Finite Group Databasebeta

← C89×#25081 #36402929

Subgroups — C89×#25081 #36402929

Order 22784.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C89C211yesmaximal, characteristic, complemented
2C2×#459×C89C211yesmaximal, characteristic, complemented
3C2×#449×C89C211yesmaximal, characteristic, complemented
4C2×#416×C89C211yesmaximal, characteristic, complemented
5C89×#2431C211yesmaximal, characteristic, complemented
6C89×#2363C211yesmaximal, characteristic, complemented
7C89×#2068C211yesmaximal, characteristic, complemented
8C89×#2054C211yesmaximal, characteristic, complemented
9C89×#2041C211yesmaximal, characteristic, complemented
10C89×#2012C211yesmaximal, characteristic, complemented
11C89×#1983C211yesmaximal, characteristic, complemented
12C89×#1925C211yesmaximal, characteristic, complemented
13C89×#1877C211yesmaximal, characteristic, complemented
14C89×#1875C211yesmaximal, characteristic, complemented
15C89×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C89C2211yescharacteristic
17C22×SD16×C89C2211yescharacteristic
18C22×D8×C89C2211yescharacteristic
19C22×D8×C89C2211yescharacteristic
20C23×C8×C89C2211yescharacteristic
21C2×#127×C89C2211yescharacteristic
22C2×#124×C89C2211yescharacteristic
23C2×#121×C89C2211yescharacteristic
24C2×#121×C89C2211yescharacteristic
25C2×C4×D4×C89C2211yescharacteristic
26C2×#117×C89C2211yescharacteristic
27#466×C89—24no—
28#459×C89—24no—
29#449×C89—24no—
30C2×#107×C89C2211yescharacteristic
31C2×C4⋊C8×C89C2211yescharacteristic
32C2×C4⋊C8×C89C2211yescharacteristic
33#416×C89—24no—
34C2×#103×C89C2211yescharacteristic
35C2×#103×C89C2211yescharacteristic
36C2×#103×C89C2211yescharacteristic
37C2×#102×C89C2211yescharacteristic
38C2×#102×C89C2211yescharacteristic
39C2×#102×C89C2211yescharacteristic
40C2×#102×C89C2211yescharacteristic
41C2×#102×C89C2211yescharacteristic
42C2×#102×C89C2211yescharacteristic
43C2×#102×C89C2211yescharacteristic
44C2×C22⋊C8×C89C2211yescharacteristic
45#392×C89—21no—
46#392×C89—21no—
47#391×C89C2211yescharacteristic
48#390×C89—21no—
49#390×C89C2211yescharacteristic
50#390×C89C2211yescharacteristic
51#389×C89C2211yescharacteristic
52#388×C89—21no—
53#386×C89—21no—
54#386×C89—21no—
55#386×C89—21no—
56C4×C4⋊C4×C89C2211yescharacteristic
57C4×C22⋊C4×C89—21no—
58C4×C22⋊C4×C89C2211yescharacteristic
59#340×C89C2211yescharacteristic
60#340×C89C2211yescharacteristic
61#336×C89C2211yescharacteristic
62#336×C89C2211yescharacteristic
63C2×#41×C89—22no—
64C2×#41×C89—22no—
65C2×#41×C89—22no—
66C2×#41×C89—22no—
67C2×#41×C89—41no—
68C2×#41×C89—41no—
69C22×Q8×C89C2311yescharacteristic
70C22×D4×C89—21no—
71C22×D4×C89—21no—
72C22×D4×C89—21no—
73C22×D4×C89—21no—
74C22×D4×C89—21no—
75C22×D4×C89C2311yescharacteristic
76C22×D4×C89C2311yescharacteristic
77C22×D4×C89C2311yescharacteristic
