Finite Group Databasebeta

← #36571799

Subgroups — #36571799

Order 22784.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028910C211yesmaximal, characteristic, complemented
2#26028701C211yesmaximal, characteristic
3#26020965C211yesmaximal, characteristic, complemented
4#26020958C211yesmaximal, characteristic, complemented
5#26020902C211yesmaximal, characteristic, complemented
6#26020902C211yesmaximal, characteristic, complemented
7#26020529C211yesmaximal, characteristic, complemented
8#26020529C211yesmaximal, characteristic, complemented
9#26020351C211yesmaximal, characteristic, complemented
10#26020294C211yesmaximal, characteristic, complemented
11#26020196C211yesmaximal, characteristic
12#26020099C211yesmaximal, characteristic, complemented
13#26020092C211yesmaximal, characteristic, complemented
14#26020033C211yesmaximal, characteristic, complemented
15C89×#2896C211yesmaximal, characteristic
16C2×#15668019C2211yescharacteristic
17C2×#15668019C2211yescharacteristic
18#19151659—21no—
19#19151659—21no—
20#19151655—21no—
21#19151651—21no—
22C2×#15667948C2211yescharacteristic, complemented
23C2×#15667948C2211yescharacteristic, complemented
24#19151625C2211yescharacteristic, complemented
25#19151625C2211yescharacteristic, complemented
26C2×#15667939C2211yescharacteristic
27C2×#15667939C2211yescharacteristic
28C2×#15667939C2211yescharacteristic
29C2×#15667939C2211yescharacteristic
30#19151565—21no—
31#19151565—21no—
32#19151565C2211yescharacteristic
33#19151565C2211yescharacteristic
34#19151562—21no—
35#19151562C2211yescharacteristic
36#19151562C2211yescharacteristic
37C2×C22⋊#10623494—21no—
38C2×C22⋊#10623494C2211yescharacteristic
39#19151554C2211yescharacteristic, complemented
40#19151554C2211yescharacteristic, complemented
41C2×#15667922C2211yescharacteristic, complemented
42C2×C8×Dic89C2211yescharacteristic, complemented
43C4×C22⋊Dic89C2211yescharacteristic
44#19151363C2211yescharacteristic, complemented
45#19151363C2211yescharacteristic, complemented
46#19151357C2211yescharacteristic, complemented
47#19151357C2211yescharacteristic, complemented
48#19151357C2211yescharacteristic, complemented
49#19151357C2211yescharacteristic, complemented
50#19151352C2211yescharacteristic, complemented
51#19151352C2211yescharacteristic, complemented
52C22×#41×C89C2211yescharacteristic
53C22×M16×C89C2211yescharacteristic
54C2×#117×C89C2211yescharacteristic
55#419×C89C411yescharacteristic, complemented
56#419×C89C411yescharacteristic, complemented
57#418×C89C411yescharacteristic, complemented
58#418×C89C411yescharacteristic, complemented
59#417×C89C411yescharacteristic, complemented
60#417×C89C411yescharacteristic, complemented
61#417×C89C411yescharacteristic, complemented
62#417×C89C411yescharacteristic, complemented
63#416×C89C2211yescharacteristic
64#416×C89C2211yescharacteristic
65#416×C89C2211yescharacteristic
66#416×C89C2211yescharacteristic
67#15668019—22no—
68#15668019—22no—
69#15668019—41no—
70#15668019—41no—
71C2×#13083558—21no—
72C2×#13083558—21no—
73C2×#13083558C2311yescharacteristic
74C2×#13083558C2311yescharacteristic
75C2×#13083558C2311yescharacteristic
76C2×#13083558C2311yescharacteristic
