Finite Group Databasebeta

← C89×#10435 #36388283

Subgroups — C89×#10435 #36388283

Order 22784.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2538C211yesmaximal, characteristic
2C89×#1844C211yesmaximal, characteristic, complemented
3C89×#1803C211yesmaximal, characteristic, complemented
4C89×#1802C211yesmaximal, characteristic
5C2×Q8⋊C8×C89C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C89C211yesmaximal, characteristic
7C89×#1296C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C89—21no—
9C2×C4×Q8×C89C2211yescharacteristic
10C2×C4×D4×C89C2211yescharacteristic
11C2×#106×C89—22no—
12C2×C4⋊C8×C89C2211yescharacteristic
13C2×C4⋊C8×C89C2211yescharacteristic
14C2×#103×C89—21no—
15C2×#102×C89—21no—
16C2×C4×C8×C89C2211yescharacteristic
17#396×C89—22no—
18#390×C89—21no—
19#389×C89—21no—
20#384×C89C2211yescharacteristic
21#384×C89C2211yescharacteristic
22#380×C89—21no—
23#340×C89—21no—
24#340×C89—21no—
25Q8⋊C8×C89—22no—
26D4⋊C8×C89—22no—
27C22×Q8×C89D411yescharacteristic
28C22×D4×C89D411yescharacteristic
29C23×C4×C89—21no—
30C22×C8×C89—21no—
31C22×C8×C89—21no—
32C22×C8×C89—21no—
33C22⋊Q8×C89—42no—
34C22⋊Q8×C89—42no—
35C4×Q8×C89—21no—
36C4×Q8×C89—21no—
37C4×Q8×C89—21no—
38C4×Q8×C89—21no—
39C4×D4×C89—21no—
40C4×D4×C89—21no—
41C4×D4×C89—21no—
42C4×D4×C89—21no—
43C2×C4⋊C4×C89—22no—
44C2×C4⋊C4×C89—21no—
45C2×C4⋊C4×C89—21no—
46C2×C4⋊C4×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89—21no—
50C2×C4⋊C4×C89D411yescharacteristic
51C2×C4⋊C4×C89D411yescharacteristic
52C2×C4⋊C4×C89D412yes—
53C2×C22⋊C4×C89—22no—
54C2×C22⋊C4×C89—21no—
55C2×C22⋊C4×C89—22no—
56C2×C42×C89—21no—
57C2×C42×C89C2311yescharacteristic
58#106×C89—44no—
59C4⋊C8×C89—21no—
60C4⋊C8×C89—21no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89—21no—
63#103×C89—42no—
64#102×C89—42no—
65C4×C8×C89—21no—
66C4×C8×C89D412yes—
67#95×C89—22no—
68C24×C89—21no—
69C2×Q8×C89—21no—
70C2×Q8×C89—21no—
71C2×Q8×C89—21no—
72C2×Q8×C89—21no—
73C2×Q8×C89—21no—
74C2×Q8×C89SD1612yes—
75C2×D4×C89—21no—
76C2×D4×C89—21no—
77C2×D4×C89—21no—
78C2×D4×C89—21no—
79C2×D4×C89—21no—
80C2×D4×C89SD1612yes—
81C22×C4×C89—21no—
82C22×C4×C89—21no—
83C22×C4×C89—21no—
84C22×C4×C89—22no—
85C22×C4×C89—41no—
86C22×C4×C89—41no—
87C22×C4×C89—41no—
88C22×C4×C89—41no—
89C22×C4×C89—41no—
90C22×C4×C89—41no—
91C22×C4×C89—41no—
92C22×C4×C89C2×D411yescharacteristic
93C22×C4×C89C2×D411yescharacteristic
94C22×C4×C89C2×D411yescharacteristic
95C2×C8×C89—22no—
96C2×C8×C89—22no—
97C2×C8×C89—22no—
98C2×C8×C89—41no—
99C2×C8×C89—41no—
100C2×C8×C89—41no—
101C2×C8×C89—41no—
102C2×C8×C89—41no—
103C2×C8×C89—41no—
104C4⋊C4×C89—21no—
105C4⋊C4×C89—21no—
106C4⋊C4×C89—21no—
107C4⋊C4×C89—21no—
108C4⋊C4×C89—44no—
109C4⋊C4×C89—42no—
110C4⋊C4×C89—42no—
111C4⋊C4×C89—41no—
112C4⋊C4×C89—41no—
113C4⋊C4×C89—41no—
114C4⋊C4×C89—41no—
115C4⋊C4×C89—41no—
116C4⋊C4×C89—41no—
117C4⋊C4×C89—41no—
118C4⋊C4×C89—41no—
119C4⋊C4×C89—41no—
120C4⋊C4×C89—41no—
121C22⋊C4×C89—44no—
122C22⋊C4×C89—41no—
123C22⋊C4×C89—41no—
124C22⋊C4×C89—82no—
125C42×C89—41no—
126C42×C89—41no—
127C42×C89C2×D411yescharacteristic
128C42×C89#4111yescharacteristic
129C42×C89#4111yescharacteristic
