Finite Group Databasebeta

← #10729192

Subgroups — #10729192

Order 768.

3030 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic
3C22×#929C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4958C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#71568C212yesmaximal, complemented
9#71550C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11#71544C211yesmaximal, characteristic, complemented
12#14926—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C2×C3×#123—24no—
20C2×C3×#123—24no—
21C2×C3×#123—24no—
22C22×C3×C4⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2212yes—
27C22×#217C2211yescharacteristic
28C2×#939—24no—
29C2×#939—24no—
30C2×#939—24no—
31C2×#929—24no—
32C2×#929—24no—
33C2×#929—24no—
34C22×(C2×D3)⋊C4C2212yes—
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2212yes—
37C22×Dic3⋊C4C2212yes—
38C22×Dic3⋊C4C2211yescharacteristic
39#5220—24no—
40C2×C3⋊#95—24no—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46C2×C3⋊#95C2212yes—
47#4958—24no—
48C22×#123—31no—
49C22×#123D311yescharacteristic, complemented
50C22×#121—31no—
51C2×#386—31no—
52C2×#386—31no—
53C22×#95—31no—
54#1444—32no—
55#1439—32no—
56#1439—32no—
57#1438—32no—
58C22⋊#95—31no—
59C25×C3C2311yescharacteristic
60C25×C3C2311yescharacteristic
61C24×D3C2311yescharacteristic
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4D414yes—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4D414yescomplemented
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—24no—
89C22×#67—42no—
90C22×#67D414yes—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—24no—
95C23×Dic3—24no—
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—42no—
99C23×Dic3—42no—
100C23×Dic3D414yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2312yes—
104C23×Dic3C2312yes—
105C23×Dic3C2311yescharacteristic
106C3×#123—232no—
107C2×C3×C4⋊C4—24no—
108C2×C3×C4⋊C4—24no—
109C2×C3×C4⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4D414yescomplemented
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—24no—
122C2×#217—24no—
123C2×#217—42no—
124C2×#217D414yescomplemented
125#939—232no—
126#929—232no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—24no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—24no—
135C2×(C2×D3)⋊C4—42no—
136C2×Dic3⋊C4—24no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—24no—
139C2×Dic3⋊C4—24no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C3⋊#95—24no—
143C3⋊#95—24no—
144C3⋊#95—24no—
145C3⋊#95—24no—
146C3⋊#95—24no—
147C3⋊#95—42no—
148C23×D4—31no—
149C23×D4—31no—
150C23×D4C2×D311yescharacteristic
151C24×C4—31no—
152C24×C4—31no—
153C24×C4C2×D311yescharacteristic
154C2×#123—24no—
155C2×#123—24no—
156C2×#123—24no—
157C2×#123—64no—
158C2×#123—64no—
159C2×#123—64no—
160C2×#121—64no—
161C2×#121—64no—
162C2×#121—64no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—32no—
165C22×C4⋊C4C2×D312yes—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—32no—
170C22×C22⋊C4—32no—
171C22×C22⋊C4—32no—
172C22×C22⋊C4C2×D312yes—
173C22×C22⋊C4C2×D311yescharacteristic
174#386—64no—
175#386—64no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C2×#95—32no—
180C2×#95—32no—
181C2×#95—32no—
182C2×#95—64no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3—21no—
195C24×C3—22no—
196C24×C3—22no—
197C24×C3C2×D412yes—
198C24×C3C2×D412yes—
199C24×C3C2×D412yes—
200C24×C3C2×D412yes—
201C24×C3C2×D412yes—
202C24×C3C2×D412yes—
203C24×C3C2×D412yes—
204C24×C3#4112yes—
205C24×C3C2411yescharacteristic
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—22no—
212C23×D3—21no—
213C23×D3—22no—
214C23×D3—22no—
215C23×D3—22no—
216C23×D3C2×D412yes—
217C2×C3×D4—28no—
218C2×C3×D4—28no—
219C2×C3×D4—28no—
220C2×C3×D4—44no—