77C22×#10623494—21no—
78C22×#10623494—21no—
79C22×#10623494C2311yescharacteristic
80C22×#10623494C2311yescharacteristic
81C2×C22⋊Dic89—21no—
82C2×C4×Dic89C2311yescharacteristic
83C2×C4×Dic89C2311yescharacteristic
84#15667948—41no—
85#15667948—41no—
86C4⋊#10623494—21no—
87C4⋊#10623494—21no—
88C4⋊#10623494—21no—
89C4⋊#10623494—21no—
90#15667939—22no—
91#15667939—22no—
92#15667939—41no—
93#15667939—41no—
94C22⋊#10623494—21no—
95C22⋊#10623494—21no—
96C22⋊#10623494—21no—
97C22⋊#10623494—21no—
98C22⋊#10623494—21no—
99C22⋊#10623494—21no—
100C22⋊#10623494—21no—
101C22⋊#10623494—21no—
102C22⋊#10623494D411yescharacteristic
103C22⋊#10623494D411yescharacteristic
104C22⋊#10623494D411yescharacteristic
105C22⋊#10623494D411yescharacteristic
106#15667923—21no—
107#15667923—21no—
108#15667922—41no—
109C4×#10623494—21no—
110C4×#10623494—21no—
111C8×Dic89—41no—
112#15667919—21no—
113C2×#41×C89—21no—
114C2×#41×C89—21no—
115C2×#41×C89—22no—
116C2×#41×C89—22no—
117C2×#41×C89—41no—
118C2×#41×C89—41no—
119C2×#41×C89C2×C411yescharacteristic
120C2×#41×C89C2×C411yescharacteristic
121C2×#41×C89C2311yescharacteristic
122C2×#41×C89C2311yescharacteristic
123C22×Q8×C89C2×C411yescharacteristic
124C22×D4×C89—21no—
125C22×D4×C89C2×C411yescharacteristic
126C23×C4×C89—21no—
127C23×C4×C89C2311yescharacteristic
128C2×M16×C89—41no—
129C2×M16×C89—41no—
130C2×M16×C89C2×C411yescharacteristic
131C2×M16×C89C2×C411yescharacteristic
132C2×M16×C89C2×C411yescharacteristic
133C2×M16×C89C2×C411yescharacteristic
134C22×C8×C89C2311yescharacteristic
135C22×C8×C89C2311yescharacteristic
136#117×C89—21no—
137#117×C89—21no—
138#117×C89C2×C411yescharacteristic
139#117×C89C2×C411yescharacteristic
140#117×C89C2311yescharacteristic
141#117×C89C2311yescharacteristic
142C2×C4⋊C4×C89C2×C411yescharacteristic
143C2×C4⋊C4×C89C2×C411yescharacteristic
144C2×C22⋊C4×C89—21no—
145C2×C42×C89—21no—
146#103×C89C2×C411yescharacteristic
147#103×C89C2×C411yescharacteristic
148#103×C89C2×C411yescharacteristic
149#103×C89C2×C411yescharacteristic
150#103×C89C2×C411yescharacteristic
151#103×C89C2×C411yescharacteristic
152#103×C89C2×C411yescharacteristic
153#103×C89C2×C411yescharacteristic
154#102×C89C2×C411yescharacteristic
155#102×C89C2×C411yescharacteristic
156#102×C89C2×C411yescharacteristic
157#102×C89C2×C411yescharacteristic
158#102×C89C2×C411yescharacteristic
159#102×C89C2×C411yescharacteristic
160#102×C89C2×C411yescharacteristic
161#102×C89C2×C411yescharacteristic
162C22×Dic89—21no—
163C22×Dic89—21no—
164#13083558—21no—
165#13083558—21no—
166#13083558—21no—
167#13083558—21no—
168#13083558—21no—
169#13083558—21no—
170#13083558—21no—
171#13083558—21no—
172#13083558—42no—
173#13083558—42no—
174C2×#10623494—21no—
175C2×#10623494—21no—
176C2×#10623494—21no—
177C2×#10623494—21no—
178C2×#10623494—21no—
179C2×#10623494—21no—
180C2×#10623494—21no—
181C2×#10623494—21no—
182C2×#10623494—42no—
183C2×#10623494—42no—
184C2×#10623494C2×D411yescharacteristic
185C2×#10623494C2×D411yescharacteristic
186C2×#10623494C2×D411yescharacteristic
187C2×#10623494C2×D411yescharacteristic
188C22⋊Dic89—42no—
189C4×Dic89—21no—
190C4×Dic89—21no—
191C4×Dic89—21no—
192C4×Dic89—21no—
