Finite Group Databasebeta

← C89×#32730 #36410578

Subgroups — C89×#32730 #36410578

Order 22784.

824 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2624C211yesmaximal, characteristic, complemented
2C89×#2619C211yesmaximal, characteristic, complemented
3C89×#2101C211yesmaximal, characteristic, complemented
4C89×#2092C211yesmaximal, characteristic, complemented
5C89×#2067C211yesmaximal, characteristic, complemented
6C89×#2065C211yesmaximal, characteristic, complemented
7C89×#2054C211yesmaximal, characteristic, complemented
8C89×#2054C211yesmaximal, characteristic, complemented
9C89×#2041C211yesmaximal, characteristic, complemented
10C89×#2034C211yesmaximal, characteristic, complemented
11C89×#2033C211yesmaximal, characteristic, complemented
12C89×#2011C211yesmaximal, characteristic, complemented
13C89×#1999C211yesmaximal, characteristic, complemented
14C89×#1999C211yesmaximal, characteristic, complemented
15C89×#1798C211yesmaximal, characteristic, complemented
16C22×D8×C89C2211yescharacteristic
17C22×D8×C89C2211yescharacteristic
18C2×#127×C89C2211yescharacteristic
19C2×#121×C89C2211yescharacteristic
20C2×#121×C89C2211yescharacteristic
21C2×#121×C89C2211yescharacteristic
22C2×#117×C89C2211yescharacteristic
23C2×#107×C89C2211yescharacteristic
24C2×#106×C89C2211yescharacteristic
25C2×C4⋊C8×C89C2211yescharacteristic
26C2×C4⋊C8×C89C2211yescharacteristic
27C2×#102×C89C2211yescharacteristic
28C2×#102×C89C2211yescharacteristic
29C2×#102×C89C2211yescharacteristic
30C2×#102×C89C2211yescharacteristic
31C2×#102×C89C2211yescharacteristic
32C2×#102×C89C2211yescharacteristic
33C2×#102×C89C2211yescharacteristic
34C2×#102×C89C2211yescharacteristic
35C2×C22⋊C8×C89C2211yescharacteristic
36C2×C22⋊C8×C89C2211yescharacteristic
37#399×C89—21no—
38#397×C89—21no—
39#394×C89—21no—
40#394×C89—21no—
41#394×C89—21no—
42#394×C89—21no—
43#392×C89—21no—
44#392×C89—21no—
45#390×C89C2211yescharacteristic
46#390×C89C2211yescharacteristic
47#390×C89C2211yescharacteristic
48#390×C89C2211yescharacteristic
49#389×C89C2211yescharacteristic
50#389×C89C2211yescharacteristic
51#382×C89C2211yescharacteristic
52#380×C89C2211yescharacteristic
53#340×C89C2211yescharacteristic
54#340×C89C2211yescharacteristic
55#340×C89C2211yescharacteristic
56#340×C89C2211yescharacteristic
57#336×C89C2211yescharacteristic
58#336×C89C2211yescharacteristic
59C22×D4×C89—21no—
60C22×D4×C89—21no—
61C22×D4×C89—21no—
62C22×D4×C89—21no—
63C22×D4×C89—21no—
64C22×D4×C89C2311yescharacteristic
65C22×D4×C89C2311yescharacteristic
66C22×D4×C89C2311yescharacteristic
67C23×C4×C89C2311yescharacteristic
68C2×D8×C89—41no—
69C2×D8×C89—41no—
70C2×D8×C89—41no—
71C2×D8×C89—41no—
72C2×D8×C89—41no—
73C2×D8×C89—41no—
74C22×C8×C89C2311yescharacteristic
75C22×C8×C89C2311yescharacteristic
76C22×C8×C89C2311yescharacteristic
77C22×C8×C89C2311yescharacteristic
78#127×C89—41no—
79#127×C89—41no—
80#121×C89—41no—
81#121×C89—41no—
82#121×C89—41no—
83#121×C89—41no—
84#121×C89—41no—
85#121×C89—41no—
86#117×C89—41no—
87#117×C89—41no—
88C2×C4⋊C4×C89—21no—
89C2×C4⋊C4×C89—21no—