221C2×C3×D4—44no—
222C2×C3×D4—44no—
223C2×C3×D4—44no—
224C22×C3×C4—28no—
225C22×C3×C4—28no—
226C22×C3×C4—28no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—44no—
246C22×C3×C4—44no—
247C22×C3×C4—44no—
248C22×C3×C4—44no—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×D414yes—
251C22×C3×C4C2×D412yes—
252C2×#67—28no—
253C2×#67—28no—
254C2×#67—28no—
255C2×#67—28no—
256C2×#67—48no—
257C2×#67—48no—
258C2×#67—44no—
259C2×#67—44no—
260C2×#67—44no—
261C2×#67—44no—
262C2×#67—44no—
263C2×#67—44no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—22no—
267C22×Dic3—28no—
268C22×Dic3—28no—
269C22×Dic3—22no—
270C22×Dic3—21no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—21no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—28no—
292C22×Dic3—44no—
293C22×Dic3—48no—
294C22×Dic3—48no—
295C22×Dic3—48no—
296C22×Dic3—48no—
297C22×Dic3—44no—
298C22×Dic3—44no—
299C22×Dic3C2×D412yes—
300C22×Dic3C2×D414yes—
301C22×Dic3C2×D412yes—
302C22×Dic3C2×D412yes—
303C22×Dic3#4114yes—
304C22×Dic3#4114yes—
305C3×C4⋊C4—216no—
306C3×C22⋊C4—216no—
307C3×C22⋊C4—28no—
308#217—28no—
309#217—28no—
310#217—48no—
311(C2×D3)⋊C4—216no—
312(C2×D3)⋊C4—28no—
313(C2×D3)⋊C4—48no—
314Dic3⋊C4—216no—
315Dic3⋊C4—28no—
316C25—31no—
317C25C22×D311yescharacteristic
318C25C22×D311yescharacteristic
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—34no—
326C22×D4—62no—
327C22×D4—64no—
328C22×D4—62no—
329C22×D4—62no—
330C22×D4—62no—
331C22×D4—62no—
332C22×D4—62no—
333C22×D4—62no—
334C22×D4—62no—
335C22×D4—62no—
336C22×D4—122no—
337C22×D4#6714yes—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—31no—
345C23×C4—32no—
346C23×C4—31no—
347C23×C4—32no—
348C23×C4—31no—
349C23×C4—34no—
350C23×C4—64no—
351C23×C4—64no—
352C23×C4—62no—
353C23×C4—62no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
357C23×C4—122no—
358C23×C4—122no—
359C23×C4#6714yescomplemented
360C23×C4C22×D312yes—
361C23×C4C22×D312yes—
362C23×C4C22×D311yescharacteristic
363#123—232no—
364#123—632no—
365#121—632no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—64no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—64no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—34no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—64no—
393C2×C22⋊C4—64no—
394C2×C22⋊C4—64no—
395C2×C22⋊C4—64no—
396C2×C22⋊C4—122no—
397C2×C22⋊C4—122no—
398C2×C22⋊C4#6714yescomplemented
399#95—64no—
400#95—64no—
401#95—64no—
402#95—64no—
403#95—64no—
404#95—122no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—42no—
432C23×C3—41no—
433C23×C3—42no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3#12014yes—
445C23×C3#12014yes—
446C23×C3#12014yes—
447C23×C3#12114yes—
448C23×C3#12114yes—
449C23×C3#12114yes—
450C23×C3#12714yes—
451C23×C3C22×D411yescharacteristic
452C23×C3C22×D411yescharacteristic
453C23×C3C22×D411yescharacteristic
454C23×C3C22×D411yescharacteristic
455C23×C3C22×D411yescharacteristic
456C23×C3C22×D411yescharacteristic
457C23×C3C2×#4111yescharacteristic
458C23×C3C2×#4112yes—
459C23×C3C2×#4112yes—
460C23×C3H(5,𝔽2)12yes—
461C23×C32−1+412yes—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—24no—
466C22×D3—24no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—42no—
473C22×D3—41no—
474C22×D3—42no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—42no—
484C22×D3—42no—
485C3×D4—416no—
486C2×C3×C4—24no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—22no—
491C2×C3×C4—24no—
492C2×C3×C4—22no—
493C2×C3×C4—24no—
494C2×C3×C4—24no—
495C2×C3×C4—42no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—41no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—416no—
508#67—416no—
509#67—416no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—24no—
