Finite Group Databasebeta

← #10726638

Subgroups — #10726638

Order 768.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic, complemented
2C22×#893C211yesmaximal, characteristic
3C2×C3×#395C211yesmaximal, characteristic, complemented
4C2×#5231C211yesmaximal, characteristic, complemented
5C2×#4989C212yesmaximal, complemented
6#71570C212yesmaximal, complemented
7#71565C211yesmaximal, characteristic, complemented
8#69427C211yesmaximal, characteristic, complemented
9#69426C212yesmaximal
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11#69406C212yesmaximal, complemented
12#14723—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×D12C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#946—24no—
20C2×#946—28no—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2212yes—
29C22×C4×Dic3C2211yescharacteristic
30C2×#893—24no—
31C2×#893—24no—
32C2×#893—24no—
33C3×#395—24no—
34C2×C3×#95C2212yes—
35C2×C3×#95C2211yescharacteristic
36#5231—24no—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2211yescharacteristic
43#4989—28no—
44C22×C22⋊Q8—31no—
45C22×C4×D4—31no—
46C2×#395D311yescharacteristic, complemented
47C2×#393—31no—
48C2×#385—32no—
49#1441—31no—
50#1439—31no—
51#1439—32no—
52#1438—32no—
53#1436—32no—
54C22⋊#95—31no—
55C24×D3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C22×C3×Q8—24no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—42no—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×Dic3C2312yes—
68C23×Dic3C2311yescharacteristic
69C23×Dic3C2312yes—
70C23×Dic3C2311yescharacteristic
71C22×D12—22no—
72C22×D12—22no—
73C22×D12—22no—
74C22×D12—22no—
75C22×D12—22no—
76C22×D12—22no—
77C22×D12Q814yescomplemented
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—24no—
84C22×C4×D3—24no—
85C22×C4×D3—42no—
86C22×C4×D3—42no—
87C22×C4×D3D414yes—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—42no—
93C2×C3×C4⋊C4D414yes—
94#946—232no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4D414yes—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—24no—
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—24no—
117C2×Dic3⋊C4D418yescomplemented
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121#893—232no—
122C3×#95—22no—
123C3×#95—24no—
124C3⋊#95—22no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C23×Q8C2×D311yescharacteristic
131C23×D4—31no—
132C24×C4—31no—
133C24×C4—31no—
134C2×C22⋊Q8—68no—
135C2×C22⋊Q8—64no—
136C2×C4×D4—64no—
137C2×C4×D4—64no—
138C2×C4×D4—64no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4C2×D312yes—
142C22×C4⋊C4C2×D311yescharacteristic
143C22×C22⋊C4—31no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—32no—
149C22×C42—31no—
150#395—24no—
151#393—64no—
152#385—68no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95C2×D311yescharacteristic
160C2×#95C2×D312yes—
161C24×C3C2411yescharacteristic
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—21no—
165C23×D3—21no—
166C23×D3—21no—
167C23×D3—21no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—21no—
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—21no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3C2×D412yes—
179C23×D3C2×D412yes—
180C23×D3C2×Q812yes—
181C23×D3C2×Q812yes—
182C23×D3#4112yes—
183C23×D3#4112yes—
184C2×C3×Q8—28no—
185C2×C3×Q8—48no—
186C2×C3×Q8—48no—
187C2×C3×Q8—44no—
188C2×C3×Q8—44no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4C2×D414yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×Q812yes—
218C22×C3×C4#4114yes—
219C22×C3×C4#4112yes—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3C2×D412yes—
241C22×Dic3C2×D414yes—
242C22×Dic3C2×D414yes—
243C22×Dic3C2×D412yes—
244C2×D12—28no—
245C2×D12—28no—
246C2×D12—28no—
247C2×D12—28no—
248C2×D12—28no—
249C2×D12—28no—
250C2×D12—28no—
251C2×C4×D3—28no—
252C2×C4×D3—28no—
253C2×C4×D3—28no—
254C2×C4×D3—44no—
255C2×C4×D3—48no—
256C2×C4×D3—48no—
257C2×C4×D3—48no—
258C2×C4×D3—48no—
259C2×C4×D3—44no—
260C2×C4×D3—44no—
261C3×C4⋊C4—28no—
262C3×C4⋊C4—48no—
263(C2×D3)⋊C4—28no—
