Finite Group Databasebeta

← #36717135

Subgroups — #36717135

Order 22784.

2024 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152351C211yesmaximal, characteristic
2#26023440C212yesmaximal, complemented
3#26023439C212yesmaximal, complemented
4#26023434C212yesmaximal, complemented
5#26023430C212yesmaximal, complemented
6#26023422C211yesmaximal, characteristic
7#26023415C212yesmaximal, complemented
8#26023412C212yesmaximal, complemented
9#26023402C211yesmaximal, characteristic
10#26022823C212yesmaximal, complemented
11#26022809C212yesmaximal, complemented
12#26022806C212yesmaximal, complemented
13#26022806C212yesmaximal, complemented
14#26022799C211yesmaximal, characteristic
15#26022784C212yesmaximal, complemented
16#26022780C212yesmaximal, complemented
17#26022777C211yesmaximal, characteristic
18#123×Dic89C211yesmaximal, characteristic
19C89×#2376C211yesmaximal, characteristic
20#19152351C4116yescomplemented
21C2×#15668011C2212yes—
22C2×#15668005C2212yes—
23C2×#15668005C2212yes—
24C2×#15668002C2212yes—
25C2×#15667999C2211yescharacteristic
26C2×#15667993C2211yescharacteristic
27C2×#15667991C2212yes—
28C2×#15667989C2212yes—
29C2×#15667977C2212yes—
30C2×#15667977C2211yescharacteristic
31C2×D4×Dic89C2211yescharacteristic
32C22×C4×Dic89C2211yescharacteristic
33C22×C4×Dic89C2211yescharacteristic
34#19151504C2211yescharacteristic
35#19151503C2212yes—
36#19151502C2212yes—
37#19151502C2212yes—
38#19151502C2212yes—
39#19151496C2212yes—
40#19151495C2212yes—
41#19151494C2212yes—
42#19151493C2212yes—
43#19151493C2212yes—
44#19151493C2212yes—
45#19151493C2212yes—
46#19151492C2212yes—
47#19151492C2212yes—
48#19151492C2212yes—
49#19151491C2212yes—
50#19151486C2212yes—
51#19151486C2212yes—
52#19151486C2212yes—
53#19151486C2212yes—
54#19151485C2212yes—
55#19151485C2212yes—
56#19151484C2212yes—
57#19151483C2212yes—
58#19151482C2212yes—
59#19151482C2212yes—
60#19151482C2212yes—
61#19151481C2212yes—
62#19151481C2212yes—
63#19151481C2212yes—
64#19151480C2212yes—
65#19151480C2212yes—
66#19151479C2212yes—
67#19151479C2212yes—
68#19151479C2212yes—
69#19151478C2211yescharacteristic
70#19151473C2211yescharacteristic
71#19151471C2211yescharacteristic
72#19151471C2212yes—
73#19151470C2212yes—
74#19151470C2212yes—
75#19151467C2212yes—
76#19151465C2212yes—
77#19151465C2212yes—
78#19151463C2211yescharacteristic
79#19151462C2212yes—
80#19151461C2211yescharacteristic
81#19151459C2211yescharacteristic
82#19151456C2212yes—
83C4⋊C4×Dic89C2212yes—
84C4⋊C4×Dic89C2212yes—
85C4⋊C4×Dic89C2212yes—
86#19151449C2212yes—
87#19151449C2212yes—
88#19151449C2212yes—
