Finite Group Databasebeta

← #10700634

Subgroups — #10700634

Order 768.

1498 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5486C211yesmaximal, characteristic
2C22×#806C211yesmaximal, characteristic
3C22×#806C211yesmaximal, characteristic
4C2×C3×#342C211yesmaximal, characteristic, complemented
5C2×#4527C211yesmaximal, characteristic, complemented
6C2×#4527C211yesmaximal, characteristic, complemented
7C2×#4526C211yesmaximal, characteristic, complemented
8#10768—31nomaximal, Sylow
9C23×#67C2211yescharacteristic
10C22×C3×C22⋊C4C2211yescharacteristic
11C22×C3×C22⋊C4C2211yescharacteristic
12C22×C3×C22⋊C4C2211yescharacteristic
13C22×#217C2211yescharacteristic
14C22×#217C2211yescharacteristic
15C22×#217C2211yescharacteristic
16C2×C4×#67—22no—
17#5486—22no—
18#5486—22no—
19#5486—22no—
20#5486—22no—
21C2×#67⋊C4—22no—
22C2×D3×C22⋊C4C412yescomplemented
23C2×#877C412yescomplemented
24C2×#806—22no—
25C2×#806—22no—
26C2×#806—22no—
27C2×#806—22no—
28C2×#806C414yescomplemented
29C2×#806C414yescomplemented
30C3×#342—22no—
31#4527—22no—
32#4527—22no—
33#4526—22no—
34C2×#518—31no—
35C22×#99—31no—
36C22×#99—31no—
37C2×#342—31no—
38C2×#342—31no—
39C2×#342—31no—
40C2×#342D311yescharacteristic, complemented
41C25×C3C2311yescharacteristic
42C24×D3C2×C411yescharacteristic
43C23×C3×C4—21no—
44C23×C3×C4—21no—
45C23×C3×C4—21no—
46C22×#67—21no—
47C22×#67—21no—
48C22×#67—21no—
49C22×#67—21no—
50C22×#67—21no—
51C22×#67—21no—
52C22×#67—21no—
53C22×#67—21no—
54C22×#67C2×C412yes—
55C22×#67C2×C412yes—
56C22×#67D412yes—
57C22×#67D412yes—
58C22×#67D412yes—
59C22×#67Q812yes—
60C23×Dic3—21no—
61C23×Dic3—21no—
62C23×Dic3—21no—
63C23×Dic3C2×C411yescharacteristic
64C22×C4×D3—22no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—21no—
67C2×C3×C22⋊C4—21no—
68C2×C3×C22⋊C4—21no—
69C2×C3×C22⋊C4—21no—
70C2×C3×C22⋊C4—21no—
71C2×C3×C22⋊C4—21no—
72C2×C3×C22⋊C4—21no—
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—21no—
75C2×C3×C22⋊C4—21no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C22⋊C4C2×C412yes—
79C2×C3×C22⋊C4C2×C412yescomplemented
80C2×C3×C22⋊C4C2×C412yescomplemented
81C2×C3×C22⋊C4D412yes—
82C2×C3×C22⋊C4D412yes—
83C2×#217—21no—
84C2×#217—21no—
85C2×#217—21no—
86C2×#217—21no—
87C2×#217—21no—
88C2×#217—21no—
89C2×#217—21no—
90C2×#217—21no—
91C2×#217—21no—
92C2×#217—21no—
93C2×#217—21no—
94C2×#217—21no—
95C2×#217—21no—
96C2×#217C2×C412yes—
97C2×#217C2×C412yescomplemented
98C2×#217C2×C412yescomplemented
99C2×#217D412yes—
100C2×#217D412yes—
101C4×#67—28no—
102C4×#67—28no—
103C2×(C2×D3)⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×C4×Dic3—22no—
106#67⋊C4—28no—
107#67⋊C4—28no—
108D3×C22⋊C4—24no—
109D3×C22⋊C4—24no—
110#877—24no—
111#877—24no—
112#806—28no—
113#806—28no—
114C23×D4—31no—
115#518—62no—
116#518—62no—
117#518—62no—
118#518—62no—
119C2×C4×D4—62no—
120C2×C4×D4—62no—
121C2×#117—32no—
122C22×C22⋊C4—31no—
123C22×C22⋊C4—31no—
124C22×C22⋊C4—31no—
