Finite Group Databasebeta

← #10701901

Subgroups — #10701901

Order 768.

1558 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
1C22×#936C211yesmaximal, characteristic
2C22×C3×#102C211yesmaximal, characteristic
3C22×#832C211yesmaximal, characteristic
4C22×#816C211yesmaximal, characteristic, complemented
5C22×#810C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#11009—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×Dic6C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×#217—22no—
14C2×#936—22no—
15C2×#936—22no—
16C2×#936—22no—
17C2×#936—22no—
18C2×#936—22no—
19C2×#936C414yescomplemented
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4×Dic3C2211yescharacteristic
22C23×C3⋊C8C2211yescharacteristic
23C2×C3×#102—22no—
24C2×C3×#102—22no—
25C2×C3×#102—22no—
26C2×#832—22no—
27C2×#832—22no—
28C2×#832—22no—
29C2×C3⋊#95—22no—
30C2×#816—22no—
31C2×#816—22no—
32C2×#816—22no—
33C2×#810—22no—
34C2×#810—22no—
35C2×#810—22no—
36#4550—22no—
37C22×#124—31no—
38C22×#103—31no—
39C22×#103—31no—
40C22×#102—31no—
41C22×#102D311yescharacteristic
42C2×#336—31no—
43C4⋊#95—31no—
44C25×C3—21no—
45C22×C3×D4—21no—
46C22×C3×D4—21no—
47C22×C3×D4—21no—
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4—21no—
51C22×C3×D4—21no—
52C22×C3×D4—21no—
53C22×C3×D4—21no—
54C22×C3×D4—21no—
55C22×C3×D4—21no—
56C22×C3×D4C2×C412yes—
57C22×C3×D4D412yes—
58C22×C3×D4D412yes—
59C23×C3×C4—21no—
60C23×C3×C4C2311yescharacteristic
61C23×Dic3—21no—
62C23×Dic3—21no—
63C23×Dic3D412yes—
64C22×Dic6—21no—
65C22×Dic6—21no—
66C22×Dic6—21no—
67C22×Dic6—21no—
68C22×Dic6—21no—
69C22×Dic6—21no—
70C22×Dic6—21no—
71C22×Dic6—21no—
72C22×Dic6—21no—
73C22×Dic6—21no—
74C22×Dic6—21no—
75C22×Dic6C2×C412yes—
76C22×Dic6D412yes—
77C22×Dic6D412yes—
78C22×C3×C8—21no—
79C22×C3×C8—21no—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8—21no—
84C22×C3×C8D412yes—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4D412yes—
91C2×#217—28no—
92C2×#217—28no—
93C2×#217—28no—
94#936—28no—
95#936—28no—
96#936—28no—
97#936—28no—
98C2×C4⋊Dic3—21no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3—21no—
101C2×C4⋊Dic3—21no—
102C2×C4⋊Dic3—21no—
103C2×C4⋊Dic3D412yes—
104C2×C4×Dic3—21no—
105C2×C4×Dic3—21no—
106C2×C4×Dic3—21no—
107C2×C4×Dic3—21no—
108C2×C4×Dic3C2×C412yes—
109C2×C4×Dic3D412yes—
110C22×C3⋊C8—21no—
111C22×C3⋊C8—21no—
112C22×C3⋊C8—21no—
113C22×C3⋊C8—21no—
114C22×C3⋊C8—21no—
115C22×C3⋊C8—21no—
116C22×C3⋊C8D412yes—
117C3×#102—28no—
118#832—28no—
119C3⋊#95—44no—
120#816—28no—
121#810—28no—
122C23×Q8—31no—
123C23×D4C2×D311yescharacteristic
124C23×C8—31no—
125C23×C8C2×D311yescharacteristic
126C2×#124—34no—
127C2×#124—62no—
128C2×#124—62no—
129C2×#124—62no—
130C2×#124—62no—
131C2×#124—62no—
132C22×C4⋊C4—31no—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C22⋊C4—62no—
135C22×C42—31no—
136C2×#103—62no—
137C2×#103—62no—
138C2×#103—62no—
139C2×#103—62no—
140C2×#103—62no—
141C2×#103—62no—
142C2×#102—22no—
143C2×#102—22no—
144C2×#102—22no—
145C2×#102—62no—
146C2×#102—62no—
147C2×#102—62no—
148C2×#95—62no—