89#19151449C2212yes—
90#19151449C2212yes—
91C22⋊C4×Dic89C2212yes—
92C22⋊C4×Dic89C2211yescharacteristic
93C22⋊C4×Dic89C2212yes—
94C22⋊C4×Dic89C2211yescharacteristic
95C22⋊C4×Dic89C2212yes—
96C22⋊C4×Dic89C2212yes—
97C42×Dic89C2211yescharacteristic
98C42×Dic89C2212yes—
99C2×#123×C89C2211yescharacteristic
100#390×C89C2211yescharacteristic
101#389×C89C2212yes—
102#388×C89C2212yes—
103#388×C89C2212yes—
104#387×C89C2212yes—
105#386×C89C2211yescharacteristic
106#385×C89C2212yes—
107#380×C89C2212yes—
108C22×Dic178C2311yescharacteristic
109C22×Dic178C2312yes—
110C23×Dic89C2311yescharacteristic
111C23×Dic89C2311yescharacteristic
112C23×Dic89C2311yescharacteristic
113C23×Dic89C2311yescharacteristic
114#15668011C2×C4116yescomplemented
115#15668005C2×C4116yescomplemented
116#15668005C2×C4116yescomplemented
117#15668002C2×C4116yescomplemented
118#15667999C2×C418yes—
119#15667993C2×C418yes—
120#15667991C2×C4116yescomplemented
121#15667989C2×C4116yescomplemented
122#15667977—42no—
123#15667977—44no—
124D4×Dic89—42no—
125C2×C4⋊Dic89C2312yes—
126C2×C4⋊Dic89C2311yescharacteristic
127C2×C4⋊Dic89C2312yes—
128C2×C4⋊Dic89C2312yes—
129C2×#13083553C2312yes—
130C2×#13083553C2312yes—
131C2×#13083553C2312yes—
132C2×#13083553C2312yes—
133C2×#13083553C2312yes—
134C2×#13083553C2312yes—
135C2×#13083553C2312yes—
136C2×#13083553C2312yes—
137C2×#13083553C2312yes—
138C2×#13083553C2312yes—
139C2×#13083553C2312yes—
140C2×#13083553C2312yes—
141C2×#13083553C2312yes—
142C2×C22⋊Dic89C2312yes—
143C2×C22⋊Dic89C2311yescharacteristic
144C2×C22⋊Dic89C2311yescharacteristic
145C2×C22⋊Dic89C2311yescharacteristic
146C2×C22⋊Dic89C2312yes—
147C2×C22⋊Dic89C2312yes—
148C2×C22⋊Dic89C2312yes—
149C2×C22⋊Dic89C2311yescharacteristic
150C2×C4×Dic89—42no—
151C2×C4×Dic89—42no—
152C2×C4×Dic89C2312yes—
153C2×C4×Dic89C2312yes—
154C2×C4×Dic89C2312yes—
155C2×C4×Dic89C2312yes—
156C2×C4×Dic89C2311yescharacteristic
157C2×C4×Dic89C2312yes—
158C2×C4×Dic89C2312yes—
159C2×C4×Dic89C2312yes—
160C2×C4×Dic89C2312yes—
161C2×C4×Dic89C2312yes—
162C2×C4×Dic89C2312yes—
163C2×C4×Dic89C2312yes—
164C2×C4×Dic89C2312yes—
165C2×C4×Dic89C2311yescharacteristic
166#15667919C2312yes—
167#15667919C2312yes—
168#15667919C2312yes—
169#15667919C2312yes—
170#15667919C2312yes—
171#15667919C2312yes—
172#15667919C2312yes—
173#15667919C2312yes—
174#15667919C2312yes—
175#15667919C2312yes—
176#15667919C2312yes—
177#15667919C2312yes—
178#15667919C2312yes—
179#15667919C2312yes—
180#15667919C2312yes—
181#15667919C2312yes—
182#15667919C2312yes—
183#15667919C2312yes—
184#15667919C2312yes—
185#15667919C2312yes—
186#15667919C2312yes—
