Finite Group Databasebeta

← C89×#13030 #36390878

Subgroups — C89×#13030 #36390878

Order 22784.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3414C211yesmaximal, characteristic
2C89×#2952C211yesmaximal, characteristic, complemented
3C89×#2145C211yesmaximal, characteristic, complemented
4C2×#360×C89C211yesmaximal, characteristic, complemented
5C89×#1976C211yesmaximal, characteristic, complemented
6C89×#1386C211yesmaximal, characteristic, complemented
7C89×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C89C2211yescharacteristic
9C2×#135×C89C2211yescharacteristic
10#520×C89—21no—
11#510×C89—21no—
12#510×C89C412yescomplemented
13#509×C89—21no—
14#509×C89C412yescomplemented
15#508×C89—22no—
16C2×M32×C89C2211yescharacteristic
17C2×M32×C89C2211yescharacteristic
18#442×C89—21no—
19#441×C89—21no—
20C4×SD16×C89—22no—
21#427×C89C2211yescharacteristic
22C2×#106×C89C2211yescharacteristic
23#421×C89—21no—
24#417×C89—21no—
25#410×C89—21no—
26#405×C89C2211yescharacteristic
27#360×C89—22no—
28#360×C89—22no—
29C2×#41×C89—21no—
30C2×#41×C89—21no—
31#135×C89—21no—
32#135×C89—21no—
33#135×C89—21no—
34#135×C89—21no—
35#135×C89—21no—
36#135×C89—21no—
37#135×C89C2×C412yes—
38#135×C89D412yes—
39C2×Q16×C89C2×C411yescharacteristic, complemented
40C2×Q16×C89D411yescharacteristic
41C2×SD16×C89—21no—
42C2×SD16×C89—21no—
43C2×D8×C89C2×C411yescharacteristic, complemented
44C2×D8×C89D411yescharacteristic
45C2×M16×C89D411yescharacteristic
46C22×C8×C89C2311yescharacteristic
47C4×Q8×C89—22no—
48C4×D4×C89—22no—
49C4×D4×C89—42no—
50#117×C89—21no—
51#117×C89—41no—
52#117×C89D411yescharacteristic
53C2×C4⋊C4×C89—21no—
54C2×C4⋊C4×C89—41no—
55Q32×C89—22no—
56SD32×C89—22no—
57SD32×C89—22no—
58D16×C89—22no—
59M32×C89—21no—
60M32×C89—21no—
61M32×C89—21no—
62M32×C89C2×C412yescomplemented
63C2×C16×C89—21no—
64C2×C16×C89—21no—
65#107×C89—21no—
66#106×C89—21no—
67#106×C89—21no—
68#106×C89D412yes—
69#104×C89—42no—
70#103×C89—22no—
71#102×C89—22no—
72#99×C89—42no—
73#97×C89—21no—
74C4×C8×C89—21no—
75#41×C89—22no—
76#41×C89—22no—
77#41×C89—41no—
78#41×C89—41no—
79#41×C89—41no—
80#41×C89—41no—
81#41×C89—41no—
82#41×C89—41no—
83C2×Q8×C89—21no—
84C2×Q8×C89—21no—
85C2×D4×C89—21no—
86C2×D4×C89—21no—
87C2×D4×C89—41no—
88C2×D4×C89—41no—
89C22×C4×C89—42no—
90C22×C4×C89—41no—
91C22×C4×C89—41no—
92C22×C4×C89—41no—
93C22×C4×C89C2×D411yescharacteristic
94Q16×C89—21no—
95Q16×C89—21no—
96Q16×C89—21no—
97Q16×C89C22⋊C412yes—
98SD16×C89—22no—
99SD16×C89—22no—
100SD16×C89—41no—
101SD16×C89—41no—
102D8×C89—21no—
103D8×C89—21no—
104D8×C89—21no—
105D8×C89C22⋊C412yes—
106M16×C89—21no—
107M16×C89—21no—
108C2×C8×C89—21no—
109C2×C8×C89C22×C411yescharacteristic
110C2×C8×C89C2×D411yescharacteristic
111C2×C8×C89C2×D411yescharacteristic
112C2×C8×C89C2×D411yescharacteristic
113C2×C8×C89#4111yescharacteristic
114C2×C8×C89#4111yescharacteristic
115C4⋊C4×C89—21no—
116C4⋊C4×C89—22no—
117C4⋊C4×C89—42no—
118C4⋊C4×C89—41no—
119C4⋊C4×C89—41no—
