Finite Group Databasebeta

← #10701896

Subgroups — #10701896

Order 768.

2118 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#940C211yesmaximal, characteristic
2C22×C3×#102C211yesmaximal, characteristic, complemented
3C22×#832C211yesmaximal, characteristic, complemented
4C22×#821C211yesmaximal, characteristic, complemented
5C22×#809C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#11008—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×#67—22no—
11C23×D12C2211yescharacteristic
12C23×C3×C8C2211yescharacteristic
13C22×C3×C4⋊C4C2211yescharacteristic
14C2×#940—22no—
15C2×#940—22no—
16C2×#940—22no—
17C2×#940—22no—
18C2×#940—22no—
19C2×#940C414yescomplemented
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×#821—22no—
31C2×#821—22no—
32C2×#821—22no—
33C2×#809—22no—
34C2×#809—22no—
35C2×#809—22no—
36#4550—22no—
37C22×#127—31no—
38C22×#102—31no—
39C22×#102—31no—
40C22×#102—31no—
41C22×#102D311yescharacteristic, complemented
42C2×#336—31no—
43C4⋊#95—31no—
44C25×C3—21no—
45C24×D3—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×D4—21no—
57C22×C3×D4C2×C412yes—
58C22×C3×D4D412yes—
59C22×C3×D4D412yes—
60C23×C3×C4—21no—
61C23×C3×C4C2311yescharacteristic
62C22×#67—28no—
63C22×#67—28no—
64C22×#67—28no—
65C22×#67—44no—
66C22×#67—44no—
67C22×#67—44no—
68C22×#67—44no—
69C23×Dic3—21no—
70C23×Dic3D412yes—
71C22×D12—21no—
72C22×D12—21no—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12—21no—
76C22×D12—21no—
77C22×D12—21no—
78C22×D12—21no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12C2×C412yes—
83C22×D12D412yes—
84C22×D12D412yes—
85C22×C3×C8—21no—
86C22×C3×C8—21no—
87C22×C3×C8—21no—
88C22×C3×C8—21no—
89C22×C3×C8—21no—
90C22×C3×C8—21no—
91C22×C3×C8D412yescomplemented
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4D412yescomplemented
98#940—28no—
99#940—28no—
100#940—28no—
101#940—28no—
102C2×C4⋊Dic3—21no—
103C2×C4⋊Dic3—21no—
104C2×C4⋊Dic3—21no—
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3—21no—
107C2×C4⋊Dic3D412yescomplemented
108C2×C4×Dic3—21no—
109C2×C4×Dic3—21no—
110C2×C4×Dic3—21no—
111C2×C4×Dic3—21no—
112C2×C4×Dic3C2×C412yes—
113C2×C4×Dic3D412yes—
114C22×C3⋊C8—21no—
115C22×C3⋊C8—21no—
116C22×C3⋊C8—21no—
117C22×C3⋊C8—21no—
118C22×C3⋊C8—21no—
119C22×C3⋊C8—21no—
120C22×C3⋊C8D412yescomplemented
121C3×#102—28no—
122#832—28no—
123C3⋊#95—44no—
124#821—28no—
125#809—28no—
126C23×D4—31no—
127C23×D4—62no—
128C23×D4C2×D311yescharacteristic
129C23×C8—31no—
130C23×C8C2×D311yescharacteristic
131C2×#127—34no—
132C2×#127—62no—
133C2×#127—62no—
134C2×#127—62no—
135C2×#127—62no—
136C2×#127—62no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4C2×D311yescharacteristic
139C22×C42—31no—
140C2×#102—22no—
141C2×#102—22no—
142C2×#102—22no—
143C2×#102—62no—
144C2×#102—62no—
145C2×#102—62no—
146C2×#102—62no—
147C2×#102—62no—
148C2×#102—62no—
149C2×#102—62no—
150C2×#102—62no—
151C2×#102—62no—
152C2×#95—62no—
153#336—62no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—41no—
158C24×C3—41no—
159C24×C3—41no—
160C24×C3—41no—
161C24×C3—42no—
162C24×C3—42no—
163C24×C3—42no—
164C24×C3—42no—
165C24×C3C2×D411yescharacteristic
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—41no—
170C23×D3—41no—
171C23×D3—41no—
172C23×D3—41no—
173C23×D3—42no—
174C23×D3—42no—
175C23×D3—42no—