187C22×D4×C89C2311yescharacteristic
188C23×C4×C89C2311yescharacteristic
189C23×C4×C89C2311yescharacteristic
190#123×C89C2×C418yes—
191C2×C4⋊C4×C89C2312yes—
192C2×C4⋊C4×C89C2312yes—
193C2×C4⋊C4×C89C2312yes—
194C2×C4⋊C4×C89C2311yescharacteristic
195C2×C4⋊C4×C89C2312yes—
196C2×C22⋊C4×C89C2312yes—
197C2×C22⋊C4×C89C2312yes—
198C2×C22⋊C4×C89C2312yes—
199C2×C22⋊C4×C89C2311yescharacteristic
200C2×C22⋊C4×C89C2312yes—
201C2×C22⋊C4×C89C2311yescharacteristic
202C2×C42×C89C2311yescharacteristic
203C2×C42×C89C2312yes—
204#95×C89C2312yes—
205#95×C89C2312yes—
206#95×C89C2312yes—
207#95×C89C2312yes—
208#95×C89C2312yes—
209C2×Dic178—42no—
210C2×Dic178—41no—
211C2×Dic178—41no—
212C2×Dic178—42no—
213C2×Dic178C22×C418yes—
214C2×Dic178C22×C414yes—
215C22×Dic89—22no—
216C22×Dic89—22no—
217C22×Dic89—24no—
218C22×Dic89—24no—
219C22×Dic89—41no—
220C22×Dic89—42no—
221C22×Dic89—41no—
222C22×Dic89—41no—
223C22×Dic89C22×C414yes—
224C22×Dic89C2411yescharacteristic
225C22×Dic89C2411yescharacteristic
226C22×Dic89C2412yes—
227C22×Dic89C2412yes—
228C22×Dic89C2411yescharacteristic
229C22×Dic89C2412yes—
230C22×Dic89C2412yes—
231C22×Dic89C2412yes—
232C22×Dic89C2412yes—
233C22×Dic89C2411yescharacteristic
234C4⋊Dic89—41no—
235C4⋊Dic89—42no—
236C4⋊Dic89C22×C418yes—
237C4⋊Dic89C22×C418yes—
238#13083553—42no—
239#13083553—42no—
240#13083553—42no—
241#13083553—42no—
242#13083553—42no—
243#13083553—42no—
244#13083553—42no—
245#13083553—42no—
246#13083553C22×C418yes—
247#13083553C22×C418yes—
248#13083553C22×C418yes—
249#13083553C22×C418yes—
250#13083553C22×C418yes—
251C22⋊Dic89—41no—
252C22⋊Dic89—41no—
253C22⋊Dic89—41no—
254C22⋊Dic89—42no—
255C22⋊Dic89C22×C418yes—
256C22⋊Dic89C22×C418yes—
257C22⋊Dic89C22×C418yes—
258C22⋊Dic89C22×C414yes—
259C4×Dic89—22no—
260C4×Dic89—24no—
261C4×Dic89—24no—
262C4×Dic89—24no—
263C4×Dic89—24no—
264C4×Dic89—24no—
265C4×Dic89—24no—
266C4×Dic89—42no—
267C4×Dic89—42no—
268C4×Dic89—42no—
269C4×Dic89—42no—
270C4×Dic89—42no—
271C4×Dic89C22×C414yes—
272C4×Dic89C22×C418yes—
273C24×C89C2411yescharacteristic
274C24×C89C2411yescharacteristic
275C2×D4×C89—41no—
276C2×D4×C89—41no—
277C2×D4×C89C22×C414yes—
278C22×C4×C89—41no—
279C22×C4×C89—42no—
280C22×C4×C89—41no—
281C22×C4×C89—41no—
282C22×C4×C89C22×C414yes—
283C22×C4×C89C2412yes—
284C22×C4×C89C2412yes—
285C22×C4×C89C2412yes—
286C22×C4×C89C2412yes—
287C22×C4×C89C2411yescharacteristic
288C22×C4×C89C2412yes—
289C22×C4×C89C2412yes—
290C4⋊C4×C89—42no—
291C4⋊C4×C89—41no—
292C4⋊C4×C89—42no—
293C4⋊C4×C89—42no—
294C4⋊C4×C89C22×C418yes—
295C22⋊C4×C89—42no—
296C22⋊C4×C89—42no—
297C22⋊C4×C89—42no—
