Finite Group Databasebeta

← #10702109

Subgroups — #10702109

Order 768.

1454 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#99C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C22×#834C211yesmaximal, characteristic
4C2×#4942C211yesmaximal, characteristic, complemented
5#71544C211yesmaximal, characteristic, complemented
6C2×#4527C211yesmaximal, characteristic, complemented
7C2×#4527C211yesmaximal, characteristic, complemented
8#11043—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C24×Dic3C2211yescharacteristic
11C22×C3×C22⋊C4C2211yescharacteristic
12C22×C3×C22⋊C4C2211yescharacteristic
13C22×#217C412yescomplemented
14C22×#217C2211yescharacteristic
15C22×#217C2211yescharacteristic
16C22×#217C2211yescharacteristic
17C22×Dic3⋊C4—21no—
18C2×C3×#99—22no—
19C2×C3×#99—22no—
20C2×C3×#99—22no—
21#5220—21no—
22#5220—22no—
23#5220—21no—
24C2×#834—22no—
25C2×#834—22no—
26C2×#834—22no—
27C2×C3⋊#95—21no—
28C2×C3⋊#95—22no—
29C2×C3⋊#95C412yescomplemented
30#4942—22no—
31#4942—22no—
32#4527—22no—
33#4527—22no—
34C22×#99—31no—
35C22×#99D311yescharacteristic
36C2×#386—31no—
37C2×#380—31no—
38C2×#342—31no—
39C2×#342—31no—
40C22⋊#95—31no—
41C25×C3C2×C411yescharacteristic
42C25×C3C2311yescharacteristic
43C22×C3×D4—21no—
44C22×C3×D4—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×D4D412yes—
56C22×C3×D4Q812yes—
57C23×C3×C4—21no—
58C23×C3×C4—21no—
59C23×C3×C4C2×C411yescharacteristic
60C23×Dic3—21no—
61C23×Dic3—21no—
62C23×Dic3—21no—
63C23×Dic3—21no—
64C23×Dic3—21no—
65C23×Dic3—21no—
66C23×Dic3—44no—
67C23×Dic3C2×C412yes—
68C23×Dic3C2×C412yes—
69C23×Dic3D411yescharacteristic
70C23×Dic3D412yes—
71C23×Dic3D411yescharacteristic
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⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C22⋊C4—21no—
81C2×C3×C22⋊C4—21no—
82C2×C3×C22⋊C4D412yes—
83C2×C3×C22⋊C4D412yes—
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×#217—21no—
97C2×#217—21no—
98C2×#217—21no—
99C2×#217—21no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—44no—
103C2×#217D412yes—
104C2×#217D412yes—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—44no—
107C3×#99—28no—
108#834—28no—
109C3⋊#95—24no—
110C3⋊#95—22no—
111C3⋊#95—22no—
112C3⋊#95—44no—
113C23×D4C2×D311yescharacteristic
114C24×C4—31no—
115C22×C4⋊C4—61no—
116C22×C22⋊C4—31no—
117C22×C22⋊C4—31no—
118C22×C22⋊C4—31no—
119C22×C22⋊C4—32no—
120C22×C22⋊C4C2×D311yescharacteristic
121C22×C22⋊C4C2×D311yescharacteristic
122C2×#99—22no—
123C2×#99—22no—
124C2×#99—22no—
125C2×#99—62no—
126C2×#99—62no—
127C2×#99—62no—
128#386—61no—
129#386—62no—
130#386—61no—
131#380—62no—
132#380—62no—
133C2×#95—32no—
134C2×#95—61no—
135C2×#95—62no—
136#342—62no—
137#342—62no—
138C24×C3—21no—
139C24×C3—21no—
140C24×C3—21no—
141C24×C3—21no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—42no—
145C24×C3—42no—
146C24×C3—42no—
147C24×C3—42no—
148C24×C3C4⋊C412yescomplemented
149C24×C3C22×C411yescharacteristic
150C24×C3C2×D411yescharacteristic
151C24×C3C2×D411yescharacteristic
152C24×C3C2×D411yescharacteristic
153C24×C3C2×D411yescharacteristic
154C24×C3C2×D411yescharacteristic
155C24×C3C2×D411yescharacteristic
156C24×C3C2×D411yescharacteristic
157C24×C3C2×Q811yescharacteristic
158C24×C3#4111yescharacteristic
159C24×C3#4111yescharacteristic
160C24×C3#4111yescharacteristic
161C24×C3#4111yescharacteristic
162C24×C3#4111yescharacteristic
163C24×C3#4111yescharacteristic
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—41no—
