Finite Group Databasebeta

← #10944113

Subgroups — #10944113

Order 768.

1406 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic
2C2×C3×#452C211yesmaximal, characteristic
3C2×#5239C211yesmaximal, characteristic
4C2×#5182C211yesmaximal, characteristic, complemented
5C2×#5162C211yesmaximal, characteristic, complemented
6#82786C211yesmaximal, characteristic, complemented
7#72065C211yesmaximal, characteristic, complemented
8#72047C211yesmaximal, characteristic, complemented
9#71692C211yesmaximal, characteristic, complemented
10#70239C211yesmaximal, characteristic, complemented
11#70222C211yesmaximal, characteristic, complemented
12#70171C211yesmaximal, characteristic, complemented
13#70154C211yesmaximal, characteristic, complemented
14#69930C211yesmaximal, characteristic, complemented
15#69909C211yesmaximal, characteristic, complemented
16#32916—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21#5827—24no—
22#5827—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×#944C2211yescharacteristic
26C22×#216C2211yescharacteristic
27C2×D4×Dic3—21no—
28C2×D4×Dic3—21no—
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C2×#926—21no—
33C2×#926C2211yescharacteristic
34C22×C4⋊Dic3—21no—
35C22×C4⋊Dic3C2211yescharacteristic
36C2×#924C2211yescharacteristic
37C3×#452—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41#5239—24no—
42#5229C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#835C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5182—24no—
49#5162—24no—
50C2×#816C2211yescharacteristic
51C2×#816C2211yescharacteristic
52C2×Dic3⋊C8C2211yescharacteristic
53C2×Dic3⋊C8C2211yescharacteristic
54#4982—21no—
55#4982—21no—
56#4977C2211yescharacteristic
57#4973C2211yescharacteristic
58#4952—21no—
59#4952—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#520—31no—
67C2×#462—31no—
68C2×#461—31no—
69C2×#452—31no—
70C2×#452D311yescharacteristic
71#2621—31no—
72#1878—31no—
73#1878—31no—
74#1877—31no—
75#1877—31no—
76#1872—31no—
77#1872—31no—
78#1805—31no—
79#1804—31no—
80#1798—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×Dic3—21no—
94C23×Dic3—21no—
95C23×Dic3—21no—
96C22×Dic6C2311yescharacteristic
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114C2×#217D411yescharacteristic
115Q8×Dic3—22no—
116Q8×Dic3—22no—
117Q8×Dic3—22no—
118Q8×Dic3D414yes—
119#944—22no—
120#944—22no—
121C2×#216—22no—
122C2×#216—22no—
123C2×#216—22no—
124D4×Dic3—28no—
125D4×Dic3—28no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128D4×Dic3—22no—
129D4×Dic3D414yes—
130C2×#214—22no—
131C2×#214—22no—
132C2×#214—22no—
133#926—28no—
134#926—22no—
135#926—22no—
136C2×C4⋊Dic3—28no—
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3—22no—
141C2×C4⋊Dic3—22no—
142C2×C4⋊Dic3D411yescharacteristic
143C2×C4⋊Dic3D411yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147#924—22no—
148#924—22no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4—21no—
152C2×C4×Dic3—21no—
153C2×C4×Dic3—21no—
154C2×C4×Dic3C2311yescharacteristic
155C2×C4×Dic3C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C3×#103—22no—
159C3×#102—22no—
160C3×C22⋊C8—22no—
161#835—22no—
162#835—22no—
163#835—22no—
164#832—22no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#816—22no—
173#816—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176C22×#41C2×D311yescharacteristic
177C22×Q16—31no—
178C22×Q16C2×D311yescharacteristic
179C22×SD16—31no—
180C22×SD16C2×D311yescharacteristic
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8C2×D311yescharacteristic
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#462—64no—
197#461—64no—
198#452—24no—
199#452—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#398—61no—
213#398—61no—
214#397—61no—
215#397—61no—
216#391—31no—
217#391—31no—
