Finite Group Databasebeta

← #10724536

Subgroups — #10724536

Order 768.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 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×#5221C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#4670C211yesmaximal, characteristic, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71549C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#69415C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14520—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×C4⋊Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C3×#386—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41#5223C418yescomplemented
42#5221—24no—
43#5213—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56#4670—24no—
57C2×#392—31no—
58C2×#390—31no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386D311yescharacteristic, complemented
62#1442—31no—
63#1440—31no—
64#1438—31no—
65#1438—31no—
66#1438—31no—
67#1437—31no—
68#1437—31no—
69#1437—31no—
70#1434—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C25×C3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—41no—
80C22×C3×D4—41no—
81C22×C3×D4C2×C414yes—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—41no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C22×#67C2×C414yes—
107C22×#67C2×C414yescomplemented
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4—41no—
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×#217—41no—
138C2×#217—41no—
139C2×#217C2×C414yes—
140C2×#217C2×C414yescomplemented
141C2×#217D414yescomplemented
142C2×(C2×D3)⋊C4—22no—
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—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4C2×C414yescomplemented
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—41no—
160C2×C4×Dic3—22no—
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3—41no—
164C2×C4×Dic3—41no—
165C2×C4×Dic3—41no—
166C3×#95—22no—
167C3×#95D414yescomplemented
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C3⋊#95—41no—
174C3⋊#95—41no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95C2×C414yescomplemented
180C23×D4—31no—
181C23×D4—31no—
182C23×D4C2×D311yescharacteristic
183C24×C4C2×D311yescharacteristic
184C22×C4⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊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⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C42—31no—
200C22×C42—31no—
201#392—38no—
202#390—64no—
203#388—64no—
204#386—24no—
205#386—64no—
206C2×#95—31no—
207C2×#95—31no—
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×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
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×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×C3C22×C412yes—
247C24×C3C22×C412yes—
248C24×C3C2×D412yes—
249C24×C3#4112yes—
250C24×C3C2411yescharacteristic
251C23×D3—21no—
252C23×D3—21no—
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×D3C22×C412yes—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
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×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—44no—
303C22×C3×C4—44no—
304C22×C3×C4—44no—
305C22×C3×C4—44no—
306C22×C3×C4—44no—
307C22×C3×C4—44no—
308C22×C3×C4—44no—
309C22×C3×C4C22×C412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4#4112yes—
314C22×C3×C4#4112yes—
315C2×#67—28no—
316C2×#67—44no—
317C2×#67—44no—
318C2×#67—44no—
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—
329C22×Dic3—21no—
330C22×Dic3—21no—
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×Dic3C22×C412yes—
373C22×Dic3C22×C412yes—
374C22×Dic3C22×C412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3#4112yes—
378C3×C22⋊C4—44no—
379C3×C22⋊C4—44no—
380C3×C22⋊C4—44no—
381#217—44no—
382#217—44no—
383#217—44no—
384#217—44no—
385#217—44no—
386#217—44no—
387(C2×D3)⋊C4—28no—
388(C2×D3)⋊C4—44no—
389(C2×D3)⋊C4—44no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392C4⋊Dic3—44no—
393C4×Dic3—44no—
394C4×Dic3—44no—
395C25—31no—
396C25C22×D311yescharacteristic
397C25C22×D311yescharacteristic
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4—34no—
403C22×D4—34no—
404C22×D4—41no—
405C22×D4—41no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4—121no—
409C22×D4—121no—
410C22×D4—121no—
411C22×D4—121no—
412C22×D4—121no—
413C22×D4—121no—
414C22×D4—121no—
415C22×D4—121no—
416C22×D4—121no—
417C22×D4—121no—
418C22×D4C4×D314yes—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—121no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—41no—
451C2×C22⋊C4—41no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—62no—
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—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C22⋊C4—121no—