514C2×Dic3—22no—
515C2×Dic3—24no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—24no—
521C2×Dic3—22no—
522C2×Dic3—24no—
523C2×Dic3—24no—
524C2×Dic3—24no—
525C2×Dic3—24no—
526C2×Dic3—416no—
527C2×Dic3—416no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—42no—
532C2×Dic3—41no—
533C2×Dic3—42no—
534C2×Dic3—42no—
535C2×Dic3—42no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3#12314yescomplemented
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—32no—
558C24—61no—
559C24—61no—
560C24—61no—
561C24—62no—
562C24—62no—
563C24—62no—
564C24—62no—
565C24—61no—
566C24—61no—
567C24—61no—
568C24D3×D412yes—
569C24D3×D412yes—
570C24D3×D412yes—
571C24#23712yes—
572C24C2×#6712yes—
573C24C2×#6712yes—
574C24C2×#6712yes—
575C24C2×#6712yes—
576C24C23×D311yescharacteristic
577C2×D4—28no—
578C2×D4—28no—
579C2×D4—28no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—68no—
585C2×D4—68no—
586C2×D4—68no—
587C2×D4—68no—
588C2×D4—124no—
589C2×D4—128no—
590C2×D4—128no—
591C2×D4—124no—
592C2×D4—124no—
593C2×D4—124no—
594C2×D4—124no—
595C2×D4—124no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—32no—
618C22×C4—34no—
619C22×C4—32no—
620C22×C4—34no—
621C22×C4—32no—
622C22×C4—34no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—68no—
628C22×C4—61no—
629C22×C4—62no—
630C22×C4—61no—
631C22×C4—68no—
632C22×C4—68no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—61no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—124no—
656C22×C4—128no—
657C22×C4—128no—
658C22×C4—128no—
659C22×C4—128no—
660C22×C4—124no—
661C22×C4—124no—
662C22×C4C2×#6714yes—
663C22×C4C2×#6714yes—
664C22×C4C2×#6712yes—
665C4⋊C4—216no—
666C4⋊C4—68no—
667C4⋊C4—616no—
668C22⋊C4—216no—
669C22⋊C4—28no—
670C22⋊C4—68no—
671C22⋊C4—616no—
672C22⋊C4—68no—
673C22⋊C4—68no—
674C22⋊C4—128no—
675C22⋊C4—128no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—28no—
681C22×C3—28no—
682C22×C3—28no—
683C22×C3—28no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—44no—
690C22×C3—44no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—82no—
694C22×C3—82no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3#39218yes—
698C22×C3C2×#12011yescharacteristic
699C22×C3C2×#12011yescharacteristic
700C22×C3C2×#12011yescharacteristic
701C22×C3C2×#12111yescharacteristic
702C22×C3C2×#12111yescharacteristic
703C22×C3C2×#12111yescharacteristic
704C22×C3C2×#12311yescharacteristic
705C22×C3#52511yescharacteristic
706C22×C3#52912yes—
707C22×C3C2×#12711yescharacteristic
708C22×C3#53212yes—
709C22×C3#53411yescharacteristic
710C22×C3#53611yescharacteristic
711C22×C3#53712yes—
712C22×C3#53912yes—
713C22×C3#54612yes—
714C22×C3#54612yes—
715C22×C3#54612yes—
716C22×C3#54612yes—
717C22×C3#54712yes—
718C22×C3#54712yes—
719C22×C3#54712yes—
720C22×C3#54712yes—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—44no—
725C2×D3—44no—
726C2×D3—81no—
727C2×D3—81no—
728C2×D3—82no—
729C2×D3—82no—
730C2×D3—81no—
731C2×D3—81no—
732C3×C4—44no—
733C3×C4—42no—
734C3×C4—44no—
735Dic3—24no—
736Dic3—42no—
737Dic3—42no—
738Dic3—44no—
739Dic3—44no—
740C23—22no—
741C23—24no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—22no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—22no—
757C23—22no—
758C23—24no—
759C23—24no—
760C23—22no—
761C23—41no—
762C23—42no—
763C23—41no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—41no—
770C23—42no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—64no—
780C23—64no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—121no—
785C23—122no—
786C23—121no—
787C23—121no—
788C23—122no—
789C23—122no—
790C23—121no—
791C23—122no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—122no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—122no—