125C22×C22⋊C4—32no—
126C22×C22⋊C4C2×D311yescharacteristic
127C22×C22⋊C4C2×D311yescharacteristic
128C22×C22⋊C4C2×D311yescharacteristic
129C2×#99—34no—
130C2×#99—34no—
131C2×#99—62no—
132C2×#99—62no—
133C2×#99—62no—
134C2×#99—62no—
135#342—22no—
136#342—62no—
137#342—62no—
138#342—62no—
139C24×C3—82no—
140C24×C3C22×C411yescharacteristic
141C24×C3C22×C411yescharacteristic
142C24×C3C22×C411yescharacteristic
143C24×C3C2×D411yescharacteristic
144C24×C3C2×D411yescharacteristic
145C24×C3C2×D411yescharacteristic
146C24×C3C2×D411yescharacteristic
147C24×C3C2×D411yescharacteristic
148C24×C3C2×D411yescharacteristic
149C24×C3C2×D411yescharacteristic
150C24×C3C2×Q811yescharacteristic
151C24×C3#4111yescharacteristic
152C24×C3#4111yescharacteristic
153C24×C3#4111yescharacteristic
154C24×C3#4111yescharacteristic
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—82no—
160C23×D3C4212yes—
161C23×D3C22⋊C412yes—
162C23×D3C4⋊C412yes—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—82no—
173C22×C3×C4—82no—
174C22×C3×C4—82no—
175C2×#67—22no—
176C2×#67—22no—
177C2×#67—22no—
178C2×#67—22no—
179C2×#67—22no—
180C2×#67—22no—
181C2×#67—22no—
182C2×#67—22no—
183C2×#67—22no—
184C2×#67—22no—
185C2×#67—22no—
186C2×#67—22no—
187C2×#67—22no—
188C2×#67—22no—
189C2×#67—22no—
190C2×#67—22no—
191C2×#67—22no—
192C2×#67—22no—
193C2×#67—22no—
194C2×#67—22no—
195C2×#67—22no—
196C2×#67—22no—
197C2×#67—22no—
198C2×#67—22no—
199C2×#67C22⋊C414yes—
200C2×#67C22⋊C414yes—
201C2×#67C4⋊C414yes—
202C2×#67C4⋊C414yes—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—41no—
213C22×Dic3—41no—
214C22×Dic3—41no—
215C22×Dic3—41no—
216C22×Dic3—82no—
217C22×Dic3—82no—
218C22×Dic3—82no—
219C22×Dic3C4212yes—
220C22×Dic3C22⋊C412yes—
221C22×Dic3C4⋊C412yes—
222C2×C4×D3—28no—
223C2×C4×D3—84no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—22no—
226C3×C22⋊C4—22no—
227C3×C22⋊C4—22no—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—22no—
231C3×C22⋊C4—41no—
232C3×C22⋊C4—41no—
233C3×C22⋊C4—41no—
234C3×C22⋊C4—41no—
235C3×C22⋊C4C22⋊C414yes—
236#217—22no—
237#217—22no—
238#217—22no—
239#217—22no—
240#217—22no—
241#217—22no—
242#217—22no—
243#217—41no—
244#217—41no—
245#217—41no—
246#217—41no—
247#217C22⋊C414yes—
248(C2×D3)⋊C4—28no—
249Dic3⋊C4—28no—
250C4×Dic3—28no—
251C25—31no—
252C25C22×D311yescharacteristic
253C22×D4—32no—
254C22×D4—32no—
255C22×D4—32no—
256C22×D4—32no—
257C22×D4—32no—
258C22×D4—32no—
259C22×D4—61no—
260C22×D4—61no—
261C22×D4—61no—
262C22×D4—61no—
263C22×D4—61no—
264C22×D4—61no—
265C22×D4—61no—
266C22×D4—61no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—31no—
271C23×C4—62no—
272C23×C4—61no—
273C23×C4—61no—
274C23×C4—61no—
275C4×D4—68no—
276C4×D4—68no—
277C4×D4—68no—
278C4×D4—68no—
279#117—64no—
280#117—64no—
281C2×C4⋊C4—62no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—32no—
296C2×C22⋊C4—32no—
297C2×C22⋊C4—32no—
298C2×C22⋊C4—32no—