120C22⋊C4×C89—42no—
121C22⋊C4×C89—41no—
122C22⋊C4×C89D812yes—
123C42×C89—21no—
124C42×C89—42no—
125C42×C89—41no—
126C16×C89—22no—
127C16×C89—41no—
128C23×C89—41no—
129C23×C89—41no—
130C23×C89C2×D811yescharacteristic
131Q8×C89—22no—
132Q8×C89—41no—
133Q8×C89—41no—
134Q8×C89—41no—
135D4×C89—22no—
136D4×C89—42no—
137D4×C89—42no—
138D4×C89—41no—
139D4×C89—41no—
140D4×C89—41no—
141D4×C89—81no—
142D4×C89—81no—
143C2×C4×C89—22no—
144C2×C4×C89—41no—
145C2×C4×C89—42no—
146C2×C4×C89—42no—
147C2×C4×C89—41no—
148C2×C4×C89—42no—
149C2×C4×C89—81no—
150C2×C4×C89—81no—
151C2×C4×C89—81no—
152C2×C4×C89—162no—
153C2×C4×C89—161no—
154C2×C4×C89C4×D411yescharacteristic
155C2×C4×C89#12011yescharacteristic
156C2×C4×C89#12111yescharacteristic
157C2×C4×C89#13511yescharacteristic
158C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
160C8×C89—41no—
161C8×C89C2×C22⋊C411yescharacteristic
162C8×C89C4×D411yescharacteristic
163C8×C89#12111yescharacteristic
164C8×C89#12311yescharacteristic
165C22×C89—41no—
166C22×C89—42no—
167C22×C89—81no—
168C22×C89—81no—
169C22×C89—81no—
170C22×C89—161no—
171C22×C89C4×D811yescharacteristic
172C22×C89#44711yescharacteristic
173C22×C89#45911yescharacteristic
174C4×C89—42no—
175C4×C89—42no—
176C4×C89—82no—
177C4×C89—81no—
178C4×C89—161no—
179C4×C89#38611yescharacteristic
180C4×C89#44211yescharacteristic
181C4×C89#44911yescharacteristic
182C4×C89#46311yescharacteristic
183#13030C8911yesmaximal, characteristic, direct product factor, Sylow
184C2×C89—21no—
185C2×C89—21no—
186C2×C89—21no—
187C2×C89—82no—
188C2×C89—161no—
189C2×C89#187911yescharacteristic
190#3414C2×C8911yescharacteristic
191#2952C2×C8911yescharacteristic, complemented
192#2145C2×C8911yescharacteristic, complemented
193C2×#360C2×C8911yescharacteristic, complemented
194#1976C2×C8911yescharacteristic, complemented
195#1386C2×C8911yescharacteristic, complemented
196#1378C2×C8911yescharacteristic, complemented
197C89#1303011yescharacteristic, direct product factor, Sylow
198C2×#135C22×C8911yescharacteristic
199C2×#135C22×C8911yescharacteristic
200#520—21no—
201#510—21no—
202#510C4×C8912yescomplemented
203#509—21no—
204#509C4×C8912yescomplemented
205#508—22no—
206C2×M32C22×C8911yescharacteristic
207C2×M32C22×C8911yescharacteristic
208#442—21no—
209#441—21no—
210C4×SD16—22no—
211#427C22×C8911yescharacteristic
212C2×#106C22×C8911yescharacteristic
213#421—21no—
214#417—21no—
215#410—21no—
216#405C22×C8911yescharacteristic
217#360—22no—
218#360—22no—
219C2×#41—21no—
220C2×#41—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135C2×C4×C8912yes—
228#135D4×C8912yes—
229C2×Q16C2×C4×C8911yescharacteristic, complemented
230C2×Q16D4×C8911yescharacteristic
231C2×SD16—21no—
232C2×SD16—21no—
233C2×D8C2×C4×C8911yescharacteristic, complemented
234C2×D8D4×C8911yescharacteristic
235C2×M16D4×C8911yescharacteristic
236C22×C8C23×C8911yescharacteristic
237C4×Q8—22no—
238C4×D4—22no—
239C4×D4—42no—
240#117—21no—
241#117—41no—