149#336—62no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—41no—
154C24×C3—41no—
155C24×C3—41no—
156C24×C3—41no—
157C24×C3—42no—
158C24×C3—42no—
159C24×C3—42no—
160C24×C3—42no—
161C24×C3C2×D411yescharacteristic
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4—22no—
167C2×C3×D4—22no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4—22no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—41no—
178C2×C3×D4—41no—
179C2×C3×D4—41no—
180C2×C3×D4—41no—
181C2×C3×D4—41no—
182C2×C3×D4—41no—
183C2×C3×D4—41no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4C22⋊C414yes—
190C22×C3×C4—22no—
191C22×C3×C4—41no—
192C22×C3×C4—41no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4C22×C411yescharacteristic
196C22×C3×C4C2×D411yescharacteristic
197C22×C3×C4C2×D411yescharacteristic
198C22×C3×C4C2×D411yescharacteristic
199C22×C3×C4C2×D411yescharacteristic
200C22×C3×C4C2×D411yescharacteristic
201C22×C3×C4C2×D411yescharacteristic
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4#4111yescharacteristic
206C22×C3×C4#4111yescharacteristic
207C22×C3×C4#4111yescharacteristic
208C22×C3×C4#4111yescharacteristic
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—41no—
220C22×Dic3—41no—
221C22×Dic3—41no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3—41no—
225C22×Dic3—42no—
226C22×Dic3—42no—
227C22×Dic3C22⋊C414yes—
228C2×Dic6—22no—
229C2×Dic6—22no—
230C2×Dic6—22no—
231C2×Dic6—22no—
232C2×Dic6—22no—
233C2×Dic6—22no—
234C2×Dic6—22no—
235C2×Dic6—22no—
236C2×Dic6—22no—
237C2×Dic6—22no—
238C2×Dic6—22no—
239C2×Dic6—22no—
240C2×Dic6—22no—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6—41no—
244C2×Dic6—41no—
245C2×Dic6—41no—
246C2×Dic6—41no—
247C2×Dic6—41no—
248C2×Dic6—41no—
249C2×Dic6—41no—
250C2×Dic6—41no—
251C2×Dic6—41no—
252C2×Dic6—41no—
253C2×Dic6—41no—
254C2×Dic6—41no—
255C2×Dic6C22⋊C414yes—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—41no—
260C2×C3×C8—41no—
261C2×C3×C8—41no—
262C2×C3×C8—41no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—41no—
267#217—232no—
268C4⋊Dic3—22no—
269C4⋊Dic3—22no—
270C4⋊Dic3—41no—
271C4⋊Dic3—41no—
272C4×Dic3—22no—
273C4×Dic3—22no—
274C4×Dic3—22no—
275C4×Dic3—22no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8—41no—
280C2×C3⋊C8—41no—
281C2×C3⋊C8—41no—
282C2×C3⋊C8—41no—
283C25—21no—
284C22×Q8—32no—
285C22×Q8—32no—
286C22×Q8—32no—
287C22×Q8—61no—
288C22×Q8—61no—
289C22×Q8—61no—
290C22×Q8—61no—
291C22×Q8—61no—
292C22×Q8—61no—
293C22×Q8—61no—
294C22×Q8—61no—
295C22×Q8—61no—
296C22×Q8—61no—
297C22×Q8—61no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4C4×D312yes—
310C22×D4D1212yes—
311C22×D4#6712yes—
312C23×C4—21no—
313C23×C4—32no—
314C23×C4—61no—
315C23×C4—61no—
316C23×C4C22×D311yescharacteristic
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—32no—
324C22×C8—61no—
325C22×C8—61no—
326C22×C8—61no—
327C22×C8—61no—
328C22×C8—61no—
329C22×C8—61no—
330C22×C8#6712yes—
331#124—68no—
332#124—68no—
333#124—68no—
334#124—68no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—32no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—61no—
