Finite Group Databasebeta

← C89×#10413 #36388261

Subgroups — C89×#10413 #36388261

Order 22784.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2563C211yesmaximal, characteristic
2C89×#1956C211yesmaximal, characteristic, complemented
3C89×#1947C211yesmaximal, characteristic, complemented
4C89×#1802C211yesmaximal, characteristic
5C2×#333×C89C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C89C211yesmaximal, characteristic
7C89×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C89C2211yescharacteristic
9C2×C4×D4×C89C2211yescharacteristic
10C2×#107×C89—21no—
11C2×C4⋊C8×C89C2211yescharacteristic
12C2×C4⋊C8×C89C2211yescharacteristic
13C2×#103×C89—22no—
14C2×#102×C89—21no—
15C2×C4×C8×C89C2211yescharacteristic
16#393×C89—22no—
17#390×C89—21no—
18#384×C89C2211yescharacteristic
19#382×C89—21no—
20#380×C89—21no—
21#380×C89—21no—
22C4×C4⋊C4×C89C2211yescharacteristic
23#340×C89—21no—
24#340×C89—21no—
25#333×C89—22no—
26D4⋊C8×C89—22no—
27C22×Q8×C89D412yes—
28C22×D4×C89D411yescharacteristic
29C23×C4×C89—21no—
30C22×C8×C89—21no—
31C22×C8×C89—21no—
32C22×C8×C89—21no—
33C4⋊Q8×C89—21no—
34C4⋊Q8×C89—21no—
35C4⋊Q8×C89—21no—
36C4⋊Q8×C89—21no—
37C4×D4×C89—21no—
38C4×D4×C89—21no—
39C4×D4×C89—21no—
40C4×D4×C89—21no—
41C2×C4⋊C4×C89—21no—
42C2×C4⋊C4×C89—21no—
43C2×C4⋊C4×C89—21no—
44C2×C4⋊C4×C89—21no—
45C2×C4⋊C4×C89—21no—
46C2×C4⋊C4×C89D411yescharacteristic
47C2×C4⋊C4×C89D411yescharacteristic
48C2×C4⋊C4×C89D411yescharacteristic
49C2×C22⋊C4×C89—21no—
50C2×C22⋊C4×C89—22no—
51C2×C22⋊C4×C89—22no—
52C2×C42×C89—21no—
53C2×C42×C89C2311yescharacteristic
54#107×C89—42no—
55C4⋊C8×C89—21no—
56C4⋊C8×C89—21no—
57C4⋊C8×C89—21no—
58C4⋊C8×C89D412yes—
59#103×C89—44no—
60#102×C89—42no—
61C4×C8×C89—21no—
62C4×C8×C89—21no—
63#95×C89—22no—
64#95×C89—22no—
65#95×C89—21no—
66C24×C89—21no—
67C2×Q8×C89—22no—
68C2×Q8×C89—22no—
69C2×Q8×C89—42no—
70C2×Q8×C89—42no—
71C2×D4×C89—21no—
72C2×D4×C89—21no—
73C2×D4×C89—21no—
74C2×D4×C89—21no—
75C2×D4×C89—21no—
76C2×D4×C89Q1612yes—
77C22×C4×C89—21no—
78C22×C4×C89—21no—
79C22×C4×C89—21no—
80C22×C4×C89—22no—
81C22×C4×C89—41no—
82C22×C4×C89—41no—
83C22×C4×C89—41no—
84C22×C4×C89—41no—
85C22×C4×C89—41no—
86C22×C4×C89—41no—
87C22×C4×C89—41no—
88C22×C4×C89C2×D411yescharacteristic
89C22×C4×C89C2×D411yescharacteristic
90C22×C4×C89C2×D411yescharacteristic
91C2×C8×C89—22no—
92C2×C8×C89—22no—
93C2×C8×C89—41no—
94C2×C8×C89—41no—
95C2×C8×C89—41no—
96C2×C8×C89—41no—
97C2×C8×C89—41no—
98C2×C8×C89—41no—
99C2×C8×C89—41no—
100C4⋊C4×C89—21no—
101C4⋊C4×C89—21no—
102C4⋊C4×C89—21no—
103C4⋊C4×C89—21no—
104C4⋊C4×C89—21no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89—42no—
107C4⋊C4×C89—41no—
108C4⋊C4×C89—41no—
109C4⋊C4×C89—41no—
110C4⋊C4×C89—41no—
111C4⋊C4×C89—41no—
112C4⋊C4×C89—41no—
113C4⋊C4×C89—41no—
114C4⋊C4×C89—41no—
115C22⋊C4×C89—41no—
116C22⋊C4×C89—41no—
117C22⋊C4×C89—82no—
118C22⋊C4×C89—82no—
119C42×C89—41no—
120C42×C89—41no—
121C42×C89C2×D411yescharacteristic
122C42×C89#4111yescharacteristic
123C42×C89#4111yescharacteristic
124C42×C89#4111yescharacteristic
125C23×C89—22no—
126C23×C89—41no—
