383×C89C2213yes—
55#383×C89C2211yescharacteristic
56#382×C89C2213yes—
57C4×C4⋊C4×C89C2213yes—
58C4×C4⋊C4×C89C2213yes—
59C4×C4⋊C4×C89C2213yes—
60C4×C4⋊C4×C89C2213yes—
61C4×C4⋊C4×C89C2213yes—
62C4×C4⋊C4×C89C2213yes—
63C4×C4⋊C4×C89C2213yes—
64C4×C4⋊C4×C89C2213yes—
65#376×C89C2213yes—
66C43×C89C2211yescharacteristic
67C22×Q8×C89C2311yescharacteristic
68#125×C89—212no—
69#125×C89—212no—
70C4×Q8×C89—212no—
71C2×C4⋊C4×C89C2313yes—
72C2×C4⋊C4×C89C2313yes—
73C2×C4⋊C4×C89C2313yes—
74C2×C4⋊C4×C89C2313yes—
75C2×C4⋊C4×C89C2313yes—
76C2×C4⋊C4×C89C2313yes—
77C2×C4⋊C4×C89C2313yes—
78C2×C4⋊C4×C89C2313yes—
79C2×C4⋊C4×C89C2313yes—
80C2×C4⋊C4×C89C2313yes—
81C2×C4⋊C4×C89C2313yes—
82C2×C4⋊C4×C89C2313yes—
83C2×C4⋊C4×C89C2313yes—
84C2×C4⋊C4×C89C2313yes—
85C2×C4⋊C4×C89C2313yes—
86C2×C4⋊C4×C89C2313yes—
87C2×C4⋊C4×C89C2313yes—
88C2×C4⋊C4×C89C2313yes—
89C2×C4⋊C4×C89C2313yes—
90C2×C42×C89C2313yes—
91C2×C42×C89C2313yes—
92C2×C42×C89C2313yes—
93C2×C42×C89C2313yes—
94C2×C42×C89C2313yes—
95C2×C42×C89C2313yes—
96C2×C42×C89C2311yescharacteristic
97C2×C42×C89C2313yes—
98C2×C42×C89C2311yescharacteristic
99C2×C42×C89C2311yescharacteristic
100C2×C42×C89C2313yes—
101#95×C89C2311yescharacteristic
102#95×C89C2313yes—
103#95×C89C2313yes—
104#95×C89C2313yes—
105#95×C89C2313yes—
106#95×C89C2313yes—
107#95×C89C2313yes—
108#95×C89C2313yes—
109#95×C89C2313yes—
110#95×C89C2313yes—
111#95×C89C2313yes—
112#95×C89C2313yes—
113#95×C89C2313yes—
114#95×C89C2313yes—
115#95×C89C2313yes—
116#95×C89C2313yes—
117#95×C89C2313yes—
118#95×C89C2313yes—
119#95×C89C2313yes—
120#95×C89C2313yes—
121#95×C89C2313yes—
122#95×C89C2313yes—
123#95×C89C2313yes—
124#95×C89C2313yes—
125C2×Q8×C89—26no—
126C22×C4×C89C2413yes—
127C22×C4×C89C2413yes—
128C22×C4×C89C2413yes—
129C22×C4×C89C2413yes—
130C22×C4×C89C2413yes—
131C22×C4×C89C2411yescharacteristic
132C22×C4×C89C2413yes—
133C22×C4×C89C2413yes—
134C22×C4×C89C2413yes—
135C22×C4×C89C2413yes—
136C22×C4×C89C2413yes—
137C4⋊C4×C89—26no—
138C4⋊C4×C89—26no—
139C4⋊C4×C89—26no—
140C4⋊C4×C89—26no—
141C4⋊C4×C89—26no—
142C4⋊C4×C89—26no—
143C4⋊C4×C89—26no—
144C4⋊C4×C89—26no—
145C4⋊C4×C89—26no—
146C4⋊C4×C89—26no—
147C4⋊C4×C89—26no—
148C4⋊C4×C89—26no—
149C4⋊C4×C89—26no—
150C4⋊C4×C89—26no—
151C4⋊C4×C89—26no—
152C4⋊C4×C89—26no—
153C4⋊C4×C89—43no—
154C4⋊C4×C89—43no—
155C4⋊C4×C89#41112yes—
156C42×C89—26no—
157C42×C89—26no—
158C42×C89—26no—
159C42×C89—26no—
160C42×C89—26no—
161C42×C89—26no—
162C42×C89—41no—
163C42×C89—43no—
164C42×C89—43no—
165C42×C89—41no—
166C42×C89—41no—
167C23×C89C2511yescharacteristic
168Q8×C89—28no—
169C2×C4×C89—23no—
170C2×C4×C89—23no—
171C2×C4×C89—23no—
172C2×C4×C89—23no—
173C2×C4×C89—23no—
174C2×C4×C89—23no—
175C2×C4×C89—23no—
176C2×C4×C89—23no—
177C2×C4×C89—23no—
178C2×C4×C89—23no—
179C2×C4×C89—23no—
180C2×C4×C89—23no—
181C2×C4×C89—23no—
182C2×C4×C89—23no—
183C2×C4×C89—23no—
184C2×C4×C89—23no—
