Finite Group Databasebeta

← #10735629

Subgroups — #10735629

Order 768.

2162 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5213C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic, complemented
5C2×#4945C211yesmaximal, characteristic, complemented
6C2×#4675C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#72127C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#69429C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#15450—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#386—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41#5223—24no—
42#5213—24no—
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#4957—24no—
56#4945—24no—
57#4675—24no—
58C2×#397—31no—
59C2×#392—31no—
60C2×#390—31no—
61C2×#388—31no—
62C2×#386—31no—
63C2×#386D311yescharacteristic, complemented
64#1442—31no—
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69#1438—31no—
70#1438—31no—
71#1434—31no—
72C22⋊#95—31no—
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—41no—
82C22×C3×D4—41no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C22×#67—41no—
107C22×#67—41no—
108C22×#67D414yes—
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—41no—
138C2×#217—41no—
139C2×#217—41no—
140C2×#217—41no—
141C2×#217—41no—
142C2×#217—41no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—41no—
162C2×Dic3⋊C4—41no—
163C2×Dic3⋊C4—41no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—22no—
166C2×C4×Dic3—22no—
167C3×#95—22no—
168C3×#95D414yescomplemented
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95—41no—
180C3⋊#95D414yescomplemented
181C23×D4—31no—
182C23×D4—31no—
183C23×D4C2×D311yescharacteristic
184C24×C4C2×D311yescharacteristic
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C22⋊C4C2×D311yescharacteristic
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C42—31no—
202#397—64no—
203#392—64no—
204#390—64no—
205#388—64no—
206#386—24no—
207#386—64no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
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×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3C2×D412yes—
249C24×C3#4112yes—
250C24×C3#4112yes—
251C24×C3#4112yes—
252C24×C3C2411yescharacteristic
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3C2×D412yes—
268C2×C3×D4—28no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—44no—
307C22×C3×C4—44no—
308C22×C3×C4—44no—
309C22×C3×C4—44no—
310C22×C3×C4—44no—
311C22×C3×C4—44no—
312C22×C3×C4—44no—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C2×#67—28no—
318C2×#67—28no—
319C2×#67—44no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3C2×D412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3#4112yes—
378C22×Dic3#4112yes—
379C22×Dic3#4112yes—
380C3×C22⋊C4—44no—
381C3×C22⋊C4—44no—
382C3×C22⋊C4—44no—
383#217—28no—
384#217—44no—
385#217—44no—
386#217—44no—
387#217—44no—
388#217—44no—
389(C2×D3)⋊C4—44no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394Dic3⋊C4—44no—
395Dic3⋊C4—44no—
396C4×Dic3—44no—
397C25—31no—
398C25C22×D311yescharacteristic
399C25C22×D311yescharacteristic
400C22×D4—22no—
401C22×D4—22no—
402C22×D4—22no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—34no—
406C22×D4—41no—
407C22×D4—41no—
408C22×D4—62no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—62no—
412C22×D4—62no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—121no—
416C22×D4—121no—
417C22×D4—121no—
418C22×D4—121no—
419C22×D4—121no—
420C22×D4—121no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—41no—
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—121no—
444C2×C4⋊C4—121no—
445C2×C4⋊C4—121no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—41no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—41no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—121no—
477C2×C22⋊C4—121no—
478C2×C22⋊C4—121no—
479C2×C22⋊C4—121no—
480C2×C22⋊C4—121no—
481C2×C22⋊C4—121no—
482C2×C22⋊C4—121no—
483C2×C22⋊C4—121no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C42—62no—
489C2×C42—62no—
490C2×C42—62no—
491#95—22no—
492#95—34no—
493#95—62no—
494#95—62no—
495#95—62no—
496#95—62no—
497#95—62no—
498#95—62no—
499#95—121no—
500#95—121no—
501#95—121no—
502#95—121no—
503#95—121no—
504#95#6714yescomplemented
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3#12314yes—
575C23×C3C22×D411yescharacteristic
576C23×C3C22×D411yescharacteristic