242#117D4×C8911yescharacteristic
243C2×C4⋊C4—21no—
244C2×C4⋊C4—41no—
245Q32—22no—
246SD32—22no—
247SD32—22no—
248D16—22no—
249M32—21no—
250M32—21no—
251M32—21no—
252M32C2×C4×C8912yescomplemented
253C2×C16—21no—
254C2×C16—21no—
255#107—21no—
256#106—21no—
257#106—21no—
258#106D4×C8912yes—
259#104—42no—
260#103—22no—
261#102—22no—
262#99—42no—
263#97—21no—
264C4×C8—21no—
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C2×D4×C8911yescharacteristic
284Q16—21no—
285Q16—21no—
286Q16—21no—
287Q16C22⋊C4×C8912yes—
288SD16—22no—
289SD16—22no—
290SD16—41no—
291SD16—41no—
292D8—21no—
293D8—21no—
294D8—21no—
295D8C22⋊C4×C8912yes—
296M16—21no—
297M16—21no—
298C2×C8—21no—
299C2×C8C22×C4×C8911yescharacteristic
300C2×C8C2×D4×C8911yescharacteristic
301C2×C8C2×D4×C8911yescharacteristic
302C2×C8C2×D4×C8911yescharacteristic
303C2×C8#41×C8911yescharacteristic
304C2×C8#41×C8911yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4D8×C8912yes—
313C42—21no—
314C42—42no—
315C42—41no—
316C16—22no—
317C16—41no—
318C23—41no—
319C23—41no—
320C23C2×D8×C8911yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—162no—
343C2×C4—161no—
344C2×C4C4×D4×C8911yescharacteristic
345C2×C4#120×C8911yescharacteristic
346C2×C4#121×C8911yescharacteristic
347C2×C4#135×C8911yescharacteristic
348C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
349C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
350C8—41no—
351C8C2×C22⋊C4×C8911yescharacteristic
352C8C4×D4×C8911yescharacteristic
353C8#121×C8911yescharacteristic
354C8#123×C8911yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22C4×D8×C8911yescharacteristic
362C22#447×C8911yescharacteristic
363C22#459×C8911yescharacteristic
364C4—42no—
365C4—42no—
366C4—82no—
367C4—81no—
368C4—161no—
369C4#386×C8911yescharacteristic
370C4#442×C8911yescharacteristic
371C4#449×C8911yescharacteristic
372C4#463×C8911yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2C89×#187911yescharacteristic
subgroupG/H
center, socleC2×C89#1879
commutatorC2×C8C22×C4×C89
Frattini, cosocleC22×C8C23×C89
prime radicalC89×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C89 ◁ C22×C4×C89 ◁ #405×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#2952C2semidirect
3. C89×#2145C2semidirect
4. C2×#360×C89C2semidirect
5. C89×#1976C2semidirect
6. C89×#1386C2semidirect
7. C89×#1378C2semidirect
12. #510×C89C4semidirect
14. #509×C89C4semidirect
39. C2×Q16×C89C2×C4semidirect
43. C2×D8×C89C2×C4semidirect
62. M32×C89C2×C4semidirect
183. #13030C89direct (N × H)
191. #2952C2×C89semidirect
192. #2145C2×C89semidirect
193. C2×#360C2×C89semidirect
194. #1976C2×C89semidirect
195. #1386C2×C89semidirect
196. #1378C2×C89semidirect
197. C89#13030direct (N × H)
202. #510C4×C89semidirect
204. #509C4×C89semidirect
229. C2×Q16C2×C4×C89semidirect
233. C2×D8C2×C4×C89semidirect
252. M32C2×C4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#34142
C89×#29522
C89×#21452
C2×#360×C892
C89×#19762
C89×#13862
C89×#13782
#1303089