Finite Group Databasebeta

← #10733269

Subgroups — #10733269

Order 768.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic
2C2×#5222C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#4945C211yesmaximal, characteristic, complemented
5C2×#4951C211yesmaximal, characteristic, complemented
6C2×#4942C211yesmaximal, characteristic, complemented
7#71568C211yesmaximal, characteristic, complemented
8#71564C211yesmaximal, characteristic, complemented
9#71549C211yesmaximal, characteristic, complemented
10#71549C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71546C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#69421C211yesmaximal, characteristic, complemented
15#69410C211yesmaximal, characteristic, complemented
16#15289—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×#394—24no—
37C2×C3×#95C2211yescharacteristic
38#5222—24no—
39#5220—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
55#4951—24no—
56#4945—24no—
57#4942—24no—
58C2×#394—31no—
59C2×#394D311yescharacteristic
60C2×#388—31no—
61C2×#388—31no—
62C2×#386—31no—
63C2×#380—31no—
64#1445—31no—
65#1444—31no—
66#1441—31no—
67#1440—31no—
68#1440—31no—
69#1439—31no—
70#1439—31no—
71#1436—31no—
72C22⋊#95—31no—
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—41no—
81C22×C3×D4—41no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—41no—
93C23×Dic3—41no—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—41no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
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—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217—41no—
133C2×#217—41no—
134C2×#217—41no—
135C2×#217—41no—
136C2×#217D414yes—
137C2×#217D414yes—
138C2×C4⋊Dic3—22no—
139C2×C4⋊Dic3—41no—
140C2×C4⋊Dic3—41no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—41no—
148C2×Dic3⋊C4—41no—
149C2×Dic3⋊C4—41no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—41no—
153C3×#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—41no—
167C3⋊#95—41no—
168C3⋊#95—41no—
169C23×D4C2×D311yescharacteristic
170C24×C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4C2×D311yescharacteristic
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C22⋊C4C2×D311yescharacteristic
185C22×C22⋊C4C2×D311yescharacteristic
186C22×C22⋊C4C2×D311yescharacteristic
187C22×C42—31no—
188#394—24no—
189#394—64no—
190#388—64no—
191#388—64no—
192#386—64no—
193#380—64no—
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×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95C2×D311yescharacteristic
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×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3C2×D412yes—
237C24×C3C2×D412yes—
238C24×C3C2×D412yes—
239C24×C3#4112yes—
240C24×C3C2411yescharacteristic
241C2×C3×D4—28no—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
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—21no—
278C22×C3×C4—21no—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—28no—
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—44no—
334C22×Dic3—44no—
335C22×Dic3—44no—
336C22×Dic3—44no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3#4112yes—
344C22×Dic3#4112yes—
345C22×Dic3#4112yes—
346C3×C4⋊C4—44no—
347C3×C22⋊C4—28no—
348C3×C22⋊C4—44no—
349C3×C22⋊C4—44no—
350C3×C22⋊C4—44no—
351#217—28no—
352#217—44no—
353#217—44no—
354#217—44no—
355#217—44no—
356#217—44no—
357#217—44no—
358C4⋊Dic3—44no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361Dic3⋊C4—44no—
362C4×Dic3—44no—
363C25C22×D311yescharacteristic
364C25C22×D311yescharacteristic
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—41no—
371C22×D4—41no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—62no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—121no—
386C23×C4—121no—
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—121no—
403C2×C4⋊C4—121no—
404C2×C4⋊C4—121no—
405C2×C4⋊C4—121no—
406C2×C4⋊C4—121no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
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—62no—
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—62no—
442C2×C42—121no—
443#95—22no—
444#95—62no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—121no—
457#95—121no—
458#95—121no—
459C23×C3—22no—
460C23×C3—22no—
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—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
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#12114yes—
529C23×C3C22×D411yescharacteristic
530C23×C3C22×D411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
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×C32−1+411yescharacteristic
543C23×C32−1+411yescharacteristic
544C3×D4—416no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
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—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
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×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
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—416no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
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#12314yes—
637C24—21no—
638C24—21no—
639C24—21no—
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—
663C24D3×D412yes—
664C24D3×D412yes—
665C24#23712yes—
666C24C2×#6712yes—
667C24C23×D311yescharacteristic
668C2×D4—28no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
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—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—68no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
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—124no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4—124no—
769C22×C4#23712yes—
770C22×C4#23712yes—
771C22×C4C2×#6712yes—
772C22×C4C2×#6712yes—
773C4⋊C4—44no—
774C4⋊C4—124no—
775C4⋊C4—124no—
776C4⋊C4—124no—