176C23×D3—42no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—41no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—41no—
197C2×C3×D4—41no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4C22⋊C414yes—
205C22×C3×C4—22no—
206C22×C3×C4—41no—
207C22×C3×C4—41no—
208C22×C3×C4—42no—
209C22×C3×C4—42no—
210C22×C3×C4C22×C411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4C2×D411yescharacteristic
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4#4111yescharacteristic
221C22×C3×C4#4111yescharacteristic
222C22×C3×C4#4111yescharacteristic
223C22×C3×C4#4111yescharacteristic
224C2×#67—232no—
225C2×#67—416no—
226C2×#67—416no—
227C2×#67—416no—
228C2×#67—416no—
229C2×#67—416no—
230C2×#67—416no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—41no—
237C22×Dic3—41no—
238C22×Dic3—42no—
239C22×Dic3—42no—
240C22×Dic3C22⋊C414yes—
241C22×Dic3D814yes—
242C22×Dic3SD1614yes—
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—22no—
249C2×D12—22no—
250C2×D12—22no—
251C2×D12—22no—
252C2×D12—22no—
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—22no—
256C2×D12—22no—
257C2×D12—22no—
258C2×D12—41no—
259C2×D12—41no—
260C2×D12—41no—
261C2×D12—41no—
262C2×D12—41no—
263C2×D12—41no—
264C2×D12—41no—
265C2×D12—41no—
266C2×D12—41no—
267C2×D12—41no—
268C2×D12—41no—
269C2×D12—41no—
270C2×D12C22⋊C414yes—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C2×C3×C8—22no—
274C2×C3×C8—41no—
275C2×C3×C8—41no—
276C2×C3×C8—41no—
277C2×C3×C8—41no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—41no—
281C3×C4⋊C4—41no—
282C4⋊Dic3—22no—
283C4⋊Dic3—22no—
284C4⋊Dic3—41no—
285C4⋊Dic3—41no—
286C4×Dic3—22no—
287C4×Dic3—22no—
288C4×Dic3—22no—
289C4×Dic3—22no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8—22no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8—41no—
294C2×C3⋊C8—41no—
295C2×C3⋊C8—41no—
296C2×C3⋊C8—41no—
297C25—21no—
298C25—61no—
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×D4—21no—
310C22×D4—32no—
311C22×D4—32no—
312C22×D4—32no—
313C22×D4—68no—
314C22×D4—68no—
315C22×D4—68no—
316C22×D4—61no—
317C22×D4—61no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—124no—
328C22×D4—124no—
329C22×D4—124no—
330C22×D4—124no—
331C22×D4C4×D312yes—
332C22×D4D1212yes—
333C22×D4#6712yes—
334C23×C4—21no—
335C23×C4—32no—
336C23×C4—61no—
337C23×C4C22×D311yescharacteristic
338C22×C8—21no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—32no—
345C22×C8—61no—
346C22×C8—61no—
347C22×C8—61no—
348C22×C8—61no—
349C22×C8—61no—
350C22×C8—61no—
351C22×C8#6712yescomplemented
352#127—68no—
353#127—68no—
354#127—68no—
355#127—68no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4#6712yescomplemented
368C2×C42—32no—
369C2×C42—32no—
370C2×C42—61no—
371C2×C42—61no—
372C2×C42—61no—
373C2×C42—61no—
374#102—28no—
375#102—68no—
376#102—68no—
377#102—68no—
378#95—124no—
379C23×C3—24no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—44no—
387C23×C3—44no—
388C23×C3—44no—
389C23×C3—44no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—82no—
393C23×C3—82no—
394C23×C3—82no—
395C23×C3—82no—
396C23×C3—82no—
397C23×C3—82no—
398C23×C3—81no—
399C23×C3—81no—
400C23×C3—81no—
401C23×C3—81no—
402C23×C3C2×C22⋊C411yescharacteristic
403C23×C3#12011yescharacteristic
404C23×C3#12011yescharacteristic
405C23×C3#12111yescharacteristic
406C23×C3#12111yescharacteristic