127C23×C89—41no—
128C23×C89—41no—
129C23×C89—41no—
130C23×C89—41no—
131C23×C89—41no—
132C23×C89#12011yescharacteristic
133Q8×C89—44no—
134Q8×C89—82no—
135D4×C89—22no—
136D4×C89—22no—
137D4×C89—41no—
138D4×C89—41no—
139C2×C4×C89—21no—
140C2×C4×C89—21no—
141C2×C4×C89—41no—
142C2×C4×C89—42no—
143C2×C4×C89—41no—
144C2×C4×C89—41no—
145C2×C4×C89—41no—
146C2×C4×C89—41no—
147C2×C4×C89—41no—
148C2×C4×C89—41no—
149C2×C4×C89—41no—
150C2×C4×C89—42no—
151C2×C4×C89—41no—
152C2×C4×C89—42no—
153C2×C4×C89—81no—
154C2×C4×C89—81no—
155C2×C4×C89—81no—
156C2×C4×C89—81no—
157C2×C4×C89—81no—
158C2×C4×C89—81no—
159C2×C4×C89—81no—
160C2×C4×C89#12111yescharacteristic
161C2×C4×C89#12111yescharacteristic
162C2×C4×C89#12111yescharacteristic
163C2×C4×C89#12311yescharacteristic
164C2×C4×C89#12311yescharacteristic
165C2×C4×C89#12411yescharacteristic
166C2×C4×C89C2×Q1611yescharacteristic
167C2×C4×C89#13511yescharacteristic
168C2×C4×C89#13511yescharacteristic
169C2×C4×C89#13511yescharacteristic
170C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C89#13711yescharacteristic
173C2×C4×C89#13711yescharacteristic
174C8×C89—42no—
175C8×C89—42no—
176C8×C89—81no—
177C22×C89—42no—
178C22×C89—42no—
179C22×C89—42no—
180C22×C89—81no—
181C22×C89—81no—
182C22×C89—81no—
183C22×C89—81no—
184C22×C89#39411yescharacteristic
185C22×C89#44911yescharacteristic
186C22×C89#44911yescharacteristic
187C22×C89#45111yescharacteristic
188C22×C89#45211yescharacteristic
189C22×C89#45311yescharacteristic
190C22×C89#45511yescharacteristic
191C4×C89—21no—
192C4×C89—21no—
193C4×C89—81no—
194C4×C89—81no—
195C4×C89—82no—
196C4×C89—81no—
197C4×C89—161no—
198C4×C89#46311yescharacteristic
199C4×C89#46411yescharacteristic
200C4×C89#46711yescharacteristic
201C4×C89#46811yescharacteristic
202C4×C89#48411yescharacteristic
203C4×C89#48511yescharacteristic
204C4×C89#48811yescharacteristic
205C4×C89#48911yescharacteristic
206#10413C8911yesmaximal, characteristic, direct product factor, Sylow
207C2×C89—82no—
208C2×C89#162411yescharacteristic
209C2×C89#163211yescharacteristic
210C2×C89#164411yescharacteristic
211C2×C89#164611yescharacteristic
212C2×C89#203611yescharacteristic
213C2×C89#203711yescharacteristic
214C2×C89#204211yescharacteristic
215#2563C2×C8911yescharacteristic
216#1956C2×C8911yescharacteristic, complemented
217#1947C2×C8911yescharacteristic, complemented
218#1802C2×C8911yescharacteristic
219C2×#333C2×C8911yescharacteristic, complemented
220C2×D4⋊C8C2×C8911yescharacteristic
221#1279C2×C8911yescharacteristic, complemented
222C89#1041311yescharacteristic, direct product factor, Sylow
223C2×C4⋊Q8C22×C8911yescharacteristic
224C2×C4×D4C22×C8911yescharacteristic
225C2×#107—21no—
226C2×C4⋊C8C22×C8911yescharacteristic
227C2×C4⋊C8C22×C8911yescharacteristic
228C2×#103—22no—
229C2×#102—21no—
230C2×C4×C8C22×C8911yescharacteristic
231#393—22no—
232#390—21no—
233#384C22×C8911yescharacteristic
234#382—21no—
235#380—21no—
236#380—21no—
237C4×C4⋊C4C22×C8911yescharacteristic
238#340—21no—
239#340—21no—
240#333—22no—
241D4⋊C8—22no—
242C22×Q8D4×C8912yes—
243C22×D4D4×C8911yescharacteristic
