Finite Group Databasebeta

← C89×#10540 #36388388

Subgroups — C89×#10540 #36388388

Order 22784.

506 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C89C211yesmaximal, characteristic
2C89×#1982C211yesmaximal, characteristic
3C89×#1981C211yesmaximal, characteristic, complemented
4C89×#1939C211yesmaximal, characteristic, complemented
5C2×#332×C89C211yesmaximal, characteristic, complemented
6C2×#331×C89C211yesmaximal, characteristic
7C89×#1277C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C89C2211yescharacteristic
9C2×#127×C89C2211yescharacteristic
10#486×C89—22no—
11#486×C89—22no—
12C2×C4⋊C8×C89—21no—
13C2×C4⋊C8×C89C2211yescharacteristic
14C2×C4⋊C8×C89C2211yescharacteristic
15C2×C4⋊C8×C89C2211yescharacteristic
16C2×#103×C89—21no—
17C2×#103×C89—21no—
18C2×#102×C89—21no—
19C2×#102×C89—21no—
20C2×#102×C89—21no—
21C2×#102×C89—21no—
22C2×C4×C8×C89C2211yescharacteristic
23C4×C4⋊C4×C89C2211yescharacteristic
24#336×C89—21no—
25#332×C89—22no—
26#331×C89—22no—
27C22×Q8×C89—21no—
28C22×D4×C89—21no—
29C22×D4×C89—21no—
30C22×D4×C89—21no—
31C22×C8×C89—21no—
32C22×C8×C89—21no—
33C22×C8×C89—21no—
34C22×C8×C89D411yescharacteristic
35C22×C8×C89D411yescharacteristic
36C4⋊Q8×C89—21no—
37C4⋊Q8×C89—21no—
38C4⋊Q8×C89—21no—
39C4⋊Q8×C89D412yes—
40#127×C89—21no—
41#127×C89—21no—
42#127×C89—21no—
43#127×C89D412yes—
44C2×C4⋊C4×C89—21no—
45C2×C4⋊C4×C89—21no—
46C2×C4⋊C4×C89D411yescharacteristic
47C2×C4⋊C4×C89D411yescharacteristic
48C2×C42×C89—21no—
49C2×C42×C89C2311yescharacteristic
50C4⋊C8×C89—21no—
51C4⋊C8×C89—21no—
52C4⋊C8×C89—21no—
53C4⋊C8×C89—21no—
54C4⋊C8×C89—21no—
55C4⋊C8×C89—21no—
56C4⋊C8×C89—42no—
57#103×C89—42no—
58#103×C89—42no—
59#102×C89—24no—
60#102×C89—24no—
61#102×C89—42no—
62#102×C89—42no—
63C4×C8×C89—21no—
64C4×C8×C89—21no—
65#95×C89—21no—
66C24×C89—41no—
67C2×Q8×C89—22no—
68C2×Q8×C89—41no—
69C2×Q8×C89—41no—
70C2×Q8×C89—41no—
71C2×Q8×C89—41no—
72C2×Q8×C89—41no—
73C2×D4×C89—22no—
74C2×D4×C89—22no—
75C2×D4×C89—22no—
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—41no—
85C2×D4×C89—41no—
86C2×D4×C89—41no—
87C2×D4×C89—81no—
88C2×D4×C89—81no—
89C22×C4×C89—21no—
90C22×C4×C89—21no—
91C22×C4×C89—41no—
92C22×C4×C89C2×D411yescharacteristic
93C22×C4×C89C2×D411yescharacteristic
94C22×C4×C89#4111yescharacteristic
95C2×C8×C89—21no—
96C2×C8×C89—21no—
97C2×C8×C89—21no—
98C2×C8×C89—21no—
99C2×C8×C89—21no—
100C2×C8×C89—21no—
101C2×C8×C89—41no—
102C2×C8×C89—41no—
103C2×C8×C89—41no—
104C2×C8×C89—41no—
105C2×C8×C89—41no—
106C2×C8×C89—41no—
107C2×C8×C89—41no—
108C2×C8×C89—41no—
109C2×C8×C89—41no—
110C4⋊C4×C89—21no—
111C4⋊C4×C89—22no—
112C4⋊C4×C89—22no—
113C4⋊C4×C89—21no—
114C4⋊C4×C89—21no—
115C4⋊C4×C89—41no—
116C4⋊C4×C89—41no—
117C4⋊C4×C89D812yes—
118C42×C89—41no—
119C42×C89—41no—
120C42×C89C2×D411yescharacteristic
121C42×C89C2×D411yescharacteristic
122C42×C89#4111yescharacteristic
123C42×C89#4111yescharacteristic
124C23×C89—42no—
125C23×C89—81no—
126C23×C89—81no—
127C23×C89—81no—
128C23×C89—81no—
129C23×C89—81no—
130C23×C89—81no—
131C23×C89#12111yescharacteristic
132Q8×C89—42no—