407C23×C3#12411yescharacteristic
408C23×C3#12711yescharacteristic
409C23×C3C2×D812yes—
410C23×C3C2×SD1612yes—
411C23×C3AGL(1,ℤ/8)12yes—
412C23×C3AGL(1,ℤ/8)12yes—
413C22×D3—24no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—44no—
421C22×D3—44no—
422C22×D3—44no—
423C22×D3—44no—
424C22×D3—44no—
425C22×D3—44no—
426C22×D3—82no—
427C22×D3—82no—
428C22×D3—82no—
429C22×D3—82no—
430C22×D3—82no—
431C22×D3—82no—
432C22×D3—81no—
433C22×D3—81no—
434C22×D3—81no—
435C22×D3—81no—
436C3×D4—24no—
437C3×D4—24no—
438C3×D4—42no—
439C3×D4—42no—
440C3×D4—42no—
441C3×D4—42no—
442C3×D4—42no—
443C3×D4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—44no—
446C2×C3×C4—82no—
447C2×C3×C4—81no—
448C2×C3×C4—81no—
449C2×C3×C4C2×C22⋊C411yescharacteristic
450C2×C3×C4C2×C22⋊C411yescharacteristic
451C2×C3×C4C4×D411yescharacteristic
452C2×C3×C4C4×D411yescharacteristic
453C2×C3×C4C4×D411yescharacteristic
454C2×C3×C4C4×D411yescharacteristic
455C2×C3×C4#12011yescharacteristic
456C2×C3×C4#12011yescharacteristic
457C2×C3×C4#12011yescharacteristic
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12011yescharacteristic
461C2×C3×C4#12111yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4#12111yescharacteristic
466C2×C3×C4#12111yescharacteristic
467C2×C3×C4#12111yescharacteristic
468C2×C3×C4#12111yescharacteristic
469C2×C3×C4#12111yescharacteristic
470C2×C3×C4#12111yescharacteristic
471C2×C3×C4#12311yescharacteristic
472C2×C3×C4#12311yescharacteristic
473C2×C3×C4#12311yescharacteristic
474C2×C3×C4#12311yescharacteristic
475C2×C3×C4#12411yescharacteristic
476C2×C3×C4#12711yescharacteristic
477#67—464no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—24no—
481C2×Dic3—24no—
482C2×Dic3—24no—
483C2×Dic3—24no—
484C2×Dic3—42no—
485C2×Dic3—44no—
486C2×Dic3—82no—
487C2×Dic3—81no—
488C2×Dic3—81no—
489C2×Dic3#10218yescomplemented
490D12—24no—
491D12—24no—
492D12—42no—
493D12—42no—
494D12—42no—
495D12—42no—
496D12—42no—
497D12—42no—
498C3×C8—42no—
499C3⋊C8—42no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—41no—
504C24—41no—
505C24—42no—
506C24—42no—
507C24—42no—
508C24—42no—
509C24—41no—
510C24—41no—
511C24—62no—
512C24—62no—
513C24—62no—
514C24—121no—
515C24—121no—
516C24—122no—
517C24—122no—
518C24—122no—
519C24—122no—
520C24—121no—
521C24—121no—
522C24D3×D411yescharacteristic
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—34no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—632no—
552C2×D4—62no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—62no—
566C2×D4—62no—
567C2×D4—1216no—
568C2×D4—1216no—
569C2×D4—1216no—
570C2×D4—1216no—
571C2×D4—1216no—
572C2×D4—1216no—
573C2×D4—121no—
574C2×D4—121no—
575C2×D4—121no—
576C2×D4—121no—
577C2×D4—121no—
578C2×D4—121no—
579C2×D4—121no—
580C2×D4—121no—
581C2×D4—121no—
582C2×D4—121no—
583C2×D4—121no—
584C2×D4—121no—
585C2×D4(C2×D3)⋊C414yes—
586C22×C4—22no—
587C22×C4—34no—
588C22×C4—34no—
589C22×C4—34no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—121no—
600C22×C4—122no—
601C22×C4—122no—
602C22×C4—121no—
603C22×C4C2×C4×D311yescharacteristic
604C22×C4C2×D1211yescharacteristic
605C22×C4#23511yescharacteristic
606C22×C4#23511yescharacteristic
607C22×C4D3×D411yescharacteristic
608C22×C4D3×D411yescharacteristic
609C22×C4D3×D411yescharacteristic
610C22×C4D3×D411yescharacteristic