244C23×C4—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C8911yescharacteristic
262C2×C4⋊C4D4×C8911yescharacteristic
263C2×C4⋊C4D4×C8911yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C42—21no—
268C2×C42C23×C8911yescharacteristic
269#107—42no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C8912yes—
274#103—44no—
275#102—42no—
276C4×C8—21no—
277C4×C8—21no—
278#95—22no—
279#95—22no—
280#95—21no—
281C24—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4Q16×C8912yes—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C8911yescharacteristic
304C22×C4C2×D4×C8911yescharacteristic
305C22×C4C2×D4×C8911yescharacteristic
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—82no—
333C22⋊C4—82no—
334C42—41no—
335C42—41no—
336C42C2×D4×C8911yescharacteristic
337C42#41×C8911yescharacteristic
338C42#41×C8911yescharacteristic
339C42#41×C8911yescharacteristic
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#120×C8911yescharacteristic
348Q8—44no—
349Q8—82no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4#121×C8911yescharacteristic
376C2×C4#121×C8911yescharacteristic
377C2×C4#121×C8911yescharacteristic
378C2×C4#123×C8911yescharacteristic
379C2×C4#123×C8911yescharacteristic
380C2×C4#124×C8911yescharacteristic
381C2×C4C2×Q16×C8911yescharacteristic
382C2×C4#135×C8911yescharacteristic
383C2×C4#135×C8911yescharacteristic
384C2×C4#135×C8911yescharacteristic
385C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
386C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
387C2×C4#137×C8911yescharacteristic
388C2×C4#137×C8911yescharacteristic
389C8—42no—
390C8—42no—
391C8—81no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22#394×C8911yescharacteristic
400C22#449×C8911yescharacteristic
401C22#449×C8911yescharacteristic
402C22#451×C8911yescharacteristic
403C22#452×C8911yescharacteristic
404C22#453×C8911yescharacteristic
405C22#455×C8911yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—82no—
412C4—161no—
413C4#463×C8911yescharacteristic
414C4#464×C8911yescharacteristic
415C4#467×C8911yescharacteristic
416C4#468×C8911yescharacteristic
417C4#484×C8911yescharacteristic
418C4#485×C8911yescharacteristic
419C4#488×C8911yescharacteristic
420C4#489×C8911yescharacteristic
421C2—82no—
422C2C89×#162411yescharacteristic
423C2C89×#163211yescharacteristic
424C2C89×#164411yescharacteristic
425C2C89×#164611yescharacteristic
426C2C89×#203611yescharacteristic
427C2C89×#203711yescharacteristic
428C2C89×#204211yescharacteristic
subgroupG/H
center, socleC23×C89#120
commutator, Frattini, cosocleC2×C42C23×C89
prime radicalC22×D4×C89D4
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
2. C89×#1956C2semidirect
3. C89×#1947C2semidirect
5. C2×#333×C89C2semidirect
7. C89×#1279C2semidirect
206. #10413C89direct (N × H)
216. #1956C2×C89semidirect
217. #1947C2×C89semidirect
219. C2×#333C2×C89semidirect
221. #1279C2×C89semidirect
222. C89#10413direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#25632
C89×#19562
C89×#19472
C89×#18022
C2×#333×C892
C2×D4⋊C8×C892
C89×#12792
#1041389