Finite Group Databasebeta

← C89×#10431 #36388279

Subgroups — C89×#10431 #36388279

Order 22784.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2537C211yesmaximal, characteristic
2C89×#1834C211yesmaximal, characteristic, complemented
3C89×#1802C211yesmaximal, characteristic, complemented
4C89×#1802C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C89C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C89C211yesmaximal, characteristic, complemented
7C89×#1296C211yesmaximal, characteristic, complemented
8C2×#121×C89—21no—
9C2×#121×C89—21no—
10C2×C4×D4×C89C2211yescharacteristic
11C2×C4×D4×C89C2211yescharacteristic
12C2×C4⋊C8×C89C2211yescharacteristic
13C2×C4⋊C8×C89C2211yescharacteristic
14C2×#102×C89—21no—
15C2×#102×C89—21no—
16C2×C4×C8×C89C2211yescharacteristic
17#394×C89—22no—
18#384×C89C2211yescharacteristic
19#384×C89C2211yescharacteristic
20#380×C89—21no—
21#380×C89—21no—
22#340×C89—21no—
23#340×C89—21no—
24#340×C89—22no—
25D4⋊C8×C89—22no—
26D4⋊C8×C89—22no—
27C22×D4×C89—22no—
28C22×D4×C89D411yescharacteristic
29C22×D4×C89D411yescharacteristic
30C23×C4×C89—21no—
31C23×C4×C89—21no—
32C22×C8×C89—21no—
33C22×C8×C89—21no—
34C22×C8×C89—21no—
35#121×C89—42no—
36#121×C89—42no—
37#121×C89—42no—
38#121×C89—42no—
39C4×D4×C89—21no—
40C4×D4×C89—21no—
41C4×D4×C89—21no—
42C4×D4×C89—21no—
43C4×D4×C89—21no—
44C4×D4×C89—21no—
45C4×D4×C89—21no—
46C4×D4×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89—21no—
50C2×C4⋊C4×C89—21no—
51C2×C4⋊C4×C89—21no—
52C2×C4⋊C4×C89D411yescharacteristic
53C2×C4⋊C4×C89D411yescharacteristic
54C2×C4⋊C4×C89D412yes—
55C2×C22⋊C4×C89—22no—
56C2×C22⋊C4×C89—22no—
57C2×C22⋊C4×C89—21no—
58C2×C22⋊C4×C89—21no—
59C2×C42×C89C2311yescharacteristic
60C4⋊C8×C89—21no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89—21no—
63C4⋊C8×C89—21no—
64#102×C89—42no—
65#102×C89—42no—
66C4×C8×C89—21no—
67C4×C8×C89D412yescomplemented
68#95×C89—22no—
69C24×C89—21no—
70C24×C89—21no—
71C2×D4×C89—21no—
72C2×D4×C89—21no—
73C2×D4×C89—21no—
74C2×D4×C89—21no—
75C2×D4×C89—21no—
76C2×D4×C89—21no—
77C2×D4×C89—21no—
78C2×D4×C89—21no—
79C2×D4×C89—21no—
80C2×D4×C89—21no—
81C2×D4×C89—44no—
82C2×D4×C89—44no—
83C2×D4×C89—82no—
84C2×D4×C89D812yes—
85C2×D4×C89SD1612yes—
86C22×C4×C89—21no—
87C22×C4×C89—21no—
88C22×C4×C89—22no—
89C22×C4×C89—41no—
90C22×C4×C89—41no—
91C22×C4×C89—41no—
92C22×C4×C89—41no—
93C22×C4×C89—41no—
94C22×C4×C89—41no—
95C22×C4×C89—41no—
96C22×C4×C89—41no—
97C22×C4×C89—41no—
98C22×C4×C89—41no—
99C22×C4×C89—41no—
100C22×C4×C89—41no—
101C22×C4×C89—41no—
102C22×C4×C89C2×D411yescharacteristic
103C22×C4×C89C2×D411yescharacteristic
104C22×C4×C89C2×D411yescharacteristic
105C2×C8×C89—22no—
106C2×C8×C89—41no—
107C2×C8×C89—41no—
108C2×C8×C89—41no—
109C2×C8×C89—41no—
110C2×C8×C89—41no—
111C2×C8×C89—41no—
112C2×C8×C89—41no—
113C2×C8×C89—41no—
114C4⋊C4×C89—21no—
115C4⋊C4×C89—21no—
116C4⋊C4×C89—21no—
117C4⋊C4×C89—21no—
118C4⋊C4×C89—42no—
119C4⋊C4×C89—42no—
120C4⋊C4×C89—41no—
121C4⋊C4×C89—41no—
122C4⋊C4×C89—41no—
123C4⋊C4×C89—41no—
124C4⋊C4×C89—41no—
125C4⋊C4×C89—41no—
126C4⋊C4×C89—41no—
127C4⋊C4×C89—41no—
128C22⋊C4×C89—44no—
129C22⋊C4×C89—44no—
130C22⋊C4×C89—41no—
131C22⋊C4×C89—41no—
132C22⋊C4×C89—41no—
133C22⋊C4×C89—41no—
134C42×C89C2×D411yescharacteristic
135C42×C89#4111yescharacteristic
136C42×C89#4111yescharacteristic
137C42×C89#4111yescharacteristic
138C23×C89—22no—
139C23×C89—22no—
140C23×C89—41no—
141C23×C89—41no—