611C22×C4D3×D411yescharacteristic
612C22×C4#23711yescharacteristic
613C22×C4#23711yescharacteristic
614C22×C4C2×#6711yescharacteristic
615C22×C4C2×#6711yescharacteristic
616C22×C4C2×#6711yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—62no—
625C2×C8—62no—
626C2×C8—62no—
627C2×C8—121no—
628C2×C8—121no—
629C2×C8—121no—
630C2×C8—121no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—121no—
638C4⋊C4—121no—
639C42—62no—
640C42—62no—
641C42—62no—
642C42—62no—
643C22×C3—44no—
644C22×C3—48no—
645C22×C3—82no—
646C22×C3—82no—
647C22×C3—84no—
648C22×C3—82no—
649C22×C3—82no—
650C22×C3—82no—
651C22×C3—82no—
652C22×C3—84no—
653C22×C3—84no—
654C22×C3#37911yescharacteristic
655C22×C3#39011yescharacteristic
656C22×C3#39011yescharacteristic
657C22×C3#39211yescharacteristic
658C22×C3#39211yescharacteristic
659C22×C3#39411yescharacteristic
660C22×C3#39411yescharacteristic
661C22×C3C2×#10212yes—
662C22×C3#41812yes—
663C22×C3#44712yes—
664C22×C3#44712yes—
665C22×C3#45012yes—
666C22×C3#45012yes—
667C22×C3#45912yes—
668C22×C3#45912yes—
669C22×C3#46012yes—
670C22×C3#46012yes—
671C22×C3#48612yes—
672C22×C3#49012yes—
673C22×C3#49211yescharacteristic
674C22×C3#49311yescharacteristic
675C22×C3#49611yescharacteristic
676C22×C3#49611yescharacteristic
677C2×D3—44no—
678C2×D3—48no—
679C2×D3—82no—
680C2×D3—82no—
681C2×D3—84no—
682C2×D3—82no—
683C2×D3—82no—
684C2×D3—82no—
685C2×D3—82no—
686C2×D3—84no—
687C2×D3—84no—
688C3×C4—82no—
689C3×C4#38611yescharacteristic
690C3×C4#38611yescharacteristic
691C3×C4#38611yescharacteristic
692C3×C4#38611yescharacteristic
693C3×C4#39211yescharacteristic
694C3×C4#39211yescharacteristic
695C3×C4#39411yescharacteristic
696C3×C4#39411yescharacteristic
697Dic3—28no—
698Dic3—82no—
699C23—24no—
700C23—44no—
701C23—44no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—64no—
713C23—82no—
714C23—81no—
715C23—81no—
716C23—82no—
717C23—81no—
718C23—81no—
719C23—82no—
720C23—82no—
721C23—82no—
722C23—82no—
723C23—124no—
724C23—124no—
725C23—122no—
726C23—122no—
727C23—122no—
728C23—122no—
729C23—122no—
730C23—122no—
731C23—124no—
732C23—124no—
733C23—124no—
734C23—124no—
735C23—242no—
736C23—241no—
737C23—241no—
738C23—242no—
739C23—241no—
740C23—241no—
741C23—242no—
742C23—242no—
743C23—242no—
744C23—242no—
745C23D3×C22⋊C411yescharacteristic
746C23#88211yescharacteristic
747C23#88411yescharacteristic
748C23#88511yescharacteristic
749C23D3×D812yes—
750C23#91112yes—
751C23D3×SD1612yes—
752C23#91412yes—
753C23#93711yescharacteristic
754C23#93911yescharacteristic
755C23#94011yescharacteristic
756D4—24no—
757D4—24no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—64no—
765D4—64no—
766D4—1264no—
767D4—122no—
768D4—122no—
769D4—122no—
770D4—122no—
771D4—122no—
772D4—122no—
773C2×C4—38no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—64no—
777C2×C4—64no—
778C2×C4—64no—
779C2×C4—64no—
780C2×C4—64no—
781C2×C4—64no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—122no—
786C2×C4—124no—
787C2×C4—241no—
788C2×C4—241no—
789C2×C4—242no—
790C2×C4D3×C22⋊C411yescharacteristic
791C2×C4#67⋊C411yescharacteristic
792C2×C4#67⋊C411yescharacteristic
793C2×C4#88211yescharacteristic
794C2×C4#88211yescharacteristic
795C2×C4#88311yescharacteristic
796C2×C4#88311yescharacteristic
797C2×C4#88411yescharacteristic
