Finite Group Databasebeta

← #10716865

Subgroups — #10716865

Order 768.

2702 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic
2C22×#872C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#217C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#71550C212yesmaximal
7#71547C212yesmaximal, complemented
8C4×C3⋊#95C211yesmaximal, characteristic, complemented
9C4×C3⋊#95C211yesmaximal, characteristic, complemented
10#69429C212yesmaximal, complemented
11#69409C212yesmaximal, complemented
12#13839—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2211yescharacteristic
21C2×C4×#67—24no—
22C2×C4×#67—24no—
23C2×C4×#67C418yescomplemented
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×#872—24no—
33C2×#872—24no—
34C2×#872—24no—
35C3×C4×C22⋊C4—24no—
36C2×C3×#95C2212yes—
37C4×#217—24no—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44C4×(C2×D3)⋊C4—24no—
45C22×C4×D4—31no—
46C22×#117—31no—
47C2×C4×C22⋊C4—31no—
48C2×C4×C22⋊C4—31no—
49C2×C4×C22⋊C4D311yescharacteristic, complemented
50#1441—32no—
51#1440—32no—
52#1439—32no—
53#1438—32no—
54C4×#95—31no—
55C4×#95—31no—
56C25×C3C2311yescharacteristic
57C24×D3C2311yescharacteristic
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4C2×C414yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C22×#67—24no—
70C22×#67—22no—
71C22×#67—22no—
72C22×#67—24no—
73C22×#67C2×C414yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3C2×C414yes—
84C22×C4×D3D414yes—
85C22×C4×D3D414yes—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×C3×C42—22no—
93C2×C3×C42—22no—
94C2×C3×C42D414yescomplemented
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—24no—
100C2×#217C2×C414yes—
101C4×#67—232no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4C2×C414yes—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—24no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4C2×C414yes—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122C2×C4×Dic3—22no—
123C2×C4×Dic3—22no—
124C2×C4×Dic3C2×C414yes—
125C2×C4×Dic3D414yescomplemented
126#872—232no—
127C3×#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—24no—
134C23×D4—31no—
135C24×C4—31no—
136C24×C4C2×D311yescharacteristic
137C2×C4×D4—38no—
138C2×C4×D4—64no—
139C2×C4×D4—64no—
140C2×#117—64no—
141C2×#117—64no—
142C2×#117—64no—
143C22×C4⋊C4—31no—
144C22×C4⋊C4—32no—
145C22×C22⋊C4—31no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4C2×D312yes—
151C22×C42—31no—
152C22×C42—31no—
153C22×C42—31no—
154C22×C42C2×D311yescharacteristic
155C22×C42C2×D311yescharacteristic
156C4×C22⋊C4—24no—
157C4×C22⋊C4—64no—
158C4×C22⋊C4—64no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C2×#95—32no—
164C2×#95—32no—
165C2×#95C2×D312yes—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3C22×C412yes—
176C24×C3#4114yes—
177C24×C3C2411yescharacteristic
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3C22×C412yes—
187C23×D3C2×D412yes—
188C23×D3C2×D412yes—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—28no—
208C22×C3×C4—28no—
209C22×C3×C4—28no—
210C22×C3×C4—44no—
211C22×C3×C4—44no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C22×C412yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D414yes—
220C22×C3×C4C2×D412yes—
221C22×C3×C4#4114yes—
222C22×C3×C4#4112yes—
223C22×C3×C4#4112yes—
224C2×#67—216no—
225C2×#67—216no—
226C2×#67—28no—
227C2×#67—28no—
228C2×#67—28no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3C22×C412yes—
253C22×Dic3C22×C412yes—
254C22×Dic3C22×C412yes—
255C22×Dic3C2×D414yes—
256C22×Dic3C2×D412yes—
257C22×Dic3C2×D412yes—
258C22×Dic3#4114yes—
259C22×Dic3#4114yes—
260C2×C4×D3—28no—
261C2×C4×D3—28no—
262C2×C4×D3—28no—
263C2×C4×D3—28no—
264C2×C4×D3—28no—
265C2×C4×D3—28no—
266C2×C4×D3C22⋊C4116yescomplemented
267C3×C22⋊C4—216no—
268C3×C42—28no—
269C3×C42—44no—
270#217—216no—
271#217—28no—
272(C2×D3)⋊C4—216no—
273(C2×D3)⋊C4—216no—
274(C2×D3)⋊C4—28no—
275Dic3⋊C4—216no—
276Dic3⋊C4—28no—
277C4×Dic3—28no—