577C23×C3C22×D411yescharacteristic
578C23×C3C2×#4111yescharacteristic
579C23×C3C2×#4111yescharacteristic
580C23×C3C2×#4111yescharacteristic
581C23×C3C2×#4111yescharacteristic
582C23×C3C2×#4111yescharacteristic
583C23×C3C2×#4111yescharacteristic
584C23×C3H(5,𝔽2)11yescharacteristic
585C23×C3H(5,𝔽2)11yescharacteristic
586C23×C3H(5,𝔽2)11yescharacteristic
587C23×C3H(5,𝔽2)11yescharacteristic
588C23×C3H(5,𝔽2)11yescharacteristic
589C23×C3H(5,𝔽2)11yescharacteristic
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C3×D4—416no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—416no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662#67—416no—
663#67—416no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687C2×Dic3—41no—
688C2×Dic3—41no—
689C2×Dic3—41no—
690C2×Dic3—41no—
691C2×Dic3—41no—
692C2×Dic3—41no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3#12114yes—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—32no—
740C24—61no—
741C24—61no—
742C24—61no—
743C24—61no—
744C24—61no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24#23512yes—
755C24#23512yes—
756C24D3×D412yes—
757C24#23712yes—
758C24C23×D311yescharacteristic
759C2×D4—28no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—68no—
767C2×D4—68no—
768C2×D4—124no—
769C2×D4—124no—
770C2×D4—124no—
771C2×D4—124no—
772C2×D4—124no—
773C2×D4—124no—
774C2×D4—124no—
775C2×D4—124no—
776C2×D4—124no—
777C2×D4—124no—
778C2×D4—124no—
779C2×D4—124no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—32no—
812C22×C4—32no—
813C22×C4—32no—
814C22×C4—32no—
815C22×C4—32no—
816C22×C4—32no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—61no—
825C22×C4—61no—
826C22×C4—61no—
827C22×C4—61no—
828C22×C4—61no—
829C22×C4—61no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4D3×D412yes—
868C22×C4C2×#6712yes—
869C22×C4C2×#6712yes—
870C22×C4C2×#6712yes—
871C4⋊C4—124no—
872C4⋊C4—124no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—68no—
877C22⋊C4—124no—
878C22⋊C4—124no—
879C22⋊C4—124no—
880C22⋊C4—124no—
881C22⋊C4—124no—
882C22⋊C4—124no—
883C22⋊C4—124no—
884C22⋊C4—124no—
885C22⋊C4—124no—
886C22⋊C4—124no—
887C42—124no—
888C22×C3—24no—
889C22×C3—24no—
890C22×C3—24no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3—42no—
904C22×C3—42no—
905C22×C3—42no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—42no—
910C22×C3—81no—
911C22×C3—81no—
912C22×C3—81no—
913C22×C3—81no—
914C22×C3—81no—
915C22×C3—81no—
916C22×C3—81no—
917C22×C3—81no—
918C22×C3C2×#12111yescharacteristic
919C22×C3C2×#12311yescharacteristic
920C22×C3#52511yescharacteristic
921C22×C3#52511yescharacteristic
922C22×C3#52911yescharacteristic
923C22×C3#53211yescharacteristic
924C22×C3#53411yescharacteristic
925C22×C3#53511yescharacteristic
926C22×C3#53511yescharacteristic
927C22×C3#53811yescharacteristic
928C22×C3#53811yescharacteristic
929C22×C3#53811yescharacteristic
930C22×C3#53811yescharacteristic
931C22×C3#54011yescharacteristic
932C22×C3#54011yescharacteristic
933C22×C3D4211yescharacteristic
934C22×C3D4211yescharacteristic
935C22×C3#54611yescharacteristic
936C22×C3#54611yescharacteristic
937C22×C3#54611yescharacteristic
938C22×C3#54611yescharacteristic
939C22×C3#54611yescharacteristic
940C22×C3#54611yescharacteristic
941C22×C3#55011yescharacteristic
942C22×C3#55011yescharacteristic
943C22×C3#55111yescharacteristic
944C22×C3#55111yescharacteristic
945C22×C3#55111yescharacteristic
946C22×C3#55111yescharacteristic
947C22×C3#55311yescharacteristic
948C22×C3#55311yescharacteristic
949C22×C3#55311yescharacteristic
950C22×C3#55311yescharacteristic
951C22×C3#56011yescharacteristic
952C22×C3H(3,𝔽4)11yescharacteristic
953C2×D3—42no—
954C2×D3—42no—
955C2×D3—42no—
956C2×D3—42no—
957C2×D3—42no—
958C2×D3—42no—
959C2×D3—42no—
960C2×D3—81no—
961C2×D3—81no—
962C2×D3—81no—
963C2×D3—81no—
964C2×D3—81no—
965C2×D3—81no—
966C2×D3—81no—
967C2×D3—81no—
968C3×C4—42no—
969C3×C4—42no—
970C3×C4—42no—
971C3×C4—42no—
972C3×C4—81no—
973Dic3—24no—
974Dic3—42no—
975Dic3—42no—
976Dic3—42no—
977Dic3—81no—
978Dic3—81no—
979Dic3—81no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23#88314yes—
1085C23C2×#23511yescharacteristic
1086C23C2×#23511yescharacteristic
1087C23C2×D3×D411yescharacteristic
1088C23C2×D3×D411yescharacteristic
1089C23C2×#23711yescharacteristic
1090C23#100411yescharacteristic