142C23×C89—41no—
143C23×C89—41no—
144C23×C89—41no—
145C23×C89—41no—
146C23×C89—41no—
147C23×C89—41no—
148C23×C89—41no—
149C23×C89—41no—
150C23×C89—41no—
151C23×C89—41no—
152C23×C89#12011yescharacteristic
153D4×C89—22no—
154D4×C89—22no—
155D4×C89—22no—
156D4×C89—22no—
157D4×C89—41no—
158D4×C89—41no—
159D4×C89—41no—
160D4×C89—41no—
161D4×C89—88no—
162C2×C4×C89—21no—
163C2×C4×C89—21no—
164C2×C4×C89—41no—
165C2×C4×C89—41no—
166C2×C4×C89—41no—
167C2×C4×C89—42no—
168C2×C4×C89—41no—
169C2×C4×C89—41no—
170C2×C4×C89—42no—
171C2×C4×C89—41no—
172C2×C4×C89—42no—
173C2×C4×C89—81no—
174C2×C4×C89—81no—
175C2×C4×C89—81no—
176C2×C4×C89—81no—
177C2×C4×C89—81no—
178C2×C4×C89—81no—
179C2×C4×C89—81no—
180C2×C4×C89—81no—
181C2×C4×C89—81no—
182C2×C4×C89—81no—
183C2×C4×C89—81no—
184C2×C4×C89#12111yescharacteristic
185C2×C4×C89#12111yescharacteristic
186C2×C4×C89#12111yescharacteristic
187C2×C4×C89#12311yescharacteristic
188C2×C4×C89#12311yescharacteristic
189C2×C4×C89#12411yescharacteristic
190C2×C4×C89C2×D811yescharacteristic
191C2×C4×C89C2×SD1611yescharacteristic
192C2×C4×C89#13511yescharacteristic
193C2×C4×C89#13511yescharacteristic
194C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C89#13711yescharacteristic
198C8×C89—42no—
199C8×C89—81no—
200C8×C89—81no—
201C22×C89—42no—
202C22×C89—42no—
203C22×C89—42no—
204C22×C89—42no—
205C22×C89—42no—
206C22×C89—42no—
207C22×C89—81no—
208C22×C89—81no—
209C22×C89—81no—
210C22×C89—81no—
211C22×C89—81no—
212C22×C89—81no—
213C22×C89—81no—
214C22×C89—81no—
215C22×C89#39411yescharacteristic
216C22×C89#44711yescharacteristic
217C22×C89#44911yescharacteristic
218C22×C89#45011yescharacteristic
219C22×C89#45211yescharacteristic
220C22×C89#45411yescharacteristic
221C22×C89#45511yescharacteristic
222C4×C89—21no—
223C4×C89—21no—
224C4×C89—82no—
225C4×C89—81no—
226C4×C89—81no—
227C4×C89—161no—
228C4×C89#46511yescharacteristic
229C4×C89#46611yescharacteristic
230C4×C89#46811yescharacteristic
231C4×C89#46911yescharacteristic
232C4×C89#48011yescharacteristic
233C4×C89#48111yescharacteristic
234C4×C89#48211yescharacteristic
235C4×C89#48211yescharacteristic
236#10431C8911yesmaximal, characteristic, direct product factor, Sylow
237C2×C89—82no—
238C2×C89—82no—
239C2×C89#162511yescharacteristic
240C2×C89#163511yescharacteristic
241C2×C89#163911yescharacteristic
242C2×C89#164611yescharacteristic
243C2×C89#203311yescharacteristic
244C2×C89#203411yescharacteristic
245C2×C89#204011yescharacteristic
246#2537C2×C8911yescharacteristic
247#1834C2×C8911yescharacteristic, complemented
248#1802C2×C8911yescharacteristic, complemented
249#1802C2×C8911yescharacteristic, complemented
250C2×D4⋊C8C2×C8911yescharacteristic, complemented
251C2×D4⋊C8C2×C8911yescharacteristic, complemented
252#1296C2×C8911yescharacteristic, complemented
253C89#1043111yescharacteristic, direct product factor, Sylow
254C2×#121—21no—
255C2×#121—21no—
256C2×C4×D4C22×C8911yescharacteristic
257C2×C4×D4C22×C8911yescharacteristic
258C2×C4⋊C8C22×C8911yescharacteristic
259C2×C4⋊C8C22×C8911yescharacteristic
260C2×#102—21no—
261C2×#102—21no—
262C2×C4×C8C22×C8911yescharacteristic
263#394—22no—
264#384C22×C8911yescharacteristic
265#384C22×C8911yescharacteristic
266#380—21no—
267#380—21no—
268#340—21no—
269#340—21no—
270#340—22no—
271D4⋊C8—22no—
272D4⋊C8—22no—
273C22×D4—22no—
274C22×D4D4×C8911yescharacteristic
275C22×D4D4×C8911yescharacteristic
276C23×C4—21no—