90C2×C4⋊C4×C89D411yescharacteristic
91C2×C4⋊C4×C89D411yescharacteristic
92C2×C4⋊C4×C89C2311yescharacteristic
93C2×C4⋊C4×C89C2311yescharacteristic
94C2×C4⋊C4×C89C2311yescharacteristic
95C2×C4⋊C4×C89C2311yescharacteristic
96C2×C4⋊C4×C89C2311yescharacteristic
97C2×C22⋊C4×C89—21no—
98C2×C22⋊C4×C89—21no—
99C2×C22⋊C4×C89—21no—
100C2×C22⋊C4×C89—21no—
101C2×C22⋊C4×C89—21no—
102C2×C22⋊C4×C89—21no—
103C2×C22⋊C4×C89—21no—
104C2×C22⋊C4×C89—21no—
105C2×C22⋊C4×C89—21no—
106C2×C22⋊C4×C89—21no—
107C2×C22⋊C4×C89—21no—
108C2×C22⋊C4×C89—21no—
109C2×C22⋊C4×C89D411yescharacteristic
110C2×C22⋊C4×C89D411yescharacteristic
111C2×C42×C89C2311yescharacteristic
112C2×C42×C89C2311yescharacteristic
113#107×C89—41no—
114#106×C89—41no—
115C4⋊C8×C89—41no—
116C4⋊C8×C89—41no—
117#102×C89—41no—
118#102×C89—41no—
119#102×C89—41no—
120#102×C89—41no—
121#102×C89—41no—
122#102×C89—41no—
123#102×C89—41no—
124#102×C89—41no—
125C22⋊C8×C89—41no—
126C22⋊C8×C89—41no—
127#95×C89—21no—
128#95×C89—21no—
129#95×C89—21no—
130#95×C89—21no—
131#95×C89—21no—
132C24×C89—21no—
133C24×C89—21no—
134C24×C89—21no—
135C24×C89C2×D411yescharacteristic
136C2×D4×C89—21no—
137C2×D4×C89—21no—
138C2×D4×C89—21no—
139C2×D4×C89—21no—
140C2×D4×C89—21no—
141C2×D4×C89—21no—
142C2×D4×C89—21no—
143C2×D4×C89—21no—
144C2×D4×C89—21no—
145C2×D4×C89—21no—
146C2×D4×C89—21no—
147C2×D4×C89—21no—
148C2×D4×C89—21no—
149C2×D4×C89—21no—
150C2×D4×C89—21no—
151C2×D4×C89—21no—
152C2×D4×C89—21no—
153C2×D4×C89—21no—
154C2×D4×C89—42no—
155C2×D4×C89—42no—
156C2×D4×C89—42no—
157C2×D4×C89—42no—
158C2×D4×C89—42no—
159C2×D4×C89—81no—
160C2×D4×C89—81no—
161C2×D4×C89—81no—
162C2×D4×C89—81no—
163C2×D4×C89—81no—
164C2×D4×C89—81no—
165C2×D4×C89—81no—
166C2×D4×C89—81no—
167C2×D4×C89—81no—
168C2×D4×C89—81no—
169C22×C4×C89—21no—
170C22×C4×C89—21no—
171C22×C4×C89—21no—
172C22×C4×C89—21no—
173C22×C4×C89—21no—
174C22×C4×C89—21no—
175C22×C4×C89—21no—
176C22×C4×C89—21no—
177C22×C4×C89—21no—
178C22×C4×C89—21no—
179C22×C4×C89—21no—
180C22×C4×C89C2×D411yescharacteristic
181C22×C4×C89C2×D411yescharacteristic
182C22×C4×C89C2×D411yescharacteristic
183C22×C4×C89C2×D411yescharacteristic
184C22×C4×C89C2×D411yescharacteristic
185C22×C4×C89C2411yescharacteristic
186D8×C89—44no—
187D8×C89—44no—
188C2×C8×C89—21no—
189C2×C8×C89—21no—
190C2×C8×C89—21no—
191C2×C8×C89—21no—
192C2×C8×C89—21no—
193C2×C8×C89—21no—
194C2×C8×C89—21no—
195C2×C8×C89—21no—
196C2×C8×C89—21no—
197C2×C8×C89—21no—
198C2×C8×C89—21no—
199C2×C8×C89—21no—
200C4⋊C4×C89—21no—
201C4⋊C4×C89—21no—
202C4⋊C4×C89—21no—
203C4⋊C4×C89—21no—
204C4⋊C4×C89—21no—
205C4⋊C4×C89—21no—
206C4⋊C4×C89—21no—
207C4⋊C4×C89—21no—
208C4⋊C4×C89—21no—
209C4⋊C4×C89—21no—
210C4⋊C4×C89—41no—
211C4⋊C4×C89—41no—
212C4⋊C4×C89—81no—
213C4⋊C4×C89—81no—
214C22⋊C4×C89—41no—
215C22⋊C4×C89—41no—
216C22⋊C4×C89—42no—
217C22⋊C4×C89—42no—
218C22⋊C4×C89—42no—
219C22⋊C4×C89—81no—
220C22⋊C4×C89—81no—
221C22⋊C4×C89—81no—
222C22⋊C4×C89—81no—
223C22⋊C4×C89—81no—
224C22⋊C4×C89—81no—
225C22⋊C4×C89—81no—
226C22⋊C4×C89—81no—
227C22⋊C4×C89—81no—
228C42×C89—21no—
229C42×C89—21no—
230C42×C89—21no—
231C42×C89—21no—
232C23×C89—21no—