78C23×C4×C89—21no—
79C23×C4×C89—21no—
80C23×C4×C89C2311yescharacteristic
81C2×SD16×C89—22no—
82C2×SD16×C89—22no—
83C2×SD16×C89—41no—
84C2×D8×C89—22no—
85C2×D8×C89—22no—
86C2×D8×C89—22no—
87C2×D8×C89—22no—
88C2×D8×C89—41no—
89C2×D8×C89—41no—
90C22×C8×C89—22no—
91C22×C8×C89—22no—
92C22×C8×C89—41no—
93C22×C8×C89C2311yescharacteristic
94C22×C8×C89C2311yescharacteristic
95C22×C8×C89C2311yescharacteristic
96C22×C8×C89C2311yescharacteristic
97#127×C89—22no—
98#127×C89—41no—
99#124×C89—22no—
100#124×C89—41no—
101#121×C89—22no—
102#121×C89—22no—
103#121×C89—22no—
104#121×C89D414yescomplemented
105C4×D4×C89—22no—
106C4×D4×C89—41no—
107#117×C89—22no—
108#117×C89—41no—
109C2×C4⋊C4×C89—21no—
110C2×C4⋊C4×C89C2311yescharacteristic
111C2×C4⋊C4×C89C2311yescharacteristic
112C2×C4⋊C4×C89C2311yescharacteristic
113C2×C4⋊C4×C89C2311yescharacteristic
114C2×C22⋊C4×C89—21no—
115C2×C22⋊C4×C89—21no—
116C2×C22⋊C4×C89—21no—
117C2×C22⋊C4×C89—21no—
118C2×C22⋊C4×C89—21no—
119C2×C22⋊C4×C89—21no—
120C2×C22⋊C4×C89—21no—
121C2×C22⋊C4×C89—21no—
122C2×C22⋊C4×C89—21no—
123C2×C22⋊C4×C89—21no—
124C2×C22⋊C4×C89D411yescharacteristic
125C2×C22⋊C4×C89D411yescharacteristic
126C2×C42×C89—21no—
127C2×C42×C89—21no—
128C2×C42×C89C2311yescharacteristic
129C2×C42×C89C2311yescharacteristic
130#107×C89—22no—
131C4⋊C8×C89—22no—
132C4⋊C8×C89—41no—
133#103×C89—22no—
134#103×C89—22no—
135#103×C89—22no—
136#102×C89—22no—
137#102×C89—22no—
138#102×C89—22no—
139#102×C89—22no—
140#102×C89—22no—
141#102×C89—41no—
142#102×C89D414yescomplemented
143C22⋊C8×C89—22no—
144#95×C89—21no—
145#95×C89—21no—
146#95×C89—21no—
147#95×C89—21no—
148#95×C89D411yescharacteristic
149#95×C89D411yescharacteristic
150C24×C89—21no—
151C24×C89—21no—
152C24×C89—21no—
153C24×C89C2×D411yescharacteristic
154#41×C89—28no—
155#41×C89—44no—
156#41×C89—44no—
157#41×C89—44no—
158C2×Q8×C89—21no—
159C2×Q8×C89—21no—
160C2×Q8×C89—21no—
161C2×Q8×C89—21no—
162C2×Q8×C89—21no—
163C2×Q8×C89#4112yes—
164C2×D4×C89—24no—
165C2×D4×C89—21no—
166C2×D4×C89—21no—
167C2×D4×C89—21no—
168C2×D4×C89—21no—
169C2×D4×C89—21no—
170C2×D4×C89—21no—
171C2×D4×C89—21no—
172C2×D4×C89—21no—
173C2×D4×C89—21no—
174C2×D4×C89—21no—
175C2×D4×C89—21no—
176C2×D4×C89—21no—
177C2×D4×C89—21no—
178C2×D4×C89—21no—
179C2×D4×C89—21no—
180C2×D4×C89—21no—
181C2×D4×C89—42no—
182C2×D4×C89—42no—
183C2×D4×C89—42no—
184C2×D4×C89—42no—
185C2×D4×C89—42no—
186C2×D4×C89—42no—
187C2×D4×C89—42no—
188C2×D4×C89—42no—
189C2×D4×C89—81no—
190C2×D4×C89—81no—
191C2×D4×C89—81no—
192C2×D4×C89—81no—
193C2×D4×C89—81no—
194C2×D4×C89—81no—
195C2×D4×C89C2×D412yes—
196C2×D4×C89C2×D412yes—
197C22×C4×C89—21no—
198C22×C4×C89—21no—
199C22×C4×C89—21no—
200C22×C4×C89—21no—
201C22×C4×C89—21no—
202C22×C4×C89—21no—
203C22×C4×C89—21no—
204C22×C4×C89—21no—
205C22×C4×C89—21no—