299C2×C22⋊C4—32no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—62no—
302C2×C22⋊C4—61no—
303C2×C22⋊C4—61no—
304C2×C22⋊C4—61no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—61no—
307C2×C22⋊C4—61no—
308C2×C22⋊C4—61no—
309C2×C22⋊C4—61no—
310C2×C22⋊C4—61no—
311C2×C22⋊C4—61no—
312C2×C22⋊C4—61no—
313C2×C22⋊C4—61no—
314C2×C22⋊C4—61no—
315C2×C22⋊C4—61no—
316C2×C22⋊C4C4×D312yes—
317C2×C22⋊C4C4×D312yescomplemented
318C2×C22⋊C4C4×D312yescomplemented
319C2×C22⋊C4D1212yes—
320C2×C22⋊C4#6712yes—
321C2×C42—62no—
322#99—68no—
323#99—68no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—81no—
332C23×C3—81no—
333C23×C3—81no—
334C23×C3—81no—
335C23×C3—81no—
336C23×C3—81no—
337C23×C3—81no—
338C23×C3—81no—
339C23×C3C2×C4211yescharacteristic
340C23×C3C2×C22⋊C411yescharacteristic
341C23×C3C2×C22⋊C411yescharacteristic
342C23×C3C2×C22⋊C411yescharacteristic
343C23×C3C2×C22⋊C411yescharacteristic
344C23×C3C2×C22⋊C411yescharacteristic
345C23×C3C2×C4⋊C411yescharacteristic
346C23×C3C2×C4⋊C411yescharacteristic
347C23×C3C2×C4⋊C411yescharacteristic
348C23×C3#11711yescharacteristic
349C23×C3#11711yescharacteristic
350C23×C3C4×D411yescharacteristic
351C23×C3C4×D411yescharacteristic
352C23×C3C4×D411yescharacteristic
353C23×C3C4×D411yescharacteristic
354C23×C3C4×D411yescharacteristic
355C23×C3C4×D411yescharacteristic
356C23×C3C4×D411yescharacteristic
357C23×C3C4×D411yescharacteristic
358C23×C3#12011yescharacteristic
359C23×C3#12011yescharacteristic
360C23×C3#12011yescharacteristic
361C23×C3#12011yescharacteristic
362C23×C3#12111yescharacteristic
363C23×C3#12111yescharacteristic
364C23×C3#12111yescharacteristic
365C23×C3#12111yescharacteristic
366C23×C3C22⋊Q811yescharacteristic
367C23×C3C22⋊Q811yescharacteristic
368C23×C3C22⋊Q811yescharacteristic
369C23×C3C22⋊Q811yescharacteristic
370C23×C3#12311yescharacteristic
371C23×C3#12311yescharacteristic
372C23×C3#12311yescharacteristic
373C23×C3#12311yescharacteristic
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—44no—
381C22×D3—82no—
382C22×D3—82no—
383C22×D3—82no—
384C22×D3—82no—
385C22×D3—82no—
386C22×D3—82no—
387C22×D3#9514yes—
388C2×C3×C4—24no—
389C2×C3×C4—44no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—82no—
393C2×C3×C4—82no—
394C2×C3×C4—82no—
395C2×C3×C4—82no—
396C2×C3×C4—82no—
397C2×C3×C4—82no—
398C2×C3×C4—82no—
399C2×C3×C4—82no—
400#67—24no—
401#67—24no—
402#67—24no—
403#67—24no—
404#67—24no—
405#67—24no—
406#67—24no—
407#67—24no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—24no—
415C2×Dic3—44no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—82no—
419C2×Dic3—82no—
420C2×Dic3—82no—
421C2×Dic3—82no—
422C2×Dic3—82no—
423C2×Dic3—82no—
424C2×Dic3—82no—
425C2×Dic3—82no—
426C2×Dic3#9514yes—
427C4×D3—88no—
428C24—32no—
429C24—32no—
430C24—32no—
431C24—61no—
432C24—61no—
433C24—61no—
434C24—61no—
435C24—82no—
436C24—242no—
437C24C2×C4×D311yescharacteristic
438C24C2×C4×D311yescharacteristic