473C2×C22⋊C4—121no—
474C2×C22⋊C4—121no—
475C2×C22⋊C4—121no—
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×C42—62no—
484C2×C42—62no—
485C2×C42—62no—
486C2×C42—121no—
487C2×C42—121no—
488C2×C42—121no—
489#95—22no—
490#95—34no—
491#95—62no—
492#95—62no—
493#95—62no—
494#95—121no—
495#95—121no—
496#95—121no—
497#95—121no—
498#95—121no—
499#95—121no—
500#95—121no—
501#95—121no—
502#95#6714yescomplemented
503C23×C3—22no—
504C23×C3—22no—
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—41no—
529C23×C3—41no—
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×C3C4×D414yes—
573C23×C3C23×C411yescharacteristic
574C23×C3C22×D411yescharacteristic
575C23×C3C22×D411yescharacteristic
576C23×C3C2×#4111yescharacteristic
577C23×C3C2×#4111yescharacteristic
578C23×C3C2×#4111yescharacteristic
579C23×C3C2×#4111yescharacteristic
580C23×C3H(5,𝔽2)11yescharacteristic
581C23×C3H(5,𝔽2)11yescharacteristic
582C23×C3H(5,𝔽2)11yescharacteristic
583C23×C3H(5,𝔽2)11yescharacteristic
584C23×C3H(5,𝔽2)11yescharacteristic
585C23×C3H(5,𝔽2)11yescharacteristic
586C23×C3H(5,𝔽2)11yescharacteristic
587C23×C3H(5,𝔽2)11yescharacteristic
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—41no—
596C22×D3—41no—
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—
623C3×D4—416no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
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—22no—
639C2×C3×C4—416no—
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×C4C4×D414yes—
660#67—416no—
661#67—416no—
662C2×Dic3—22no—
663C2×Dic3—22no—
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—22no—
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—
711C24—21no—
712C24—21no—
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—32no—
738C24—61no—
739C24—61no—
740C24—61no—
741C24—61no—
742C24—61no—
743C24—61no—
744C24—61no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24C2×C4×D312yes—
753C24C2×C4×D312yes—
754C24D3×D412yes—
755C24#23712yes—
756C24C23×D311yescharacteristic
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—68no—
765C2×D4—124no—
766C2×D4—124no—
767C2×D4—124no—
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—
778C22×C4—21no—
779C22×C4—21no—
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—32no—
808C22×C4—32no—
809C22×C4—32no—
810C22×C4—32no—
811C22×C4—32no—
812C22×C4—32no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—61no—
821C22×C4—61no—
822C22×C4—61no—
823C22×C4—61no—
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×C4C2×C4×D312yes—
864C22×C4#23512yes—
865C22×C4#23712yes—
866C22×C4C2×#6712yes—
867C22×C4C2×#6712yes—
868C22×C4C2×#6712yes—
869C4⋊C4—124no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—68no—
874C22⋊C4—124no—
875C22⋊C4—124no—
876C22⋊C4—124no—
877C22⋊C4—124no—
878C22⋊C4—124no—
879C22⋊C4—124no—
880C22⋊C4—124no—
881C22⋊C4—124no—
882C22⋊C4—124no—
883C22⋊C4—124no—
884C42—124no—
885C42—124no—
886C22×C3—24no—
887C22×C3—24no—
888C22×C3—24no—
889C22×C3—42no—
890C22×C3—42no—
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—81no—
909C22×C3—81no—
910C22×C3—81no—
911C22×C3—81no—
912C22×C3—81no—
913C22×C3—81no—
914C22×C3—81no—
915C22×C3—81no—
916C22×C3C2×C4×D411yescharacteristic
917C22×C3C2×C4×D411yescharacteristic
918C22×C3C4×#4111yescharacteristic
919C22×C3#51811yescharacteristic
920C22×C3#51811yescharacteristic
921C22×C3#51811yescharacteristic
922C22×C3#51811yescharacteristic
923C22×C3#53411yescharacteristic
924C22×C3#53511yescharacteristic
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×C3#54011yescharacteristic
934C22×C3#54011yescharacteristic
935C22×C3D4211yescharacteristic
936C22×C3#54611yescharacteristic
937C22×C3#54611yescharacteristic
938C22×C3#54611yescharacteristic
939C22×C3#54611yescharacteristic
940C22×C3#54611yescharacteristic
941C22×C3#55011yescharacteristic
942C22×C3#55111yescharacteristic
943C22×C3#55311yescharacteristic
944C22×C3#55311yescharacteristic
945C22×C3#55311yescharacteristic
946C22×C3#55511yescharacteristic
947C22×C3#56011yescharacteristic
948C22×C3#56011yescharacteristic
949C22×C3#56011yescharacteristic
950C22×C3H(3,𝔽4)11yescharacteristic
951C2×D3—42no—
952C2×D3—42no—
953C2×D3—42no—
954C2×D3—42no—
955C2×D3—42no—
956C2×D3—42no—
957C2×D3—42no—
958C2×D3—81no—
959C2×D3—81no—
960C2×D3—81no—
961C2×D3—81no—
962C2×D3—81no—
963C2×D3—81no—
964C2×D3—81no—
965C2×D3—81no—
966C3×C4—24no—
967C3×C4—42no—
968C3×C4—42no—
969C3×C4—42no—
970C3×C4—81no—
971Dic3—42no—
972Dic3—42no—
973Dic3—42no—
974Dic3—42no—
975Dic3—42no—
976Dic3—42no—
977Dic3—81no—
978C23—22no—
979C23—22no—
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—41no—
1004C23—41no—
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—62no—