343C2×C4⋊C4—61no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4—61no—
346C2×C4⋊C4#6712yes—
347C2×C22⋊C4—68no—
348C2×C22⋊C4—68no—
349C2×C22⋊C4—68no—
350C2×C42—32no—
351C2×C42—32no—
352C2×C42—61no—
353C2×C42—61no—
354C2×C42—61no—
355C2×C42—61no—
356#103—68no—
357#103—68no—
358#102—28no—
359#102—68no—
360#95—124no—
361C23×C3—24no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—44no—
369C23×C3—44no—
370C23×C3—44no—
371C23×C3—44no—
372C23×C3—44no—
373C23×C3—44no—
374C23×C3—82no—
375C23×C3—82no—
376C23×C3—82no—
377C23×C3—82no—
378C23×C3—82no—
379C23×C3—82no—
380C23×C3—81no—
381C23×C3—81no—
382C23×C3—81no—
383C23×C3—81no—
384C23×C3C2×C22⋊C411yescharacteristic
385C23×C3#12011yescharacteristic
386C23×C3#12011yescharacteristic
387C23×C3#12111yescharacteristic
388C23×C3#12111yescharacteristic
389C23×C3#12411yescharacteristic
390C23×C3#12711yescharacteristic
391C23×C3#13512yes—
392C23×C3#13512yes—
393C23×C3AGL(1,ℤ/8)12yes—
394C23×C3#13712yes—
395C3×D4—24no—
396C3×D4—24no—
397C3×D4—42no—
398C3×D4—42no—
399C3×D4—42no—
400C3×D4—42no—
401C3×D4—42no—
402C3×D4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—44no—
405C2×C3×C4—82no—
406C2×C3×C4—81no—
407C2×C3×C4—81no—
408C2×C3×C4C2×C22⋊C411yescharacteristic
409C2×C3×C4C2×C22⋊C411yescharacteristic
410C2×C3×C4C4×D411yescharacteristic
411C2×C3×C4C4×D411yescharacteristic
412C2×C3×C4C4×D411yescharacteristic
413C2×C3×C4C4×D411yescharacteristic
414C2×C3×C4#12011yescharacteristic
415C2×C3×C4#12011yescharacteristic
416C2×C3×C4#12011yescharacteristic
417C2×C3×C4#12011yescharacteristic
418C2×C3×C4#12011yescharacteristic
419C2×C3×C4#12011yescharacteristic
420C2×C3×C4#12111yescharacteristic
421C2×C3×C4#12111yescharacteristic
422C2×C3×C4#12111yescharacteristic
423C2×C3×C4#12111yescharacteristic
424C2×C3×C4#12111yescharacteristic
425C2×C3×C4#12111yescharacteristic
426C2×C3×C4#12111yescharacteristic
427C2×C3×C4#12111yescharacteristic
428C2×C3×C4#12111yescharacteristic
429C2×C3×C4#12111yescharacteristic
430C2×C3×C4#12311yescharacteristic
431C2×C3×C4#12311yescharacteristic
432C2×C3×C4#12311yescharacteristic
433C2×C3×C4#12311yescharacteristic
434C2×C3×C4#12411yescharacteristic
435C2×C3×C4#12711yescharacteristic
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—44no—
452C2×Dic3—82no—
453C2×Dic3—81no—
454C2×Dic3—81no—
455Dic6—24no—
456Dic6—24no—
457Dic6—42no—
458Dic6—42no—
459Dic6—42no—
460Dic6—42no—
461Dic6—42no—
462Dic6—42no—
463C3×C8—42no—
464C3⋊C8—42no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—41no—
469C24—41no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—41no—
475C24—41no—
476C24D3×D411yescharacteristic
477C2×Q8—34no—
478C2×Q8—62no—
479C2×Q8—62no—
480C2×Q8—62no—
481C2×Q8—62no—
482C2×Q8—62no—
483C2×Q8—62no—
484C2×Q8—62no—
485C2×Q8—62no—
486C2×Q8—62no—
487C2×Q8—62no—
488C2×Q8—62no—
489C2×Q8—62no—
490C2×Q8—62no—
491C2×Q8—62no—
492C2×Q8—62no—
493C2×Q8—121no—
494C2×Q8—121no—
495C2×Q8—121no—
496C2×Q8—121no—
497C2×Q8—121no—
498C2×Q8—121no—
499C2×Q8—121no—
500C2×Q8—121no—
501C2×Q8—121no—
502C2×Q8—121no—
503C2×Q8—121no—