206C22×C4×C89—42no—
207C22×C4×C89—42no—
208C22×C4×C89—42no—
209C22×C4×C89—42no—
210C22×C4×C89—42no—
211C22×C4×C89—81no—
212C22×C4×C89C2×D411yescharacteristic
213C22×C4×C89C2×D411yescharacteristic
214C22×C4×C89C2×D411yescharacteristic
215C22×C4×C89C2×D411yescharacteristic
216C22×C4×C89C2×D412yes—
217C22×C4×C89C2×D411yescharacteristic
218C22×C4×C89#4112yes—
219C22×C4×C89C2411yescharacteristic
220SD16×C89—44no—
221D8×C89—44no—
222D8×C89—44no—
223C2×C8×C89—21no—
224C2×C8×C89—21no—
225C2×C8×C89—21no—
226C2×C8×C89—21no—
227C2×C8×C89—21no—
228C2×C8×C89—21no—
229C2×C8×C89—21no—
230C2×C8×C89—21no—
231C2×C8×C89—21no—
232C2×C8×C89—21no—
233C2×C8×C89—21no—
234C2×C8×C89—44no—
235C2×C8×C89C2×D412yes—
236C4⋊C4×C89—21no—
237C4⋊C4×C89—21no—
238C4⋊C4×C89—21no—
239C4⋊C4×C89—21no—
240C4⋊C4×C89—21no—
241C4⋊C4×C89—21no—
242C4⋊C4×C89—81no—
243C4⋊C4×C89C2×D412yes—
244C4⋊C4×C89C2×D412yes—
245C22⋊C4×C89—24no—
246C22⋊C4×C89—22no—
247C22⋊C4×C89—41no—
248C22⋊C4×C89—42no—
249C22⋊C4×C89—42no—
250C22⋊C4×C89—42no—
251C22⋊C4×C89—42no—
252C22⋊C4×C89—42no—
253C22⋊C4×C89—42no—
254C22⋊C4×C89—81no—
255C22⋊C4×C89—81no—
256C22⋊C4×C89—81no—
257C42×C89—21no—
258C42×C89—21no—
259C42×C89—21no—
260C42×C89—21no—
261C42×C89—42no—
262C42×C89—81no—
263C23×C89—21no—
264C23×C89—21no—
265C23×C89—21no—
266C23×C89—21no—
267C23×C89—21no—
268C23×C89—21no—
269C23×C89—22no—
270C23×C89—22no—
271C23×C89—41no—
272C23×C89—41no—
273C23×C89—41no—
274C23×C89—41no—
275C23×C89—41no—
276C23×C89—41no—
277C23×C89—41no—
278C23×C89—41no—
279C23×C89—41no—
280C23×C89—41no—
281C23×C89—41no—
282C23×C89—41no—
283C23×C89—41no—
284C23×C89—41no—
285C23×C89—41no—
286C23×C89—41no—
287C23×C89—41no—
288C23×C89—41no—
289C23×C89—41no—
290C23×C89#12112yes—
291C23×C89C22×D411yescharacteristic
292Q8×C89—22no—
293Q8×C89—22no—
294Q8×C89—41no—
295Q8×C89—41no—
296D4×C89—22no—
297D4×C89—22no—
298D4×C89—22no—
299D4×C89—22no—
300D4×C89—48no—
301D4×C89—41no—
302D4×C89—41no—
303D4×C89—41no—
304D4×C89—41no—
305D4×C89—41no—
306D4×C89—41no—
307D4×C89—41no—
308D4×C89—41no—
309D4×C89—84no—
310D4×C89—84no—
311D4×C89—84no—
312D4×C89—84no—
313C2×C4×C89—21no—
314C2×C4×C89—21no—
315C2×C4×C89—21no—
316C2×C4×C89—21no—
317C2×C4×C89—22no—
318C2×C4×C89—22no—
319C2×C4×C89—22no—
320C2×C4×C89—22no—
321C2×C4×C89—22no—
322C2×C4×C89—21no—
323C2×C4×C89—22no—
324C2×C4×C89—21no—
325C2×C4×C89—21no—
326C2×C4×C89—22no—
327C2×C4×C89—21no—
328C2×C4×C89—21no—
329C2×C4×C89—21no—
330C2×C4×C89—21no—
331C2×C4×C89—21no—
332C2×C4×C89—21no—
333C2×C4×C89—48no—
334C2×C4×C89—41no—
335C2×C4×C89—41no—
336C2×C4×C89—41no—
337C2×C4×C89—41no—
338C2×C4×C89—41no—
339C2×C4×C89—41no—
340C2×C4×C89—41no—
341C2×C4×C89—41no—
342C2×C4×C89—41no—
343C2×C4×C89—41no—
344C2×C4×C89—41no—
345C2×C4×C89—41no—
346C2×C4×C89—84no—
347C2×C4×C89#12112yes—
