Finite Group Databasebeta

← #10723732

Subgroups — #10723732

Order 768.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4942C211yesmaximal, characteristic
2C3×#1439C211yesmaximal, characteristic
3#71566C211yesmaximal, characteristic, complemented
4#71564C211yesmaximal, characteristic, complemented
5#71547C211yesmaximal, characteristic
6#71545C211yesmaximal, characteristic
7#71545C211yesmaximal, characteristic
8#71544C211yesmaximal, characteristic
9#71544C211yesmaximal, characteristic
10#69418C211yesmaximal, characteristic, complemented
11#69418C211yesmaximal, characteristic, complemented
12#69409C211yesmaximal, characteristic, complemented
13#69406C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#14453—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
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
52#4942C418yescomplemented
53C2×#380—31no—
54#1443—31no—
55#1443—31no—
56#1441—31no—
57#1441—31no—
58#1439—31no—
59#1439D311yescharacteristic
60#1437—31no—
61#1437—31no—
62#1436—31no—
63#1436—31no—
64#1436—31no—
65#1436—31no—
66C22⋊#95—31no—
67C22⋊#95—31no—
68C25×C3C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×Dic3—22no—
76C23×Dic3—22no—
77C23×Dic3—41no—
78C23×Dic3—41no—
79C23×Dic3—41no—
80C23×Dic3—41no—
81C23×Dic3C2×C414yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—41no—
92C2×C3×C4⋊C4—41no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—41no—
97C2×C3×C22⋊C4—41no—
98C2×C3×C22⋊C4—41no—
99C2×C3×C22⋊C4—41no—
100C2×C3×C22⋊C4—41no—
101C2×C3×C22⋊C4C2×C414yes—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—41no—
105C2×#217—41no—
106C2×#217—41no—
107C2×#217—41no—
108C2×#217—41no—
109C2×#217C2×C414yes—
110C2×#217Q814yes—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—41no—
113C2×Dic3⋊C4—41no—
114C2×Dic3⋊C4—41no—
115C2×Dic3⋊C4—41no—
116C2×Dic3⋊C4—41no—
117C2×Dic3⋊C4—41no—
118C2×Dic3⋊C4C2×C414yes—
119C2×Dic3⋊C4C2×C414yes—
120C2×C4×Dic3—41no—
121C2×C4×Dic3—41no—
122C2×C4×Dic3—41no—
123C2×C4×Dic3—41no—
124C2×C4×Dic3—41no—
125C2×C4×Dic3—41no—
126C3×#95—41no—
127C3×#95—41no—
128C3×#95—41no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—41no—
136C3⋊#95—41no—
137C3⋊#95—41no—
138C3⋊#95—41no—
139C3⋊#95—41no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95C2×C414yes—
147C3⋊#95C2×C414yes—
148C24×C4—31no—
149C22×C4⋊C4—31no—
150C22×C4⋊C4—31no—
151C22×C4⋊C4—31no—
152C22×C4⋊C4C2×D311yescharacteristic
153C22×C22⋊C4—31no—
154C22×C22⋊C4—31no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4C2×D311yescharacteristic
157C22×C22⋊C4C2×D311yescharacteristic
158C22×C22⋊C4C2×D311yescharacteristic
159C22×C42—31no—
160C22×C42—31no—
161#380—38no—
162C2×#95—31no—
163C2×#95—31no—
164C2×#95—31no—
165C2×#95—31no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95C2×D311yescharacteristic
182C2×#95C2×D311yescharacteristic
183C2×#95C2×D311yescharacteristic
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3C22×C412yes—
197C24×C3C2×Q812yes—
198C24×C3#4112yes—
199C24×C3C2411yescharacteristic
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×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4C22×C412yes—
240C22×C3×C4C22×C412yes—
241C22×C3×C4#4112yes—
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×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—28no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—44no—
291C22×Dic3—44no—
292C22×Dic3—44no—
293C22×Dic3—44no—
294C22×Dic3—44no—
295C22×Dic3—44no—
296C22×Dic3C22×C412yes—
297C22×Dic3C22×C412yes—
298C22×Dic3C22×C412yes—
299C22×Dic3C22×C412yes—
300C22×Dic3C2×Q812yes—
301C22×Dic3C2×Q812yes—
302C22×Dic3#4112yes—
303C22×Dic3#4112yes—
304C22×Dic3#4112yes—
305C3×C4⋊C4—44no—
306C3×C22⋊C4—44no—
307C3×C22⋊C4—44no—
308C3×C22⋊C4—44no—
309#217—44no—
310#217—44no—
311#217—44no—