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×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4—41no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4—42no—
203C22×C3×C4—42no—
204C22×C3×C4—41no—
205C22×C3×C4—41no—
206C22×C3×C4—41no—
207C22×C3×C4—41no—
208C22×C3×C4C4⋊C412yescomplemented
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—24no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—24no—
219C22×Dic3—24no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—42no—
226C22×Dic3—42no—
227C22×Dic3—42no—
228C22×Dic3—44no—
229C22×Dic3—44no—
230C22×Dic3—44no—
231C22×Dic3—44no—
232C22×Dic3—42no—
233C22×Dic3—42no—
234C22×Dic3—42no—
235C22×Dic3—42no—
236C22×Dic3—41no—
237C22×Dic3—41no—
238C22×Dic3—41no—
239C22×Dic3—41no—
240C22×Dic3—42no—
241C22×Dic3—42no—
242C22×Dic3C22⋊C412yes—
243C22×Dic3C22⋊C412yes—
244C3×C22⋊C4—22no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—22no—
248C3×C22⋊C4—41no—
249C3×C22⋊C4—41no—
250C3×C22⋊C4—41no—
251C3×C22⋊C4—41no—
252#217—22no—
253#217—22no—
254#217—22no—
255#217—22no—
256#217—44no—
257#217—41no—
258#217—41no—
259#217—41no—
260#217—41no—
261#217—41no—
262#217—41no—
263#217—41no—
264#217—41no—
265#217—44no—
266Dic3⋊C4—48no—
267C25C4×D311yescharacteristic
268C25C22×D311yescharacteristic
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4Dic612yes—
282C22×D4#6712yes—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—31no—
286C23×C4—32no—
287C23×C4—32no—
288C23×C4—31no—
289C23×C4—32no—
290C23×C4—61no—
291C23×C4—61no—
292C23×C4—61no—
293C23×C4—61no—
294C23×C4—61no—
295C23×C4—61no—
296C23×C4—124no—
297C23×C4C4×D311yescharacteristic
298C2×C4⋊C4—64no—
299C2×C4⋊C4—124no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—32no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—61no—
313C2×C22⋊C4—61no—
314C2×C22⋊C4—61no—
315C2×C22⋊C4—61no—
316C2×C22⋊C4—61no—
317C2×C22⋊C4—61no—
318C2×C22⋊C4—61no—
319C2×C22⋊C4—61no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—61no—
323C2×C22⋊C4—61no—
324C2×C22⋊C4—61no—
325C2×C22⋊C4—61no—
326C2×C22⋊C4—61no—
327C2×C22⋊C4—61no—
328C2×C22⋊C4—61no—
329C2×C22⋊C4—61no—
330C2×C22⋊C4—124no—
331C2×C22⋊C4#6712yes—
332C2×C22⋊C4#6712yes—
333#99—28no—
334#99—68no—
335#95—62no—
336#95—62no—
337#95—64no—
338#95—124no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—41no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—41no—
363C23×C3—42no—
364C23×C3—44no—
365C23×C3—44no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—81no—
373C23×C3—81no—
374C23×C3—81no—
375C23×C3—81no—
376C23×C3—82no—
377C23×C3—82no—
378C23×C3C2×C22⋊C411yescharacteristic
379C23×C3C2×C4⋊C411yescharacteristic
380C23×C3#11711yescharacteristic
381C23×C3C4×D411yescharacteristic
382C23×C3C4×D411yescharacteristic
383C23×C3C4×D411yescharacteristic
384C23×C3C4×D411yescharacteristic
385C23×C3#12011yescharacteristic
386C23×C3#12011yescharacteristic
387C23×C3#12011yescharacteristic
388C23×C3#12111yescharacteristic
389C23×C3#12111yescharacteristic
390C23×C3#12111yescharacteristic
391C23×C3#12111yescharacteristic
392C23×C3#12111yescharacteristic
393C23×C3#12111yescharacteristic
394C23×C3#12111yescharacteristic
395C23×C3#12111yescharacteristic
396C23×C3C22⋊Q811yescharacteristic
397C23×C3C22⋊Q811yescharacteristic
398C23×C3C22⋊Q811yescharacteristic
399C23×C3C22⋊Q811yescharacteristic
400C23×C3C22⋊Q811yescharacteristic
401C23×C3C22⋊Q811yescharacteristic
402C23×C3#12311yescharacteristic