264(C2×D3)⋊C4—216no—
265(C2×D3)⋊C4—216no—
266(C2×D3)⋊C4—28no—
267(C2×D3)⋊C4—48no—
268(C2×D3)⋊C4—48no—
269C4⋊Dic3—28no—
270Dic3⋊C4—216no—
271C4×Dic3—28no—
272C25—31no—
273C25—31no—
274C22×Q8—24no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—42no—
279C22×D4—34no—
280C22×D4—62no—
281C22×D4—62no—
282C22×D4—62no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—62no—
286C23×C4—31no—
287C23×C4—32no—
288C23×C4—31no—
289C23×C4—34no—
290C23×C4—32no—
291C23×C4—62no—
292C23×C4—64no—
293C23×C4—64no—
294C23×C4—62no—
295C23×C4—62no—
296C23×C4—62no—
297C23×C4—62no—
298C23×C4—122no—
299C23×C4—122no—
300C23×C4C22×D312yes—
301C23×C4C22×D312yes—
302C23×C4C22×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304C23×C4C22×D311yescharacteristic
305C22⋊Q8—632no—
306C4×D4—632no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—38no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—64no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—64no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4#6714yes—
318C2×C22⋊C4—34no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—62no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4—122no—
336C2×C42—62no—
337C2×C42—62no—
338C2×C42—62no—
339#95—22no—
340#95—24no—
341#95—64no—
342#95—64no—
343#95—64no—
344#95—62no—
345#95—64no—
346#95—64no—
347C23×C3C22×D411yescharacteristic
348C23×C3C22×D411yescharacteristic
349C23×C3C22×D412yes—
350C23×C3C22×D411yescharacteristic
351C23×C3C22×Q811yescharacteristic
352C23×C3C2×#4111yescharacteristic
353C23×C3C2×#4112yes—
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3H(5,𝔽2)12yes—
357C23×C32−1+412yes—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—24no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—41no—
385C22×D3—42no—
386C22×D3—41no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—41no—
390C22×D3—41no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3C22⋊Q814yes—
403C22×D3C22⋊Q814yescomplemented
404C3×Q8—416no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4#12014yes—
435C2×C3×C4C22⋊Q814yescomplemented
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—22no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3#12014yes—
460D12—232no—
461C4×D3—416no—
462C4×D3—416no—
463C24—32no—
464C24—32no—
465C24—32no—
466C24—32no—
467C24—32no—
468C24—32no—
469C24—62no—
470C24—62no—
471C24—61no—
472C24—61no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—61no—
478C24—61no—
479C24—62no—
480C24—62no—
481C24—61no—
482C24—61no—
483C24—61no—
484C24—61no—
485C24C23×D311yescharacteristic
486C2×Q8—28no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×D4—68no—
492C2×D4—68no—
493C2×D4—68no—
494C2×D4—68no—
495C2×D4—68no—
496C2×D4—68no—
497C2×D4—68no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—34no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—34no—
524C22×C4—68no—
525C22×C4—68no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—68no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—124no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4—128no—
551C22×C4—124no—
552C22×C4—128no—
553C22×C4—124no—
554C22×C4D3×D414yes—
555C22×C4D3×D412yes—
556C22×C4D3×D412yes—
557C22×C4D3×Q812yes—
558C22×C4#23914yes—
559C22×C4#23912yes—
560C22×C4C2×#6712yes—
561C22×C4C2×#6712yes—
562C22×C4C2×#6712yes—
563C4⋊C4—28no—
564C4⋊C4—48no—
565C4⋊C4—616no—
566C4⋊C4—68no—
567C22⋊C4—68no—
568C22⋊C4—616no—
569C22⋊C4—616no—
570C22⋊C4—68no—
571C22⋊C4—128no—
572C22⋊C4—128no—
573C42—68no—
574C22×C3C2×#12011yescharacteristic
575C22×C3C2×#12011yescharacteristic
576C22×C3C2×C22⋊Q811yescharacteristic
577C22×C3C2×C22⋊Q811yescharacteristic
578C22×C3C2×C22⋊Q811yescharacteristic
579C22×C3#52511yescharacteristic
580C22×C3#52511yescharacteristic
581C22×C3#52511yescharacteristic
582C22×C3#52512yes—
583C22×C3#53211yescharacteristic
584C22×C3#53212yes—
585C22×C3#53411yescharacteristic
586C22×C3#53611yescharacteristic
587C22×C3#53912yes—
588C22×C3#54212yes—
589C22×C3D4212yes—
