Finite Group Databasebeta

← C89×#19346 #36397194

Subgroups — C89×#19346 #36397194

Order 22784.

582 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3237C211yesmaximal, characteristic, complemented
2C89×#3216C211yesmaximal, characteristic
3C89×#3167C211yesmaximal, characteristic
4C89×#2960C211yesmaximal, characteristic, complemented
5C89×#1692C212yesmaximal, complemented
6C89×#1686C212yesmaximal, complemented
7C89×#1680C212yesmaximal, complemented
8C89×#1678C212yesmaximal, complemented
9C89×#1568C211yesmaximal, characteristic, complemented
10C89×#1559C211yesmaximal, characteristic, complemented
11C89×#1557C211yesmaximal, characteristic
12#533×C89C2211yescharacteristic
13#533×C89C2211yescharacteristic
14#532×C89C2211yescharacteristic
15#501×C89—21no—
16#498×C89C2211yescharacteristic
17#497×C89—21no—
18#492×C89C2211yescharacteristic
19#491×C89—21no—
20#489×C89—21no—
21#487×C89C2211yescharacteristic
22#486×C89C2211yescharacteristic
23#485×C89—22no—
24#477×C89C2212yes—
25#475×C89C2212yes—
26#465×C89—21no—
27#465×C89—21no—
28#462×C89C2212yes—
29#460×C89C2212yes—
30#452×C89—22no—
31#446×C89—21no—
32#446×C89C2212yes—
33C8×Q8×C89—21no—
34C8×Q8×C89C2212yes—
35C4×SD16×C89—21no—
36C4×SD16×C89—21no—
37#432×C89C2211yescharacteristic
38#432×C89C2211yescharacteristic
39#424×C89—21no—
40#423×C89C2211yescharacteristic
41#405×C89—21no—
42C2×C4×C8×C89C2211yescharacteristic
43#335×C89C2212yes—
44#334×C89C2212yes—
45#333×C89C2212yes—
46#332×C89C2212yes—
47#332×C89C2212yes—
48#331×C89C2212yes—
49C2×#41×C89—21no—
50C2×Q16×C89—22no—
51C2×SD16×C89—22no—
52C2×SD16×C89—21no—
53C2×SD16×C89—21no—
54C2×M16×C89—21no—
55C22×C8×C89D411yescharacteristic
56C22×C8×C89D411yescharacteristic
57C4⋊Q8×C89D411yescharacteristic
58C4⋊Q8×C89D411yescharacteristic
59C4⋊Q8×C89C2311yescharacteristic
60C4⋊Q8×C89C2311yescharacteristic
61C4⋊Q8×C89C2311yescharacteristic
62#127×C89C2311yescharacteristic
63#125×C89—21no—
64#125×C89—21no—
65#124×C89—21no—
66C22⋊Q8×C89—21no—
67C22⋊Q8×C89—21no—
68C22⋊Q8×C89—21no—
69C22⋊Q8×C89D412yes—
70#121×C89—21no—
71#121×C89—21no—
72C4×Q8×C89—21no—
73C4×Q8×C89—21no—
74C4×Q8×C89—21no—
75C4×Q8×C89C2312yes—
76C4×D4×C89—21no—
77C4×D4×C89—21no—
78#117×C89—21no—
79#117×C89—21no—
80C2×C42×C89C2311yescharacteristic
81#107×C89—22no—
82#106×C89—21no—
83#106×C89—21no—
84#106×C89—22no—
85C4⋊C8×C89—22no—
86C4⋊C8×C89—22no—
87C4⋊C8×C89—21no—
88C4⋊C8×C89C2312yes—
89C4⋊C8×C89C2312yes—
90C4⋊C8×C89C2312yes—
91#103×C89—22no—
92#103×C89—22no—
93#103×C89—21no—
94#103×C89—21no—
95#103×C89—22no—
96#102×C89—21no—
97#102×C89—21no—
98#102×C89—22no—
99C22⋊C8×C89—21no—
100C22⋊C8×C89—21no—
101#97×C89—22no—
102#97×C89—21no—
103#97×C89—21no—
104C4×C8×C89—22no—
105C4×C8×C89D411yescharacteristic
106C4×C8×C89D411yescharacteristic
107C4×C8×C89C2311yescharacteristic
108C4×C8×C89C2311yescharacteristic
109#41×C89—82no—
110C2×Q8×C89—21no—
111C2×Q8×C89—21no—
112C2×Q8×C89—21no—
113C2×Q8×C89—21no—
114C2×Q8×C89C2×D412yes—
115C2×D4×C89—21no—
116C2×D4×C89—21no—
117C2×D4×C89—21no—
118C2×D4×C89—41no—
119C22×C4×C89—41no—
120C22×C4×C89C2×D411yescharacteristic
121C22×C4×C89C2×D411yescharacteristic
122C22×C4×C89#4111yescharacteristic
123Q16×C89—82no—
124SD16×C89—42no—
125SD16×C89—42no—
126SD16×C89—82no—
127M16×C89—42no—
128C2×C8×C89—22no—
129C2×C8×C89—22no—
130C2×C8×C89—22no—
131C2×C8×C89—22no—
132C2×C8×C89—41no—
133C2×C8×C89C2×D411yescharacteristic
134C2×C8×C89C2×D411yescharacteristic
135C2×C8×C89C2×D411yescharacteristic
136C2×C8×C89C2×D411yescharacteristic