348C2×C4×C89#13512yes—
349C2×C4×C89C22×D411yescharacteristic
350C2×C4×C89C22×D411yescharacteristic
351C2×C4×C89C2×#4111yescharacteristic
352C2×C4×C89C2×#4111yescharacteristic
353C2×C4×C89H(5,𝔽2)11yescharacteristic
354C2×C4×C89H(5,𝔽2)11yescharacteristic
355C8×C89—22no—
356C8×C89—41no—
357C8×C89—41no—
358C8×C89—41no—
359C22×C89—22no—
360C22×C89—22no—
361C22×C89—22no—
362C22×C89—41no—
363C22×C89—41no—
364C22×C89—41no—
365C22×C89—41no—
366C22×C89—42no—
367C22×C89—42no—
368C22×C89—42no—
369C22×C89—42no—
370C22×C89—42no—
371C22×C89—42no—
372C22×C89—81no—
373C22×C89—81no—
374C22×C89—81no—
375C22×C89—81no—
376C22×C89—81no—
377C22×C89—81no—
378C22×C89—81no—
379C22×C89—81no—
380C22×C89—81no—
381C22×C89—81no—
382C22×C89—81no—
383C22×C89—81no—
384C22×C89—81no—
385C22×C89—81no—
386C22×C89—81no—
387C22×C89C2×#12111yescharacteristic
388C22×C89D4211yescharacteristic
389C22×C89#54611yescharacteristic
390C22×C89C2×#13511yescharacteristic
391C22×C89#57511yescharacteristic
392C22×C89#57611yescharacteristic
393C22×C89#57611yescharacteristic
394C4×C89—22no—
395C4×C89—22no—
396C4×C89—42no—
397C4×C89—41no—
398C4×C89—42no—
399C4×C89—42no—
400C4×C89—41no—
401C4×C89—41no—
402C4×C89—81no—
403C4×C89—81no—
404C4×C89#52511yescharacteristic
405C4×C89#53811yescharacteristic
406C4×C89D4211yescharacteristic
407C4×C89#54611yescharacteristic
408#25081C8911yesmaximal, characteristic, direct product factor, Sylow
409C2×C89—42no—
410C2×C89—82no—
411C2×C89—82no—
412C2×C89—161no—
413C2×C89#242411yescharacteristic
414C2×C89#303511yescharacteristic
415C2×C89#304111yescharacteristic
416C2×C89#326811yescharacteristic
417C2×C89#328011yescharacteristic
418C2×C89#330511yescharacteristic
419C2×C89#330911yescharacteristic
420C2×#466C2×C8911yescharacteristic, complemented
421C2×#459C2×C8911yescharacteristic, complemented
422C2×#449C2×C8911yescharacteristic, complemented
423C2×#416C2×C8911yescharacteristic, complemented
424#2431C2×C8911yescharacteristic, complemented
425#2363C2×C8911yescharacteristic, complemented
426#2068C2×C8911yescharacteristic, complemented
427#2054C2×C8911yescharacteristic, complemented
428#2041C2×C8911yescharacteristic, complemented
429#2012C2×C8911yescharacteristic, complemented
430#1983C2×C8911yescharacteristic, complemented
431#1925C2×C8911yescharacteristic, complemented
432#1877C2×C8911yescharacteristic, complemented
433#1875C2×C8911yescharacteristic, complemented
434#1850C2×C8911yescharacteristic, complemented
435C89#2508111yescharacteristic, direct product factor, Sylow
436C22×#41C22×C8911yescharacteristic
437C22×SD16C22×C8911yescharacteristic
438C22×D8C22×C8911yescharacteristic
439C22×D8C22×C8911yescharacteristic
440C23×C8C22×C8911yescharacteristic
441C2×#127C22×C8911yescharacteristic
442C2×#124C22×C8911yescharacteristic
443C2×#121C22×C8911yescharacteristic