133Q8×C89—42no—
134Q8×C89—81no—
135Q8×C89—81no—
136D4×C89—42no—
137D4×C89—42no—
138D4×C89—42no—
139D4×C89—42no—
140D4×C89—82no—
141D4×C89—82no—
142D4×C89—81no—
143D4×C89—81no—
144D4×C89—81no—
145D4×C89—81no—
146C2×C4×C89—21no—
147C2×C4×C89—21no—
148C2×C4×C89—22no—
149C2×C4×C89—41no—
150C2×C4×C89—41no—
151C2×C4×C89—42no—
152C2×C4×C89—41no—
153C2×C4×C89—41no—
154C2×C4×C89—41no—
155C2×C4×C89—81no—
156C2×C4×C89—81no—
157C2×C4×C89#12011yescharacteristic
158C2×C4×C89#12111yescharacteristic
159C2×C4×C89#12111yescharacteristic
160C2×C4×C89#12311yescharacteristic
161C2×C4×C89#12311yescharacteristic
162C2×C4×C89#12411yescharacteristic
163C2×C4×C89C2×D811yescharacteristic
164C2×C4×C89#13511yescharacteristic
165C2×C4×C89#13511yescharacteristic
166C2×C4×C89#13511yescharacteristic
167C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C89#13711yescharacteristic
171C8×C89—41no—
172C8×C89—41no—
173C8×C89—81no—
174C8×C89—81no—
175C8×C89—81no—
176C22×C89—82no—
177C22×C89—82no—
178C22×C89—82no—
179C22×C89—161no—
180C22×C89—161no—
181C22×C89—161no—
182C22×C89—161no—
183C22×C89#39411yescharacteristic
184C22×C89#46311yescharacteristic
185C22×C89#46411yescharacteristic
186C22×C89#46611yescharacteristic
187C22×C89#46911yescharacteristic
188C22×C89#47111yescharacteristic
189C22×C89#47111yescharacteristic
190C4×C89—21no—
191C4×C89—21no—
192C4×C89—42no—
193C4×C89—82no—
194C4×C89—81no—
195C4×C89#44911yescharacteristic
196C4×C89#45211yescharacteristic
197C4×C89#45911yescharacteristic
198C4×C89#45911yescharacteristic
199C4×C89#46311yescharacteristic
200C4×C89#46311yescharacteristic
201C4×C89#48811yescharacteristic
202C4×C89#48911yescharacteristic
203#10540C8911yesmaximal, characteristic, direct product factor, Sylow
204C2×C89—162no—
205C2×C89#168111yescharacteristic
206C2×C89#168211yescharacteristic
207C2×C89#170111yescharacteristic
208C2×C89#170211yescharacteristic
209C2×C89#204211yescharacteristic
210C2×C89#204611yescharacteristic
211C2×C89#205411yescharacteristic
212C2×#486C2×C8911yescharacteristic
213#1982C2×C8911yescharacteristic
214#1981C2×C8911yescharacteristic, complemented
215#1939C2×C8911yescharacteristic, complemented
216C2×#332C2×C8911yescharacteristic, complemented
217C2×#331C2×C8911yescharacteristic
218#1277C2×C8911yescharacteristic, complemented
219C89#1054011yescharacteristic, direct product factor, Sylow
220C2×C4⋊Q8C22×C8911yescharacteristic
221C2×#127C22×C8911yescharacteristic
222#486—22no—
223#486—22no—
224C2×C4⋊C8—21no—
225C2×C4⋊C8C22×C8911yescharacteristic
226C2×C4⋊C8C22×C8911yescharacteristic
227C2×C4⋊C8C22×C8911yescharacteristic
228C2×#103—21no—
229C2×#103—21no—
230C2×#102—21no—
231C2×#102—21no—
232C2×#102—21no—
233C2×#102—21no—
234C2×C4×C8C22×C8911yescharacteristic
235C4×C4⋊C4C22×C8911yescharacteristic
236#336—21no—
237#332—22no—
238#331—22no—
239C22×Q8—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8D4×C8911yescharacteristic
247C22×C8D4×C8911yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8D4×C8912yes—
252#127—21no—
253#127—21no—
254#127—21no—