233C23×C89—21no—
234C23×C89—21no—
235C23×C89—21no—
236C23×C89—21no—
237C23×C89—21no—
238C23×C89—21no—
239C23×C89—41no—
240C23×C89—41no—
241C23×C89—41no—
242C23×C89—41no—
243C23×C89—41no—
244C23×C89—41no—
245C23×C89—41no—
246C23×C89—41no—
247C23×C89—41no—
248C23×C89—41no—
249C23×C89—41no—
250C23×C89—41no—
251C23×C89—41no—
252C23×C89—41no—
253C23×C89—41no—
254C23×C89—41no—
255C23×C89—41no—
256C23×C89—41no—
257C23×C89—41no—
258C23×C89—41no—
259C23×C89—41no—
260C23×C89C22×D411yescharacteristic
261D4×C89—41no—
262D4×C89—41no—
263D4×C89—41no—
264D4×C89—41no—
265D4×C89—41no—
266D4×C89—41no—
267D4×C89—41no—
268D4×C89—41no—
269D4×C89—41no—
270D4×C89—41no—
271D4×C89—41no—
272D4×C89—41no—
273D4×C89—84no—
274D4×C89—84no—
275D4×C89—84no—
276D4×C89—84no—
277D4×C89—84no—
278C2×C4×C89—21no—
279C2×C4×C89—21no—
280C2×C4×C89—21no—
281C2×C4×C89—21no—
282C2×C4×C89—21no—
283C2×C4×C89—21no—
284C2×C4×C89—21no—
285C2×C4×C89—21no—
286C2×C4×C89—21no—
287C2×C4×C89—21no—
288C2×C4×C89—21no—
289C2×C4×C89—21no—
290C2×C4×C89—21no—
291C2×C4×C89—21no—
292C2×C4×C89—21no—
293C2×C4×C89—41no—
294C2×C4×C89—41no—
295C2×C4×C89—41no—
296C2×C4×C89—41no—
297C2×C4×C89—41no—
298C2×C4×C89—41no—
299C2×C4×C89—41no—
300C2×C4×C89—41no—
301C2×C4×C89—41no—
302C2×C4×C89—41no—
303C2×C4×C89—41no—
304C2×C4×C89—41no—
305C2×C4×C89—41no—
306C2×C4×C89—41no—
307C2×C4×C89—41no—
308C2×C4×C89—41no—
309C2×C4×C89—41no—
310C2×C4×C89—41no—
311C2×C4×C89—41no—
312C2×C4×C89H(5,𝔽2)11yescharacteristic
313C2×C4×C89H(5,𝔽2)11yescharacteristic
314C2×C4×C89H(5,𝔽2)11yescharacteristic
315C2×C4×C89H(5,𝔽2)11yescharacteristic
316C2×C4×C89H(5,𝔽2)11yescharacteristic
317C2×C4×C892−1+411yescharacteristic
318C8×C89—41no—
319C8×C89—41no—
320C8×C89—41no—
321C8×C89—41no—
322C22×C89—41no—
323C22×C89—41no—
324C22×C89—41no—
325C22×C89—41no—
326C22×C89—41no—
327C22×C89—41no—
328C22×C89—41no—
329C22×C89—81no—
330C22×C89—81no—
331C22×C89—81no—
332C22×C89—81no—
333C22×C89—81no—
334C22×C89—81no—
335C22×C89—81no—
336C22×C89—81no—
337C22×C89—81no—
338C22×C89—81no—
339C22×C89—81no—
340C22×C89—81no—
341C22×C89—81no—
342C22×C89—81no—
343C22×C89—81no—
344C22×C89—81no—
345C22×C89—81no—
346C22×C89—81no—
347C22×C89—81no—
348C22×C89—81no—
349C22×C89—81no—
350C22×C89#53411yescharacteristic
351C22×C89#53511yescharacteristic
352C22×C89#53711yescharacteristic
353C22×C89#57611yescharacteristic
354C22×C89#57611yescharacteristic
355C22×C89#57611yescharacteristic
356C22×C89#57711yescharacteristic
357C4×C89—41no—
358C4×C89—41no—
359C4×C89—41no—
360C4×C89—41no—
361C4×C89—41no—
362C4×C89—81no—
363C4×C89—81no—
364C4×C89—81no—
365C4×C89—81no—
366C4×C89—81no—
367C4×C89#56011yescharacteristic
368C4×C89#56011yescharacteristic
369C4×C89#56211yescharacteristic
370C4×C89#56211yescharacteristic
371#32730C8911yesmaximal, characteristic, direct product factor, Sylow
372C2×C89—81no—
373C2×C89—161no—
374C2×C89—161no—
375C2×C89—161no—
376C2×C89#281311yescharacteristic
377C2×C89#319811yescharacteristic
378C2×C89#319911yescharacteristic
379C2×C89#322011yescharacteristic
380C2×C89#322411yescharacteristic
381C2×C89#325711yescharacteristic