504C2×Q8—121no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4(C2×D3)⋊C414yes—
533C22×C4—22no—
534C22×C4—34no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—121no—
550C22×C4—121no—
551C22×C4—121no—
552C22×C4—121no—
553C22×C4—121no—
554C22×C4—122no—
555C22×C4—122no—
556C22×C4—121no—
557C22×C4C2×C4×D311yescharacteristic
558C22×C4C2×D1211yescharacteristic
559C22×C4#23511yescharacteristic
560C22×C4#23511yescharacteristic
561C22×C4D3×D411yescharacteristic
562C22×C4D3×D411yescharacteristic
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4D3×D411yescharacteristic
566C22×C4#23711yescharacteristic
567C22×C4#23711yescharacteristic
568C22×C4C2×#6711yescharacteristic
569C22×C4C2×#6711yescharacteristic
570C22×C4C2×#6711yescharacteristic
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—62no—
579C2×C8—62no—
580C2×C8—62no—
581C2×C8—121no—
582C2×C8—121no—
583C2×C8—121no—
584C2×C8—121no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—121no—
592C4⋊C4—121no—
593C22⋊C4—632no—
594C42—62no—
595C42—62no—
596C42—62no—
597C42—62no—
598C22×C3—44no—
599C22×C3—48no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3—84no—
603C22×C3—82no—
604C22×C3—82no—
605C22×C3—82no—
606C22×C3—82no—
607C22×C3—84no—
608C22×C3—84no—
609C22×C3#37911yescharacteristic
610C22×C3#39011yescharacteristic
611C22×C3#39011yescharacteristic
612C22×C3#39211yescharacteristic
613C22×C3#39211yescharacteristic
614C22×C3#39411yescharacteristic
615C22×C3#39411yescharacteristic
616C22×C3#41612yes—
617C22×C3#41712yes—
618C22×C3#44912yes—
619C22×C3#44912yes—
620C22×C3#45212yes—
621C22×C3#45212yes—
622C22×C3#46312yes—
623C22×C3#46312yes—
624C22×C3#46412yes—
625C22×C3#46412yes—
626C22×C3#48812yes—
627C22×C3#48912yes—
628C22×C3#49511yescharacteristic
629C22×C3#49511yescharacteristic
630C22×C3#49611yescharacteristic
631C22×C3#49711yescharacteristic
632C3×C4—82no—
633C3×C4#38611yescharacteristic
634C3×C4#38611yescharacteristic
635C3×C4#38611yescharacteristic
636C3×C4#38611yescharacteristic
637C3×C4#39211yescharacteristic
638C3×C4#39211yescharacteristic
639C3×C4#39411yescharacteristic
640C3×C4#39411yescharacteristic
641Dic3—44no—
642Dic3—44no—
643Dic3—82no—
644C23—24no—
645C23—44no—
646C23—44no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—82no—
658C23—81no—
659C23—81no—
660C23—82no—
661C23—81no—
662C23—81no—
663C23—82no—
664C23—82no—
665C23—82no—
666C23—82no—
667C23D3×C22⋊C411yescharacteristic
668C23#88211yescharacteristic
669C23#88411yescharacteristic
670C23#88511yescharacteristic
671C23#91112yes—
672C23#91212yes—
673C23#91512yes—
674C23#91612yes—
675C23#93711yescharacteristic
676C23#93911yescharacteristic
677C23#94011yescharacteristic
678Q8—64no—
679Q8—64no—
680Q8—122no—
681Q8—122no—
682Q8—122no—
683Q8—122no—
684Q8—122no—
685Q8—122no—
686D4—24no—
687D4—24no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—64no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—124no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—242no—
718C2×C4D3×C22⋊C411yescharacteristic
719C2×C4#67⋊C411yescharacteristic
720C2×C4#67⋊C411yescharacteristic