255#127D4×C8912yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C8911yescharacteristic
259C2×C4⋊C4D4×C8911yescharacteristic
260C2×C42—21no—
261C2×C42C23×C8911yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—42no—
269#103—42no—
270#103—42no—
271#102—24no—
272#102—24no—
273#102—42no—
274#102—42no—
275C4×C8—21no—
276C4×C8—21no—
277#95—21no—
278C24—41no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—81no—
300C2×D4—81no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4C2×D4×C8911yescharacteristic
305C22×C4C2×D4×C8911yescharacteristic
306C22×C4#41×C8911yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4D8×C8912yes—
330C42—41no—
331C42—41no—
332C42C2×D4×C8911yescharacteristic
333C42C2×D4×C8911yescharacteristic
334C42#41×C8911yescharacteristic
335C42#41×C8911yescharacteristic
336C23—42no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—81no—
343C23#121×C8911yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4#120×C8911yescharacteristic
370C2×C4#121×C8911yescharacteristic
371C2×C4#121×C8911yescharacteristic
372C2×C4#123×C8911yescharacteristic
373C2×C4#123×C8911yescharacteristic
374C2×C4#124×C8911yescharacteristic
375C2×C4C2×D8×C8911yescharacteristic
376C2×C4#135×C8911yescharacteristic
377C2×C4#135×C8911yescharacteristic
378C2×C4#135×C8911yescharacteristic
379C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
380C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
381C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
382C2×C4#137×C8911yescharacteristic
383C8—41no—
384C8—41no—
385C8—81no—
386C8—81no—
387C8—81no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—161no—
392C22—161no—
393C22—161no—
394C22—161no—
395C22#394×C8911yescharacteristic
396C22#463×C8911yescharacteristic
397C22#464×C8911yescharacteristic
398C22#466×C8911yescharacteristic
399C22#469×C8911yescharacteristic
400C22#471×C8911yescharacteristic
401C22#471×C8911yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—82no—
406C4—81no—
407C4#449×C8911yescharacteristic
408C4#452×C8911yescharacteristic
409C4#459×C8911yescharacteristic
410C4#459×C8911yescharacteristic
411C4#463×C8911yescharacteristic
412C4#463×C8911yescharacteristic
413C4#488×C8911yescharacteristic
414C4#489×C8911yescharacteristic
415C2—162no—
416C2C89×#168111yescharacteristic
417C2C89×#168211yescharacteristic
418C2C89×#170111yescharacteristic
419C2C89×#170211yescharacteristic
420C2C89×#204211yescharacteristic
421C2C89×#204611yescharacteristic
422C2C89×#205411yescharacteristic
subgroupG/H
center, socleC23×C89#121
commutator, Frattini, cosocleC2×C42C23×C89
prime radicalC2×#127×C89C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C89×#1981C2semidirect
4. C89×#1939C2semidirect
5. C2×#332×C89C2semidirect
7. C89×#1277C2semidirect
203. #10540C89direct (N × H)
214. #1981C2×C89semidirect
215. #1939C2×C89semidirect
216. C2×#332C2×C89semidirect
218. #1277C2×C89semidirect
219. C89#10540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#486×C892
C89×#19822
C89×#19812
C89×#19392
C2×#332×C892
C2×#331×C892
C89×#12772
#1054089