Finite Group Databasebeta

← #10728016

Subgroups — #10728016

Order 768.

1434 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4992C211yesmaximal, characteristic
2C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
3C3×#1436C211yesmaximal, characteristic, complemented
4#71566C211yesmaximal, characteristic, complemented
5#71534C211yesmaximal, characteristic, complemented
6#69429C211yesmaximal, characteristic
7#69429C211yesmaximal, characteristic
8#69428C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic
11#69418C211yesmaximal, characteristic, complemented
12#69417C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14828—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
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
52#4992—24no—
53C4×(C2×D3)⋊C4—24no—
54C2×#397—31no—
55C2×C4×C22⋊C4—31no—
56#1443—31no—
57#1443—31no—
58#1443—31no—
59#1441—31no—
60#1440—31no—
61#1440—31no—
62#1439—31no—
63#1436—31no—
64#1436D311yescharacteristic, complemented
65#1434—31no—
66#1434—31no—
67C22⋊#95—31no—
68C22⋊#95—31no—
69C24×D3C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—22no—
89C22×C4×D3—41no—
90C22×C4×D3—41no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—41no—
94C2×C3×C42—22no—
95C2×C3×C42—22no—
96C2×C3×C42—41no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4—41no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4D414yes—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—41no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—41no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—41no—
125C3×#95—41no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C3⋊#95—22no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—41no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C24×C4—31no—
146C22×C4⋊C4—31no—
147C22×C4⋊C4C2×D311yescharacteristic
148C22×C22⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—31no—
151C22×C22⋊C4—31no—
152C22×C22⋊C4—31no—
153C22×C22⋊C4—31no—
154C22×C42—31no—
155C22×C42C2×D311yescharacteristic
156#397—64no—
157C4×C22⋊C4—64no—
158C2×#95—31no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95—31no—
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×#95C2×D311yescharacteristic
178C2×#95C2×D311yescharacteristic
179C2×#95C2×D311yescharacteristic
180C2×#95C2×D311yescharacteristic
181C2×#95C2×D311yescharacteristic
182C24×C3C2411yescharacteristic
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—21no—
186C23×D3—21no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—21no—
190C23×D3—21no—
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—21no—
195C23×D3C2×D412yes—
196C23×D3#4112yes—
197C23×D3#4112yes—
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×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×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4C2×D412yes—
242C22×C3×C4#4112yes—
243C22×C3×C4#4112yes—
244C22×C3×C4#4112yes—
245C22×C3×C4#4112yes—
246C22×C3×C4#4112yes—
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—21no—
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×Dic3C2×D412yes—
293C22×Dic3#4112yes—
294C22×Dic3#4112yes—
295C22×Dic3#4112yes—
296C2×C4×D3—28no—
297C2×C4×D3—44no—
298C2×C4×D3—44no—
299C2×C4×D3—44no—
300C2×C4×D3—44no—
301C2×C4×D3—44no—
302C2×C4×D3—44no—
303C3×C4⋊C4—44no—
304C3×C42—44no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—28no—
307(C2×D3)⋊C4—44no—
308(C2×D3)⋊C4—44no—
309(C2×D3)⋊C4—44no—
310(C2×D3)⋊C4—44no—
311Dic3⋊C4—44no—
312C4×Dic3—44no—
313C25—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—62no—
322C23×C4—62no—
323C23×C4—62no—
324C23×C4—62no—
325C23×C4—62no—
326C23×C4—121no—
327C23×C4—121no—
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—121no—
341C2×C22⋊C4—34no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—62no—
344C2×C22⋊C4—62no—
345C2×C22⋊C4—62no—
346C2×C22⋊C4—62no—
347C2×C22⋊C4—62no—
348C2×C22⋊C4—62no—
349C2×C22⋊C4—62no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—62no—