439C24C2×C4×D311yescharacteristic
440C24C2×D1211yescharacteristic
441C24#23511yescharacteristic
442C24#23511yescharacteristic
443C24D3×D411yescharacteristic
444C24D3×D411yescharacteristic
445C24D3×D411yescharacteristic
446C24D3×D411yescharacteristic
447C24D3×D411yescharacteristic
448C24#23711yescharacteristic
449C24D3×Q811yescharacteristic
450C24#23911yescharacteristic
451C24C2×#6711yescharacteristic
452C2×D4—34no—
453C2×D4—34no—
454C2×D4—34no—
455C2×D4—34no—
456C2×D4—62no—
457C2×D4—62no—
458C2×D4—62no—
459C2×D4—62no—
460C2×D4—62no—
461C2×D4—62no—
462C2×D4—62no—
463C2×D4—62no—
464C2×D4—62no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4—62no—
469C2×D4—62no—
470C2×D4—62no—
471C2×D4—62no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—62no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—68no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—82no—
503C22×C4—82no—
504C22×C4—82no—
505C22×C4—121no—
506C22×C4—121no—
507C22×C4—121no—
508C22×C4—121no—
509C22×C4—244no—
510C22×C4—242no—
511C22×C4—242no—
512C22×C4—242no—
513C4⋊C4—68no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—34no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—68no—
527C22⋊C4—62no—
528C22⋊C4—62no—
529C22⋊C4—62no—
530C22⋊C4—62no—
531C22⋊C4—62no—
532C22⋊C4—62no—
533C22⋊C4—62no—
534C22⋊C4—121no—
535C22⋊C4—121no—
536C22⋊C4—121no—
537C22⋊C4—121no—
538C22⋊C4(C2×D3)⋊C414yes—
539C42—68no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3C2×#9511yescharacteristic
576C22×C3C4×C22⋊C411yescharacteristic
577C22×C3C4×C22⋊C411yescharacteristic
578C22×C3#37911yescharacteristic
579C22×C3#38011yescharacteristic
580C22×C3#38011yescharacteristic
581C22×C3#38111yescharacteristic
582C22×C3#38511yescharacteristic
583C22×C3#38511yescharacteristic
584C22×C3#38511yescharacteristic
585C22×C3#38511yescharacteristic
586C22×C3#38611yescharacteristic
587C22×C3#38611yescharacteristic
588C22×C3#38611yescharacteristic
589C22×C3#38611yescharacteristic
590C2×D3—24no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—44no—
594C2×D3—82no—
595C2×D3—82no—
596C2×D3—82no—
597C2×D3—82no—
598C3×C4—44no—
599C3×C4—82no—
600C3×C4—82no—
601Dic3—24no—
602Dic3—44no—
603Dic3—82no—
604Dic3—82no—
605C23—34no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—62no—
614C23—62no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—124no—
628C23—242no—
629C23—242no—
630C23—242no—
631C23—242no—
632C23—242no—
633C23—242no—
634C23C42×D311yescharacteristic
635C23#87211yescharacteristic
636C23C4×D1211yescharacteristic
637C23C4×D1211yescharacteristic
638C23D3×C22⋊C411yescharacteristic
639C23D3×C22⋊C411yescharacteristic
640C23D3×C22⋊C411yescharacteristic
641C23D3×C22⋊C411yescharacteristic
642C23#67⋊C411yescharacteristic
643C23#67⋊C411yescharacteristic
644C23#88211yescharacteristic
645C23#88211yescharacteristic
646C23#88311yescharacteristic
647C23#88311yescharacteristic