298C22⋊C4×C89—41no—
299C22⋊C4×C89C22×C418yes—
300C22⋊C4×C89C22×C414yes—
301C42×C89—42no—
302C42×C89—41no—
303C23×C89—21no—
304C23×C89—21no—
305C23×C89—22no—
306C23×C89—22no—
307C23×C89—22no—
308C23×C89—22no—
309C23×C89—21no—
310C23×C89—21no—
311C23×C89C23×C412yes—
312C23×C89C23×C412yes—
313C23×C89C2511yescharacteristic
314D4×C89—44no—
315C2×C4×C89—22no—
316C2×C4×C89—21no—
317C2×C4×C89—22no—
318C2×C4×C89—22no—
319C2×C4×C89—21no—
320C2×C4×C89—22no—
321C2×C4×C89—22no—
322C2×C4×C89—22no—
323C2×C4×C89—22no—
324C2×C4×C89—22no—
325C2×C4×C89—22no—
326C2×C4×C89—22no—
327C2×C4×C89—22no—
328C2×C4×C89—22no—
329C2×C4×C89—22no—
330C2×C4×C89—22no—
331C2×C4×C89—22no—
332C2×C4×C89—22no—
333C2×C4×C89—44no—
334C2×C4×C89—44no—
335C2×C4×C89C23×C414yes—
336C2×C4×C89C23×C414yes—
337C2×C4×C89C23×C412yes—
338C2×Dic89—22no—
339C2×Dic89—22no—
340C2×Dic89—22no—
341C2×Dic89—22no—
342C2×Dic89—22no—
343C2×Dic89—22no—
344C2×Dic89—22no—
345C2×Dic89—22no—
346C2×Dic89—22no—
347C2×Dic89—21no—
348C2×Dic89—21no—
349C2×Dic89—21no—
350C2×Dic89—22no—
351C2×Dic89—22no—
352C2×Dic89—22no—
353C2×Dic89—22no—
354C2×Dic89—22no—
355C2×Dic89—22no—
356C2×Dic89—22no—
357C2×Dic89—22no—
358C2×Dic89—44no—
359C2×Dic89—44no—
360C2×Dic89—44no—
361C2×Dic89—44no—
362C2×Dic89C23×C414yes—
363C2×Dic89C23×C414yes—
364C2×Dic89C23×C414yes—
365C2×Dic89C23×C414yes—
366C2×Dic89H(5,𝔽2)12yes—
367C2×Dic892−1+414yes—
368Dic178—44no—
369Dic178—48no—
370C22×C89—22no—
371C22×C89—22no—
372C22×C89—24no—
373C22×C89—24no—
374C22×C89—41no—
375C22×C89—41no—
376C22×C89—41no—
377C22×C89—41no—
378C22×C89—42no—
379C22×C89—42no—
380C22×C89C24×C411yescharacteristic
381C22×C89C2×H(5,𝔽2)11yescharacteristic
382C22×C89C2×2−1+412yes—
383C22×C89#58511yescharacteristic
384C22×C89#58512yes—
385C4×C89—24no—
386C4×C89—22no—
387C4×C89—24no—
388C4×C89—42no—
389C4×C89—42no—
390C4×C89—42no—
391C4×C89—42no—
392Dic89—24no—
393Dic89—24no—
394Dic89—24no—
395Dic89—24no—
396Dic89—41no—
397Dic89—41no—
398Dic89—41no—
399Dic89—42no—
400Dic89—42no—
401Dic89#56314yescomplemented
402C4×#563—891nomaximal, Sylow
403C2×C89—42no—
404C2×C89—42no—
405C2×C89C4×H(5,𝔽2)11yescharacteristic
406C2×C89C4×2−1+412yes—
407C2×C89C2×#56311yescharacteristic
408C2×C89#352911yescharacteristic
409C2×C89#353112yes—
410C2×#563—891no—
411#2383—892no—
412#2383—892no—
413#2382—892no—
414#2381—892no—
415#2379—891no—
416#2378—892no—
417#2378—892no—
418#2376—891no—
419#2376D8911yescharacteristic
420C4×C4⋊Q8—892no—
421C4×#125—892no—
422C4×#126—892no—
423C4×#126—892no—
424C4×#124—891no—
425C4×C22⋊Q8—892no—
426C4×C22⋊Q8—892no—
427C4×#123—891no—
428C4×#123—891no—