403C23×C3#12311yescharacteristic
404C23×C3#12311yescharacteristic
405C23×C3#12311yescharacteristic
406C23×C3#12311yescharacteristic
407C23×C3#12411yescharacteristic
408C23×C3#12411yescharacteristic
409C23×C3#12411yescharacteristic
410C23×C3#12611yescharacteristic
411C23×C3#12611yescharacteristic
412C23×C3#12711yescharacteristic
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—42no—
417C3×D4—42no—
418C3×D4—42no—
419C3×D4—42no—
420C3×D4—42no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—44no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—82no—
434C2×C3×C4—82no—
435C2×C3×C4—81no—
436C2×C3×C4—81no—
437C2×C3×C4—82no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—44no—
446C2×Dic3—44no—
447C2×Dic3—44no—
448C2×Dic3—44no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—44no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—82no—
460C2×Dic3—82no—
461C2×Dic3—81no—
462C2×Dic3—81no—
463C2×Dic3—82no—
464C2×Dic3—82no—
465C2×Dic3—82no—
466C2×Dic3#9914yescomplemented
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24Dic3⋊C412yescomplemented
478C24C2×Dic611yescharacteristic
479C24C2×C4×D311yescharacteristic
480C24#23511yescharacteristic
481C24#23511yescharacteristic
482C24D3×D411yescharacteristic
483C24D3×D411yescharacteristic
484C24D3×D411yescharacteristic
485C24D3×D411yescharacteristic
486C24#23711yescharacteristic
487C24#23711yescharacteristic
488C24#23711yescharacteristic
489C24#23711yescharacteristic
490C24C2×#6711yescharacteristic
491C24C2×#6711yescharacteristic
492C24C2×#6711yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—64no—
540C22×C4—64no—
541C22×C4—64no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—122no—
556C22×C4—122no—
557C22×C4—122no—
558C22×C4—124no—
559C22×C4—124no—
560C22×C4—124no—
561C22×C4—124no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4—122no—
566C22×C4—121no—
567C22×C4—121no—
568C22×C4—121no—
569C22×C4—121no—
570C22×C4—122no—
571C22×C4—122no—
572C22×C4Dic3⋊C412yescomplemented
573C4⋊C4—128no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—62no—
583C22⋊C4—62no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—124no—
587C22⋊C4—124no—
588C22⋊C4—121no—
589C22⋊C4—121no—
590C22⋊C4—121no—
591C22⋊C4—121no—
592C22⋊C4—121no—
593C22⋊C4—121no—
594C22⋊C4—121no—
595C22⋊C4—121no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—44no—
637C22×C3—42no—
638C22×C3—82no—
639C22×C3—82no—
640C22×C3—82no—
641C22×C3—82no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—82no—
645C22×C3#38011yescharacteristic
646C22×C3#38511yescharacteristic
647C22×C3#38511yescharacteristic
648C22×C3#38611yescharacteristic
649C22×C3#38811yescharacteristic
650C22×C3#38811yescharacteristic
651C22×C3#39011yescharacteristic
652C22×C3#39211yescharacteristic
653C22×C3#39311yescharacteristic
654C22×C3#39411yescharacteristic
655C22×C3#39411yescharacteristic
656C22×C3#39611yescharacteristic
657C22×C3#39611yescharacteristic
658C22×C3#39711yescharacteristic
659C22×C3#39911yescharacteristic
660C22×C3C2×#9912yes—
661C22×C3#41012yes—
662C3×C4—42no—
663C3×C4—82no—
664C3×C4—82no—
665Dic3—24no—
666Dic3—42no—
667Dic3—82no—
668Dic3—82no—
669Dic3—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—44no—
696C23—44no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23—81no—
704C23—81no—
705C23—82no—
706C23—82no—
707C23—81no—
708C23—81no—
709C23#87711yescharacteristic
710C23#87811yescharacteristic
711C23#87811yescharacteristic