137C4⋊C4×C89—21no—
138C4⋊C4×C89—21no—
139C4⋊C4×C89—21no—
140C4⋊C4×C89—22no—
141C4⋊C4×C89—22no—
142C4⋊C4×C89—21no—
143C4⋊C4×C89—21no—
144C4⋊C4×C89—21no—
145C4⋊C4×C89—21no—
146C4⋊C4×C89—21no—
147C4⋊C4×C89—21no—
148C4⋊C4×C89—41no—
149C4⋊C4×C89—41no—
150C4⋊C4×C89C2×D412yes—
151C22⋊C4×C89—22no—
152C22⋊C4×C89—41no—
153C22⋊C4×C89—41no—
154C22⋊C4×C89—41no—
155C42×C89—22no—
156C42×C89—41no—
157C42×C89C2×D411yescharacteristic
158C42×C89C2×D411yescharacteristic
159C42×C89#4111yescharacteristic
160C42×C89C2411yescharacteristic
161C23×C89—41no—
162C23×C89#12111yescharacteristic
163Q8×C89—22no—
164Q8×C89—22no—
165Q8×C89—42no—
166Q8×C89—41no—
167Q8×C89—41no—
168Q8×C89—42no—
169Q8×C89—81no—
170D4×C89—41no—
171D4×C89—41no—
172D4×C89—42no—
173D4×C89—81no—
174D4×C89—82no—
175C2×C4×C89—21no—
176C2×C4×C89—21no—
177C2×C4×C89—22no—
178C2×C4×C89—22no—
179C2×C4×C89—22no—
180C2×C4×C89—41no—
181C2×C4×C89—41no—
182C2×C4×C89—41no—
183C2×C4×C89—41no—
184C2×C4×C89—82no—
185C2×C4×C89#12111yescharacteristic
186C2×C4×C89#12111yescharacteristic
187C2×C4×C89#12111yescharacteristic
188C2×C4×C89C22×D411yescharacteristic
189C2×C4×C89C22×D411yescharacteristic
190C2×C4×C89C2×#4111yescharacteristic
191C8×C89—21no—
192C8×C89—21no—
193C8×C89—21no—
194C8×C89—42no—
195C8×C89—42no—
196C8×C89—42no—
197C8×C89#13712yes—
198C22×C89—21no—
199C22×C89—21no—
200C22×C89—21no—
201C22×C89—81no—
202C22×C89—81no—
203C22×C89—81no—
204C22×C89C2×#12111yescharacteristic
205C4×C89—21no—
206C4×C89—21no—
207C4×C89—21no—
208C4×C89—21no—
209C4×C89—42no—
210C4×C89—42no—
211C4×C89—81no—
212C4×C89—81no—
213C4×C89—81no—
214C4×C89C2×#13711yescharacteristic
215C4×C89#57511yescharacteristic
216C4×C89#57712yes—
217#19346C8911yesmaximal, characteristic, direct product factor, Sylow
218C2×C89—41no—
219C2×C89—161no—
220C2×C89#303711yescharacteristic
221C2×C89#305711yescharacteristic
222C2×C89#306711yescharacteristic
223#3237C2×C8911yescharacteristic, complemented
224#3216C2×C8911yescharacteristic
225#3167C2×C8911yescharacteristic
226#2960C2×C8911yescharacteristic, complemented
227#1692C2×C8912yescomplemented
228#1686C2×C8912yescomplemented
229#1680C2×C8912yescomplemented
230#1678C2×C8912yescomplemented
231#1568C2×C8911yescharacteristic, complemented
232#1559C2×C8911yescharacteristic, complemented
233#1557C2×C8911yescharacteristic
234C89#1934611yescharacteristic, direct product factor, Sylow
235#533C22×C8911yescharacteristic
236#533C22×C8911yescharacteristic
237#532C22×C8911yescharacteristic
238#501—21no—
239#498C22×C8911yescharacteristic
240#497—21no—
241#492C22×C8911yescharacteristic
242#491—21no—
243#489—21no—
244#487C22×C8911yescharacteristic
245#486C22×C8911yescharacteristic
246#485—22no—
247#477C22×C8912yes—
248#475C22×C8912yes—
249#465—21no—
250#465—21no—
251#462C22×C8912yes—
252#460C22×C8912yes—
253#452—22no—
254#446—21no—
255#446C22×C8912yes—
256C8×Q8—21no—
257C8×Q8C22×C8912yes—
258C4×SD16—21no—
259C4×SD16—21no—
260#432C22×C8911yescharacteristic
261#432C22×C8911yescharacteristic
262#424—21no—
263#423C22×C8911yescharacteristic
264#405—21no—
265C2×C4×C8C22×C8911yescharacteristic
266#335C22×C8912yes—
267#334C22×C8912yes—
268#333C22×C8912yes—
269#332C22×C8912yes—
270#332C22×C8912yes—
271#331C22×C8912yes—
272C2×#41—21no—
273C2×Q16—22no—
274C2×SD16—22no—
275C2×SD16—21no—
276C2×SD16—21no—
277C2×M16—21no—
278C22×C8D4×C8911yescharacteristic
279C22×C8D4×C8911yescharacteristic
280C4⋊Q8D4×C8911yescharacteristic
281C4⋊Q8D4×C8911yescharacteristic
