Finite Group Databasebeta

← #10724491

Subgroups — #10724491

Order 768.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5222C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#4944C211yesmaximal, characteristic, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71549C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69421C211yesmaximal, characteristic, complemented
13#69418C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14517—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C3×#386—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37#5222C418yescomplemented
38#5220—24no—
39#5210—24no—
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4944—24no—
57C2×#394—31no—
58C2×#388—31no—
59C2×#386—31no—
60C2×#386D311yescharacteristic
61C2×#385—31no—
62#1445—31no—
63#1443—31no—
64#1441—31no—
65#1440—31no—
66#1439—31no—
67#1437—31no—
68#1436—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C25×C3C2311yescharacteristic
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—41no—
79C22×C3×D4—41no—
80C22×C3×D4C2×C414yes—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—41no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—41no—
97C23×Dic3—41no—
98C23×Dic3—41no—
99C23×Dic3—41no—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4—41no—
116C2×C3×C22⋊C4D414yes—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—41no—
126C2×#217—41no—
127C2×#217—41no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217—41no—
133C2×#217C2×C414yescomplemented
134C2×#217C2×C414yescomplemented
135C2×#217C2×C414yescomplemented
136C2×#217C2×C414yescomplemented
137C2×#217D414yes—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—41no—
143C2×Dic3⋊C4—41no—
144C2×Dic3⋊C4—41no—
145C2×Dic3⋊C4—41no—
146C2×Dic3⋊C4C2×C414yescomplemented
147C2×C4×Dic3—22no—
148C2×C4×Dic3—41no—
149C2×C4×Dic3—41no—
150C3×#95—22no—
151C3×#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95C2×C414yescomplemented
168C23×D4C2×D311yescharacteristic
169C24×C4—31no—
170C24×C4C2×D311yescharacteristic
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4C2×D311yescharacteristic
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C42—31no—
185#394—38no—
186#388—64no—
187#386—24no—
188#386—64no—
189#385—64no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3C22×C412yes—
233C24×C3C22×C412yes—
234C24×C3C2×D412yes—
235C24×C3C2×D412yes—
236C24×C3#4112yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C2×C3×D4—28no—
240C2×C3×D4—28no—
241C2×C3×D4—44no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—44no—
278C22×C3×C4—44no—
279C22×C3×C4—44no—
280C22×C3×C4—44no—
281C22×C3×C4—44no—
282C22×C3×C4—44no—
283C22×C3×C4—44no—
284C22×C3×C4C22×C412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C22×C3×C4#4112yes—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3—44no—
342C22×Dic3—44no—
343C22×Dic3—44no—
344C22×Dic3C22×C412yes—
345C22×Dic3C22×C412yes—
346C22×Dic3C22×C412yes—
347C22×Dic3C22×C412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3#4112yes—
351C3×C22⋊C4—44no—
352C3×C22⋊C4—44no—
353C3×C22⋊C4—44no—
354#217—28no—
355#217—28no—
356#217—44no—
357#217—44no—
358#217—44no—
359#217—44no—
360#217—44no—
361Dic3⋊C4—44no—
362Dic3⋊C4—44no—
363Dic3⋊C4—44no—
364C4×Dic3—44no—
365C25C22×D311yescharacteristic
366C25C22×D311yescharacteristic
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C4×D314yes—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—41no—
388C23×C4—41no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4—121no—
395C23×C4—121no—
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C2×C4⋊C4—34no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—121no—
407C2×C4⋊C4—121no—
408C2×C4⋊C4—121no—
409C2×C4⋊C4—121no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—41no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4—121no—
439C2×C22⋊C4#6714yes—
440C2×C42—62no—
441C2×C42—121no—
442C2×C42—121no—
443#95—22no—
444#95—22no—
445#95—34no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—121no—
454#95—121no—
455#95—121no—
456#95—121no—
457#95—121no—
458#95—121no—
459#95—121no—
460#95—121no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3C4×D414yes—
530C23×C3C4×D414yes—
531C23×C3C23×C411yescharacteristic
532C23×C3C22×D411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3H(5,𝔽2)11yescharacteristic
539C23×C3H(5,𝔽2)11yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C3H(5,𝔽2)11yescharacteristic
544C23×C32−1+411yescharacteristic
545C23×C32−1+411yescharacteristic
546C3×D4—416no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—416no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—416no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C2×C4×D312yes—
665C24C2×C4×D312yes—
666C24#23512yes—
667C24D3×D412yes—
668C24#23712yes—
669C24C2×#6712yes—
670C24C23×D311yescharacteristic
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—32no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—124no—
778C22×C4—124no—
779C22×C4C2×C4×D312yes—
780C22×C4#23712yes—
781C22×C4C2×#6712yes—
782C22×C4C2×#6712yes—
783C4⋊C4—124no—
784C4⋊C4—124no—
785C4⋊C4—124no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—68no—
790C22⋊C4—68no—
791C22⋊C4—124no—
792C22⋊C4—124no—
793C22⋊C4—124no—
794C22⋊C4—124no—
795C22⋊C4—124no—
796C42—124no—
797C22×C3—24no—
798C22×C3—24no—
799C22×C3—24no—