218#382—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C3×#41—28no—
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—28no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8C2×D412yes—
241C2×C3×Q8C2×D412yes—
242C2×C3×Q8#4112yes—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4C2×D412yes—
250C2×C3×D4C2×D412yes—
251C2×C3×D4#4112yes—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4—21no—
255C22×C3×C4—24no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4#4112yes—
265C22×C3×C4C2411yescharacteristic
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—24no—
269C22×Dic3—24no—
270C22×Dic3—24no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—81no—
274C22×Dic3—81no—
275C22×Dic3—81no—
276C22×Dic3—81no—
277C22×Dic3—81no—
278C22×Dic3—81no—
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C3×Q16—44no—
290C3×SD16—44no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—42no—
300C3×C22⋊C4—42no—
301#217—24no—
302#217—22no—
303#217—22no—
304#217—24no—
305#217—42no—
306#216—44no—
307#214—44no—
308C4⋊Dic3—24no—
309C4⋊Dic3—24no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—22no—
313C4⋊Dic3—24no—
314C4⋊Dic3—22no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3C2×D412yes—
318C4⋊Dic3C2×D412yes—
319Dic3⋊C4—42no—
320Dic3⋊C4—42no—
321Dic3⋊C4—42no—
322C4×Dic3—24no—
323C4×Dic3—21no—
324C4×Dic3—21no—
325C4×Dic3—24no—
326C4×Dic3C2×D412yes—
327C4×Dic3C2×D412yes—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41#6714yes—
340C22×Q8—31no—
341C22×Q8C22×D311yescharacteristic
342C22×Q8C22×D311yescharacteristic
343C22×D4—21no—
344C22×D4C22×D311yescharacteristic
345C23×C4—21no—
346C23×C4—61no—
347C23×C4—61no—
348C23×C4—61no—
349C23×C4C22×D311yescharacteristic
350C2×Q16—22no—
351C2×Q16—22no—
352C2×Q16—22no—
353C2×Q16—62no—
354C2×Q16—62no—
355C2×Q16—62no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—62no—
360C2×SD16—62no—
361C2×SD16—62no—
362C22×C8—31no—
363C22×C8—31no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366C4⋊Q8—62no—
367C4⋊Q8—62no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—62no—
371C22⋊Q8—62no—
372C4×Q8—34no—
373C4×Q8—62no—
374C4×Q8—62no—
375C4×Q8—62no—
376C4×D4—34no—
377C4×D4—62no—
378C4×D4—62no—
379C4×D4—68no—
380C4×D4—68no—
381C4×D4—62no—
382#117—62no—
383#117—62no—
384#117—68no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—68no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—61no—
410C2×C42—61no—
411C4⋊C8—62no—
412C4⋊C8—62no—
413#103—22no—
414#103—62no—
415#103—62no—
416#103—62no—
417#103—62no—
418#103—62no—
419#102—22no—
420#102—62no—
421C22⋊C8—22no—
422C22⋊C8—62no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427#95—61no—
428#95—61no—
429C23×C3—21no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—21no—
433C23×C3—22no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3#12112yes—
443C23×C3C22×D411yescharacteristic
444C3×Q8—22no—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8#12114yes—
452C3×D4—216no—
453C3×D4—22no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4#12114yes—
457C2×C3×C4—216no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4#12112yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—84no—
503C2×Dic3—84no—
504C2×Dic3—84no—
505C2×Dic3#12012yes—
506C2×Dic3#12012yes—
507Dic6—41no—
508Dic6—41no—
509Dic6—41no—
510Dic6—41no—
511C3×C8—41no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—21no—
516C24D3×D411yescharacteristic
517#41—28no—
518#41—28no—
519#41—28no—
520#41—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8D3×D412yes—
537C2×Q8#23712yes—
538C2×Q8C2×#6712yes—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4D3×D412yes—
546C2×D4#23712yes—
547C2×D4C2×#6712yes—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—64no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—241no—
570C22×C4—241no—
571C22×C4—241no—