193C24×C89—21no—
194C24×C89#4111yescharacteristic
195#41×C89—21no—
196#41×C89—21no—
197#41×C89—22no—
198#41×C89—22no—
199#41×C89—21no—
200#41×C89—21no—
201#41×C89—21no—
202#41×C89—21no—
203#41×C89—42no—
204#41×C89—42no—
205#41×C89—41no—
206#41×C89—41no—
207#41×C89—42no—
208#41×C89—42no—
209#41×C89#4112yes—
210#41×C89#4112yes—
211C2×Q8×C89—21no—
212C2×Q8×C89—22no—
213C2×Q8×C89—41no—
214C2×Q8×C89C22×C411yescharacteristic
215C2×Q8×C89C22×C411yescharacteristic
216C2×D4×C89—21no—
217C2×D4×C89—22no—
218C2×D4×C89—21no—
219C2×D4×C89—21no—
220C2×D4×C89—21no—
221C2×D4×C89—21no—
222C2×D4×C89—41no—
223C2×D4×C89—42no—
224C2×D4×C89—42no—
225C2×D4×C89C22×C411yescharacteristic
226C2×D4×C89C22×C411yescharacteristic
227C22×C4×C89—21no—
228C22×C4×C89—21no—
229C22×C4×C89—21no—
230C22×C4×C89—21no—
231C22×C4×C89—21no—
232C22×C4×C89—21no—
233C22×C4×C89—21no—
234C22×C4×C89—21no—
235C22×C4×C89—21no—
236C22×C4×C89—21no—
237C22×C4×C89—21no—
238C22×C4×C89—42no—
239C22×C4×C89—42no—
240C22×C4×C89C22×C411yescharacteristic
241C22×C4×C89C22×C411yescharacteristic
242C22×C4×C89C2×D411yescharacteristic
243C22×C4×C89C2×D411yescharacteristic
244C22×C4×C89#4111yescharacteristic
245C22×C4×C89C2411yescharacteristic
246M16×C89—41no—
247M16×C89—41no—
248M16×C89—41no—
249M16×C89—41no—
250C2×C8×C89—21no—
251C2×C8×C89—21no—
252C2×C8×C89—21no—
253C2×C8×C89—21no—
254C2×C8×C89C22×C411yescharacteristic
255C2×C8×C89C22×C411yescharacteristic
256C2×C8×C89C22×C411yescharacteristic
257C2×C8×C89C22×C411yescharacteristic
258C4⋊C4×C89—21no—
259C4⋊C4×C89—21no—
260C4⋊C4×C89C22×C411yescharacteristic
261C4⋊C4×C89C22×C411yescharacteristic
262C4⋊C4×C89C22×C411yescharacteristic
263C4⋊C4×C89C22×C411yescharacteristic
264C22⋊C4×C89—21no—
265C22⋊C4×C89—21no—
266C22⋊C4×C89—21no—
267C22⋊C4×C89—21no—
268C42×C89—21no—
269C42×C89—21no—
270C42×C89—21no—
271C42×C89—21no—
272C23×C89—21no—
273C23×C89—21no—
274C23×C89—21no—
275C23×C89—21no—
276C23×C89—41no—
277C23×C89—41no—
278C23×C89—42no—
279C23×C89—42no—
280C23×C89—81no—
281C23×C89C4×D411yescharacteristic
282C23×C89C4×D411yescharacteristic
283C23×C89C2×#4111yescharacteristic
284Q8×C89—21no—
285Q8×C89—21no—
286Q8×C89—21no—
287Q8×C89—42no—
288Q8×C89#11712yes—
289D4×C89—22no—
290D4×C89—22no—
291D4×C89—21no—
292D4×C89—21no—
293D4×C89—21no—
294D4×C89—42no—
295D4×C89—42no—
296D4×C89—42no—
297D4×C89—41no—
298D4×C89—41no—
299D4×C89#11712yes—
300C2×C4×C89—21no—
301C2×C4×C89—21no—
302C2×C4×C89—21no—
303C2×C4×C89—21no—
304C2×C4×C89—21no—
305C2×C4×C89—21no—
306C2×C4×C89—21no—
307C2×C4×C89—21no—
308C2×C4×C89—21no—
309C2×C4×C89—21no—
310C2×C4×C89—21no—
311C2×C4×C89—22no—
312C2×C4×C89—22no—
313C2×C4×C89—21no—
314C2×C4×C89—21no—
315C2×C4×C89—21no—
316C2×C4×C89—21no—
317C2×C4×C89—21no—
318C2×C4×C89—42no—
319C2×C4×C89—42no—
320C2×C4×C89—42no—
321C2×C4×C89—42no—
322C2×C4×C89—41no—
323C2×C4×C89—41no—
324C2×C4×C89—81no—
325C2×C4×C89C4×D411yescharacteristic
326C2×C4×C89C4×D411yescharacteristic
327C2×C4×C89C23×C411yescharacteristic
328C2×C4×C89C22×D411yescharacteristic
329C2×C4×C89C2×#4111yescharacteristic
330C2×C4×C89C2×#4111yescharacteristic
331C2×C4×C89H(5,𝔽2)11yescharacteristic
332C2×C4×C89H(5,𝔽2)11yescharacteristic
333C2×Dic89—22no—
