Finite Group Databasebeta

← #10742735

Subgroups — #10742735

Order 768.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C2×#5211C211yesmaximal, characteristic, complemented
4C2×#4943C211yesmaximal, characteristic, complemented
5#72131C211yesmaximal, characteristic
6#72127C211yesmaximal, characteristic, complemented
7#71547C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69421C211yesmaximal, characteristic, complemented
13#69418C211yesmaximal, characteristic, complemented
14#69417C211yesmaximal, characteristic, complemented
15#69413C211yesmaximal, characteristic, complemented
16#15952—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
32C3×#386—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35#5220—24no—
36#5211—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4943—24no—
56C2×#386—31no—
57C2×#386D311yescharacteristic
58C2×#381—31no—
59C2×#381—31no—
60#1445—31no—
61#1443—31no—
62#1443—31no—
63#1442—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69C22⋊#95—31no—
70C22⋊#95—31no—
71C25×C3C2311yescharacteristic
72C25×C3C2311yescharacteristic
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—41no—
78C22×C3×D4—41no—
79C22×C3×D4D414yes—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—41no—
98C23×Dic3—41no—
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
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—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4—41no—
116C2×#217—22no—
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×#217—41no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×Dic3⋊C4—41no—
143C3×#95—22no—
144C3×#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95D414yescomplemented
163C23×D4C2×D311yescharacteristic
164C24×C4—31no—
165C24×C4C2×D311yescharacteristic
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4C2×D311yescharacteristic
176C22×C22⋊C4C2×D311yescharacteristic
177C22×C22⋊C4C2×D311yescharacteristic
178#386—24no—
179#386—64no—
180#381—64no—
181#381—64no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
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×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
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×C3C2×D412yes—
227C24×C3C2×D412yes—
228C24×C3#4112yes—
229C24×C3#4112yes—
230C24×C3#4112yes—
231C24×C3#4112yes—
232C24×C3C2411yescharacteristic
233C2×C3×D4—28no—
234C2×C3×D4—28no—
235C2×C3×D4—44no—
236C2×C3×D4—44no—
237C2×C3×D4—44no—
238C2×C3×D4—44no—
239C2×C3×D4—44no—
240C22×C3×C4—28no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
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—44no—
274C22×C3×C4—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4—44no—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4#4112yes—
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—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—44no—
336C22×Dic3—44no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3#4112yes—
344C22×Dic3#4112yes—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347C3×C22⋊C4—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351#217—44no—
352#217—44no—
353#217—44no—
354#217—44no—
355Dic3⋊C4—44no—
356Dic3⋊C4—44no—
357C25C22×D311yescharacteristic
358C25C22×D311yescharacteristic
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4#6714yes—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—62no—
386C23×C4—121no—
387C23×C4—121no—
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C2×C4⋊C4—62no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4—121no—
398C2×C4⋊C4—121no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4—121no—
429#95—22no—
430#95—22no—
431#95—34no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—62no—
441#95—62no—
442#95—121no—
443#95—121no—
444#95—121no—
445#95—121no—
446#95—121no—
447#95—121no—
448#95—121no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
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—22no—
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#12314yes—
518C23×C3#12314yes—
519C23×C3C22×D411yescharacteristic
520C23×C3C22×D411yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3C2×#4111yescharacteristic
524C23×C3C2×#4111yescharacteristic
525C23×C3C2×#4111yescharacteristic
526C23×C3C2×#4111yescharacteristic
527C23×C3C2×#4111yescharacteristic
528C23×C3H(5,𝔽2)11yescharacteristic
529C23×C3H(5,𝔽2)11yescharacteristic
530C23×C3H(5,𝔽2)11yescharacteristic
531C23×C3H(5,𝔽2)11yescharacteristic
532C23×C3H(5,𝔽2)11yescharacteristic
533C23×C32−1+411yescharacteristic
534C3×D4—416no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—416no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
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×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—416no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
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—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
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#23512yes—
653C24#23512yes—
654C24#23712yes—
655C24#23712yes—
656C24C2×#6712yes—
657C24C2×#6712yes—
658C24C23×D311yescharacteristic
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C22×C4—28no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
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—32no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—68no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
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—124no—
763C22×C4—124no—
764C22×C4—124no—
765C22×C4—124no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4D3×D412yes—
769C22×C4#23712yes—
770C22×C4C2×#6712yes—
771C4⋊C4—124no—
772C4⋊C4—124no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22×C3—24no—
784C22×C3—24no—
785C22×C3—24no—