353C2×C22⋊C4—62no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—121no—
356C2×C22⋊C4—121no—
357C2×C22⋊C4—121no—
358C2×C22⋊C4—121no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—41no—
362C2×C42—62no—
363C2×C42—62no—
364C2×C42—121no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—41no—
369#95—41no—
370#95—62no—
371#95—62no—
372#95—62no—
373#95—62no—
374#95—62no—
375#95—62no—
376#95—62no—
377#95—62no—
378#95—62no—
379#95—62no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—121no—
384#95—121no—
385#95—121no—
386#95—121no—
387#95—121no—
388#95—121no—
389C23×C3C22×D411yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4111yescharacteristic
394C23×C3C2×#4111yescharacteristic
395C23×C3C2×#4111yescharacteristic
396C23×C3C2×#4111yescharacteristic
397C23×C3C2×#4111yescharacteristic
398C23×C3C2×#4111yescharacteristic
399C23×C3C2×#4111yescharacteristic
400C23×C3H(5,𝔽2)11yescharacteristic
401C23×C3H(5,𝔽2)11yescharacteristic
402C23×C3H(5,𝔽2)11yescharacteristic
403C23×C32−1+411yescharacteristic
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3#12314yes—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
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—41no—
455C2×C3×C4—41no—
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#12614yes—
488C2×Dic3—22no—
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—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
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—
537C4×D3—416no—
538C24—32no—
539C24—32no—
540C24—32no—
541C24—61no—
542C24—61no—
543C24—61no—
544C24—61no—
545C24—61no—
546C24—61no—
547C24—61no—
548C24—61no—
549C24—61no—
550C24—61no—
551C24—61no—
552C24—61no—
553C24C23×D311yescharacteristic
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
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—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—68no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
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—124no—
648C22×C4—124no—
649C22×C4—124no—
650C22×C4—124no—
651C22×C4—124no—
652C22×C4—124no—
653C22×C4#23512yes—
654C22×C4#23512yes—
655C22×C4#23512yes—
656C22×C4D3×D412yes—
657C22×C4#23712yes—
658C22×C4#23912yes—
659C4⋊C4—44no—
660C4⋊C4—124no—
661C22⋊C4—68no—
662C22⋊C4—68no—
663C22⋊C4—124no—
664C22⋊C4—124no—
665C22⋊C4—124no—
666C22⋊C4—124no—
667C42—44no—
668C42—124no—
669C22×C3C2×#12311yescharacteristic
670C22×C3#52511yescharacteristic
671C22×C3#52511yescharacteristic
672C22×C3C2×#12611yescharacteristic
673C22×C3#52911yescharacteristic
674C22×C3#52911yescharacteristic
675C22×C3#52911yescharacteristic
676C22×C3#52911yescharacteristic
677C22×C3#52911yescharacteristic
678C22×C3#52911yescharacteristic
679C22×C3#52911yescharacteristic
680C22×C3#52911yescharacteristic
681C22×C3#52911yescharacteristic
682C22×C3#53811yescharacteristic
683C22×C3#53811yescharacteristic
684C22×C3#53911yescharacteristic
685C22×C3#53911yescharacteristic
686C22×C3#54011yescharacteristic
687C22×C3#54211yescharacteristic
688C22×C3#54611yescharacteristic
689C22×C3#54611yescharacteristic
690C22×C3#54611yescharacteristic
691C22×C3#54711yescharacteristic
692C22×C3#55111yescharacteristic
693C22×C3#55111yescharacteristic
694C22×C3#55111yescharacteristic
695C22×C3#55111yescharacteristic
696C22×C3#55211yescharacteristic
697C22×C3#55311yescharacteristic
698C22×C3#55311yescharacteristic
699C22×C3#55311yescharacteristic
700C22×C3#55311yescharacteristic
701C22×C3#55511yescharacteristic
702C22×C3#55611yescharacteristic
703C22×C3#55611yescharacteristic
704C2×D3—24no—
705C2×D3—24no—
706C2×D3—24no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—42no—
718C2×D3—42no—
719C3×C4—24no—
720C3×C4—42no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—81no—
724C3×C4—81no—
725C3×C4—81no—
726Dic3—42no—
727Dic3—42no—
728Dic3—42no—
729Dic3—42no—
730Dic3—81no—
731Dic3—81no—
732Dic3—81no—
733C23—34no—
734C23—62no—
735C23—62no—
736C23—62no—
737C23—62no—
738C23—62no—
739C23—62no—
740C23—62no—