382C2×C89#325911yescharacteristic
383#2624C2×C8911yescharacteristic, complemented
384#2619C2×C8911yescharacteristic, complemented
385#2101C2×C8911yescharacteristic, complemented
386#2092C2×C8911yescharacteristic, complemented
387#2067C2×C8911yescharacteristic, complemented
388#2065C2×C8911yescharacteristic, complemented
389#2054C2×C8911yescharacteristic, complemented
390#2054C2×C8911yescharacteristic, complemented
391#2041C2×C8911yescharacteristic, complemented
392#2034C2×C8911yescharacteristic, complemented
393#2033C2×C8911yescharacteristic, complemented
394#2011C2×C8911yescharacteristic, complemented
395#1999C2×C8911yescharacteristic, complemented
396#1999C2×C8911yescharacteristic, complemented
397#1798C2×C8911yescharacteristic, complemented
398C89#3273011yescharacteristic, direct product factor, Sylow
399C22×D8C22×C8911yescharacteristic
400C22×D8C22×C8911yescharacteristic
401C2×#127C22×C8911yescharacteristic
402C2×#121C22×C8911yescharacteristic
403C2×#121C22×C8911yescharacteristic
404C2×#121C22×C8911yescharacteristic
405C2×#117C22×C8911yescharacteristic
406C2×#107C22×C8911yescharacteristic
407C2×#106C22×C8911yescharacteristic
408C2×C4⋊C8C22×C8911yescharacteristic
409C2×C4⋊C8C22×C8911yescharacteristic
410C2×#102C22×C8911yescharacteristic
411C2×#102C22×C8911yescharacteristic
412C2×#102C22×C8911yescharacteristic
413C2×#102C22×C8911yescharacteristic
414C2×#102C22×C8911yescharacteristic
415C2×#102C22×C8911yescharacteristic
416C2×#102C22×C8911yescharacteristic
417C2×#102C22×C8911yescharacteristic
418C2×C22⋊C8C22×C8911yescharacteristic
419C2×C22⋊C8C22×C8911yescharacteristic
420#399—21no—
421#397—21no—
422#394—21no—
423#394—21no—
424#394—21no—
425#394—21no—
426#392—21no—
427#392—21no—
428#390C22×C8911yescharacteristic
429#390C22×C8911yescharacteristic
430#390C22×C8911yescharacteristic
431#390C22×C8911yescharacteristic
432#389C22×C8911yescharacteristic
433#389C22×C8911yescharacteristic
434#382C22×C8911yescharacteristic
435#380C22×C8911yescharacteristic
436#340C22×C8911yescharacteristic
437#340C22×C8911yescharacteristic
438#340C22×C8911yescharacteristic
439#340C22×C8911yescharacteristic
440#336C22×C8911yescharacteristic
441#336C22×C8911yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C23×C8911yescharacteristic
448C22×D4C23×C8911yescharacteristic
449C22×D4C23×C8911yescharacteristic
450C23×C4C23×C8911yescharacteristic
451C2×D8—41no—
452C2×D8—41no—
453C2×D8—41no—
454C2×D8—41no—
455C2×D8—41no—
456C2×D8—41no—
457C22×C8C23×C8911yescharacteristic
458C22×C8C23×C8911yescharacteristic
459C22×C8C23×C8911yescharacteristic
460C22×C8C23×C8911yescharacteristic
461#127—41no—
462#127—41no—
463#121—41no—
464#121—41no—
465#121—41no—
466#121—41no—
467#121—41no—
468#121—41no—
469#117—41no—
470#117—41no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4D4×C8911yescharacteristic
474C2×C4⋊C4D4×C8911yescharacteristic
475C2×C4⋊C4C23×C8911yescharacteristic
476C2×C4⋊C4C23×C8911yescharacteristic
477C2×C4⋊C4C23×C8911yescharacteristic
478C2×C4⋊C4C23×C8911yescharacteristic