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3C2×C4×D411yescharacteristic
828C22×C3C2×C4×D411yescharacteristic
829C22×C3C4×#4111yescharacteristic
830C22×C3#51811yescharacteristic
831C22×C3#51811yescharacteristic
832C22×C3#52011yescharacteristic
833C22×C3#52011yescharacteristic
834C22×C3#53411yescharacteristic
835C22×C3#53411yescharacteristic
836C22×C3#53611yescharacteristic
837C22×C3#53711yescharacteristic
838C22×C3#53811yescharacteristic
839C22×C3#53811yescharacteristic
840C22×C3#53811yescharacteristic
841C22×C3#53911yescharacteristic
842C22×C3#53911yescharacteristic
843C22×C3#53911yescharacteristic
844C22×C3#54211yescharacteristic
845C22×C3#54211yescharacteristic
846C22×C3D4211yescharacteristic
847C22×C3#54611yescharacteristic
848C22×C3#54611yescharacteristic
849C22×C3#54611yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54611yescharacteristic
852C22×C3#54711yescharacteristic
853C22×C3#55111yescharacteristic
854C22×C3#55111yescharacteristic
855C22×C3#55211yescharacteristic
856C22×C3#55311yescharacteristic
857C22×C3#55311yescharacteristic
858C22×C3#56011yescharacteristic
859C22×C3#56011yescharacteristic
860C22×C3#56211yescharacteristic
861C22×C3#56211yescharacteristic
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—81no—
867Dic3—42no—
868Dic3—42no—
869Dic3—42no—
870Dic3—42no—
871Dic3—42no—
872Dic3—42no—
873Dic3—42no—
874Dic3—81no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23#67⋊C414yes—
944C23C4×#6714yes—
945C23C22×C4×D311yescharacteristic
946C23C2×#23511yescharacteristic
947C23C2×D3×D411yescharacteristic
948C23C2×#23711yescharacteristic
949C23C2×#23711yescharacteristic
950C23#100411yescharacteristic
951C23#100411yescharacteristic
952C23#100411yescharacteristic
953C23#100411yescharacteristic
954C23#100411yescharacteristic
955C23D3×#4111yescharacteristic
956C23#100911yescharacteristic
957C23#101011yescharacteristic
958C23#101011yescharacteristic
959C23C22×#6711yescharacteristic
960D4—416no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—416no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—1216no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C3—44no—
1055C2×C3—44no—
1056C2×C3#232211yescharacteristic
1057C2×C3#232511yescharacteristic
1058C2×C3#233711yescharacteristic
1059C2×C3#235811yescharacteristic
1060C2×C3#235911yescharacteristic
1061C2×C3#236411yescharacteristic
1062C2×C3#237711yescharacteristic
1063C2×C3#266811yescharacteristic
1064C2×C3#267211yescharacteristic
1065C2×C3#268711yescharacteristic
1066C2×C3#269111yescharacteristic
1067C2×C3#269711yescharacteristic
1068C2×C3#270811yescharacteristic
1069C2×C3#274611yescharacteristic
1070C2×C3#275011yescharacteristic
1071C22—24no—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22C2×#67⋊C411yescharacteristic
1102C22#548611yescharacteristic
1103C22#549011yescharacteristic
1104C22#549511yescharacteristic
1105C22C4×#23711yescharacteristic
1106C22#554111yescharacteristic
1107C22#554511yescharacteristic
1108C22#554611yescharacteristic
1109C22#554611yescharacteristic
1110C22#555611yescharacteristic
1111C22#556011yescharacteristic
1112C22#556411yescharacteristic
1113C22#558911yescharacteristic
1114C22#559111yescharacteristic
1115C22#559311yescharacteristic
1116C22#559511yescharacteristic
1117C22#560111yescharacteristic
1118C22#560211yescharacteristic
1119C22#560211yescharacteristic
1120C22#560311yescharacteristic
1121C22#561311yescharacteristic
1122C22#561811yescharacteristic
1123C22#562011yescharacteristic
1124C22#562111yescharacteristic
1125C22#564811yescharacteristic
1126C22#565411yescharacteristic
1127C22#566211yescharacteristic
1128C22#566711yescharacteristic
1129C22C2×C4×#6711yescharacteristic
1130C22D4×#6711yescharacteristic
1131C22#580411yescharacteristic
1132C22#580611yescharacteristic
1133C22#580611yescharacteristic
1134C22#582411yescharacteristic
1135C22#583311yescharacteristic
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—81no—
1141C4—122no—
1142C4—122no—
1143C4—122no—
1144C4—122no—
1145C4—122no—
1146C4—122no—
1147C4—122no—
1148C4—241no—
1149C3#1451711yescharacteristic, complemented, Sylow
1150C2—44no—
1151C2—44no—
1152C2#7466411yescharacteristic
1153C2#7467111yescharacteristic
1154C2#7467811yescharacteristic
1155C2#7479711yescharacteristic
1156C2#7483711yescharacteristic
1157C2#7484311yescharacteristic
1158C2#7488311yescharacteristic
1159C2#7492411yescharacteristic
1160C2#8209911yescharacteristic
1161C2#8232711yescharacteristic
1162C2#8233911yescharacteristic
1163C2#8260811yescharacteristic
1164C2#8269011yescharacteristic
1165C2#8269411yescharacteristic
1166C2#8286911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14517
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×#5210C2semidirect
5. C2×#4944C2semidirect
6. #72127C2semidirect
7. #71549C2semidirect
8. #71547C2semidirect
9. #71545C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
12. #69421C2semidirect
13. #69418C2semidirect
14. #69409C2semidirect
15. #69406C2semidirect
37. #5222C4semidirect
133. C2×#217C2×C4semidirect
134. C2×#217C2×C4semidirect
135. C2×#217C2×C4semidirect
136. C2×#217C2×C4semidirect
146. C2×Dic3⋊C4C2×C4semidirect
167. C3⋊#95C2×C4semidirect
1149. C3#14517semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52222
C2×#52202
C2×#52102
C2×#49442
#721272
#715492
#715472
#715452
#715442
#694212
#694182
#694092
#694062
#145173