278C4×Dic3—28no—
279C4×Dic3—44no—
280C25—31no—
281C25C22×D311yescharacteristic
282C22×D4—34no—
283C22×D4—64no—
284C22×D4—62no—
285C22×D4—62no—
286C22×D4—64no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—31no—
294C23×C4—31no—
295C23×C4—34no—
296C23×C4—34no—
297C23×C4—34no—
298C23×C4—32no—
299C23×C4—31no—
300C23×C4—32no—
301C23×C4—62no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—62no—
305C23×C4C4×D314yes—
306C23×C4C22×D311yescharacteristic
307C23×C4C22×D312yes—
308C23×C4C22×D312yes—
309C23×C4C22×D311yescharacteristic
310C4×D4—632no—
311#117—632no—
312C2×C4⋊C4—34no—
313C2×C4⋊C4—64no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4—64no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—34no—
322C2×C22⋊C4—34no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—62no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—62no—
330C2×C22⋊C4—62no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—34no—
342C2×C42—34no—
343C2×C42—62no—
344C2×C42—62no—
345C2×C42—62no—
346C2×C42—62no—
347C2×C42—62no—
348C2×C42—62no—
349C2×C42—62no—
350C2×C42#6714yescomplemented
351#95—24no—
352#95—64no—
353#95—64no—
354#95—64no—
355#95—64no—
356#95—64no—
357#95—64no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3#11714yescomplemented
381C23×C3C23×C411yescharacteristic
382C23×C3C22×D411yescharacteristic
383C23×C3C22×D411yescharacteristic
384C23×C3C22×D411yescharacteristic
385C23×C3C22×D411yescharacteristic
386C23×C3C2×#4112yes—
387C23×C3C2×#4111yescharacteristic
388C23×C3C2×#4112yes—
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4112yes—
391C23×C3C2×#4112yes—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3C2×C22⋊C414yes—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—416no—
437C2×C3×C4C2×C22⋊C414yes—
438C2×C3×C4C4×D414yes—
439C2×C3×C4C4×D414yes—
440C2×C3×C4#12014yes—
441C2×C3×C4#12114yes—
442C2×C3×C4#12114yes—
443C2×C3×C4#12314yes—
444#67—232no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—24no—
454C2×Dic3—24no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—24no—
459C2×Dic3—24no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3C2×C22⋊C414yes—
475C2×Dic3#11714yescomplemented
476C4×D3—232no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—32no—
487C24—32no—
488C24—32no—
489C24—62no—
490C24—61no—
491C24—62no—
492C24—61no—
493C24—61no—
494C24—62no—
495C24—62no—
496C24—61no—
497C24C2×C4×D312yes—
498C24#23514yes—
499C24C23×D311yescharacteristic
500C2×D4—68no—
501C2×D4—68no—
502C2×D4—616no—
503C2×D4—616no—
504C2×D4—68no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—34no—
531C22×C4—316no—
532C22×C4—32no—
533C22×C4—34no—
534C22×C4—34no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—68no—
547C22×C4—68no—
548C22×C4—68no—
549C22×C4—68no—
550C22×C4—68no—
551C22×C4—68no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4C2×C4×D312yes—
569C22×C4C2×C4×D312yes—
570C22×C4#23514yes—
571C22×C4#23512yes—
572C22×C4D3×D412yes—
573C22×C4D3×D412yes—
574C22×C4D3×D412yes—
575C22×C4#23712yes—
576C22×C4C2×#6714yes—
577C22×C4C2×#6712yes—
578C4⋊C4—68no—
579C4⋊C4—616no—
580C22⋊C4—216no—
581C22⋊C4—68no—
582C22⋊C4—616no—
583C22⋊C4—616no—
584C22⋊C4—68no—
585C22⋊C4—616no—
586C42—28no—
587C42—44no—
588C42—68no—
589C42—68no—
590C42—124no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3C22×C22⋊C411yescharacteristic
603C22×C3C2×#11711yescharacteristic
604C22×C3C2×#11711yescharacteristic
605C22×C3C2×C4×D411yescharacteristic
606C22×C3C2×C4×D411yescharacteristic
607C22×C3C4×#4111yescharacteristic
608C22×C3C4×#4111yescharacteristic
609C22×C3C2×#12011yescharacteristic
610C22×C3C2×#12111yescharacteristic
611C22×C3C2×#12111yescharacteristic
612C22×C3C2×#12311yescharacteristic
613C22×C3#52512yes—
614C22×C3#52512yes—
615C22×C3#52512yes—
616C22×C3#52512yes—
617C22×C3#52512yes—
618C22×C3#52912yes—
619C22×C3#52912yes—
620C22×C3#52912yes—
621C22×C3#52912yes—
622C22×C3#53212yes—
623C22×C3#53212yes—