277C23×C4—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281#121—42no—
282#121—42no—
283#121—42no—
284#121—42no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4×C8911yescharacteristic
299C2×C4⋊C4D4×C8911yescharacteristic
300C2×C4⋊C4D4×C8912yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C42C23×C8911yescharacteristic
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310#102—42no—
311#102—42no—
312C4×C8—21no—
313C4×C8D4×C8912yescomplemented
314#95—22no—
315C24—21no—
316C24—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—44no—
328C2×D4—44no—
329C2×D4—82no—
330C2×D4D8×C8912yes—
331C2×D4SD16×C8912yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4C2×D4×C8911yescharacteristic
349C22×C4C2×D4×C8911yescharacteristic
350C22×C4C2×D4×C8911yescharacteristic
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C42C2×D4×C8911yescharacteristic
381C42#41×C8911yescharacteristic
382C42#41×C8911yescharacteristic
383C42#41×C8911yescharacteristic
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23#120×C8911yescharacteristic
399D4—22no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—88no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4#121×C8911yescharacteristic
431C2×C4#121×C8911yescharacteristic
432C2×C4#121×C8911yescharacteristic
433C2×C4#123×C8911yescharacteristic
434C2×C4#123×C8911yescharacteristic
435C2×C4#124×C8911yescharacteristic
436C2×C4C2×D8×C8911yescharacteristic
437C2×C4C2×SD16×C8911yescharacteristic
438C2×C4#135×C8911yescharacteristic
439C2×C4#135×C8911yescharacteristic
440C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
441C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
442C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
443C2×C4#137×C8911yescharacteristic
444C8—42no—
445C8—81no—
446C8—81no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#394×C8911yescharacteristic
462C22#447×C8911yescharacteristic
463C22#449×C8911yescharacteristic
464C22#450×C8911yescharacteristic
465C22#452×C8911yescharacteristic
466C22#454×C8911yescharacteristic
467C22#455×C8911yescharacteristic
468C4—21no—
469C4—21no—
470C4—82no—
471C4—81no—
472C4—81no—
473C4—161no—
474C4#465×C8911yescharacteristic
475C4#466×C8911yescharacteristic
476C4#468×C8911yescharacteristic
477C4#469×C8911yescharacteristic
478C4#480×C8911yescharacteristic
479C4#481×C8911yescharacteristic
480C4#482×C8911yescharacteristic
481C4#482×C8911yescharacteristic
482C2—82no—
483C2—82no—
484C2C89×#162511yescharacteristic
485C2C89×#163511yescharacteristic
486C2C89×#163911yescharacteristic
487C2C89×#164611yescharacteristic
488C2C89×#203311yescharacteristic
489C2C89×#203411yescharacteristic
490C2C89×#204011yescharacteristic
subgroupG/H
center, socleC23×C89#120
commutator, Frattini, cosocleC2×C42C23×C89
prime radicalC89×#2537C2
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×#1834C2semidirect
3. C89×#1802C2semidirect
4. C89×#1802C2semidirect
5. C2×D4⋊C8×C89C2semidirect
6. C2×D4⋊C8×C89C2semidirect
7. C89×#1296C2semidirect
67. C4×C8×C89D4semidirect
236. #10431C89direct (N × H)
247. #1834C2×C89semidirect
248. #1802C2×C89semidirect
249. #1802C2×C89semidirect
250. C2×D4⋊C8C2×C89semidirect
251. C2×D4⋊C8C2×C89semidirect
252. #1296C2×C89semidirect
253. C89#10431direct (N × H)
313. C4×C8D4×C89semidirect

Maximal subgroups

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

subgroupindex
C89×#25372
C89×#18342
C89×#18022
C2×D4⋊C8×C892
C89×#12962
#1043189