312Dic3⋊C4—44no—
313Dic3⋊C4—44no—
314Dic3⋊C4—44no—
315C4×Dic3—44no—
316C4×Dic3—44no—
317C25C22×D311yescharacteristic
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—34no—
326C23×C4—31no—
327C23×C4—62no—
328C23×C4—62no—
329C23×C4—121no—
330C23×C4—121no—
331C23×C4—121no—
332C23×C4—121no—
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C2×C4⋊C4—22no—
340C2×C4⋊C4—34no—
341C2×C4⋊C4—34no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—121no—
346C2×C4⋊C4—121no—
347C2×C4⋊C4—121no—
348C2×C4⋊C4—121no—
349C2×C4⋊C4—121no—
350C2×C4⋊C4—121no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—34no—
355C2×C22⋊C4—34no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—62no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4—121no—
364C2×C22⋊C4—121no—
365C2×C22⋊C4—121no—
366C2×C22⋊C4—121no—
367C2×C22⋊C4—121no—
368C2×C22⋊C4C4×D314yes—
369C2×C42—121no—
370C2×C42—121no—
371C2×C42—121no—
372C2×C42—121no—
373C2×C42—121no—
374C2×C42—121no—
375#95—34no—
376#95—34no—
377#95—41no—
378#95—41no—
379#95—41no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—121no—
387#95—121no—
388#95—121no—
389#95—121no—
390#95—121no—
391#95—121no—
392#95—121no—
393#95—121no—
394#95—121no—
395#95—121no—
396#95—121no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3C4×Q814yes—
432C23×C3C23×C411yescharacteristic
433C23×C3C22×Q811yescharacteristic
434C23×C3C2×#4111yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3H(5,𝔽2)11yescharacteristic
440C23×C3H(5,𝔽2)11yescharacteristic
441C23×C3H(5,𝔽2)11yescharacteristic
442C23×C3H(5,𝔽2)11yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C23×C3H(5,𝔽2)11yescharacteristic
445C23×C3H(5,𝔽2)11yescharacteristic
446C23×C32−1+411yescharacteristic
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—416no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3#11714yes—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24C2×C4×D312yes—
559C24#23712yes—
560C24D3×Q812yes—
561C24C23×D311yescharacteristic
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—32no—
610C22×C4—68no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—124no—
659C22×C4—124no—
660C22×C4—124no—
661C22×C4—124no—
662C22×C4—124no—
663C22×C4—124no—
664C22×C4C2×C4×D312yes—
665C22×C4C2×C4×D312yes—
666C22×C4#23712yes—
667C4⋊C4—44no—
668C4⋊C4—124no—
669C4⋊C4—124no—
670C4⋊C4—124no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—124no—
675C22⋊C4—124no—
676C22⋊C4—124no—
677C42—124no—
678C42—124no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3C2×#11711yescharacteristic
695C22×C3C2×C4×Q811yescharacteristic
696C22×C3C4×#4111yescharacteristic
697C22×C3#51811yescharacteristic
698C22×C3#51811yescharacteristic
699C22×C3#51811yescharacteristic
700C22×C3#52011yescharacteristic
701C22×C3#53811yescharacteristic
702C22×C3#53811yescharacteristic
703C22×C3#53811yescharacteristic
704C22×C3#53811yescharacteristic
705C22×C3#53811yescharacteristic
706C22×C3#53811yescharacteristic
707C22×C3#53811yescharacteristic
708C22×C3#53911yescharacteristic
709C22×C3#54011yescharacteristic
710C22×C3#54011yescharacteristic
711C22×C3#54311yescharacteristic
712C22×C3#54411yescharacteristic
713C22×C3#55111yescharacteristic
714C22×C3#55111yescharacteristic
715C22×C3#55311yescharacteristic
716C22×C3#55311yescharacteristic
717C22×C3#55311yescharacteristic
718C22×C3#55311yescharacteristic
719C22×C3#55411yescharacteristic
720C22×C3#55411yescharacteristic
721C22×C3#55411yescharacteristic
722C22×C3#55411yescharacteristic
723C22×C3#55611yescharacteristic
724C22×C3#55611yescharacteristic
725C22×C3#56011yescharacteristic
726C22×C3#56011yescharacteristic
727C22×C3#56211yescharacteristic
728C22×C3#56211yescharacteristic
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4—81no—
735Dic3—24no—
736Dic3—42no—