429C89C4×#56311yescharacteristic, complemented, Sylow
430#563—8916no—
431C2×C4⋊Q8—892no—
432C2×#126—892no—
433C2×#126—892no—
434C2×#125—892no—
435C2×#124—891no—
436C2×#123—891no—
437C2×#123C2×D8911yescharacteristic
438C2×C22⋊Q8—892no—
439C2×C22⋊Q8—892no—
440C2×C4×Q8—891no—
441C2×C4×Q8—892no—
442C2×C4×D4—891no—
443C22×C42—891no—
444C22×C42—891no—
445#391—892no—
446#391—891no—
447#391—892no—
448#391—892no—
449#391—892no—
450#390C2×D8911yescharacteristic
451#389—892no—
452#389—892no—
453#389—892no—
454#389—892no—
455#389—892no—
456#389—892no—
457#389—892no—
458#389C2×D8912yes—
459#388—892no—
460#388—892no—
461#388—892no—
462#388—892no—
463#388—892no—
464#388—892no—
465#388—892no—
466#388—892no—
467#388C2×D8912yes—
468#388C2×D8912yes—
469#387—892no—
470#387—892no—
471#387—892no—
472#387—892no—
473#387—892no—
474#387—892no—
475#387—892no—
476#387—892no—
477#387—892no—
478#387—892no—
479#387—892no—
480#387—892no—
481#387—892no—
482#387—892no—
483#387—892no—
484#387C2×D8912yes—
485#386—891no—
486#386C2×D8911yescharacteristic
487#385—892no—
488#385—891no—
489#385—892no—
490#385—892no—
491#385—891no—
492#385C2×D8912yes—
493#384—892no—
494#383—892no—
495#383—892no—
496#382—891no—
497#382—892no—
498#381—891no—
499#381—891no—
500#380—892no—
501#380C2×D8912yes—
502C4×C4⋊C4—892no—
503C4×C4⋊C4—892no—
504C4×C4⋊C4—892no—
505C4×C4⋊C4—892no—
506C4×C4⋊C4—892no—
507C4×C4⋊C4—892no—
508C4×C4⋊C4—892no—
509C4×C4⋊C4—892no—
510C4×C22⋊C4—891no—
511C4×C22⋊C4—891no—
512C4×C22⋊C4—892no—
513C4×C22⋊C4—892no—
514C4×C22⋊C4—892no—
515C4×C22⋊C4—892no—
516C43—892no—
517C43—891no—
518C22×Q8—892no—
519C22×Q8—891no—
520C22×D4C22×D8911yescharacteristic
521C23×C4—891no—
522C23×C4—891no—
523C23×C4—891no—
524C23×C4—891no—
525C23×C4C22×D8911yescharacteristic
526C23×C4C22×D8911yescharacteristic
527C4⋊Q8—8916no—
528#126—8916no—
529#126—8916no—
530#125—8916no—
531#124—898no—
532#123—898no—
533#123C4×D8918yes—
534C22⋊Q8—8916no—
535C22⋊Q8—8916no—
536C4×Q8—3564no—
537C4×Q8—3562no—
538C4×D4—3562no—
539C2×C4⋊C4—892no—
540C2×C4⋊C4—892no—
541C2×C4⋊C4—892no—
542C2×C4⋊C4—892no—
543C2×C4⋊C4—892no—
544C2×C4⋊C4—892no—
545C2×C4⋊C4—892no—
546C2×C4⋊C4—891no—
547C2×C4⋊C4—892no—
548C2×C4⋊C4—892no—
549C2×C4⋊C4—892no—
550C2×C4⋊C4—892no—
551C2×C4⋊C4—892no—
552C2×C4⋊C4—892no—
553C2×C4⋊C4—892no—
554C2×C4⋊C4—892no—
555C2×C4⋊C4—892no—
556C2×C4⋊C4C22×D8912yes—
557C2×C4⋊C4C22×D8911yescharacteristic
558C2×C4⋊C4C22×D8912yes—
559C2×C4⋊C4C22×D8912yes—
560C2×C4⋊C4C22×D8912yes—
561C2×C22⋊C4—892no—
562C2×C22⋊C4—892no—
563C2×C22⋊C4—892no—
564C2×C22⋊C4—891no—
565C2×C22⋊C4—891no—
566C2×C22⋊C4—891no—
567C2×C22⋊C4—892no—