721C2×C4#88211yescharacteristic
722C2×C4#88211yescharacteristic
723C2×C4#88311yescharacteristic
724C2×C4#88311yescharacteristic
725C2×C4#88411yescharacteristic
726C2×C4#88411yescharacteristic
727C2×C4#88411yescharacteristic
728C2×C4#88511yescharacteristic
729C2×C4#88611yescharacteristic
730C2×C4C2×(C2×D3)⋊C411yescharacteristic
731C2×C4C4×#6711yescharacteristic
732C2×C4C4×#6711yescharacteristic
733C2×C4#92911yescharacteristic
734C2×C4#93011yescharacteristic
735C2×C4#93011yescharacteristic
736C2×C4#93711yescharacteristic
737C2×C4#93711yescharacteristic
738C2×C4#93711yescharacteristic
739C2×C4#93811yescharacteristic
740C2×C4#93811yescharacteristic
741C2×C4#93911yescharacteristic
742C2×C4#93911yescharacteristic
743C2×C4#93911yescharacteristic
744C2×C4#94011yescharacteristic
745C2×C4#95311yescharacteristic
746C8—42no—
747C8—122no—
748C2×C3—84no—
749C2×C3#143811yescharacteristic
750C2×C3#178812yes—
751C2×C3#195811yescharacteristic
752C2×C3#195911yescharacteristic
753C2×C3#198312yes—
754C2×C3#201211yescharacteristic
755C2×C3#201211yescharacteristic
756C2×C3#201511yescharacteristic
757C2×C3#201511yescharacteristic
758C2×C3#204212yes—
759C2×C3#204212yes—
760C22—48no—
761C22—44no—
762C22—82no—
763C22—82no—
764C22—84no—
765C22—84no—
766C22—82no—
767C22—82no—
768C22—84no—
769C22—82no—
770C22—82no—
771C22#476512yes—
772C22#476712yes—
773C22#476812yes—
774C22#477112yes—
775C22#477212yes—
776C22#478112yes—
777C22#478312yes—
778C22#478712yes—
779C22#495511yescharacteristic
780C22#495711yescharacteristic
781C22#495711yescharacteristic
782C22#495911yescharacteristic
783C22#496011yescharacteristic
784C22#496111yescharacteristic
785C22#515312yes—
786C22#515411yescharacteristic
787C22#515511yescharacteristic
788C22#515812yes—
789C22#516612yes—
790C22#516711yescharacteristic
791C22#516811yescharacteristic
792C22#517312yes—
793C22#522311yescharacteristic
794C4—82no—
795C4—124no—
796C4—124no—
797C4—242no—
798C4#495611yescharacteristic
799C4#495611yescharacteristic
800C4#495811yescharacteristic
801C4#495911yescharacteristic
802C4#496011yescharacteristic
803C4#496111yescharacteristic
804C4#521311yescharacteristic
805C4#522311yescharacteristic
806C3#1100911yescharacteristic, complemented, Sylow
807C2—84no—
808C2#7015811yescharacteristic
809C2#7015911yescharacteristic
810C2#7016212yes—
811C2#7017812yes—
812C2#7019912yes—
813C2#7021411yescharacteristic
814C2#7021511yescharacteristic
815C2#7021612yes—
816C2#7155011yescharacteristic
817C2#7204511yescharacteristic
818C2#7205811yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#102C2
socleC24×C3C2×D4
prime radicalC23×C3×D4C22
cosocleC23×C3×C4C23
hypercenterC22×#102D3
hypocenterC3#11009
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
4. C22×#816C2semidirect
5. C22×#810C2semidirect
6. C2×#4550C2semidirect
7. #71563C2semidirect
19. C2×#936C4semidirect
806. C3#11009semidirect

Maximal subgroups

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

subgroupindex
C22×#9362
C22×C3×#1022
C22×#8322
C22×#8162
C22×#8102
C2×#45502
#715632
#110093