786C22×C3—24no—
787C22×C3—24no—
788C22×C3—24no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
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—42no—
813C22×C3C2×#12311yescharacteristic
814C22×C3C2×#12311yescharacteristic
815C22×C3#52511yescharacteristic
816C22×C3#52511yescharacteristic
817C22×C3#52911yescharacteristic
818C22×C3#52911yescharacteristic
819C22×C3#53411yescharacteristic
820C22×C3#53711yescharacteristic
821C22×C3#53811yescharacteristic
822C22×C3#53811yescharacteristic
823C22×C3#53811yescharacteristic
824C22×C3#53911yescharacteristic
825C22×C3#53911yescharacteristic
826C22×C3#54011yescharacteristic
827C22×C3#54011yescharacteristic
828C22×C3D4211yescharacteristic
829C22×C3#54611yescharacteristic
830C22×C3#54611yescharacteristic
831C22×C3#54611yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54711yescharacteristic
834C22×C3#55011yescharacteristic
835C22×C3#55111yescharacteristic
836C22×C3#55111yescharacteristic
837C22×C3#55111yescharacteristic
838C22×C3#55111yescharacteristic
839C22×C3#55111yescharacteristic
840C22×C3#55111yescharacteristic
841C22×C3#55111yescharacteristic
842C22×C3#55111yescharacteristic
843C22×C3#55211yescharacteristic
844C22×C3#55211yescharacteristic
845C22×C3#55511yescharacteristic
846C22×C3#56011yescharacteristic
847C22×C3#56211yescharacteristic
848C3×C4—42no—
849C3×C4—42no—
850C3×C4—42no—
851C3×C4—81no—
852C3×C4—81no—
853Dic3—42no—
854Dic3—42no—
855Dic3—42no—
856Dic3—42no—
857Dic3—81no—
858Dic3—81no—
859Dic3—81no—
860Dic3—81no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
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—22no—
894C23—22no—
895C23—22no—
896C23—22no—
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#92914yes—
930C23#93514yes—
931C23C2×#23511yescharacteristic
932C23C2×#23511yescharacteristic
933C23C2×D3×D411yescharacteristic
934C23C2×#23711yescharacteristic
935C23C2×#23711yescharacteristic
936C23C2×#23711yescharacteristic
937C23#100411yescharacteristic
938C23#100411yescharacteristic
939C23#100411yescharacteristic
940C23#100411yescharacteristic
941C23D3×#4111yescharacteristic
942C23D3×#4111yescharacteristic
943C23#100911yescharacteristic
944C23#101011yescharacteristic
945C23C22×#6711yescharacteristic
946D4—416no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—416no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
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—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—1216no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
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×C3—44no—
1041C2×C3—44no—
1042C2×C3#241811yescharacteristic
1043C2×C3#241811yescharacteristic
1044C2×C3#241911yescharacteristic
1045C2×C3#241911yescharacteristic
1046C2×C3#247111yescharacteristic
1047C2×C3#247111yescharacteristic
1048C2×C3#248311yescharacteristic
1049C2×C3#257211yescharacteristic
1050C2×C3#260911yescharacteristic
1051C2×C3#268211yescharacteristic
1052C2×C3#269311yescharacteristic
1053C2×C3#269911yescharacteristic
1054C2×C3#274311yescharacteristic
1055C2×C3#274311yescharacteristic
1056C2×C3#276011yescharacteristic
1057C22—24no—
1058C22—24no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
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—42no—
1086C22—42no—
1087C22#549511yescharacteristic
1088C22#549511yescharacteristic
1089C22#549511yescharacteristic
1090C22#549511yescharacteristic
1091C22#553811yescharacteristic
1092C22#554111yescharacteristic
1093C22#554711yescharacteristic
1094C22#555011yescharacteristic
1095C22#555611yescharacteristic
1096C22#555611yescharacteristic
1097C22#556011yescharacteristic
1098C22#556411yescharacteristic
1099C22#558611yescharacteristic
1100C22#558711yescharacteristic
1101C22#559111yescharacteristic
1102C22#559311yescharacteristic
1103C22#559911yescharacteristic
1104C22#560811yescharacteristic
1105C22#561311yescharacteristic
1106C22#561511yescharacteristic
1107C22#561611yescharacteristic
1108C22#561911yescharacteristic
1109C22#562011yescharacteristic
1110C22#562111yescharacteristic
1111C22#564911yescharacteristic
1112C22#565011yescharacteristic
1113C22#565811yescharacteristic
1114C22#566511yescharacteristic
1115C22C2×#92911yescharacteristic
1116C22C2×#93511yescharacteristic
1117C22D4×#6711yescharacteristic
1118C22#580411yescharacteristic
1119C22#580611yescharacteristic
1120C22#582411yescharacteristic
1121C22#582911yescharacteristic
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—81no—
1126C4—81no—
1127C4—122no—
1128C4—122no—
1129C4—122no—
1130C4—122no—
1131C4—241no—
1132C4—241no—
1133C4—241no—
1134C4—241no—
1135C3#1595211yescharacteristic, complemented, Sylow
1136C2—44no—
1137C2—44no—
1138C2#7472411yescharacteristic
1139C2#7472511yescharacteristic
1140C2#7476411yescharacteristic
1141C2#7477911yescharacteristic
1142C2#7480411yescharacteristic
1143C2#7483411yescharacteristic
1144C2#7483511yescharacteristic
1145C2#7485111yescharacteristic
1146C2#8211411yescharacteristic
1147C2#8235411yescharacteristic
1148C2#8240411yescharacteristic
1149C2#8258511yescharacteristic
1150C2#8268611yescharacteristic
1151C2#8269111yescharacteristic
1152C2#8284411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#15952
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#5211C2semidirect
4. C2×#4943C2semidirect
6. #72127C2semidirect
7. #71547C2semidirect
8. #71547C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #71544C2semidirect
12. #69421C2semidirect
13. #69418C2semidirect
14. #69417C2semidirect
15. #69413C2semidirect
162. C3⋊#95D4semidirect
1135. C3#15952semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52202
C2×#52112
C2×#49432
#721312
#721272
#715472
#715442
#694212
#694182
#694172
#694132
#159523