334C2×Dic89—41no—
335C2×Dic89—41no—
336C2×Dic89—41no—
337C2×Dic89—41no—
338C2×Dic89—41no—
339C8×C89—21no—
340C8×C89—21no—
341C8×C89—21no—
342C8×C89—21no—
343#10623494—21no—
344#10623494—21no—
345#10623494—21no—
346#10623494—21no—
347#10623494—41no—
348#10623494—41no—
349#10623494—41no—
350#10623494—41no—
351C22×C89—21no—
352C22×C89—21no—
353C22×C89—21no—
354C22×C89—21no—
355C22×C89—22no—
356C22×C89—21no—
357C22×C89—21no—
358C22×C89—21no—
359C22×C89—21no—
360C22×C89—41no—
361C22×C89—41no—
362C22×C89—41no—
363C22×C89—41no—
364C22×C89—41no—
365C22×C89—81no—
366C22×C89—81no—
367C22×C89—84no—
368C22×C89C2×C4×D411yescharacteristic
369C22×C89#55111yescharacteristic
370C22×C89#55111yescharacteristic
371C4×C89—21no—
372C4×C89—21no—
373C4×C89—22no—
374C4×C89—41no—
375C4×C89—41no—
376C4×C89—41no—
377C4×C89—41no—
378C4×C89—41no—
379C4×C89C2×#11711yescharacteristic
380C4×C89#51811yescharacteristic
381C4×C89#54611yescharacteristic
382C4×C89#54611yescharacteristic
383Dic89—42no—
384Dic89—81no—
385#22588—891nomaximal, Sylow
386C2×C89—21no—
387C2×C89—21no—
388C2×C89—41no—
389C2×C89—41no—
390C2×C89—42no—
391C2×C89—81no—
392C2×C89#234211yescharacteristic
393C2×C89#295511yescharacteristic
394C2×C89#295611yescharacteristic
395#2924—891no—
396#2896D8911yescharacteristic
397#2880—891no—
398#1938—891no—
399#1937—891no—
400#1929—891no—
401#1929—891no—
402#1866—891no—
403#1866—891no—
404#1826—891no—
405#1811—891no—
406#1789—891no—
407#1765—891no—
408#1764—891no—
409#1753—891no—
410C89#2258811yescharacteristic, complemented, Sylow
411C22×#41C2×D8911yescharacteristic
412C2×#131—891no—
413C2×#131—891no—
414C22×M16C2×D8911yescharacteristic
415C2×#117C2×D8911yescharacteristic
416#433—1781no—
417#433—1781no—
418#432—1781no—
419#431—1781no—
420C2×#108—891no—
421C2×#108—891no—
422#424—891no—
423#424—891no—
424C2×#104—891no—
425C2×#104—891no—
426C2×#104—891no—
427C2×#104—891no—
428#419Dic8911yescharacteristic, complemented
429#419Dic8911yescharacteristic, complemented
430#418Dic8911yescharacteristic, complemented
431#418Dic8911yescharacteristic, complemented
432#417Dic8911yescharacteristic, complemented
433#417Dic8911yescharacteristic, complemented
434#417Dic8911yescharacteristic, complemented
435#417Dic8911yescharacteristic, complemented
436#416C2×D8911yescharacteristic
437#416C2×D8911yescharacteristic
438#416C2×D8911yescharacteristic
439#416C2×D8911yescharacteristic
440#408—891no—
441#408—891no—
442#408—1781no—
443#408—1781no—
444#407—891no—
445#407—891no—
446#407—1781no—
447C2×C22⋊C8—891no—
448C2×C22⋊C8—1781no—
449#405—891no—
450#405—891no—
451C2×#97—891no—
452C2×C4×C8—891no—
453C4×C22⋊C4—891no—
454#341—891no—
455#341—891no—
456#339—891no—
457#339—891no—
458#339—891no—
459#339—891no—
460#336—891no—
461#336—891no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic8911yescharacteristic
469C2×#41C2×Dic8911yescharacteristic
470C2×#41C22×D8911yescharacteristic
471C2×#41C22×D8911yescharacteristic
472C22×Q8C2×Dic8911yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic8911yescharacteristic
475C23×C4—21no—
476C23×C4C22×D8911yescharacteristic
477#131—3561no—
478#131—3561no—
479#131—1782no—