590C22×C3D4212yes—
591C22×C3#54712yes—
592C22×C3#54812yes—
593C22×C3#54812yes—
594C22×C3D4×Q812yes—
595C22×C3#55112yes—
596C22×C3#55412yes—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—28no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—44no—
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C3×C4—24no—
620C3×C4—24no—
621C3×C4—42no—
622C3×C4—44no—
623C3×C4—44no—
624Dic3—24no—
625Dic3—44no—
626Dic3—42no—
627Dic3—82no—
628C23—34no—
629C23—34no—
630C23—64no—
631C23—64no—
632C23—64no—
633C23—62no—
634C23—62no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23—64no—
639C23—64no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—62no—
648C23—64no—
649C23—62no—
650C23—62no—
651C23—64no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—121no—
660C23—122no—
661C23—122no—
662C23—121no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—122no—
669C23—122no—
670C23—121no—
671C23—121no—
672C23—122no—
673C23—122no—
674C23C2×D3×D412yes—
675C23C2×D3×D411yescharacteristic
676C23C2×D3×D411yescharacteristic
677C23#100412yes—
678C23C2×D3×Q811yescharacteristic
679C23C2×#23912yes—
680C23C2×#23911yescharacteristic
681C23#100712yes—
682C23D3×#4111yescharacteristic
683C23D3×#4111yescharacteristic
684C23C22×#6711yescharacteristic
685Q8—416no—
686D4—632no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—34no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—62no—
718C2×C4—64no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—1216no—
727C2×C4—1216no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4#93714yes—
743C2×C4#94614yescomplemented
744C2×C3#238811yescharacteristic
745C2×C3#240311yescharacteristic
746C2×C3#240911yescharacteristic
747C2×C3#243211yescharacteristic
748C2×C3#244912yes—
749C2×C3#245212yes—
750C2×C3#246112yes—
751C2×C3#246312yes—
752C2×C3#256411yescharacteristic
753C2×C3#263811yescharacteristic
754C2×C3#284811yescharacteristic
755D3—44no—
756D3—44no—
757C22—64no—
758C22—64no—
759C22—64no—
760C22—68no—
761C22—64no—
762C22—124no—
763C22—124no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22—124no—
770C22—124no—
771C22—124no—
772C22—124no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—124no—
778C22—122no—
779C22D3×#12011yescharacteristic
780C22#558911yescharacteristic
781C22#559012yes—
782C22D3×C22⋊Q811yescharacteristic
783C22D3×C22⋊Q811yescharacteristic
784C22#562712yes—
785C22#562711yescharacteristic
786C22#562711yescharacteristic
787C22#563312yes—
788C22#563712yes—
789C22#563812yes—
790C22#572411yescharacteristic
791C22#572512yes—
792C22#572511yescharacteristic
793C22#572612yes—
794C22#572712yes—
795C22#573012yes—
796C22#573312yes—
797C22C2×#93711yescharacteristic
798C22D4×#6712yes—
799C22C2×#94611yescharacteristic
800C22#581712yes—
801C22#582811yescharacteristic
802C4—24no—
803C4—24no—
804C4—44no—
805C4—42no—
806C4—44no—
807C4—64no—
808C4—122no—
809C4—124no—
810C4—242no—
811C3#1472311yescharacteristic, complemented, Sylow
812C2—124no—
813C2—124no—
814C2#7716911yescharacteristic
815C2#7717211yescharacteristic
816C2#7717612yes—
817C2#7720611yescharacteristic
818C2#7725212yes—
819C2#7725411yescharacteristic
820C2#8260411yescharacteristic
821C2#8281812yes—
822C2#8283411yescharacteristic
823C2#8323612yes—
824C2#8325511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#395C2
prime radicalC23×D12C22
hypercenterC2×#395D3
hypocenterC3#14723
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#946C2semidirect
3. C2×C3×#395C2semidirect
4. C2×#5231C2semidirect
5. C2×#4989C2semidirect
6. #71570C2semidirect
7. #71565C2semidirect
8. #69427C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. #69406C2semidirect
46. C2×#395D3semidirect
77. C22×D12Q8semidirect
117. C2×Dic3⋊C4D4semidirect
403. C22×D3C22⋊Q8semidirect
435. C2×C3×C4C22⋊Q8semidirect
743. C2×C4#946semidirect
811. C3#14723semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C22×#8932
C2×C3×#3952
C2×#52312
C2×#49892
#715702
#715652
#694272
#694262
(C2×D3)⋊#952
#694062
#147233