Finite Group Databasebeta

← #10725813

Subgroups — #10725813

Order 768.

1094 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊#401C211yesmaximal, characteristic
2C3×#1442C211yesmaximal, characteristic
3#71567C211yesmaximal, characteristic
4#71567C211yesmaximal, characteristic
5#69420C211yesmaximal, characteristic
6#69417C211yesmaximal, characteristic
7#69407C211yesmaximal, characteristic
8#69407C211yesmaximal, characteristic
9#69406C211yesmaximal, characteristic
10#69406C211yesmaximal, characteristic
11#69405C211yesmaximal, characteristic
12#69405C211yesmaximal, characteristic
13#69403C211yesmaximal, characteristic
14#69402C211yesmaximal, characteristic
15#69401C211yesmaximal, characteristic
16#14620—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic3C2211yescharacteristic
19C22×Dic3⋊C4C2211yescharacteristic
20C22×Dic3⋊C4C2211yescharacteristic
21C22×C4×Dic3C2211yescharacteristic
22C22×C4×Dic3C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24C2×C3×#95C2211yescharacteristic
25C2×C3×#95C2211yescharacteristic
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
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
52C3⋊#401C418yescomplemented
53C2×#401—31no—
54#1444—31no—
55#1443—31no—
56#1442—31no—
57#1442—31no—
58#1442D311yescharacteristic
59#1436—31no—
60#1436—31no—
61#1436—31no—
62#1436—31no—
63#1436—31no—
64#1436—31no—
65#1434—31no—
66#1434—31no—
67#1434—31no—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C2×C3×C4⋊C4—41no—
84C2×C3×C4⋊C4—41no—
85C2×C3×C4⋊C4—41no—
86C2×C4⋊Dic3—22no—
87C2×C4⋊Dic3—22no—
88C2×C4⋊Dic3—41no—
89C2×Dic3⋊C4—22no—
90C2×Dic3⋊C4—22no—
91C2×Dic3⋊C4—22no—
92C2×Dic3⋊C4—22no—
93C2×Dic3⋊C4—41no—
94C2×Dic3⋊C4—41no—
95C2×C4×Dic3—22no—
96C2×C4×Dic3—22no—
97C2×C4×Dic3—22no—
98C2×C4×Dic3—41no—
99C2×C4×Dic3—41no—
100C2×C4×Dic3—41no—
101C2×C4×Dic3—41no—
102C2×C4×Dic3—41no—
103C2×C4×Dic3—41no—
104C3×#95—22no—
105C3×#95—22no—
106C3×#95—41no—
107C3×#95—41no—
108C3×#95—41no—
109C3×#95C2×C414yes—
110C3⋊#95—22no—
111C3⋊#95—22no—
112C3⋊#95—22no—
113C3⋊#95—22no—
114C3⋊#95—22no—
115C3⋊#95—22no—
116C3⋊#95—22no—
117C3⋊#95—41no—
118C3⋊#95—41no—
119C3⋊#95—41no—
120C3⋊#95—41no—
121C3⋊#95—41no—
122C3⋊#95—41no—
123C3⋊#95—41no—
124C3⋊#95—41no—
125C3⋊#95—41no—
126C3⋊#95C2×C414yes—
127C3⋊#95C2×C414yes—
128C3⋊#95C2×C414yes—
129C3⋊#95C2×C414yes—
130C3⋊#95C2×C414yes—
131C3⋊#95C2×C414yes—
132C22×C4⋊C4—31no—
133C22×C4⋊C4—31no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4C2×D311yescharacteristic
136C22×C42—31no—
137C22×C42—31no—
138C22×C42—31no—
139#401—38no—
140C2×#95—31no—
141C2×#95—31no—
142C2×#95—31no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—31no—
146C2×#95—31no—
147C2×#95—31no—
148C2×#95—31no—
149C2×#95—31no—
150C2×#95—31no—
151C2×#95—31no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—31no—
155C2×#95—31no—
156C2×#95—31no—
157C2×#95—31no—
158C2×#95—31no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95—31no—
162C2×#95C2×D311yescharacteristic
163C2×#95C2×D311yescharacteristic
164C2×#95C2×D311yescharacteristic
165C2×#95C2×D311yescharacteristic
166C2×#95C2×D311yescharacteristic
167C2×#95C2×D311yescharacteristic
168C24×C3C2411yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4C22×C412yes—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C22×C412yes—
216C22×C3×C4#4112yes—