480#131—1782no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—891no—
484C2×M16—891no—
485C2×M16—891no—
486C2×M16—891no—
487C2×M16—1781no—
488C2×M16—1781no—
489C2×M16C2×Dic8911yescharacteristic
490C2×M16C2×Dic8911yescharacteristic
491C2×M16C2×Dic8911yescharacteristic
492C2×M16C2×Dic8911yescharacteristic
493C22×C8—891no—
494C22×C8—891no—
495C22×C8—1781no—
496C22×C8—1781no—
497C22×C8C22×D8911yescharacteristic
498C22×C8C22×D8911yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic8911yescharacteristic
502#117C2×Dic8911yescharacteristic
503#117C22×D8911yescharacteristic
504#117C22×D8911yescharacteristic
505C2×C4⋊C4C2×Dic8911yescharacteristic
506C2×C4⋊C4C2×Dic8911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1781no—
509C2×C42—21no—
510C2×C42—891no—
511C2×C42—891no—
512#108—3561no—
513#108—3561no—
514C4⋊C8—1781no—
515C4⋊C8—1781no—
516C4⋊C8—1781no—
517C4⋊C8—1781no—
518#104—3561no—
519#104—3561no—
520#104—1782no—
521#104—1782no—
522#103C2×Dic8911yescharacteristic
523#103C2×Dic8911yescharacteristic
524#103C2×Dic8911yescharacteristic
525#103C2×Dic8911yescharacteristic
526#103C2×Dic8911yescharacteristic
527#103C2×Dic8911yescharacteristic
528#103C2×Dic8911yescharacteristic
529#103C2×Dic8911yescharacteristic
530#102C2×Dic8911yescharacteristic
531#102C2×Dic8911yescharacteristic
532#102C2×Dic8911yescharacteristic
533#102C2×Dic8911yescharacteristic
534#102C2×Dic8911yescharacteristic
535#102C2×Dic8911yescharacteristic
536#102C2×Dic8911yescharacteristic
537#102C2×Dic8911yescharacteristic
538C22⋊C8—891no—
539C22⋊C8—891no—
540C22⋊C8—891no—
541C22⋊C8—891no—
542C22⋊C8—1781no—
543C22⋊C8—1781no—
544C22⋊C8—1781no—
545C22⋊C8—1781no—
546C22⋊C8—1781no—
547C22⋊C8—1781no—
548C22⋊C8—1781no—
549C22⋊C8—1781no—
550#97—3561no—
551#97—1781no—
552#97—1781no—
553C4×C8—3561no—
554C4×C8—1781no—
555C4×C8—1781no—
556#95—1781no—
557C24—21no—
558C24#1308357311yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1308357412yes—
574#41#1308357412yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic8911yescharacteristic
579C2×Q8C22×Dic8911yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic8911yescharacteristic
590C2×D4C22×Dic8911yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1781no—
605C22×C4—1781no—
606C22×C4C22×Dic8911yescharacteristic
607C22×C4C22×Dic8911yescharacteristic
608C22×C4D4×D8911yescharacteristic
609C22×C4D4×D8911yescharacteristic
610C22×C4#1308357311yescharacteristic
611C22×C4C23×D8911yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—3562no—
617M16—3562no—
618M16—1781no—
619M16—1781no—
620M16—1781no—
621M16—1781no—
622M16—1781no—
623M16—1781no—
624M16—1781no—
625M16—1781no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—891no—
631C2×C8—891no—
632C2×C8—891no—
633C2×C8—891no—
634C2×C8—3562no—
635C2×C8—3562no—
636C2×C8—1781no—
637C2×C8—1781no—
638C2×C8—1781no—
639C2×C8—1781no—
640C2×C8—1781no—
641C2×C8—1781no—
642C2×C8—1781no—
643C2×C8—1781no—
644C2×C8C22×Dic8911yescharacteristic
645C2×C8C22×Dic8911yescharacteristic
646C2×C8C22×Dic8911yescharacteristic
647C2×C8C22×Dic8911yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic8911yescharacteristic
651C4⋊C4C22×Dic8911yescharacteristic
652C4⋊C4C22×Dic8911yescharacteristic