1048C23—62no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—121no—
1055C23—121no—
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#67⋊C414yes—
1083C23C22×C4×D311yescharacteristic
1084C23C2×#23511yescharacteristic
1085C23C2×D3×D411yescharacteristic
1086C23C2×#23711yescharacteristic
1087C23C2×#23711yescharacteristic
1088C23#100411yescharacteristic
1089C23#100411yescharacteristic
1090C23#100411yescharacteristic
1091C23#100411yescharacteristic
1092C23#100411yescharacteristic
1093C23D3×#4111yescharacteristic
1094C23#100911yescharacteristic
1095C23#100911yescharacteristic
1096C23#100911yescharacteristic
1097C23C22×#6711yescharacteristic
1098D4—416no—
1099D4—1216no—
1100D4—1216no—
1101C2×C4—22no—
1102C2×C4—22no—
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—22no—
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—62no—
1137C2×C4—62no—
1138C2×C4—62no—
1139C2×C4—62no—
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—121no—
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×C4C4×#6714yes—
1186C2×C3—44no—
1187C2×C3—82no—
1188C2×C3#232111yescharacteristic
1189C2×C3#232811yescharacteristic
1190C2×C3#233311yescharacteristic
1191C2×C3#235811yescharacteristic
1192C2×C3#236311yescharacteristic
1193C2×C3#236411yescharacteristic
1194C2×C3#237511yescharacteristic
1195C2×C3#267011yescharacteristic
1196C2×C3#267311yescharacteristic
1197C2×C3#269911yescharacteristic
1198C2×C3#270311yescharacteristic
1199C2×C3#270311yescharacteristic
1200C2×C3#271411yescharacteristic
1201C2×C3#275311yescharacteristic
1202C2×C3#275611yescharacteristic
1203D3—82no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—42no—
1208C22—42no—
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—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—122no—
1235C22—122no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22—122no—
1240C22—122no—
1241C22—241no—
1242C22—241no—
1243C22—241no—
1244C22—241no—
1245C22—241no—
1246C22—241no—
1247C22—241no—
1248C22—241no—
1249C22C2×#67⋊C411yescharacteristic
1250C22#548611yescharacteristic
1251C22#549011yescharacteristic
1252C22#549511yescharacteristic
1253C22C4×#23711yescharacteristic
1254C22#554511yescharacteristic
1255C22#554511yescharacteristic
1256C22#554511yescharacteristic
1257C22#555811yescharacteristic
1258C22#556211yescharacteristic
1259C22#556211yescharacteristic
1260C22#556311yescharacteristic
1261C22#559111yescharacteristic
1262C22#559211yescharacteristic
1263C22#559311yescharacteristic
1264C22#559411yescharacteristic
1265C22#560111yescharacteristic
1266C22#561311yescharacteristic
1267C22#561711yescharacteristic
1268C22#561711yescharacteristic
1269C22#561811yescharacteristic
1270C22#561911yescharacteristic
1271C22#562011yescharacteristic
1272C22#562011yescharacteristic
1273C22#565311yescharacteristic
1274C22#565411yescharacteristic
1275C22#566311yescharacteristic
1276C22#566611yescharacteristic
1277C22C2×C4×#6711yescharacteristic
1278C22D4×#6711yescharacteristic
1279C22#580511yescharacteristic
1280C22#580611yescharacteristic
1281C22#580611yescharacteristic
1282C22#583011yescharacteristic
1283C22#583411yescharacteristic
1284C4—24no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—81no—
1289C4—122no—
1290C4—122no—
1291C4—122no—
1292C4—122no—
1293C4—122no—
1294C4—122no—
1295C4—241no—
1296C3#1452011yescharacteristic, complemented, Sylow
1297C2—44no—
1298C2—82no—
1299C2—242no—
1300C2#7466811yescharacteristic
1301C2#7467811yescharacteristic
1302C2#7481011yescharacteristic
1303C2#7481511yescharacteristic
1304C2#7484611yescharacteristic
1305C2#7484811yescharacteristic
1306C2#7487511yescharacteristic
1307C2#7488211yescharacteristic
1308C2#8209911yescharacteristic
1309C2#8232911yescharacteristic
1310C2#8234111yescharacteristic
1311C2#8259511yescharacteristic
1312C2#8269311yescharacteristic
1313C2#8269611yescharacteristic
1314C2#8290611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC2×#5223C2
hypercenterC2×#386D3
hypocenterC3#14520
LCSG ▷ C23×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×#5221C2semidirect
4. C2×#5213C2semidirect
5. C2×#4670C2semidirect
6. #72127C2semidirect
7. #71550C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71549C2semidirect
11. #71545C2semidirect
12. #71545C2semidirect
13. #69415C2semidirect
14. #69408C2semidirect
15. #69401C2semidirect
41. #5223C4semidirect
61. C2×#386D3semidirect
107. C22×#67C2×C4semidirect
140. C2×#217C2×C4semidirect
141. C2×#217D4semidirect
156. C2×(C2×D3)⋊C4C2×C4semidirect
167. C3×#95D4semidirect
179. C3⋊#95C2×C4semidirect
502. #95#67semidirect
1296. C3#14520semidirect

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×#52212
C2×#52132
C2×#46702
#721272
#715502
#715492
#715452
#694152
#694082
#694012
#145203