217C22×C3×C4#4112yes—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3C22×C412yes—
267C22×Dic3C22×C412yes—
268C22×Dic3C22×C412yes—
269C22×Dic3C22×C412yes—
270C22×Dic3#4112yes—
271C22×Dic3#4112yes—
272C22×Dic3#4112yes—
273C22×Dic3#4112yes—
274C3×C4⋊C4—44no—
275C4⋊Dic3—44no—
276Dic3⋊C4—44no—
277Dic3⋊C4—44no—
278C4×Dic3—44no—
279C4×Dic3—44no—
280C4×Dic3—44no—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—31no—
286C23×C4—31no—
287C23×C4—31no—
288C23×C4—31no—
289C23×C4C22×D311yescharacteristic
290C23×C4C22×D311yescharacteristic
291C23×C4C22×D311yescharacteristic
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D311yescharacteristic
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—62no—
304C2×C4⋊C4—62no—
305C2×C4⋊C4—121no—
306C2×C4⋊C4—121no—
307C2×C4⋊C4—121no—
308C2×C42—62no—
309C2×C42—62no—
310C2×C42—62no—
311C2×C42—121no—
312C2×C42—121no—
313C2×C42—121no—
314C2×C42—121no—
315C2×C42—121no—
316C2×C42—121no—
317#95—22no—
318#95—22no—
319#95—34no—
320#95—34no—
321#95—34no—
322#95—34no—
323#95—34no—
324#95—34no—
325#95—41no—
326#95—41no—
327#95—41no—
328#95—62no—
329#95—62no—
330#95—62no—
331#95—62no—
332#95—62no—
333#95—62no—
334#95—62no—
335#95—121no—
336#95—121no—
337#95—121no—
338#95—121no—
339#95—121no—
340#95—121no—
341#95—121no—
342#95—121no—
343#95—121no—
344#95C4×D314yes—
345C23×C3C23×C411yescharacteristic
346C23×C3C2×#4111yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3C2×#4111yescharacteristic
352C23×C3H(5,𝔽2)11yescharacteristic
353C23×C3H(5,𝔽2)11yescharacteristic
354C23×C3H(5,𝔽2)11yescharacteristic
355C23×C3H(5,𝔽2)11yescharacteristic
356C23×C32−1+411yescharacteristic
357C23×C32−1+411yescharacteristic
358C23×C32−1+411yescharacteristic
359C23×C32−1+411yescharacteristic
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C24C23×D311yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—32no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4C2×C4×D312yes—
567C22×C4C2×C4×D312yes—
568C22×C4C2×C4×D312yes—
569C22×C4#23712yes—
570C22×C4#23912yes—
571C4⋊C4—44no—
572C4⋊C4—124no—
573C4⋊C4—124no—
574C4⋊C4—124no—
575C42—124no—
576C42—124no—
577C42—124no—
578C22×C3C4×#4111yescharacteristic
579C22×C3C4×#4111yescharacteristic
580C22×C3C4×#4111yescharacteristic
581C22×C3#52011yescharacteristic
582C22×C3#52011yescharacteristic
583C22×C3#52011yescharacteristic
584C22×C3#52011yescharacteristic
585C22×C3#53811yescharacteristic
586C22×C3#53811yescharacteristic
587C22×C3#53811yescharacteristic
588C22×C3#53911yescharacteristic
589C22×C3#53911yescharacteristic
590C22×C3#53911yescharacteristic
591C22×C3#54111yescharacteristic
592C22×C3#54111yescharacteristic
593C22×C3#54111yescharacteristic
594C22×C3#54211yescharacteristic
595C22×C3#54211yescharacteristic
596C22×C3#54211yescharacteristic
597C22×C3#55111yescharacteristic
598C22×C3#55111yescharacteristic
599C22×C3#55111yescharacteristic
600C22×C3#55211yescharacteristic
601C22×C3#55211yescharacteristic
602C22×C3#55211yescharacteristic
603C22×C3#55311yescharacteristic
604C22×C3#55311yescharacteristic
605C22×C3#55311yescharacteristic
606C22×C3#55611yescharacteristic
607C22×C3#55611yescharacteristic
608C22×C3#55611yescharacteristic
609C22×C3#56011yescharacteristic
610C22×C3#56311yescharacteristic
611C22×C3#56311yescharacteristic
612C22×C3#56311yescharacteristic
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—81no—