800C23—122no—
801C23—121no—
802C23#93714yes—
803C23#93714yes—
804C23#93814yes—
805C23#93914yes—
806C23#93914yes—
807C23#94014yes—
808C23#95314yes—
809C23C2×D3×D411yescharacteristic
810C23C2×D3×D411yescharacteristic
811C23C2×D3×D411yescharacteristic
812C23C2×#23711yescharacteristic
813C23D3×#4112yes—
814C23D3×#4112yes—
815C23#100912yes—
816C23#101012yes—
817C23C22×#6711yescharacteristic
818C23C22×#6711yescharacteristic
819C23C22×#6711yescharacteristic
820D4—416no—
821D4—1216no—
822D4—1216no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—34no—
833C2×C4—416no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—62no—
847C2×C4—64no—
848C2×C4—62no—
849C2×C4—64no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—64no—
853C2×C4—64no—
854C2×C4—64no—
855C2×C4—64no—
856C2×C4—64no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—64no—
862C2×C4—1216no—
863C2×C4—1216no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—122no—
872C2×C4—121no—
873C2×C4—122no—
874C2×C4—122no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—121no—
878C2×C3—28no—
879C2×C3—82no—
880C2×C3C2×#39211yescharacteristic
881C2×C3#240511yescharacteristic
882C2×C3#240611yescharacteristic
883C2×C3#242512yes—
884C2×C3#242512yes—
885C2×C3#243012yes—
886C2×C3#243012yes—
887C2×C3#250111yescharacteristic
888C2×C3#253911yescharacteristic
889C2×C3#261811yescharacteristic
890C2×C3#285411yescharacteristic
891D3—82no—
892C22—28no—
893C22—24no—
894C22—28no—
895C22—28no—
896C22—28no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—42no—
903C22—44no—
904C22—42no—
905C22—44no—
906C22—42no—
907C22—82no—
908C22—82no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—122no—
914C22—122no—
915C22—124no—
916C22—124no—
917C22—122no—
918C22—242no—
919C22—242no—
920C22—241no—
921C22—241no—
922C22—241no—
923C22—241no—
924C22#522318yes—
925C22#564811yescharacteristic
926C22#564912yes—
927C22D3×#12311yescharacteristic
928C22#565311yescharacteristic
929C22#565412yes—
930C22#565412yes—
931C22#565512yes—
932C22#565512yes—
933C22#565611yescharacteristic
934C22#566512yes—
935C22C2×#93711yescharacteristic
936C22C2×#93711yescharacteristic
937C22C2×#93811yescharacteristic
938C22C2×#93911yescharacteristic
939C22C2×#93911yescharacteristic
940C22C2×#94011yescharacteristic
941C22#582412yes—
942C22#582412yes—
943C22#582912yes—
944C22#582912yes—
945C22#583212yes—
946C22#583312yes—
947C22C2×#95311yescharacteristic
948C4—44no—
949C4—42no—
950C4—44no—
951C4—64no—
952C4—122no—
953C4—124no—
954C4—122no—
955C4—124no—
956C3#1492611yescharacteristic, complemented, Sylow
957C2—28no—
958C2—82no—
959C2—242no—
960C2#8284111yescharacteristic
961C2#8284612yes—
962C2#8284712yes—
963C2#8284812yes—
964C2#8285911yescharacteristic
965C2#8286511yescharacteristic
966C2#8289111yescharacteristic
967C2#8289311yescharacteristic
968C2#8290111yescharacteristic
969C2C2×#522311yescharacteristic
970C2#8409112yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#123C2
prime radicalC22×#939C2
hypercenterC22×#123D3
hypocenterC3#14926
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
3. C22×#929C2semidirect
4. C2×#5220C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4958C2semidirect
7. #71570C2semidirect
8. #71568C2semidirect
9. #71550C2semidirect
10. #71547C2semidirect
11. #71544C2semidirect
49. C22×#123D3semidirect
75. C23×C3×C4D4semidirect
115. C2×C3×C22⋊C4D4semidirect
124. C2×#217D4semidirect
359. C23×C4#67semidirect
398. C2×C22⋊C4#67semidirect
542. C2×Dic3#123semidirect
956. C3#14926semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9392
C22×#9292
C2×#52202
C22×C3⋊#952
C2×#49582
#715702
#715682
#715502
#715472
#715442
#149263