737Dic3—42no—
738Dic3—42no—
739Dic3—42no—
740Dic3—42no—
741Dic3—42no—
742Dic3—81no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#88714yes—
778C23C22×C4×D311yescharacteristic
779C23C2×#23711yescharacteristic
780C23C2×#23711yescharacteristic
781C23#100411yescharacteristic
782C23#100411yescharacteristic
783C23#100411yescharacteristic
784C23#100411yescharacteristic
785C23#100411yescharacteristic
786C23C2×D3×Q811yescharacteristic
787C23D3×#4111yescharacteristic
788C23D3×#4111yescharacteristic
789C23D3×#4111yescharacteristic
790C23#100911yescharacteristic
791C23#100911yescharacteristic
792C23#101011yescharacteristic
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—34no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—1216no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C3—44no—
893C2×C3#231211yescharacteristic
894C2×C3#232911yescharacteristic
895C2×C3#233311yescharacteristic
896C2×C3#234511yescharacteristic
897C2×C3#234711yescharacteristic
898C2×C3#236811yescharacteristic
899C2×C3#237711yescharacteristic
900C2×C3#277811yescharacteristic
901C2×C3#277811yescharacteristic
902C2×C3#278011yescharacteristic
903C2×C3#278011yescharacteristic
904C2×C3#278611yescharacteristic
905C2×C3#278611yescharacteristic
906C2×C3#278811yescharacteristic
907C2×C3#278811yescharacteristic
908C22—24no—
909C22—24no—
910C22—24no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22#548611yescharacteristic
924C22C2×#88711yescharacteristic
925C22D3×#11711yescharacteristic
926C22C4×#23711yescharacteristic
927C22#554511yescharacteristic
928C22#554511yescharacteristic
929C22#554611yescharacteristic
930C22#558711yescharacteristic
931C22#559311yescharacteristic
932C22#559311yescharacteristic
933C22#560111yescharacteristic
934C22#560111yescharacteristic
935C22#560111yescharacteristic
936C22#561311yescharacteristic
937C22#561311yescharacteristic
938C22#561911yescharacteristic
939C22#562011yescharacteristic
940C22#562111yescharacteristic
941C22#562311yescharacteristic
942C22#563411yescharacteristic
943C22#563511yescharacteristic
944C22#563611yescharacteristic
945C22#563611yescharacteristic
946C22#563611yescharacteristic
947C22#565711yescharacteristic
948C22#565811yescharacteristic
949C22#566111yescharacteristic
950C22#566311yescharacteristic
951C22#566511yescharacteristic
952C22#567111yescharacteristic
953C22#567811yescharacteristic
954C22#568411yescharacteristic
955C22#570211yescharacteristic
956C22#570411yescharacteristic
957C22#572011yescharacteristic
958C4—42no—
959C4—42no—
960C4—42no—
961C4—64no—
962C4—81no—
963C4—81no—
964C4—81no—
965C4—122no—
966C4—122no—
967C4—122no—
968C4—122no—
969C4—122no—
970C4—122no—
971C4—241no—
972C3#1445311yescharacteristic, complemented, Sylow
973C2—44no—
974C2#7388011yescharacteristic
975C2#7438711yescharacteristic
976C2#7439911yescharacteristic
977C2#7466811yescharacteristic
978C2#7547411yescharacteristic
979C2#7582511yescharacteristic
980C2#7631011yescharacteristic
981C2#7673811yescharacteristic
982C2#7684911yescharacteristic
983C2#7706411yescharacteristic
984C2#7707111yescharacteristic
985C2#7738811yescharacteristic
986C2#7739311yescharacteristic
987C2#7763211yescharacteristic
988C2#7808511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC25×C3C23
hypercenter#1439D3
hypocenterC3#14453
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. #71566C2semidirect
4. #71564C2semidirect
10. #69418C2semidirect
11. #69418C2semidirect
12. #69409C2semidirect
13. #69406C2semidirect
14. #69406C2semidirect
15. #69405C2semidirect
52. #4942C4semidirect
972. C3#14453semidirect

Maximal subgroups

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

subgroupindex
C2×#49422
C3×#14392
#715662
#715642
#715472
#715452
#715442
#694182
#694092
#694062
#694052
#144533