572C22×C4—241no—
573C22×C4—241no—
574C22×C4—241no—
575C22×C4D3×D411yescharacteristic
576C22×C4#23712yes—
577C22×C4C2×#6712yes—
578C22×C4C23×D311yescharacteristic
579Q16—44no—
580Q16—124no—
581SD16—44no—
582SD16—124no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—61no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—32no—
598C4⋊C4—32no—
599C4⋊C4—42no—
600C4⋊C4—62no—
601C4⋊C4—62no—
602C4⋊C4—64no—
603C4⋊C4—64no—
604C4⋊C4—64no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—122no—
610C4⋊C4—122no—
611C4⋊C4—122no—
612C22⋊C4—42no—
613C22⋊C4—62no—
614C22⋊C4—62no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—122no—
618C42—32no—
619C42—32no—
620C42—64no—
621C42—64no—
622C42—61no—
623C42—61no—
624C22×C3—22no—
625C22×C3—24no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—41no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3C2×#12011yescharacteristic
639C22×C3C2×#12111yescharacteristic
640C22×C3#52511yescharacteristic
641C22×C3#57711yescharacteristic
642C22×C3#57711yescharacteristic
643C22×C3#57811yescharacteristic
644C22×C3#57811yescharacteristic
645C3×C4—22no—
646C3×C4—24no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4C2×#12111yescharacteristic
650C3×C4C2×#12111yescharacteristic
651C3×C4#52511yescharacteristic
652C3×C4#52511yescharacteristic
653Dic3—22no—
654Dic3—22no—
655Dic3—41no—
656Dic3—42no—
657Dic3—42no—
658Dic3—41no—
659Dic3—81no—
660Dic3—81no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23#93912yes—
675C23C2×D3×D411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—121no—
684Q8—121no—
685Q8—121no—
686Q8—121no—
687Q8#93914yes—
688D4—216no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4#93914yes—
693C2×C4—216no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—244no—
734C2×C4—244no—
735C2×C4—244no—
736C2×C4#93912yes—
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4C2×#23711yescharacteristic
740C2×C4C2×#23711yescharacteristic
741C2×C4C2×#23711yescharacteristic
742C2×C4C22×#6711yescharacteristic
743C8—41no—
744C8—41no—
745C8—121no—
746C8—121no—
747C2×C3—42no—
748C2×C3—44no—
749C2×C3#284711yescharacteristic
750C2×C3#300911yescharacteristic
751C2×C3#301111yescharacteristic
752C2×C3#304611yescharacteristic
753C2×C3#304611yescharacteristic
754C2×C3#312011yescharacteristic
755C2×C3#312011yescharacteristic
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22#558611yescharacteristic
771C22D3×#12011yescharacteristic
772C22#577011yescharacteristic
773C22#577111yescharacteristic
774C22#577811yescharacteristic
775C22#577911yescharacteristic
776C22C2×#93911yescharacteristic
777C4—22no—
778C4—24no—
779C4—62no—
780C4—62no—
781C4—81no—
782C4—81no—
783C4—121no—
784C4—122no—
785C4—122no—
786C4—121no—
787C4—241no—
788C4—241no—
789C4#558611yescharacteristic
790C4#558611yescharacteristic
791C4C2×#93911yescharacteristic
792C4C2×#93911yescharacteristic
793C3#3291611yescharacteristic, complemented, Sylow
794C2—42no—
795C2—44no—
796C2#8021611yescharacteristic
797C2#8021711yescharacteristic
798C2#8022911yescharacteristic
799C2#8023011yescharacteristic
800C2#8260111yescharacteristic
801C2#8390211yescharacteristic
802C2#8397111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC22×C3×#41C22
hypercenterC2×#452D3
hypocenterC3#32916
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
4. C2×#5182C2semidirect
5. C2×#5162C2semidirect
6. #82786C2semidirect
7. #72065C2semidirect
8. #72047C2semidirect
9. #71692C2semidirect
10. #70239C2semidirect
11. #70222C2semidirect
12. #70171C2semidirect
13. #70154C2semidirect
14. #69930C2semidirect
15. #69909C2semidirect
793. C3#32916semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4522
C2×#52392
C2×#51822
C2×#51622
#827862
#720652
#720472
#716922
#702392
#702222
#701712
#701542
#699302
#699092
#329163