Finite Group Databasebeta

← C89×#9271 #36387119

Subgroups — C89×#9271 #36387119

Order 22784.

496 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×#3226C211yesmaximal, characteristic
2C89×#2935C211yesmaximal, characteristic
3C89×#1966C211yesmaximal, characteristic, complemented
4C89×#1547C211yesmaximal, characteristic
5C2×#332×C89C211yesmaximal, characteristic, complemented
6C89×#1301C211yesmaximal, characteristic, complemented
7C89×#1283C211yesmaximal, characteristic, complemented
8C2×#131×C89—21no—
9#532×C89C2211yescharacteristic
10C2×C4⋊Q8×C89C2211yescharacteristic
11#500×C89—21no—
12#486×C89—21no—
13#480×C89C414yes—
14#474×C89—22no—
15#436×C89—21no—
16#435×C89—22no—
17C8×D4×C89—21no—
18#431×C89C2211yescharacteristic
19#423×C89C2211yescharacteristic
20C2×C4⋊C8×C89C2211yescharacteristic
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×#101×C89—21no—
23C2×#101×C89—21no—
24#408×C89—21no—
25C4×M16×C89C2211yescharacteristic
26#332×C89—21no—
27#332×C89—21no—
28#332×C89—21no—
29#331×C89—21no—
30C2×#41×C89—21no—
31C22×Q8×C89—21no—
32#131×C89—42no—
33#131×C89—42no—
34C2×M16×C89—22no—
35C2×M16×C89—21no—
36C2×M16×C89D411yescharacteristic
37C2×M16×C89D411yescharacteristic
38C22×C8×C89—22no—
39C22×C8×C89—21no—
40C22×C8×C89—21no—
41C4⋊Q8×C89—21no—
42C4⋊Q8×C89—21no—
43C4⋊Q8×C89—21no—
44C4⋊Q8×C89—21no—
45C4⋊Q8×C89D411yescharacteristic
46#127×C89D411yescharacteristic
47#124×C89—21no—
48#121×C89—21no—
49#121×C89C2×C412yes—
50C4×D4×C89—21no—
51C4×D4×C89D412yes—
52C2×C4⋊C4×C89—21no—
53C2×C4⋊C4×C89C2×C412yes—
54C2×C42×C89C2311yescharacteristic
55#107×C89—24no—
56C4⋊C8×C89—21no—
57C4⋊C8×C89—21no—
58C4⋊C8×C89—21no—
59C4⋊C8×C89—21no—
60C4⋊C8×C89—21no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89D411yescharacteristic
63C4⋊C8×C89D411yescharacteristic
64#102×C89—24no—
65#101×C89—42no—
66#101×C89—42no—
67C22⋊C8×C89—22no—
68C22⋊C8×C89—22no—
69C22⋊C8×C89C2×C412yes—
70#97×C89—21no—
71C4×C8×C89—21no—
72C4×C8×C89—21no—
73#41×C89—41no—
74#41×C89—41no—
75#41×C89—41no—
76#41×C89—41no—
77C2×Q8×C89—21no—
78C2×Q8×C89—41no—
79C2×Q8×C89—41no—
80C2×Q8×C89—41no—
81C2×Q8×C89—41no—
82C2×Q8×C89—41no—
83C2×Q8×C89—41no—
84C2×D4×C89—22no—
85C2×D4×C89—21no—
86C2×D4×C89—21no—
87C2×D4×C89C22⋊C412yes—
88C22×C4×C89—22no—
89C22×C4×C89—22no—
90C22×C4×C89C22×C411yescharacteristic
91C22×C4×C89C2×D411yescharacteristic
92C22×C4×C89#4111yescharacteristic
93M16×C89—21no—
94M16×C89—21no—
95M16×C89—21no—
96M16×C89—44no—
97M16×C89—41no—
98M16×C89—41no—
99M16×C89D812yes—
100C2×C8×C89—21no—
101C2×C8×C89—22no—
102C2×C8×C89—21no—
103C2×C8×C89—21no—
104C2×C8×C89—21no—
105C2×C8×C89—44no—
106C2×C8×C89—41no—
107C2×C8×C89—41no—
108C2×C8×C89—41no—
109C2×C8×C89—41no—
110C2×C8×C89—81no—
111C4⋊C4×C89—21no—
112C4⋊C4×C89—22no—
113C4⋊C4×C89—22no—
114C4⋊C4×C89—41no—
115C4⋊C4×C89—41no—
116C4⋊C4×C89C22⋊C412yes—
117C22⋊C4×C89—22no—
118C22⋊C4×C89—22no—
119C42×C89C2×D411yescharacteristic
120C42×C89C2×D411yescharacteristic