185C2×C4×C89—23no—
186C2×C4×C89—23no—
187C2×C4×C89—23no—
188C2×C4×C89—23no—
189C2×C4×C89—23no—
190C2×C4×C89—23no—
191C2×C4×C89—23no—
192C2×C4×C89—23no—
193C2×C4×C89—23no—
194C2×C4×C89—23no—
195C2×C4×C89—23no—
196C2×C4×C89C2×#4116yes—
197C2×C4×C89C2×#4116yes—
198C2×C4×C89C2×#4116yes—
199C2×C4×C892−1+416yes—
200C22×C89C22×#4113yes—
201C22×C89C2×2−1+413yes—
202C22×C89#58511yescharacteristic
203C4×C89—26no—
204C4×C89—26no—
205C4×C89—26no—
206C4×C89—26no—
207C4×C89—41no—
208C4×C89—43no—
209C4×C89—43no—
210C4×C89—43no—
211C4×C89—43no—
212C4×C89—43no—
213C4×C89—43no—
214#35498C8911yesmaximal, characteristic, direct product factor, Sylow
215C2×C89#344411yescharacteristic
216C2×C89#351513yes—
217C2×C89#352313yes—
218#2590C2×C8913yes—
219#2585C2×C8913yes—
220#2533C2×C8913yes—
221#2528C2×C8913yes—
222#2524C2×C8913yes—
223#2506C2×C8913yes—
224#2462C2×C8913yes—
225#2462C2×C8913yes—
226#2336C2×C8913yes—
227C4×#125C2×C8913yes—
228#2276C2×C8911yescharacteristic
229C89#3549811yescharacteristic, direct product factor, Sylow
230C2×#125C22×C8913yes—
231C2×#125C22×C8913yes—
232C2×C4×Q8C22×C8913yes—
233#401C22×C8911yescharacteristic
234#400C22×C8913yes—
235#400C22×C8913yes—
236#400C22×C8913yes—
237#400C22×C8913yes—
238#398C22×C8913yes—
239#398C22×C8913yes—
240#398C22×C8913yes—
241#398C22×C8913yes—
242#398C22×C8913yes—
243#395C22×C8913yes—
244#395C22×C8911yescharacteristic
245#389C22×C8913yes—
246#389C22×C8913yes—
247#389C22×C8913yes—
248#389C22×C8913yes—
249#389C22×C8913yes—
250#389C22×C8913yes—
251#389C22×C8913yes—
252#387C22×C8913yes—
253#387C22×C8913yes—
254#387C22×C8913yes—
255#387C22×C8913yes—
256#387C22×C8913yes—
257#387C22×C8913yes—
258#387C22×C8913yes—
259#387C22×C8913yes—
260#387C22×C8913yes—
261#387C22×C8913yes—
262#387C22×C8913yes—
263#387C22×C8913yes—
264#387C22×C8913yes—
265#387C22×C8913yes—
266#387C22×C8913yes—
267#387C22×C8913yes—
268#387C22×C8913yes—
269#387C22×C8913yes—
270#387C22×C8913yes—
271#384C22×C8911yescharacteristic
272#383C22×C8913yes—
273#383C22×C8911yescharacteristic
274#382C22×C8913yes—
275C4×C4⋊C4C22×C8913yes—
276C4×C4⋊C4C22×C8913yes—
277C4×C4⋊C4C22×C8913yes—
278C4×C4⋊C4C22×C8913yes—
279C4×C4⋊C4C22×C8913yes—
280C4×C4⋊C4C22×C8913yes—
281C4×C4⋊C4C22×C8913yes—
282C4×C4⋊C4C22×C8913yes—
283#376C22×C8913yes—
284C43C22×C8911yescharacteristic
285C22×Q8C23×C8911yescharacteristic
286#125—212no—
287#125—212no—
288C4×Q8—212no—
289C2×C4⋊C4C23×C8913yes—
290C2×C4⋊C4C23×C8913yes—
291C2×C4⋊C4C23×C8913yes—
292C2×C4⋊C4C23×C8913yes—
293C2×C4⋊C4C23×C8913yes—
294C2×C4⋊C4C23×C8913yes—
295C2×C4⋊C4C23×C8913yes—
296C2×C4⋊C4C23×C8913yes—
297C2×C4⋊C4C23×C8913yes—
298C2×C4⋊C4C23×C8913yes—
299C2×C4⋊C4C23×C8913yes—
300C2×C4⋊C4C23×C8913yes—
301C2×C4⋊C4C23×C8913yes—
302C2×C4⋊C4C23×C8913yes—
303C2×C4⋊C4C23×C8913yes—
304C2×C4⋊C4C23×C8913yes—
305C2×C4⋊C4C23×C8913yes—
306C2×C4⋊C4C23×C8913yes—