712C23#87811yescharacteristic
713C23#87811yescharacteristic
714C23#87911yescharacteristic
715C23#87911yescharacteristic
716C23D3×C22⋊C411yescharacteristic
717C23#67⋊C411yescharacteristic
718C23#67⋊C411yescharacteristic
719C23#88311yescharacteristic
720C23#88311yescharacteristic
721C23#88411yescharacteristic
722C23#88411yescharacteristic
723C23#88511yescharacteristic
724C23#88511yescharacteristic
725C23C2×Dic3⋊C411yescharacteristic
726C23#92411yescharacteristic
727C23#92411yescharacteristic
728C23C4×#6711yescharacteristic
729C23C4×#6711yescharacteristic
730C23#92911yescharacteristic
731C23#93511yescharacteristic
732C23#93511yescharacteristic
733C23#93611yescharacteristic
734C23#93711yescharacteristic
735C23#93711yescharacteristic
736C23#93811yescharacteristic
737C23#93811yescharacteristic
738C23#93911yescharacteristic
739C23#93911yescharacteristic
740C23#93911yescharacteristic
741C23#93911yescharacteristic
742C23#94011yescharacteristic
743C23#95311yescharacteristic
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—34no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—64no—
766C2×C4—64no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—81no—
777C2×C4—124no—
778C2×C4—124no—
779C2×C4—124no—
780C2×C4—124no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—124no—
786C2×C4—122no—
787C2×C4—122no—
788C2×C4—122no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4—242no—
792C2×C4—242no—
793C2×C4—241no—
794C2×C4—242no—
795C2×C4—241no—
796C2×C4—242no—
797C2×C4—242no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—82no—
811C2×C3#143911yescharacteristic
812C2×C3#179912yes—
813C2×C3#189811yescharacteristic
814C2×C3#189911yescharacteristic
815C2×C3#196412yes—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—44no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—81no—
863C22—82no—
864C22—81no—
865C22#474012yes—
866C22D3×#9912yes—
867C22#494211yescharacteristic
868C22#494411yescharacteristic
869C22#494511yescharacteristic
870C22#494611yescharacteristic
871C22#494711yescharacteristic
872C22#494811yescharacteristic
873C22#494811yescharacteristic
874C22#494911yescharacteristic
875C22#495211yescharacteristic
876C22#495611yescharacteristic
877C22#495711yescharacteristic
878C22#495911yescharacteristic
879C22#521011yescharacteristic
880C22#522211yescharacteristic
881C22#522311yescharacteristic
882C4—42no—
883C4—64no—
884C4—82no—
885C4—82no—
886C4—122no—
887C4—242no—
888C4—242no—
889C4—242no—
890C3#1104311yescharacteristic, complemented, Sylow
891C2—21no—
892C2—21no—
893C2—21no—
894C2—21no—
895C2—21no—
896C2—21no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—82no—
904C2#7002812yes—
905C2#7002911yescharacteristic
906C2#7003012yes—
907C2#7003611yescharacteristic
908C2#7154711yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC24×C3C22×C4
FrattiniC25C22×D3
FittingC22×C3×#99C2
socleC23×C3C2×C22⋊C4
prime radicalC23×C3×D4C22
cosocleC25×C3C23
hypercenterC22×#99D3
hypocenterC3#11043
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
4. C2×#4942C2semidirect
5. #71544C2semidirect
6. C2×#4527C2semidirect
7. C2×#4527C2semidirect
13. C22×#217C4semidirect
29. C2×C3⋊#95C4semidirect
148. C24×C3C4⋊C4semidirect
208. C22×C3×C4C4⋊C4semidirect
466. C2×Dic3#99semidirect
477. C24Dic3⋊C4semidirect
572. C22×C4Dic3⋊C4semidirect
890. C3#11043semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#992
C2×#52202
C22×#8342
C2×#49422
#715442
C2×#45272
#110433