Finite Group Databasebeta

← #10702896

Subgroups — #10702896

Order 768.

1406 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82121C211yesmaximal, characteristic
2C22×#806C211yesmaximal, characteristic
3C2×#4958C211yesmaximal, characteristic
4C2×C3×#342C211yesmaximal, characteristic, complemented
5#71544C211yesmaximal, characteristic, complemented
6#71544C211yesmaximal, characteristic, complemented
7C2×#4527C211yesmaximal, characteristic, complemented
8#11174—31nomaximal, Sylow
9C23×#67C2211yescharacteristic
10C24×Dic3C2211yescharacteristic
11C22×C3×C22⋊C4C2211yescharacteristic
12C22×C3×C22⋊C4C2211yescharacteristic
13C22×C3×C22⋊C4C2211yescharacteristic
14C22×#217C2211yescharacteristic
15C22×#217C2211yescharacteristic
16C22×(C2×D3)⋊C4—21no—
17#5213—22no—
18C2×C3⋊#95—21no—
19C2×C3⋊#95—22no—
20C2×C3⋊#95—22no—
21#4958—22no—
22#4958—22no—
23#4958C414yescomplemented
24#4955—21no—
25C2×#806—22no—
26C2×#806—22no—
27C2×#806—22no—
28#4943—21no—
29C3×#342—22no—
30#4527—22no—
31C22×#99—31no—
32#2308—31no—
33C2×#386—31no—
34C2×#342—31no—
35C2×#342D311yescharacteristic, complemented
36C22⋊#95—31no—
37C22⋊#95—31no—
38C25×C3C2311yescharacteristic
39C24×D3D411yescharacteristic
40C23×C3×C4—21no—
41C23×C3×C4—21no—
42C23×C3×C4D412yes—
43C22×#67—21no—
44C22×#67—21no—
45C22×#67—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×#67—21no—
55C22×#67C2×C412yes—
56C22×#67D412yes—
57C23×Dic3—21no—
58C23×Dic3—21no—
59C23×Dic3—21no—
60C23×Dic3—21no—
61C23×Dic3—21no—
62C23×Dic3—21no—
63C23×Dic3—21no—
64C23×Dic3—44no—
65C23×Dic3C2×C412yes—
66C23×Dic3D411yescharacteristic
67C23×Dic3D412yes—
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⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C22⋊C4—21no—
81C2×C3×C22⋊C4—21no—
82C2×C3×C22⋊C4—21no—
83C2×C3×C22⋊C4—21no—
84C2×C3×C22⋊C4C2×C412yes—
85C2×C3×C22⋊C4D412yes—
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×#217D412yes—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—44no—
102C3⋊#95—24no—
103C3⋊#95—24no—
104C3⋊#95—44no—
105C3⋊#95—44no—
106#806—28no—
107C23×D4—31no—
108C24×C4—31no—
109C22×C22⋊C4—31no—
110C22×C22⋊C4—31no—
111C22×C22⋊C4—61no—
112C22×C22⋊C4C2×D311yescharacteristic
113C22×C22⋊C4C2×D311yescharacteristic
114C22×C22⋊C4C2×D311yescharacteristic
115C2×#99—62no—
116C2×#99—62no—
117C2×#99—62no—
118#386—34no—
119#386—62no—
120#386—62no—
121#386—62no—
122#381—61no—
123#379—61no—
124C2×#95—61no—
125C2×#95—62no—
126C2×#95—62no—
127#342—22no—
128#342—62no—
129C24×C3—42no—
130C24×C3—42no—
131C24×C3C22×C411yescharacteristic
132C24×C3C2×D411yescharacteristic
133C24×C3C2×D411yescharacteristic
134C24×C3C2×D411yescharacteristic
135C24×C3C2×D411yescharacteristic
136C24×C3C2×D411yescharacteristic
137C24×C3C2×D411yescharacteristic
138C24×C3#4111yescharacteristic
139C24×C3#4111yescharacteristic
140C24×C3#4111yescharacteristic
141C24×C3#4111yescharacteristic
142C24×C3#4111yescharacteristic
143C24×C3#4111yescharacteristic
144C24×C3#4111yescharacteristic
145C24×C3#4111yescharacteristic
146C23×D3—21no—
147C23×D3—21no—
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—21no—
151C23×D3—21no—
152C23×D3—42no—
153C23×D3—42no—
154C23×D3C22⋊C412yes—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—42no—
161C22×C3×C4—42no—
162C22×C3×C4—42no—
163C22×C3×C4—42no—
164C22×C3×C4—42no—
165C22×C3×C4—42no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C2×#67—22no—
171C2×#67—22no—
172C2×#67—22no—
173C2×#67—22no—