121C42×C89C2×D411yescharacteristic
122C42×C89#4111yescharacteristic
123C23×C89—22no—
124C23×C89C4×D411yescharacteristic
125Q8×C89—41no—
126Q8×C89—41no—
127Q8×C89—81no—
128Q8×C89—81no—
129Q8×C89—81no—
130Q8×C89—81no—
131D4×C89—42no—
132D4×C89—42no—
133D4×C89—42no—
134D4×C89—41no—
135D4×C89—41no—
136D4×C89—41no—
137D4×C89—41no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—22no—
141C2×C4×C89—41no—
142C2×C4×C89—42no—
143C2×C4×C89—42no—
144C2×C4×C89—42no—
145C2×C4×C89—42no—
146C2×C4×C89—42no—
147C2×C4×C89C2×C22⋊C411yescharacteristic
148C2×C4×C89C4×D411yescharacteristic
149C2×C4×C89#12011yescharacteristic
150C2×C4×C89#12111yescharacteristic
151C2×C4×C89#12111yescharacteristic
152C2×C4×C89#12311yescharacteristic
153C2×C4×C89C2×D811yescharacteristic
154C2×C4×C89#13511yescharacteristic
155C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
157C8×C89—22no—
158C8×C89—42no—
159C8×C89—41no—
160C8×C89—41no—
161C8×C89—41no—
162C8×C89—81no—
163C8×C89—81no—
164C22×C89—21no—
165C22×C89—21no—
166C22×C89—42no—
167C22×C89—42no—
168C22×C89—42no—
169C22×C89#38611yescharacteristic
170C22×C89C4×D811yescharacteristic
171C22×C89#44211yescharacteristic
172C4×C89—21no—
173C4×C89—21no—
174C4×C89—21no—
175C4×C89—42no—
176C4×C89—82no—
177C4×C89#44711yescharacteristic
178C4×C89#44911yescharacteristic
179C4×C89#45911yescharacteristic
180C4×C89#46311yescharacteristic
181C4×C89#47111yescharacteristic
182C4×C89#47311yescharacteristic
183#9271C8911yesmaximal, characteristic, direct product factor, Sylow
184C2×C89—21no—
185C2×C89—21no—
186C2×C89—82no—
187C2×C89#187911yescharacteristic
188C2×C89#190811yescharacteristic
189C2×C89#191511yescharacteristic
190#3226C2×C8911yescharacteristic
191#2935C2×C8911yescharacteristic
192#1966C2×C8911yescharacteristic, complemented
193#1547C2×C8911yescharacteristic
194C2×#332C2×C8911yescharacteristic, complemented
195#1301C2×C8911yescharacteristic, complemented
196#1283C2×C8911yescharacteristic, complemented
197C89#927111yescharacteristic, direct product factor, Sylow
198C2×#131—21no—
199#532C22×C8911yescharacteristic
200C2×C4⋊Q8C22×C8911yescharacteristic
201#500—21no—
202#486—21no—
203#480C4×C8914yes—
204#474—22no—
205#436—21no—
206#435—22no—
207C8×D4—21no—
208#431C22×C8911yescharacteristic
209#423C22×C8911yescharacteristic
210C2×C4⋊C8C22×C8911yescharacteristic
211C2×C4⋊C8C22×C8911yescharacteristic
212C2×#101—21no—
213C2×#101—21no—
214#408—21no—
215C4×M16C22×C8911yescharacteristic
216#332—21no—
217#332—21no—
218#332—21no—
219#331—21no—
220C2×#41—21no—
221C22×Q8—21no—
222#131—42no—
223#131—42no—
224C2×M16—22no—
225C2×M16—21no—
226C2×M16D4×C8911yescharacteristic
227C2×M16D4×C8911yescharacteristic
228C22×C8—22no—
229C22×C8—21no—
230C22×C8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8D4×C8911yescharacteristic
236#127D4×C8911yescharacteristic
237#124—21no—
238#121—21no—
239#121C2×C4×C8912yes—
240C4×D4—21no—
241C4×D4D4×C8912yes—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C2×C4×C8912yes—