648C23#88411yescharacteristic
649C23#88411yescharacteristic
650C23D3×C4⋊C411yescharacteristic
651C23D3×C4⋊C411yescharacteristic
652C23D3×C4⋊C411yescharacteristic
653C23#89211yescharacteristic
654C23#89311yescharacteristic
655C23#89311yescharacteristic
656C23#89411yescharacteristic
657C23#89411yescharacteristic
658C23#89511yescharacteristic
659C23#89611yescharacteristic
660C23#89611yescharacteristic
661C23#89711yescharacteristic
662C23C2×(C2×D3)⋊C411yescharacteristic
663C23C4×#6711yescharacteristic
664C23C4×#6711yescharacteristic
665C23#93711yescharacteristic
666C23#93711yescharacteristic
667C23#93811yescharacteristic
668C23#94611yescharacteristic
669D4—64no—
670D4—64no—
671D4—64no—
672D4—64no—
673D4—64no—
674D4—64no—
675D4—64no—
676D4—64no—
677C2×C4—24no—
678C2×C4—34no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—64no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—124no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—248no—
701C2×C4—242no—
702C2×C4—242no—
703C2×C4—242no—
704C2×C4—242no—
705C2×C4—242no—
706C2×C4—242no—
707C2×C4—242no—
708C2×C4—242no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3C22⋊#9511yescharacteristic
724C2×C3#182812yes—
725D3—44no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—64no—
762C22—124no—
763C22—124no—
764C22—124no—
765C22—242no—
766C22—242no—
767C22—242no—
768C22—242no—
769C22D3×#9511yescharacteristic
770C22#466411yescharacteristic
771C22#466511yescharacteristic
772C22#466511yescharacteristic
773C22#466611yescharacteristic
774C22#466711yescharacteristic
775C22#466811yescharacteristic
776C22#466811yescharacteristic
777C22C4×(C2×D3)⋊C411yescharacteristic
778C22#495511yescharacteristic
779C22#495611yescharacteristic
780C22#495611yescharacteristic
781C22#498711yescharacteristic
782C22#498911yescharacteristic
783C22#498911yescharacteristic
784C4—44no—
785C4—64no—
786C4—82no—
787C4—82no—
788C4—124no—
789C4—242no—
790C4—242no—
791C3#1076811yescharacteristic, complemented, Sylow
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—124no—
807C2#6896012yes—
808C2(C2×D3)⋊#9511yescharacteristic
subgroupG/H
centerC22#4664
commutatorC23×C3C2×C42
FrattiniC25C22×D3
FittingC2×C3×#342C2
socleC22×C3#381
prime radicalC23×#67C22
cosocleC25×C3C23
hypercenterC2×#342D3
hypocenterC3#10768
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×C3×#342C2semidirect
5. C2×#4527C2semidirect
6. C2×#4527C2semidirect
7. C2×#4526C2semidirect
22. C2×D3×C22⋊C4C4semidirect
23. C2×#877C4semidirect
28. C2×#806C4semidirect
29. C2×#806C4semidirect
40. C2×#342D3semidirect
79. C2×C3×C22⋊C4C2×C4semidirect
80. C2×C3×C22⋊C4C2×C4semidirect
97. C2×#217C2×C4semidirect
98. C2×#217C2×C4semidirect
317. C2×C22⋊C4C4×D3semidirect
318. C2×C22⋊C4C4×D3semidirect
791. C3#10768semidirect

Maximal subgroups

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

subgroupindex
C2×#54862
C22×#8062
C2×C3×#3422
C2×#45272
C2×#45262
#107683