798C2×C4#88411yescharacteristic
799C2×C4#88411yescharacteristic
800C2×C4#88511yescharacteristic
801C2×C4#88611yescharacteristic
802C2×C4C2×(C2×D3)⋊C411yescharacteristic
803C2×C4C4×#6711yescharacteristic
804C2×C4C4×#6711yescharacteristic
805C2×C4#92911yescharacteristic
806C2×C4#93011yescharacteristic
807C2×C4#93011yescharacteristic
808C2×C4#93711yescharacteristic
809C2×C4#93711yescharacteristic
810C2×C4#93711yescharacteristic
811C2×C4#93811yescharacteristic
812C2×C4#93811yescharacteristic
813C2×C4#93911yescharacteristic
814C2×C4#93911yescharacteristic
815C2×C4#93911yescharacteristic
816C2×C4#94011yescharacteristic
817C2×C4#95311yescharacteristic
818C8—42no—
819C8—122no—
820C2×C3—84no—
821C2×C3#143811yescharacteristic
822C2×C3#178612yes—
823C2×C3#195711yescharacteristic
824C2×C3#196111yescharacteristic
825C2×C3#198212yes—
826C2×C3#201111yescharacteristic
827C2×C3#201111yescharacteristic
828C2×C3#201411yescharacteristic
829C2×C3#201411yescharacteristic
830C2×C3#204112yes—
831C2×C3#204112yes—
832D3—84no—
833C22—48no—
834C22—44no—
835C22—82no—
836C22—82no—
837C22—84no—
838C22—84no—
839C22—82no—
840C22—82no—
841C22—84no—
842C22—82no—
843C22—82no—
844C22—128no—
845C22—124no—
846C22—242no—
847C22—242no—
848C22—244no—
849C22—244no—
850C22—242no—
851C22—242no—
852C22—244no—
853C22—242no—
854C22—242no—
855C22#476012yes—
856C22#476212yes—
857C22#476412yes—
858C22D3×#10212yes—
859C22#477012yes—
860C22#477312yes—
861C22#477612yes—
862C22#478612yes—
863C22#495511yescharacteristic
864C22#495711yescharacteristic
865C22#495711yescharacteristic
866C22#495911yescharacteristic
867C22#496011yescharacteristic
868C22#496111yescharacteristic
869C22#515012yes—
870C22#515111yescharacteristic
871C22#515411yescharacteristic
872C22#515612yes—
873C22#516312yes—
874C22#516912yes—
875C22#517511yescharacteristic
876C22#517611yescharacteristic
877C22#522311yescharacteristic
878C4—68no—
879C4—82no—
880C4—242no—
881C4#495611yescharacteristic
882C4#495611yescharacteristic
883C4#495811yescharacteristic
884C4#495911yescharacteristic
885C4#496011yescharacteristic
886C4#496111yescharacteristic
887C4#521311yescharacteristic
888C4#522311yescharacteristic
889C3#1100811yescharacteristic, complemented, Sylow
890C2—84no—
891C2—244no—
892C2#7015711yescharacteristic
893C2#7016011yescharacteristic
894C2#7016112yes—
895C2#7017712yes—
896C2#7019812yes—
897C2#7020911yescharacteristic
898C2#7021011yescharacteristic
899C2#7021112yes—
900C2#7155011yescharacteristic
901C2#7204411yescharacteristic
902C2#7205611yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#102C2
socleC24×C3C2×D4
prime radicalC22×#940C2
cosocleC23×C3×C4C23
hypercenterC22×#102D3
hypocenterC3#11008
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
2. C22×C3×#102C2semidirect
3. C22×#832C2semidirect
4. C22×#821C2semidirect
5. C22×#809C2semidirect
6. C2×#4550C2semidirect
7. #71563C2semidirect
19. C2×#940C4semidirect
41. C22×#102D3semidirect
91. C22×C3×C8D4semidirect
97. C2×C3×C4⋊C4D4semidirect
107. C2×C4⋊Dic3D4semidirect
120. C22×C3⋊C8D4semidirect
351. C22×C8#67semidirect
367. C2×C4⋊C4#67semidirect
489. C2×Dic3#102semidirect
889. C3#11008semidirect

Maximal subgroups

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

subgroupindex
C22×#9402
C22×C3×#1022
C22×#8322
C22×#8212
C22×#8092
C2×#45502
#715632
#110083