244C2×C42C23×C8911yescharacteristic
245#107—24no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C8911yescharacteristic
253C4⋊C8D4×C8911yescharacteristic
254#102—24no—
255#101—42no—
256#101—42no—
257C22⋊C8—22no—
258C22⋊C8—22no—
259C22⋊C8C2×C4×C8912yes—
260#97—21no—
261C4×C8—21no—
262C4×C8—21no—
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×D4—22no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊C4×C8912yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4C22×C4×C8911yescharacteristic
281C22×C4C2×D4×C8911yescharacteristic
282C22×C4#41×C8911yescharacteristic
283M16—21no—
284M16—21no—
285M16—21no—
286M16—44no—
287M16—41no—
288M16—41no—
289M16D8×C8912yes—
290C2×C8—21no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—44no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—81no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C8912yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C42C2×D4×C8911yescharacteristic
310C42C2×D4×C8911yescharacteristic
311C42C2×D4×C8911yescharacteristic
312C42#41×C8911yescharacteristic
313C23—22no—
314C23C4×D4×C8911yescharacteristic
315Q8—41no—
316Q8—41no—
317Q8—81no—
318Q8—81no—
319Q8—81no—
320Q8—81no—
321D4—42no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—41no—
327D4—41no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4C2×C22⋊C4×C8911yescharacteristic
338C2×C4C4×D4×C8911yescharacteristic
339C2×C4#120×C8911yescharacteristic
340C2×C4#121×C8911yescharacteristic
341C2×C4#121×C8911yescharacteristic
342C2×C4#123×C8911yescharacteristic
343C2×C4C2×D8×C8911yescharacteristic
344C2×C4#135×C8911yescharacteristic
345C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
346C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
347C8—22no—
348C8—42no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—81no—
353C8—81no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22#386×C8911yescharacteristic
360C22C4×D8×C8911yescharacteristic
361C22#442×C8911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—82no—
367C4#447×C8911yescharacteristic
368C4#449×C8911yescharacteristic
369C4#459×C8911yescharacteristic
370C4#463×C8911yescharacteristic
371C4#471×C8911yescharacteristic
372C4#473×C8911yescharacteristic
373C2—21no—
374C2—21no—
375C2—82no—
376C2C89×#187911yescharacteristic
377C2C89×#190811yescharacteristic
378C2C89×#191511yescharacteristic
subgroupG/H
center, socleC22×C89#386
commutatorC22×C4C22×C4×C89
Frattini, cosocleC2×C42C23×C89
prime radical#532×C89C22
LCSG ▷ C22×C4 ▷ 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×#1966C2semidirect
5. C2×#332×C89C2semidirect
6. C89×#1301C2semidirect
7. C89×#1283C2semidirect
183. #9271C89direct (N × H)
192. #1966C2×C89semidirect
194. C2×#332C2×C89semidirect
195. #1301C2×C89semidirect
196. #1283C2×C89semidirect
197. C89#9271direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#32262
C89×#29352
C89×#19662
C89×#15472
C2×#332×C892
C89×#13012
C89×#12832
#927189