568C2×C22⋊C4—891no—
569C2×C22⋊C4C22×D8912yes—
570C2×C22⋊C4C22×D8912yes—
571C2×C22⋊C4C22×D8912yes—
572C2×C22⋊C4C22×D8911yescharacteristic
573C2×C22⋊C4C22×D8912yes—
574C2×C22⋊C4C22×D8911yescharacteristic
575C2×C42—891no—
576C2×C42—892no—
577C2×C42—892no—
578C2×C42—892no—
579C2×C42—892no—
580C2×C42—892no—
581C2×C42—892no—
582C2×C42—891no—
583C2×C42—892no—
584C2×C42—892no—
585C2×C42—892no—
586C2×C42—892no—
587C2×C42—892no—
588C2×C42—892no—
589C2×C42—3562no—
590C2×C42—3562no—
591C2×C42C22×D8911yescharacteristic
592C2×C42C22×D8912yes—
593#95—892no—
594#95—892no—
595#95—892no—
596#95—892no—
597#95—892no—
598#95—892no—
599#95—892no—
600#95—892no—
601#95—892no—
602#95—892no—
603#95—892no—
604#95—892no—
605#95—892no—
606#95—892no—
607#95—892no—
608#95—892no—
609#95—892no—
610#95—892no—
611#95—892no—
612#95—892no—
613#95—892no—
614#95C22×D8912yes—
615#95C22×D8912yes—
616#95C22×D8912yes—
617#95C22×D8912yes—
618#95C22×D8912yes—
619C24C23×D8911yescharacteristic
620C24C23×D8911yescharacteristic
621C2×Q8—898no—
622C2×Q8—894no—
623C2×Q8—3562no—
624C2×Q8—3561no—
625C2×Q8—3561no—
626C2×Q8—3562no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4C2×C4×D8914yes—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—891no—
635C22×C4—894no—
636C22×C4—892no—
637C22×C4—892no—
638C22×C4—892no—
639C22×C4—892no—
640C22×C4—891no—
641C22×C4—891no—
642C22×C4—892no—
643C22×C4—892no—
644C22×C4—891no—
645C22×C4—3561no—
646C22×C4—3561no—
647C22×C4—3562no—
648C22×C4—3561no—
649C22×C4—1782no—
650C22×C4—1782no—
651C22×C4—1784no—
652C22×C4—1784no—
653C22×C4C2×C4×D8914yes—
654C22×C4C23×D8912yes—
655C22×C4C23×D8912yes—
656C22×C4C23×D8912yes—
657C22×C4C23×D8912yes—
658C22×C4C23×D8912yes—
659C22×C4C23×D8911yescharacteristic
660C22×C4C23×D8912yes—
661C4⋊C4—42no—
662C4⋊C4—41no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—898no—
666C4⋊C4—898no—
667C4⋊C4—898no—
668C4⋊C4—898no—
669C4⋊C4—898no—
670C4⋊C4—898no—
671C4⋊C4—898no—
672C4⋊C4—3561no—
673C4⋊C4—3562no—
674C4⋊C4—3562no—
675C4⋊C4—3562no—
676C4⋊C4—3562no—
677C4⋊C4—3562no—
678C4⋊C4—3562no—
679C4⋊C4—3562no—
680C4⋊C4—3562no—
681C4⋊C4—3562no—
682C4⋊C4C2×C4×D8918yes—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—41no—
687C22⋊C4—898no—
688C22⋊C4—898no—
689C22⋊C4—898no—
690C22⋊C4—894no—
691C22⋊C4—3561no—
692C22⋊C4—3561no—
693C22⋊C4—3561no—
694C22⋊C4—3562no—
695C22⋊C4C2×C4×D8918yes—
696C22⋊C4C2×C4×D8914yes—
697C42—42no—
698C42—41no—
699C42—894no—
700C42—898no—
701C42—3562no—
702C42—3562no—
703C42—3562no—
704C42—3562no—
705C42—3562no—
706C42—1784no—
707C42—1784no—
708C42—1782no—
709C42—1784no—
710C42—1784no—