619C3×C4—81no—
620Dic3—42no—
621Dic3—42no—
622Dic3—42no—
623Dic3—42no—
624Dic3—42no—
625Dic3—42no—
626Dic3—42no—
627Dic3—42no—
628C23C22×C4×D311yescharacteristic
629C23C2×#23711yescharacteristic
630C23#100411yescharacteristic
631C23#100411yescharacteristic
632C23#100411yescharacteristic
633C23C2×#23911yescharacteristic
634C23#100711yescharacteristic
635C23D3×#4111yescharacteristic
636C23D3×#4111yescharacteristic
637C23D3×#4111yescharacteristic
638C23D3×#4111yescharacteristic
639C23#100911yescharacteristic
640C23#101011yescharacteristic
641C23#101011yescharacteristic
642C23#101011yescharacteristic
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C3#233411yescharacteristic
749C2×C3#233411yescharacteristic
750C2×C3#233411yescharacteristic
751C2×C3#237311yescharacteristic
752C2×C3#237311yescharacteristic
753C2×C3#237311yescharacteristic
754C2×C3#238311yescharacteristic
755C2×C3#276011yescharacteristic
756C2×C3#276211yescharacteristic
757C2×C3#276211yescharacteristic
758C2×C3#276211yescharacteristic
759C2×C3#278711yescharacteristic
760C2×C3#278711yescharacteristic
761C2×C3#278711yescharacteristic
762C2×C3#280111yescharacteristic
763C22#550411yescharacteristic
764C22#552211yescharacteristic
765C22#552311yescharacteristic
766C22C4×#23711yescharacteristic
767C22#554611yescharacteristic
768C22#554611yescharacteristic
769C22C4×#23911yescharacteristic
770C22#559511yescharacteristic
771C22#560111yescharacteristic
772C22#560311yescharacteristic
773C22#561411yescharacteristic
774C22#563711yescharacteristic
775C22#563711yescharacteristic
776C22#564411yescharacteristic
777C22#564611yescharacteristic
778C22#564611yescharacteristic
779C22#565011yescharacteristic
780C22#565111yescharacteristic
781C22#566111yescharacteristic
782C22#566211yescharacteristic
783C22#566511yescharacteristic
784C22#566911yescharacteristic
785C22#567811yescharacteristic
786C22#567811yescharacteristic
787C22#567911yescharacteristic
788C22#569211yescharacteristic
789C22#569311yescharacteristic
790C22#569411yescharacteristic
791C22#569611yescharacteristic
792C22#569811yescharacteristic
793C22#570111yescharacteristic
794C22#570211yescharacteristic
795C22#570211yescharacteristic
796C22#570711yescharacteristic
797C22#573211yescharacteristic
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—122no—
806C4—122no—
807C4—122no—
808C4—122no—
809C4—122no—
810C4—122no—
811C4—122no—
812C4—122no—
813C3#1462011yescharacteristic, complemented, Sylow
814C2#7415511yescharacteristic
815C2#7440311yescharacteristic
816C2#7495511yescharacteristic
817C2#7497211yescharacteristic
818C2#7546711yescharacteristic
819C2#7548511yescharacteristic
820C2#7599111yescharacteristic
821C2#7684211yescharacteristic
822C2#7707811yescharacteristic
823C2#7763511yescharacteristic
824C2#7788011yescharacteristic
825C2#7800311yescharacteristic
826C2#7826111yescharacteristic
827C2#7826311yescharacteristic
828C2#7829311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1442C2
socle, prime radical, cosocleC24×C3C24
hypercenter#1442D3
hypocenterC3#14620
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
52. C3⋊#401C4semidirect
813. C3#14620semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#4012
C3×#14422
#715672
#694202
#694172
#694072
#694062
#694052
#694032
#694022
#694012
#146203