479C2×C4⋊C4C23×C8911yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C8911yescharacteristic
493C2×C22⋊C4D4×C8911yescharacteristic
494C2×C42C23×C8911yescharacteristic
495C2×C42C23×C8911yescharacteristic
496#107—41no—
497#106—41no—
498C4⋊C8—41no—
499C4⋊C8—41no—
500#102—41no—
501#102—41no—
502#102—41no—
503#102—41no—
504#102—41no—
505#102—41no—
506#102—41no—
507#102—41no—
508C22⋊C8—41no—
509C22⋊C8—41no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C2×D4×C8911yescharacteristic
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4C2×D4×C8911yescharacteristic
564C22×C4C2×D4×C8911yescharacteristic
565C22×C4C2×D4×C8911yescharacteristic
566C22×C4C2×D4×C8911yescharacteristic
567C22×C4C2×D4×C8911yescharacteristic
568C22×C4C24×C8911yescharacteristic
569D8—44no—
570D8—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C22×D4×C8911yescharacteristic
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658D4—84no—
659D4—84no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4H(5,𝔽2)×C8911yescharacteristic
696C2×C4H(5,𝔽2)×C8911yescharacteristic
697C2×C4H(5,𝔽2)×C8911yescharacteristic
698C2×C4H(5,𝔽2)×C8911yescharacteristic
699C2×C4H(5,𝔽2)×C8911yescharacteristic
700C2×C42−1+4×C8911yescharacteristic
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22#534×C8911yescharacteristic
734C22#535×C8911yescharacteristic
735C22#537×C8911yescharacteristic
736C22#576×C8911yescharacteristic
737C22#576×C8911yescharacteristic
738C22#576×C8911yescharacteristic
739C22#577×C8911yescharacteristic
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4#560×C8911yescharacteristic
751C4#560×C8911yescharacteristic
752C4#562×C8911yescharacteristic
753C4#562×C8911yescharacteristic
754C2—81no—
755C2—161no—
756C2—161no—
757C2—161no—
758C2C89×#281311yescharacteristic
759C2C89×#319811yescharacteristic
760C2C89×#319911yescharacteristic
761C2C89×#322011yescharacteristic
762C2C89×#322411yescharacteristic
763C2C89×#325711yescharacteristic
764C2C89×#325911yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C2×#117×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C89×#2624C2semidirect
2. C89×#2619C2semidirect
3. C89×#2101C2semidirect
4. C89×#2092C2semidirect
5. C89×#2067C2semidirect
6. C89×#2065C2semidirect
7. C89×#2054C2semidirect
8. C89×#2054C2semidirect
9. C89×#2041C2semidirect
10. C89×#2034C2semidirect
11. C89×#2033C2semidirect
12. C89×#2011C2semidirect
13. C89×#1999C2semidirect
14. C89×#1999C2semidirect
15. C89×#1798C2semidirect
371. #32730C89direct (N × H)
383. #2624C2×C89semidirect
384. #2619C2×C89semidirect
385. #2101C2×C89semidirect
386. #2092C2×C89semidirect
387. #2067C2×C89semidirect
388. #2065C2×C89semidirect
389. #2054C2×C89semidirect
390. #2054C2×C89semidirect
391. #2041C2×C89semidirect
392. #2034C2×C89semidirect
393. #2033C2×C89semidirect
394. #2011C2×C89semidirect
395. #1999C2×C89semidirect
396. #1999C2×C89semidirect
397. #1798C2×C89semidirect
398. C89#32730direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#26242
C89×#26192
C89×#21012
C89×#20922
C89×#20672
C89×#20652
C89×#20542
C89×#20412
C89×#20342
C89×#20332
C89×#20112
C89×#19992
C89×#17982
#3273089