711C42—1784no—
712C42—1784no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—21no—
720C23—21no—
721C23C22×C4×D8912yes—
722C23C22×C4×D8912yes—
723C23C24×D8911yescharacteristic
724Q8—3568no—
725Q8—3564no—
726D4—44no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—892no—
748C2×C4—894no—
749C2×C4—894no—
750C2×C4—894no—
751C2×C4—894no—
752C2×C4—894no—
753C2×C4—3564no—
754C2×C4—3564no—
755C2×C4—3564no—
756C2×C4—3564no—
757C2×C4—1781no—
758C2×C4—1781no—
759C2×C4—1782no—
760C2×C4—1781no—
761C2×C4—1782no—
762C2×C4—1782no—
763C2×C4—1782no—
764C2×C4—1782no—
765C2×C4—1782no—
766C2×C4—1782no—
767C2×C4—1782no—
768C2×C4—1782no—
769C2×C4—1782no—
770C2×C4—1782no—
771C2×C4—1782no—
772C2×C4—1782no—
773C2×C4—1782no—
774C2×C4—1782no—
775C2×C4—1782no—
776C2×C4—1782no—
777C2×C4C22×C4×D8914yes—
778C2×C4C22×C4×D8912yes—
779C2×C4C22×C4×D8914yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22C23×C4×D8911yescharacteristic
791C22H(5,𝔽2)×D8911yescharacteristic
792C222−1+4×D8912yes—
793C22#1915243311yescharacteristic
794C22#1915243312yes—
795C4—24no—
796C4—22no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—894no—
803C4—3561no—
804C4—3561no—
805C4—3562no—
806C4—3561no—
807C4—3562no—
808C4—1784no—
809C4—1784no—
810C4—1784no—
811C4—1784no—
812C2—42no—
813C2—42no—
814C2#2603345611yescharacteristic
815C2#2603346312yes—
816C2#563×D8911yescharacteristic
817C2#2603438711yescharacteristic
818C2#2603439612yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2376C2
socle, cosocleC23×C89C25
prime radicalC22×D4×C89C23
hypercenter#2376D89
hypocenterC89C4×#563
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2376

Complements

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

NH ≅ G/Ntype
2. #26023440C2semidirect
3. #26023439C2semidirect
4. #26023434C2semidirect
5. #26023430C2semidirect
7. #26023415C2semidirect
8. #26023412C2semidirect
10. #26022823C2semidirect
11. #26022809C2semidirect
12. #26022806C2semidirect
13. #26022806C2semidirect
15. #26022784C2semidirect
16. #26022780C2semidirect
20. #19152351C4semidirect
114. #15668011C2×C4semidirect
115. #15668005C2×C4semidirect
116. #15668005C2×C4semidirect
117. #15668002C2×C4semidirect
120. #15667991C2×C4semidirect
121. #15667989C2×C4semidirect
401. Dic89#563semidirect
429. C89C4×#563semidirect

Maximal subgroups

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

subgroupindex
C2×#191523512
#260234402
#260234392
#260234342
#260234302
#260234222
#260234152
#260234122
#260234022
#260228232
#260228092
#260228062
#260227992
#260227842
#260227802
#260227772
#123×Dic892
C89×#23762
C4×#56389