282C4⋊Q8C23×C8911yescharacteristic
283C4⋊Q8C23×C8911yescharacteristic
284C4⋊Q8C23×C8911yescharacteristic
285#127C23×C8911yescharacteristic
286#125—21no—
287#125—21no—
288#124—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8D4×C8912yes—
293#121—21no—
294#121—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8C23×C8912yes—
299C4×D4—21no—
300C4×D4—21no—
301#117—21no—
302#117—21no—
303C2×C42C23×C8911yescharacteristic
304#107—22no—
305#106—21no—
306#106—21no—
307#106—22no—
308C4⋊C8—22no—
309C4⋊C8—22no—
310C4⋊C8—21no—
311C4⋊C8C23×C8912yes—
312C4⋊C8C23×C8912yes—
313C4⋊C8C23×C8912yes—
314#103—22no—
315#103—22no—
316#103—21no—
317#103—21no—
318#103—22no—
319#102—21no—
320#102—21no—
321#102—22no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324#97—22no—
325#97—21no—
326#97—21no—
327C4×C8—22no—
328C4×C8D4×C8911yescharacteristic
329C4×C8D4×C8911yescharacteristic
330C4×C8C23×C8911yescharacteristic
331C4×C8C23×C8911yescharacteristic
332#41—82no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8C2×D4×C8912yes—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C22×C4—41no—
343C22×C4C2×D4×C8911yescharacteristic
344C22×C4C2×D4×C8911yescharacteristic
345C22×C4#41×C8911yescharacteristic
346Q16—82no—
347SD16—42no—
348SD16—42no—
349SD16—82no—
350M16—42no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—41no—
356C2×C8C2×D4×C8911yescharacteristic
357C2×C8C2×D4×C8911yescharacteristic
358C2×C8C2×D4×C8911yescharacteristic
359C2×C8C2×D4×C8911yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4C2×D4×C8912yes—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C42—22no—
379C42—41no—
380C42C2×D4×C8911yescharacteristic
381C42C2×D4×C8911yescharacteristic
382C42#41×C8911yescharacteristic
383C42C24×C8911yescharacteristic
384C23—41no—
385C23#121×C8911yescharacteristic
386Q8—22no—
387Q8—22no—
388Q8—42no—
389Q8—41no—
390Q8—41no—
391Q8—42no—
392Q8—81no—
393D4—41no—
394D4—41no—
395D4—42no—
396D4—81no—
397D4—82no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4#121×C8911yescharacteristic
409C2×C4#121×C8911yescharacteristic
410C2×C4#121×C8911yescharacteristic
411C2×C4C22×D4×C8911yescharacteristic
412C2×C4C22×D4×C8911yescharacteristic
413C2×C4C2×#41×C8911yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—42no—
418C8—42no—
419C8—42no—
420C8#137×C8912yes—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C2×#121×C8911yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—42no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4C2×#137×C8911yescharacteristic
438C4#575×C8911yescharacteristic
439C4#577×C8912yes—
440C2—41no—
441C2—161no—
442C2C89×#303711yescharacteristic
443C2C89×#305711yescharacteristic
444C2C89×#306711yescharacteristic
subgroupG/H
center, socleC22×C89C2×#121
commutator, Frattini, cosocleC42C24×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
1. C89×#3237C2semidirect
4. C89×#2960C2semidirect
5. C89×#1692C2semidirect
6. C89×#1686C2semidirect
7. C89×#1680C2semidirect
8. C89×#1678C2semidirect
9. C89×#1568C2semidirect
10. C89×#1559C2semidirect
217. #19346C89direct (N × H)
223. #3237C2×C89semidirect
226. #2960C2×C89semidirect
227. #1692C2×C89semidirect
228. #1686C2×C89semidirect
229. #1680C2×C89semidirect
230. #1678C2×C89semidirect
231. #1568C2×C89semidirect
232. #1559C2×C89semidirect
234. C89#19346direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#32372
C89×#32162
C89×#31672
C89×#29602
C89×#16922
C89×#16862
C89×#16802
C89×#16782
C89×#15682
C89×#15592
C89×#15572
#1934689