307C2×C4⋊C4C23×C8913yes—
308C2×C42C23×C8913yes—
309C2×C42C23×C8913yes—
310C2×C42C23×C8913yes—
311C2×C42C23×C8913yes—
312C2×C42C23×C8913yes—
313C2×C42C23×C8913yes—
314C2×C42C23×C8911yescharacteristic
315C2×C42C23×C8913yes—
316C2×C42C23×C8911yescharacteristic
317C2×C42C23×C8911yescharacteristic
318C2×C42C23×C8913yes—
319#95C23×C8911yescharacteristic
320#95C23×C8913yes—
321#95C23×C8913yes—
322#95C23×C8913yes—
323#95C23×C8913yes—
324#95C23×C8913yes—
325#95C23×C8913yes—
326#95C23×C8913yes—
327#95C23×C8913yes—
328#95C23×C8913yes—
329#95C23×C8913yes—
330#95C23×C8913yes—
331#95C23×C8913yes—
332#95C23×C8913yes—
333#95C23×C8913yes—
334#95C23×C8913yes—
335#95C23×C8913yes—
336#95C23×C8913yes—
337#95C23×C8913yes—
338#95C23×C8913yes—
339#95C23×C8913yes—
340#95C23×C8913yes—
341#95C23×C8913yes—
342#95C23×C8913yes—
343C2×Q8—26no—
344C22×C4C24×C8913yes—
345C22×C4C24×C8913yes—
346C22×C4C24×C8913yes—
347C22×C4C24×C8913yes—
348C22×C4C24×C8913yes—
349C22×C4C24×C8911yescharacteristic
350C22×C4C24×C8913yes—
351C22×C4C24×C8913yes—
352C22×C4C24×C8913yes—
353C22×C4C24×C8913yes—
354C22×C4C24×C8913yes—
355C4⋊C4—26no—
356C4⋊C4—26no—
357C4⋊C4—26no—
358C4⋊C4—26no—
359C4⋊C4—26no—
360C4⋊C4—26no—
361C4⋊C4—26no—
362C4⋊C4—26no—
363C4⋊C4—26no—
364C4⋊C4—26no—
365C4⋊C4—26no—
366C4⋊C4—26no—
367C4⋊C4—26no—
368C4⋊C4—26no—
369C4⋊C4—26no—
370C4⋊C4—26no—
371C4⋊C4—43no—
372C4⋊C4—43no—
373C4⋊C4#41×C89112yes—
374C42—26no—
375C42—26no—
376C42—26no—
377C42—26no—
378C42—26no—
379C42—26no—
380C42—41no—
381C42—43no—
382C42—43no—
383C42—41no—
384C42—41no—
385C23C25×C8911yescharacteristic
386Q8—28no—
387C2×C4—23no—
388C2×C4—23no—
389C2×C4—23no—
390C2×C4—23no—
391C2×C4—23no—
392C2×C4—23no—
393C2×C4—23no—
394C2×C4—23no—
395C2×C4—23no—
396C2×C4—23no—
397C2×C4—23no—
398C2×C4—23no—
399C2×C4—23no—
400C2×C4—23no—
401C2×C4—23no—
402C2×C4—23no—
403C2×C4—23no—
404C2×C4—23no—
405C2×C4—23no—
406C2×C4—23no—
407C2×C4—23no—
408C2×C4—23no—
409C2×C4—23no—
410C2×C4—23no—
411C2×C4—23no—
412C2×C4—23no—
413C2×C4—23no—
414C2×C4C2×#41×C8916yes—
415C2×C4C2×#41×C8916yes—
416C2×C4C2×#41×C8916yes—
417C2×C42−1+4×C8916yes—
418C22C22×#41×C8913yes—
419C22C2×2−1+4×C8913yes—
420C22#585×C8911yescharacteristic
421C4—26no—
422C4—26no—
423C4—26no—
424C4—26no—
425C4—41no—
426C4—43no—
427C4—43no—
428C4—43no—
429C4—43no—
430C4—43no—
431C4—43no—
432C2C89×#344411yescharacteristic
433C2C89×#351513yes—
434C2C89×#352313yes—
subgroupG/H
center, socle, prime radicalC23×C89C25
commutator, Frattini, cosocleC23C25×C89
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C89 ◁ G

Complements

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

NH ≅ G/Ntype
214. #35498C89direct (N × H)
229. C89#35498direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#25902
C89×#25852
C89×#25332
C89×#25282
C89×#25242
C89×#25062
C89×#24622
C89×#23362
C4×#125×C892
C89×#22762
#3549889