174C2×#67—22no—
175C2×#67—22no—
176C2×#67—22no—
177C2×#67—22no—
178C2×#67—22no—
179C2×#67—22no—
180C2×#67—22no—
181C2×#67—22no—
182C2×#67—41no—
183C2×#67—41no—
184C2×#67—41no—
185C2×#67—41no—
186C2×#67—41no—
187C2×#67—41no—
188C2×#67—41no—
189C2×#67—41no—
190C2×#67—41no—
191C2×#67—41no—
192C2×#67—41no—
193C2×#67—41no—
194C2×#67—41no—
195C2×#67—41no—
196C2×#67—41no—
197C2×#67—41no—
198C22×Dic3—24no—
199C22×Dic3—24no—
200C22×Dic3—24no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—22no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—44no—
215C22×Dic3—44no—
216C22×Dic3—44no—
217C22×Dic3—44no—
218C22×Dic3—42no—
219C22×Dic3—42no—
220C22×Dic3—42no—
221C22×Dic3—41no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3—41no—
225C22×Dic3—42no—
226C22×Dic3—42no—
227C22×Dic3—42no—
228C22×Dic3—42no—
229C22×Dic3—41no—
230C22×Dic3—41no—
231C22×Dic3C22⋊C412yes—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—41no—
237C3×C22⋊C4—41no—
238C3×C22⋊C4—41no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—41no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—41no—
243C3×C22⋊C4—41no—
244#217—22no—
245#217—22no—
246#217—41no—
247#217—41no—
248#217—41no—
249#217—41no—
250#217—41no—
251#217—41no—
252(C2×D3)⋊C4—48no—
253(C2×D3)⋊C4—82no—
254(C2×D3)⋊C4—82no—
255C25—31no—
256C25C22×D311yescharacteristic
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—
267C22×D4—61no—
268C22×D4—61no—
269C22×D4—61no—
270C22×D4—61no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—31no—
274C23×C4—32no—
275C23×C4—32no—
276C23×C4—61no—
277C23×C4—61no—
278C23×C4—61no—
279C23×C4—61no—
280C23×C4—61no—
281C23×C4—61no—
282C23×C4—61no—
283C23×C4—124no—
284C23×C4D1212yes—
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—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—61no—
303C2×C22⋊C4—61no—
304C2×C22⋊C4—61no—
305C2×C22⋊C4—61no—
306C2×C22⋊C4—64no—
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—62no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—124no—
317C2×C22⋊C4C4×D312yes—
318C2×C22⋊C4#6712yes—
319#99—68no—
320#95—64no—
321#95—64no—
322#95—124no—
323#95—124no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—41no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—41no—
345C23×C3—42no—
346C23×C3C2×C22⋊C411yescharacteristic
347C23×C3#11711yescharacteristic
348C23×C3#11711yescharacteristic
349C23×C3C4×D411yescharacteristic
350C23×C3C4×D411yescharacteristic
351C23×C3C4×D411yescharacteristic
352C23×C3C4×D411yescharacteristic
353C23×C3#12011yescharacteristic
354C23×C3#12011yescharacteristic
355C23×C3#12111yescharacteristic
356C23×C3#12111yescharacteristic
357C23×C3#12111yescharacteristic
358C23×C3#12111yescharacteristic
359C23×C3#12111yescharacteristic
360C23×C3#12111yescharacteristic
361C23×C3#12111yescharacteristic
362C23×C3#12111yescharacteristic
363C23×C3#12311yescharacteristic
364C23×C3#12311yescharacteristic
365C23×C3#12311yescharacteristic
366C23×C3#12311yescharacteristic
367C23×C3#12311yescharacteristic
368C23×C3#12311yescharacteristic
369C23×C3#12311yescharacteristic
370C23×C3#12311yescharacteristic
371C23×C3#12311yescharacteristic
372C23×C3#12311yescharacteristic
373C23×C3#12411yescharacteristic
374C23×C3#12411yescharacteristic
375C23×C3#12411yescharacteristic
376C23×C3#12411yescharacteristic
377C23×C3#12611yescharacteristic
378C23×C3#12611yescharacteristic
379C23×C3#12611yescharacteristic
380C23×C3#12611yescharacteristic