130C42×C89#4111yescharacteristic
131C23×C89—22no—
132C23×C89—41no—
133C23×C89—41no—
134C23×C89—41no—
135C23×C89—41no—
136C23×C89—41no—
137C23×C89—41no—
138C23×C89#12011yescharacteristic
139Q8×C89—22no—
140Q8×C89—22no—
141Q8×C89—41no—
142Q8×C89—41no—
143D4×C89—22no—
144D4×C89—22no—
145D4×C89—41no—
146D4×C89—41no—
147C2×C4×C89—21no—
148C2×C4×C89—21no—
149C2×C4×C89—22no—
150C2×C4×C89—41no—
151C2×C4×C89—41no—
152C2×C4×C89—41no—
153C2×C4×C89—41no—
154C2×C4×C89—41no—
155C2×C4×C89—42no—
156C2×C4×C89—41no—
157C2×C4×C89—42no—
158C2×C4×C89—41no—
159C2×C4×C89—42no—
160C2×C4×C89—41no—
161C2×C4×C89—81no—
162C2×C4×C89—81no—
163C2×C4×C89—81no—
164C2×C4×C89—81no—
165C2×C4×C89—81no—
166C2×C4×C89—81no—
167C2×C4×C89—81no—
168C2×C4×C89#12111yescharacteristic
169C2×C4×C89#12111yescharacteristic
170C2×C4×C89#12111yescharacteristic
171C2×C4×C89#12311yescharacteristic
172C2×C4×C89#12311yescharacteristic
173C2×C4×C89#12411yescharacteristic
174C2×C4×C89C2×SD1611yescharacteristic
175C2×C4×C89C2×SD1611yescharacteristic
176C2×C4×C89#13511yescharacteristic
177C2×C4×C89#13511yescharacteristic
178C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C89#13711yescharacteristic
181C2×C4×C89#13711yescharacteristic
182C8×C89—24no—
183C8×C89—81no—
184C8×C89—81no—
185C22×C89—42no—
186C22×C89—42no—
187C22×C89—42no—
188C22×C89—81no—
189C22×C89—81no—
190C22×C89—81no—
191C22×C89—81no—
192C22×C89#39411yescharacteristic
193C22×C89#44811yescharacteristic
194C22×C89#44911yescharacteristic
195C22×C89#45011yescharacteristic
196C22×C89#45211yescharacteristic
197C22×C89#45311yescharacteristic
198C22×C89#45611yescharacteristic
199C4×C89—21no—
200C4×C89—21no—
201C4×C89—42no—
202C4×C89—82no—
203C4×C89—81no—
204C4×C89—81no—
205C4×C89—161no—
206C4×C89#46511yescharacteristic
207C4×C89#46511yescharacteristic
208C4×C89#46911yescharacteristic
209C4×C89#47011yescharacteristic
210C4×C89#48111yescharacteristic
211C4×C89#48211yescharacteristic
212C4×C89#48311yescharacteristic
213C4×C89#48511yescharacteristic
214#10435C8911yesmaximal, characteristic, direct product factor, Sylow
215C2×C89—82no—
216C2×C89#162211yescharacteristic
217C2×C89#163111yescharacteristic
218C2×C89#165111yescharacteristic
219C2×C89#165211yescharacteristic
220C2×C89#203411yescharacteristic
221C2×C89#203511yescharacteristic
222C2×C89#203911yescharacteristic
223#2538C2×C8911yescharacteristic
224#1844C2×C8911yescharacteristic, complemented
225#1803C2×C8911yescharacteristic, complemented
226#1802C2×C8911yescharacteristic
227C2×Q8⋊C8C2×C8911yescharacteristic, complemented
228C2×D4⋊C8C2×C8911yescharacteristic
229#1296C2×C8911yescharacteristic, complemented
230C89#1043511yescharacteristic, direct product factor, Sylow
231C2×C22⋊Q8—21no—
232C2×C4×Q8C22×C8911yescharacteristic
233C2×C4×D4C22×C8911yescharacteristic
234C2×#106—22no—
235C2×C4⋊C8C22×C8911yescharacteristic
236C2×C4⋊C8C22×C8911yescharacteristic
237C2×#103—21no—
238C2×#102—21no—
239C2×C4×C8C22×C8911yescharacteristic
240#396—22no—
241#390—21no—
242#389—21no—
243#384C22×C8911yescharacteristic
244#384C22×C8911yescharacteristic
245#380—21no—
246#340—21no—
247#340—21no—
248Q8⋊C8—22no—
249D4⋊C8—22no—