741C23—62no—
742C23—62no—
743C23—62no—
744C23—62no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—121no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23C2×#23511yescharacteristic
769C23C2×#23511yescharacteristic
770C23C2×#23511yescharacteristic
771C23C2×D3×D411yescharacteristic
772C23C2×#23711yescharacteristic
773C23#100411yescharacteristic
774C23#100411yescharacteristic
775C23C2×#23911yescharacteristic
776C23#100711yescharacteristic
777C23D3×#4111yescharacteristic
778C23D3×#4111yescharacteristic
779C23D3×#4111yescharacteristic
780C23D3×#4111yescharacteristic
781C23D3×#4111yescharacteristic
782C23#100911yescharacteristic
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
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—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—1216no—
844C2×C4—121no—
845C2×C4—121no—
846C2×C4—121no—
847C2×C4—121no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
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#89814yes—
882C2×C3#240111yescharacteristic
883C2×C3#241911yescharacteristic
884C2×C3#244411yescharacteristic
885C2×C3#245711yescharacteristic
886C2×C3#246611yescharacteristic
887C2×C3#247411yescharacteristic
888C2×C3#248011yescharacteristic
889C2×C3#249411yescharacteristic
890C2×C3#251811yescharacteristic
891C2×C3#252311yescharacteristic
892C2×C3#253111yescharacteristic
893C2×C3#257711yescharacteristic
894C2×C3#257811yescharacteristic
895C2×C3#264911yescharacteristic
896C2×C3#285311yescharacteristic
897D3—44no—
898C22—64no—
899C22—64no—
900C22—64no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22#547911yescharacteristic
914C22#549011yescharacteristic
915C22C2×#89811yescharacteristic
916C22#551511yescharacteristic
917C22#552711yescharacteristic
918C22#552811yescharacteristic
919C22#552811yescharacteristic
920C22#553811yescharacteristic
921C22#554711yescharacteristic
922C22#555011yescharacteristic
923C22#555611yescharacteristic
924C22#555711yescharacteristic
925C22#555811yescharacteristic
926C22#555811yescharacteristic
927C22#556211yescharacteristic
928C22#556811yescharacteristic
929C22#558011yescharacteristic
930C22#558011yescharacteristic
931C22#558111yescharacteristic
932C22#559111yescharacteristic
933C22#561311yescharacteristic
934C22#561411yescharacteristic
935C22#562711yescharacteristic
936C22#563111yescharacteristic
937C22#564111yescharacteristic
938C22#564411yescharacteristic
939C22D3×#12311yescharacteristic
940C22#565811yescharacteristic
941C22#566111yescharacteristic
942C22#567011yescharacteristic
943C22#569111yescharacteristic
944C22#569211yescharacteristic
945C22#570511yescharacteristic
946C22#570611yescharacteristic
947C22#573311yescharacteristic
948C4—24no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4—122no—
956C4—122no—
957C4—122no—
958C4—122no—
959C4—241no—
960C4—241no—
961C4—241no—
962C3#1482811yescharacteristic, complemented, Sylow
963C2—124no—
964C2#7358911yescharacteristic
965C2#7377911yescharacteristic
966C2#7381011yescharacteristic
967C2#7443411yescharacteristic
968C2#7445311yescharacteristic
969C2#7489711yescharacteristic
970C2#7508911yescharacteristic
971C2#7531511yescharacteristic
972C2#7535011yescharacteristic
973C2#7544711yescharacteristic
974C2#7555911yescharacteristic
975C2#7587911yescharacteristic
976C2#7623411yescharacteristic
977C2#7625311yescharacteristic
978C2#7651511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC24×D3C23
hypercenter#1436D3
hypocenterC3#14828
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C3×#1436C2semidirect
4. #71566C2semidirect
5. #71534C2semidirect
11. #69418C2semidirect
12. #69417C2semidirect
13. #69417C2semidirect
14. #69406C2semidirect
15. #69401C2semidirect
64. #1436D3semidirect
962. C3#14828semidirect

Maximal subgroups

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

subgroupindex
C2×#49922
C2×C4×(C2×D3)⋊C42
C3×#14362
#715662
#715342
#694292
#694282
(C2×D3)⋊#952
#694182
#694172
#694062
#694012
#148283