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—44no—
387C22×D3—44no—
388C22×D3—41no—
389C22×D3—41no—
390C22×D3—41no—
391C22×D3—41no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—81no—
395C22×D3—81no—
396C22×D3—82no—
397C22×D3—82no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—44no—
401C2×C3×C4—44no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—81no—
408C2×C3×C4—81no—
409C2×C3×C4—82no—
410C2×C3×C4—82no—
411C2×C3×C4—82no—
412C2×C3×C4—82no—
413#67—42no—
414#67—42no—
415#67—42no—
416#67—42no—
417#67—42no—
418#67—42no—
419#67—42no—
420#67—42no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—44no—
431C2×Dic3—44no—
432C2×Dic3—44no—
433C2×Dic3—42no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—44no—
439C2×Dic3—44no—
440C2×Dic3—44no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—81no—
446C2×Dic3—81no—
447C2×Dic3—82no—
448C2×Dic3—82no—
449C24—32no—
450C24—42no—
451C24—42no—
452C24—61no—
453C24—61no—
454C24—61no—
455C24—61no—
456C24—61no—
457C24—61no—
458C24—122no—
459C24—122no—
460C24C2×C4×D311yescharacteristic
461C24C2×D1211yescharacteristic
462C24#23511yescharacteristic
463C24#23511yescharacteristic
464C24#23511yescharacteristic
465C24#23511yescharacteristic
466C24D3×D411yescharacteristic
467C24D3×D411yescharacteristic
468C24D3×D411yescharacteristic
469C24D3×D411yescharacteristic
470C24#23711yescharacteristic
471C24#23711yescharacteristic
472C24#23911yescharacteristic
473C24#23911yescharacteristic
474C24C2×#6711yescharacteristic
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—121no—
488C2×D4—121no—
489C2×D4—121no—
490C2×D4—121no—
491C2×D4—121no—
492C2×D4—121no—
493C2×D4—121no—
494C2×D4—121no—
495C2×D4—121no—
496C2×D4—121no—
497C2×D4—121no—
498C2×D4—121no—
499C2×D4—121no—
500C2×D4—121no—
501C2×D4—121no—
502C2×D4—121no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—32no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—64no—
520C22×C4—64no—
521C22×C4—64no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—124no—
536C22×C4—124no—
537C22×C4—124no—
538C22×C4—124no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—121no—
543C22×C4—121no—
544C22×C4—121no—
545C22×C4—121no—
546C22×C4—122no—
547C22×C4—122no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4—121no—
551C22×C4—121no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—62no—
565C22⋊C4—62no—
566C22⋊C4—128no—
567C22⋊C4—121no—
568C22⋊C4—121no—
569C22⋊C4—121no—
570C22⋊C4—121no—
571C22⋊C4—121no—
572C22⋊C4—121no—
573C22⋊C4—242no—
574C22⋊C4—242no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3#38111yescharacteristic
616C22×C3#38611yescharacteristic
617C22×C3#38611yescharacteristic
618C22×C3#38811yescharacteristic
619C22×C3#38811yescharacteristic
620C22×C3#38811yescharacteristic
621C22×C3#38811yescharacteristic
622C22×C3#39411yescharacteristic
623C22×C3#39411yescharacteristic
624C22×C3#39411yescharacteristic
625C22×C3#39411yescharacteristic
626C22×C3#39711yescharacteristic
627C22×C3#39711yescharacteristic
628C22×C3#39711yescharacteristic
629C22×C3#39711yescharacteristic
630C22×C3B(4,𝔽2)12yes—
631C22×C3#45812yes—
632C2×D3—44no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—82no—
637C2×D3—82no—
638C2×D3—82no—
639C2×D3—82no—
640C2×D3—82no—
641C3×C4—82no—
642C3×C4—82no—
643C3×C4—82no—
644Dic3—44no—
645Dic3—42no—
646Dic3—82no—
647Dic3—82no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—122no—
674C23—122no—