653C4⋊C4C22×Dic8911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—3562no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1781no—
664C42—1781no—
665C42—1781no—
666C42—1781no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic8911yescharacteristic
677C23D4×Dic8911yescharacteristic
678C23C2×#1308357311yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1566797112yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1566797112yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—3561no—
721C2×C4—3561no—
722C2×C4—3561no—
723C2×C4—3561no—
724C2×C4—3561no—
725C2×C4—1782no—
726C2×C4D4×Dic8911yescharacteristic
727C2×C4D4×Dic8911yescharacteristic
728C2×C4C23×Dic8911yescharacteristic
729C2×C4C2×D4×D8911yescharacteristic
730C2×C4C2×#1308357411yescharacteristic
731C2×C4C2×#1308357411yescharacteristic
732C2×C4#1566805711yescharacteristic
733C2×C4#1566805711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—3561no—
739C8—3561no—
740C8—3561no—
741C8—3561no—
742C8—1781no—
743C8—1781no—
744C8—1781no—
745C8—1781no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic8911yescharacteristic
764C22#1915227411yescharacteristic
765C22#1915227411yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—3562no—
775C4—7121no—
776C4C2×#1566797111yescharacteristic
777C4#1915207311yescharacteristic
778C4#1915223811yescharacteristic
779C4#1915223811yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2602310111yescharacteristic
787C2#2602915511yescharacteristic
788C2#2602916211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC89×#2896C2
socleC22×C89C2×C4×D4
prime radicalC22×#41×C89C22
cosocleC22×C4×C89C24
hypercenter#2896D89
hypocenterC89#22588
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #26028910C2semidirect
3. #26020965C2semidirect
4. #26020958C2semidirect
5. #26020902C2semidirect
6. #26020902C2semidirect
7. #26020529C2semidirect
8. #26020529C2semidirect
9. #26020351C2semidirect
10. #26020294C2semidirect
12. #26020099C2semidirect
13. #26020092C2semidirect
14. #26020033C2semidirect
22. C2×#15667948C22semidirect
23. C2×#15667948C22semidirect
24. #19151625C22semidirect
25. #19151625C22semidirect
39. #19151554C22semidirect
40. #19151554C22semidirect
41. C2×#15667922C22semidirect
42. C2×C8×Dic89C22semidirect
44. #19151363C22semidirect
45. #19151363C22semidirect
46. #19151357C22semidirect
47. #19151357C22semidirect
48. #19151357C22semidirect
49. #19151357C22semidirect
50. #19151352C22semidirect
51. #19151352C22semidirect
55. #419×C89C4semidirect
56. #419×C89C4semidirect
57. #418×C89C4semidirect
58. #418×C89C4semidirect
59. #417×C89C4semidirect
60. #417×C89C4semidirect
61. #417×C89C4semidirect
62. #417×C89C4semidirect
410. C89#22588semidirect
428. #419Dic89semidirect
429. #419Dic89semidirect
430. #418Dic89semidirect
431. #418Dic89semidirect
432. #417Dic89semidirect
433. #417Dic89semidirect
434. #417Dic89semidirect
435. #417Dic89semidirect

Maximal subgroups

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

subgroupindex
#260289102
#260287012
#260209652
#260209582
#260209022
#260205292
#260203512
#260202942
#260201962
#260200992
#260200922
#260200332
C89×#28962
#2258889