777C4⋊C4—124no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—68no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C22⋊C4—124no—
789C42—124no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
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—81no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3C2×#12111yescharacteristic
821C22×C3C2×#12311yescharacteristic
822C22×C3#52511yescharacteristic
823C22×C3#52511yescharacteristic
824C22×C3#52911yescharacteristic
825C22×C3#53211yescharacteristic
826C22×C3#53411yescharacteristic
827C22×C3#53611yescharacteristic
828C22×C3#53711yescharacteristic
829C22×C3#53811yescharacteristic
830C22×C3#53811yescharacteristic
831C22×C3#54011yescharacteristic
832C22×C3#54211yescharacteristic
833C22×C3#54211yescharacteristic
834C22×C3#54211yescharacteristic
835C22×C3D4211yescharacteristic
836C22×C3D4211yescharacteristic
837C22×C3#54611yescharacteristic
838C22×C3#54611yescharacteristic
839C22×C3#54611yescharacteristic
840C22×C3#54611yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54711yescharacteristic
843C22×C3#54711yescharacteristic
844C22×C3#54711yescharacteristic
845C22×C3#55111yescharacteristic
846C22×C3#55211yescharacteristic
847C22×C3#55211yescharacteristic
848C22×C3#55311yescharacteristic
849C22×C3#55311yescharacteristic
850C22×C3#55311yescharacteristic
851C22×C3#55511yescharacteristic
852C22×C3#55611yescharacteristic
853C22×C3#56211yescharacteristic
854C22×C3#56211yescharacteristic
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859C3×C4—81no—
860Dic3—24no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865Dic3—81no—
866Dic3—81no—
867Dic3—81no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
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—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
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#93914yes—
938C23C2×D3×D411yescharacteristic
939C23C2×D3×D411yescharacteristic
940C23C2×#23711yescharacteristic
941C23C2×#23711yescharacteristic
942C23C2×#23711yescharacteristic
943C23#100411yescharacteristic
944C23#100411yescharacteristic
945C23#100411yescharacteristic
946C23D3×#4111yescharacteristic
947C23D3×#4111yescharacteristic
948C23D3×#4111yescharacteristic
949C23#100911yescharacteristic
950C23#101011yescharacteristic
951C23#101011yescharacteristic
952C23C22×#6711yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—34no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
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—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
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—1216no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
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×C3—44no—
1047C2×C3—82no—
1048C2×C3#241311yescharacteristic
1049C2×C3#241811yescharacteristic
1050C2×C3#242211yescharacteristic
1051C2×C3#242411yescharacteristic
1052C2×C3#246811yescharacteristic
1053C2×C3#247611yescharacteristic
1054C2×C3#248511yescharacteristic
1055C2×C3#252111yescharacteristic
1056C2×C3#254311yescharacteristic
1057C2×C3#267111yescharacteristic
1058C2×C3#267211yescharacteristic
1059C2×C3#268611yescharacteristic
1060C2×C3#270011yescharacteristic
1061C2×C3#274111yescharacteristic
1062C2×C3#277911yescharacteristic
1063C22—24no—
1064C22—24no—
1065C22—24no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22#558611yescharacteristic
1094C22#559011yescharacteristic
1095C22#559111yescharacteristic
1096C22#559311yescharacteristic
1097C22#559611yescharacteristic
1098C22#559711yescharacteristic
1099C22#560011yescharacteristic
1100C22#560111yescharacteristic
1101C22#560111yescharacteristic
1102C22#560311yescharacteristic
1103C22#560511yescharacteristic
1104C22#561111yescharacteristic
1105C22#561511yescharacteristic
1106C22#561611yescharacteristic
1107C22#561811yescharacteristic
1108C22#562111yescharacteristic
1109C22#565011yescharacteristic
1110C22#565011yescharacteristic
1111C22D3×#12311yescharacteristic
1112C22#565411yescharacteristic
1113C22#565511yescharacteristic
1114C22#565511yescharacteristic
1115C22#565711yescharacteristic
1116C22#565911yescharacteristic
1117C22#566911yescharacteristic
1118C22#567111yescharacteristic
1119C22#568211yescharacteristic
1120C22#568411yescharacteristic
1121C22D4×#6711yescharacteristic
1122C22C2×#93911yescharacteristic
1123C22#580611yescharacteristic
1124C22#580611yescharacteristic
1125C22#582511yescharacteristic
1126C22#582811yescharacteristic
1127C22#582911yescharacteristic
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—64no—
1133C4—81no—
1134C4—122no—
1135C4—122no—
1136C4—122no—
1137C4—122no—
1138C4—241no—
1139C4—241no—
1140C4—241no—
1141C3#1528911yescharacteristic, complemented, Sylow
1142C2—44no—
1143C2—82no—
1144C2#7690011yescharacteristic
1145C2#7692211yescharacteristic
1146C2#7693311yescharacteristic
1147C2#7694011yescharacteristic
1148C2#7705111yescharacteristic
1149C2#7706511yescharacteristic
1150C2#7713011yescharacteristic
1151C2#7714511yescharacteristic
1152C2#8258711yescharacteristic
1153C2#8266011yescharacteristic
1154C2#8267011yescharacteristic
1155C2#8268211yescharacteristic
1156C2#8284311yescharacteristic
1157C2#8289611yescharacteristic
1158C2#8298511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC23×C3×D4C22
hypercenterC2×#394D3
hypocenterC3#15289
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
4. C2×#4945C2semidirect
5. C2×#4951C2semidirect
6. C2×#4942C2semidirect
7. #71568C2semidirect
8. #71564C2semidirect
9. #71549C2semidirect
10. #71549C2semidirect
11. #71547C2semidirect
12. #71546C2semidirect
13. #71544C2semidirect
14. #69421C2semidirect
15. #69410C2semidirect
1141. C3#15289semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×#52222
C2×#52202
C2×#49452
C2×#49512
C2×#49422
#715682
#715642
#715492
#715472
#715462
#715442
#694212
#694102
#152893