444C2×#121C22×C8911yescharacteristic
445C2×C4×D4C22×C8911yescharacteristic
446C2×#117C22×C8911yescharacteristic
447#466—24no—
448#459—24no—
449#449—24no—
450C2×#107C22×C8911yescharacteristic
451C2×C4⋊C8C22×C8911yescharacteristic
452C2×C4⋊C8C22×C8911yescharacteristic
453#416—24no—
454C2×#103C22×C8911yescharacteristic
455C2×#103C22×C8911yescharacteristic
456C2×#103C22×C8911yescharacteristic
457C2×#102C22×C8911yescharacteristic
458C2×#102C22×C8911yescharacteristic
459C2×#102C22×C8911yescharacteristic
460C2×#102C22×C8911yescharacteristic
461C2×#102C22×C8911yescharacteristic
462C2×#102C22×C8911yescharacteristic
463C2×#102C22×C8911yescharacteristic
464C2×C22⋊C8C22×C8911yescharacteristic
465#392—21no—
466#392—21no—
467#391C22×C8911yescharacteristic
468#390—21no—
469#390C22×C8911yescharacteristic
470#390C22×C8911yescharacteristic
471#389C22×C8911yescharacteristic
472#388—21no—
473#386—21no—
474#386—21no—
475#386—21no—
476C4×C4⋊C4C22×C8911yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4C22×C8911yescharacteristic
479#340C22×C8911yescharacteristic
480#340C22×C8911yescharacteristic
481#336C22×C8911yescharacteristic
482#336C22×C8911yescharacteristic
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C8911yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C8911yescharacteristic
496C22×D4C23×C8911yescharacteristic
497C22×D4C23×C8911yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C8911yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C8911yescharacteristic
514C22×C8C23×C8911yescharacteristic
515C22×C8C23×C8911yescharacteristic
516C22×C8C23×C8911yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C8914yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4C23×C8911yescharacteristic
531C2×C4⋊C4C23×C8911yescharacteristic
532C2×C4⋊C4C23×C8911yescharacteristic
533C2×C4⋊C4C23×C8911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C8911yescharacteristic
545C2×C22⋊C4D4×C8911yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C8911yescharacteristic
549C2×C42C23×C8911yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562#102D4×C8914yescomplemented
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C8911yescharacteristic
569#95D4×C8911yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C8911yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8#41×C8912yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C8912yes—
616C2×D4C2×D4×C8912yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C8911yescharacteristic
633C22×C4C2×D4×C8911yescharacteristic
634C22×C4C2×D4×C8911yescharacteristic
635C22×C4C2×D4×C8911yescharacteristic
636C22×C4C2×D4×C8912yes—
637C22×C4C2×D4×C8911yescharacteristic
638C22×C4#41×C8912yes—
639C22×C4C24×C8911yescharacteristic