250C22×Q8D4×C8911yescharacteristic
251C22×D4D4×C8911yescharacteristic
252C23×C4—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22⋊Q8—42no—
257C22⋊Q8—42no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C8911yescharacteristic
274C2×C4⋊C4D4×C8911yescharacteristic
275C2×C4⋊C4D4×C8912yes—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C42—21no—
280C2×C42C23×C8911yescharacteristic
281#106—44no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286#103—42no—
287#102—42no—
288C4×C8—21no—
289C4×C8D4×C8912yes—
290#95—22no—
291C24—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8SD16×C8912yes—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4SD16×C8912yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4C2×D4×C8911yescharacteristic
316C22×C4C2×D4×C8911yescharacteristic
317C22×C4C2×D4×C8911yescharacteristic
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—44no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—82no—
348C42—41no—
349C42—41no—
350C42C2×D4×C8911yescharacteristic
351C42#41×C8911yescharacteristic
352C42#41×C8911yescharacteristic
353C42#41×C8911yescharacteristic
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#120×C8911yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4#121×C8911yescharacteristic
392C2×C4#121×C8911yescharacteristic
393C2×C4#121×C8911yescharacteristic
394C2×C4#123×C8911yescharacteristic
395C2×C4#123×C8911yescharacteristic
396C2×C4#124×C8911yescharacteristic
397C2×C4C2×SD16×C8911yescharacteristic
398C2×C4C2×SD16×C8911yescharacteristic
399C2×C4#135×C8911yescharacteristic
400C2×C4#135×C8911yescharacteristic
401C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
402C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
403C2×C4#137×C8911yescharacteristic
404C2×C4#137×C8911yescharacteristic
405C8—24no—
406C8—81no—
407C8—81no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22#394×C8911yescharacteristic
416C22#448×C8911yescharacteristic
417C22#449×C8911yescharacteristic
418C22#450×C8911yescharacteristic
419C22#452×C8911yescharacteristic
420C22#453×C8911yescharacteristic
421C22#456×C8911yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—82no—
427C4—81no—
428C4—161no—
429C4#465×C8911yescharacteristic
430C4#465×C8911yescharacteristic
431C4#469×C8911yescharacteristic
432C4#470×C8911yescharacteristic
433C4#481×C8911yescharacteristic
434C4#482×C8911yescharacteristic
435C4#483×C8911yescharacteristic
436C4#485×C8911yescharacteristic
437C2—82no—
438C2C89×#162211yescharacteristic
439C2C89×#163111yescharacteristic
440C2C89×#165111yescharacteristic
441C2C89×#165211yescharacteristic
442C2C89×#203411yescharacteristic
443C2C89×#203511yescharacteristic
444C2C89×#203911yescharacteristic
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×#1844C2semidirect
3. C89×#1803C2semidirect
5. C2×Q8⋊C8×C89C2semidirect
7. C89×#1296C2semidirect
214. #10435C89direct (N × H)
224. #1844C2×C89semidirect
225. #1803C2×C89semidirect
227. C2×Q8⋊C8C2×C89semidirect
229. #1296C2×C89semidirect
230. C89#10435direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#25382
C89×#18442
C89×#18032
C89×#18022
C2×Q8⋊C8×C892
C2×D4⋊C8×C892
C89×#12962
#1043589