624C22×C3#53212yes—
625C2×D3—24no—
626C2×D3—24no—
627C2×D3—24no—
628C2×D3—44no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—44no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C3×C4—44no—
637C3×C4—44no—
638C3×C4—42no—
639C3×C4#38618yes—
640Dic3—24no—
641Dic3—24no—
642Dic3—44no—
643Dic3—44no—
644Dic3—42no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—34no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—122no—
683C23—122no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—122no—
688C23—122no—
689C23—122no—
690C23#87214yescomplemented
691C23C22×C4×D311yescharacteristic
692C23C2×#23512yes—
693C23C2×#23512yes—
694C23C2×#23511yescharacteristic
695C23C2×D3×D411yescharacteristic
696C23C2×D3×D411yescharacteristic
697C23C2×D3×D411yescharacteristic
698C23C2×#23711yescharacteristic
699C23D3×#4112yes—
700C23D3×#4112yes—
701C23C22×#6711yescharacteristic
702D4—632no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—34no—
713C2×C4—34no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—416no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—632no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—64no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—64no—
745C2×C4—64no—
746C2×C4—64no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4D3×C22⋊C414yes—
758C2×C4#67⋊C414yes—
759C2×C4#88314yes—
760C2×C4#88414yes—
761C2×C4C4×#6714yes—
762C2×C4#93714yes—
763C2×C4#93814yes—
764C2×C3—44no—
765C2×C3#228011yescharacteristic
766C2×C3C2×#38611yescharacteristic
767C2×C3#229011yescharacteristic
768C2×C3#229011yescharacteristic
769C2×C3#229311yescharacteristic
770C2×C3#229311yescharacteristic
771C2×C3#229711yescharacteristic
772C2×C3#238812yes—
773C2×C3#239212yes—
774C2×C3#239212yes—
775C2×C3#239512yes—
776D3—44no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—64no—
789C22—64no—
790C22—64no—
791C22—122no—
792C22—124no—
793C22—124no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—124no—
798C22—124no—
799C22C2×#87211yescharacteristic
800C22C4×#23511yescharacteristic
801C22#547912yes—
802C22C2×D3×C22⋊C411yescharacteristic
803C22C2×#67⋊C411yescharacteristic
804C22C2×#88311yescharacteristic
805C22C2×#88411yescharacteristic
806C22D3×#11711yescharacteristic
807C22#552211yescharacteristic
808C22#552812yes—
809C22#553812yes—
810C22#553812yes—
811C22#554712yes—
812C22#554712yes—
813C22#554712yes—
814C22#554712yes—
815C22#554812yes—
816C22#554812yes—
817C22C2×C4×#6711yescharacteristic
818C22#579112yes—
819C22C2×#93711yescharacteristic
820C22C2×#93811yescharacteristic
821C22#583212yes—
822C4—42no—
823C4—44no—
824C4—44no—
825C4—64no—
826C4—64no—
827C4—122no—
828C4—124no—
829C4—124no—
830C4#495618yes—
831C3#1383911yescharacteristic, complemented, Sylow
832C2—44no—
833C2—124no—
834C2#7343811yescharacteristic
835C2#7343911yescharacteristic
836C2#7356111yescharacteristic
837C2#7356311yescharacteristic
838C2#7358112yes—
839C2#7358212yes—
840C2#8206511yescharacteristic
841C2C2×#495611yescharacteristic
842C2#8222511yescharacteristic
843C2#8240012yes—
844C2#8240112yes—
subgroupG/H
centerC23×C4C22×D3
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×C4×C22⋊C4C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#13839
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#872C2semidirect
3. C2×C3×C4×C22⋊C4C2semidirect
4. C2×C4×#217C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
7. #71547C2semidirect
8. C4×C3⋊#95C2semidirect
9. C4×C3⋊#95C2semidirect
10. #69429C2semidirect
11. #69409C2semidirect
23. C2×C4×#67C4semidirect
49. C2×C4×C22⋊C4D3semidirect
94. C2×C3×C42D4semidirect
125. C2×C4×Dic3D4semidirect
266. C2×C4×D3C22⋊C4semidirect
350. C2×C42#67semidirect
380. C23×C3#117semidirect
475. C2×Dic3#117semidirect
690. C23#872semidirect
831. C3#13839semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C22×#8722
C2×C3×C4×C22⋊C42
C2×C4×#2172
C2×C4×(C2×D3)⋊C42
#715502
#715472
C4×C3⋊#952
#694292
#694092
#138393