640SD16—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8C2×D4×C8912yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C8912yes—
664C4⋊C4C2×D4×C8912yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#121×C8912yes—
711C23C22×D4×C8911yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—48no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—84no—
767C2×C4#121×C8912yes—
768C2×C4#135×C8912yes—
769C2×C4C22×D4×C8911yescharacteristic
770C2×C4C22×D4×C8911yescharacteristic
771C2×C4C2×#41×C8911yescharacteristic
772C2×C4C2×#41×C8911yescharacteristic
773C2×C4H(5,𝔽2)×C8911yescharacteristic
774C2×C4H(5,𝔽2)×C8911yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C8911yescharacteristic
808C22D42×C8911yescharacteristic
809C22#546×C8911yescharacteristic
810C22C2×#135×C8911yescharacteristic
811C22#575×C8911yescharacteristic
812C22#576×C8911yescharacteristic
813C22#576×C8911yescharacteristic
814C4—22no—
815C4—22no—
816C4—42no—
817C4—41no—
818C4—42no—
819C4—42no—
820C4—41no—
821C4—41no—
822C4—81no—
823C4—81no—
824C4#525×C8911yescharacteristic
825C4#538×C8911yescharacteristic
826C4D42×C8911yescharacteristic
827C4#546×C8911yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C89×#242411yescharacteristic
833C2C89×#303511yescharacteristic
834C2C89×#304111yescharacteristic
835C2C89×#326811yescharacteristic
836C2C89×#328011yescharacteristic
837C2C89×#330511yescharacteristic
838C2C89×#330911yescharacteristic
subgroupG/H
center, socleC23×C89C22×D4
commutator, Frattini, cosocleC22×C4C24×C89
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C89 ◁ C4×C22⋊C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C89C2semidirect
2. C2×#459×C89C2semidirect
3. C2×#449×C89C2semidirect
4. C2×#416×C89C2semidirect
5. C89×#2431C2semidirect
6. C89×#2363C2semidirect
7. C89×#2068C2semidirect
8. C89×#2054C2semidirect
9. C89×#2041C2semidirect
10. C89×#2012C2semidirect
11. C89×#1983C2semidirect
12. C89×#1925C2semidirect
13. C89×#1877C2semidirect
14. C89×#1875C2semidirect
15. C89×#1850C2semidirect
104. #121×C89D4semidirect
142. #102×C89D4semidirect
408. #25081C89direct (N × H)
420. C2×#466C2×C89semidirect
421. C2×#459C2×C89semidirect
422. C2×#449C2×C89semidirect
423. C2×#416C2×C89semidirect
424. #2431C2×C89semidirect
425. #2363C2×C89semidirect
426. #2068C2×C89semidirect
427. #2054C2×C89semidirect
428. #2041C2×C89semidirect
429. #2012C2×C89semidirect
430. #1983C2×C89semidirect
431. #1925C2×C89semidirect
432. #1877C2×C89semidirect
433. #1875C2×C89semidirect
434. #1850C2×C89semidirect
435. C89#25081direct (N × H)
524. #121D4×C89semidirect
562. #102D4×C89semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C892
C2×#459×C892
C2×#449×C892
C2×#416×C892
C89×#24312
C89×#23632
C89×#20682
C89×#20542
C89×#20412
C89×#20122
C89×#19832
C89×#19252
C89×#18772
C89×#18752
C89×#18502
#2508189