675C23—124no—
676C23—124no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—122no—
682C23—122no—
683C23—241no—
684C23—241no—
685C23—242no—
686C23—242no—
687C23#87211yescharacteristic
688C23C4×D1211yescharacteristic
689C23#87511yescharacteristic
690C23#87611yescharacteristic
691C23D3×C22⋊C411yescharacteristic
692C23#67⋊C411yescharacteristic
693C23#88211yescharacteristic
694C23#88311yescharacteristic
695C23#88311yescharacteristic
696C23#88311yescharacteristic
697C23#88411yescharacteristic
698C23#88411yescharacteristic
699C23#88411yescharacteristic
700C23#88511yescharacteristic
701C23#88511yescharacteristic
702C23#88611yescharacteristic
703C23#89211yescharacteristic
704C23#89311yescharacteristic
705C23#89411yescharacteristic
706C23#89411yescharacteristic
707C23#89411yescharacteristic
708C23#89411yescharacteristic
709C23#89411yescharacteristic
710C23#89511yescharacteristic
711C23#89511yescharacteristic
712C23#89811yescharacteristic
713C23#89811yescharacteristic
714C23#89811yescharacteristic
715C23C4×#6711yescharacteristic
716C23#92911yescharacteristic
717C23#93011yescharacteristic
718C23#93711yescharacteristic
719C23#93811yescharacteristic
720C23#93911yescharacteristic
721C23#94711yescharacteristic
722D4—122no—
723D4—122no—
724D4—122no—
725D4—122no—
726D4—122no—
727D4—122no—
728D4—122no—
729D4—122no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—124no—
755C2×C4—124no—
756C2×C4—124no—
757C2×C4—122no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—124no—
763C2×C4—124no—
764C2×C4—124no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—241no—
770C2×C4—241no—
771C2×C4—242no—
772C2×C4—242no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3#144011yescharacteristic
786C2×C3#188911yescharacteristic
787C2×C3#189011yescharacteristic
788C2×C3#204412yes—
789C2×C3#204412yes—
790D3—82no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—124no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—242no—
836C22—242no—
837C22—242no—
838C22—242no—
839C22—242no—
840C22#466411yescharacteristic
841C22#466511yescharacteristic
842C22#466911yescharacteristic
843C22#467011yescharacteristic
844C22#467211yescharacteristic
845C22#467411yescharacteristic
846C22#467511yescharacteristic
847C22#467511yescharacteristic
848C22#474112yes—
849C22#474212yes—
850C22#494011yescharacteristic
851C22#495611yescharacteristic
852C22#495911yescharacteristic
853C22#496111yescharacteristic
854C22#499011yescharacteristic
855C22#499111yescharacteristic
856C22#499211yescharacteristic
857C4—82no—
858C4—82no—
859C4—82no—
860C4—122no—
861C4—124no—
862C4—242no—
863C4—242no—
864C3#1117411yescharacteristic, complemented, Sylow
865C2—21no—
866C2—21no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—242no—
878C2#6895712yes—
879C2#6896211yescharacteristic
880C2#6896311yescharacteristic
881C2#6942911yescharacteristic
882C2#7003212yes—
subgroupG/H
centerC23#882
commutatorC24×C3C22×C4
FrattiniC25C22×D3
FittingC2×C3×#342C2
socleC23×C3#120
prime radicalC23×#67C22
cosocleC25×C3C23
hypercenterC2×#342D3
hypocenterC3#11174
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×C3×#342C2semidirect
5. #71544C2semidirect
6. #71544C2semidirect
7. C2×#4527C2semidirect
23. #4958C4semidirect
35. C2×#342D3semidirect
864. C3#11174semidirect

Maximal subgroups

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

subgroupindex
#821212
C22×#8062
C2×#49582
C2×C3×#3422
#715442
C2×#45272
#111743