1091C23#100411yescharacteristic
1092C23#100411yescharacteristic
1093C23#100411yescharacteristic
1094C23#100411yescharacteristic
1095C23D3×#4111yescharacteristic
1096C23D3×#4111yescharacteristic
1097C23D3×#4111yescharacteristic
1098C23#100911yescharacteristic
1099C23C22×#6711yescharacteristic
1100D4—416no—
1101D4—1216no—
1102D4—1216no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—34no—
1116C2×C4—416no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—62no—
1141C2×C4—62no—
1142C2×C4—62no—
1143C2×C4—62no—
1144C2×C4—62no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—62no—
1152C2×C4—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—121no—
1156C2×C4—121no—
1157C2×C4—121no—
1158C2×C4—121no—
1159C2×C4—121no—
1160C2×C4—121no—
1161C2×C4—121no—
1162C2×C4—121no—
1163C2×C4—121no—
1164C2×C4—121no—
1165C2×C4—121no—
1166C2×C4—121no—
1167C2×C4—121no—
1168C2×C4—121no—
1169C2×C4—121no—
1170C2×C4—121no—
1171C2×C4—121no—
1172C2×C4—121no—
1173C2×C4—121no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C3—44no—
1189C2×C3—82no—
1190C2×C3#241211yescharacteristic
1191C2×C3#241811yescharacteristic
1192C2×C3#242811yescharacteristic
1193C2×C3#244411yescharacteristic
1194C2×C3#245611yescharacteristic
1195C2×C3#247111yescharacteristic
1196C2×C3#253511yescharacteristic
1197C2×C3#255411yescharacteristic
1198C2×C3#260311yescharacteristic
1199C2×C3#267011yescharacteristic
1200C2×C3#267311yescharacteristic
1201C2×C3#268411yescharacteristic
1202C2×C3#271411yescharacteristic
1203C2×C3#274911yescharacteristic
1204C2×C3#275311yescharacteristic
1205D3—82no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22—241no—
1244C22—241no—
1245C22—241no—
1246C22—241no—
1247C22—241no—
1248C22—241no—
1249C22—241no—
1250C22—241no—
1251C22C2×#88311yescharacteristic
1252C22#549011yescharacteristic
1253C22#549411yescharacteristic
1254C22#549511yescharacteristic
1255C22#554011yescharacteristic
1256C22#554011yescharacteristic
1257C22#554011yescharacteristic
1258C22#554711yescharacteristic
1259C22#555011yescharacteristic
1260C22#555611yescharacteristic
1261C22#555611yescharacteristic
1262C22#556011yescharacteristic
1263C22#559111yescharacteristic
1264C22#559211yescharacteristic
1265C22#559311yescharacteristic
1266C22#559411yescharacteristic
1267C22#559911yescharacteristic
1268C22D3×#12111yescharacteristic
1269C22#560511yescharacteristic
1270C22#561011yescharacteristic
1271C22#561011yescharacteristic
1272C22#561511yescharacteristic
1273C22#561511yescharacteristic
1274C22#562011yescharacteristic
1275C22#564911yescharacteristic
1276C22#565711yescharacteristic
1277C22#565811yescharacteristic
1278C22#566111yescharacteristic
1279C22#579111yescharacteristic
1280C22D4×#6711yescharacteristic
1281C22D4×#6711yescharacteristic
1282C22#580511yescharacteristic
1283C22#580611yescharacteristic
1284C22#583211yescharacteristic
1285C22#583411yescharacteristic
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—64no—
1291C4—81no—
1292C4—122no—
1293C4—122no—
1294C4—122no—
1295C4—241no—
1296C4—241no—
1297C4—241no—
1298C3#1545011yescharacteristic, complemented, Sylow
1299C2—44no—
1300C2—82no—
1301C2—242no—
1302C2#7470711yescharacteristic
1303C2#7472411yescharacteristic
1304C2#7475111yescharacteristic
1305C2#7482311yescharacteristic
1306C2#7484011yescharacteristic
1307C2#7484711yescharacteristic
1308C2#7489011yescharacteristic
1309C2#7491911yescharacteristic
1310C2#8212811yescharacteristic
1311C2#8239011yescharacteristic
1312C2#8241111yescharacteristic
1313C2#8259511yescharacteristic
1314C2#8265011yescharacteristic
1315C2#8271711yescharacteristic
1316C2#8286111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC2×#5223C2
hypercenterC2×#386D3
hypocenterC3#15450
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×C3×#386C2semidirect
3. C2×#5213C2semidirect
4. C2×#4957C2semidirect
5. C2×#4945C2semidirect
6. C2×#4675C2semidirect
7. #72131C2semidirect
8. #72127C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #69429C2semidirect
14. #69413C2semidirect
15. #69401C2semidirect
63. C2×#386D3semidirect
168. C3×#95D4semidirect
180. C3⋊#95D4semidirect
504. #95#67semidirect
1298. C3#15450semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52232
C2×#52132
C2×#49572
C2×#49452
C2×#46752
#721312
#721272
#715502
#715472
#694292
#694132
#694012
#154503