Finite Group Databasebeta

← #10733710

Subgroups — #10733710

Order 768.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×#5222C211yesmaximal, characteristic, complemented
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#5221C211yesmaximal, characteristic, complemented
5C2×#4982C211yesmaximal, characteristic, complemented
6C2×#4945C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#72131C211yesmaximal, characteristic, complemented
9#72131C211yesmaximal, characteristic, complemented
10#72127C211yesmaximal, characteristic, complemented
11#72127C211yesmaximal, characteristic, complemented
12#71564C211yesmaximal, characteristic, complemented
13#71549C211yesmaximal, characteristic, complemented
14#71547C211yesmaximal, characteristic, complemented
15#71546C211yesmaximal, characteristic, complemented
16#15319—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C2×C3×#121—24no—
22C2×C3×#121—24no—
23C2×C3×#121—24no—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43#5222—24no—
44#5222—24no—
45#5221—24no—
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
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4982—24no—
59#4945—24no—
60C22×#121D311yescharacteristic
61C2×#398—31no—
62C2×#394—31no—
63C2×#394—31no—
64C2×#390—31no—
65C2×#388—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1438—31no—
72#1436—31no—
73C22⋊#95—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C25×C3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—22no—
88C22×C3×D4—22no—
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—22no—
92C22×C3×D4—41no—
93C22×C3×D4—41no—
94C22×C3×D4—41no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4D414yes—
99C23×C3×C4—22no—
100C23×C3×C4—22no—
101C23×C3×C4—22no—
102C23×C3×C4—22no—
103C23×C3×C4—22no—
104C23×C3×C4—41no—
105C23×C3×C4—41no—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C3×#121—232no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4D414yes—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4D414yes—
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—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—41no—
148C2×#217—41no—
149C2×#217—41no—
150C2×#217—41no—
151C2×#217—41no—
152C2×#217—41no—
153C2×#217—41no—
154C2×#217—41no—
155C2×#217—41no—
156C2×#217—41no—
157C2×#217—41no—
158C2×#217—41no—
159C2×#217—41no—
160C2×#217—41no—
161C2×#217—41no—
162C2×#217—41no—
163C2×#217D414yescomplemented
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—41no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—41no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—22no—
175C2×C4×Dic3—41no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—41no—
186C3⋊#95—41no—
187C3⋊#95—41no—
188C23×D4C2×D311yescharacteristic
189C23×D4C2×D311yescharacteristic
190C23×D4C2×D311yescharacteristic
191C24×C4C2×D311yescharacteristic
192C2×#121—24no—
193C2×#121—24no—
194C2×#121—24no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4C2×D311yescharacteristic
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C42—31no—
214#398—64no—
215#394—64no—
216#394—64no—
217#390—64no—
218#388—64no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
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×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—21no—
270C24×C3—21no—
271C24×C3C2×D412yes—
272C24×C3C2×D412yes—
273C24×C3C2×D412yes—
274C24×C3C2×D412yes—
275C24×C3#4112yes—
276C24×C3C2411yescharacteristic
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—28no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4—44no—
286C2×C3×D4—44no—
287C2×C3×D4—44no—
288C2×C3×D4—44no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
291C2×C3×D4—44no—
292C2×C3×D4—44no—
293C2×C3×D4—44no—
294C2×C3×D4—44no—
295C2×C3×D4—44no—
296C2×C3×D4—44no—
297C2×C3×D4—44no—
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—28no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—44no—
320C22×C3×C4—44no—
321C22×C3×C4—44no—
322C22×C3×C4—44no—
323C22×C3×C4—44no—
324C22×C3×C4—44no—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4#4112yes—
332C22×C3×C4#4112yes—
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×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3#4112yes—
388C22×Dic3#4112yes—
389C3×C4⋊C4—28no—
390C3×C22⋊C4—28no—
391C3×C22⋊C4—28no—
392#217—28no—
393#217—44no—
394#217—44no—
395#217—44no—
396#217—44no—
397#217—44no—
398#217—44no—
399#217—44no—
400#217—44no—
401#217—44no—
402#217—44no—
403#217—44no—
404C4⋊Dic3—44no—
405Dic3⋊C4—44no—
406Dic3⋊C4—44no—
407C4×Dic3—44no—
408C25C22×D311yescharacteristic
409C25C22×D311yescharacteristic
410C25C22×D311yescharacteristic
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—41no—
426C22×D4—41no—
427C22×D4—41no—
428C22×D4—41no—
429C22×D4—41no—
430C22×D4—41no—
431C22×D4#6714yes—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—41no—
446C23×C4—41no—
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451#121—232no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—121no—
462C2×C4⋊C4—121no—
463C2×C4⋊C4#6714yes—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—34no—
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—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C22⋊C4—121no—
504C2×C22⋊C4—121no—
505C2×C22⋊C4#6714yes—
506C2×C42—62no—
507C2×C42—62no—
508C2×C42—121no—
509#95—62no—
510#95—62no—
511#95—62no—
512#95—62no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—121no—
519#95—121no—
520#95—121no—
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—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
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—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3—41no—
611C23×C3—41no—
612C23×C3—41no—
613C23×C3—41no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3—41no—
625C23×C3#12114yes—
626C23×C3C22×D411yescharacteristic
627C23×C3C22×D411yescharacteristic
628C23×C3C22×D411yescharacteristic
629C23×C3C22×D411yescharacteristic
630C23×C3C2×#4111yescharacteristic
631C23×C3C2×#4111yescharacteristic
632C23×C3C2×#4111yescharacteristic
633C23×C3C2×#4111yescharacteristic
634C23×C3C2×#4111yescharacteristic
635C23×C3H(5,𝔽2)11yescharacteristic
636C23×C3H(5,𝔽2)11yescharacteristic
637C23×C3H(5,𝔽2)11yescharacteristic
638C23×C3H(5,𝔽2)11yescharacteristic
639C23×C3H(5,𝔽2)11yescharacteristic
640C23×C32−1+411yescharacteristic
641C3×D4—416no—
642C3×D4—416no—
643C3×D4—416no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—416no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4#12014yes—
672C2×C3×C4#12414yes—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
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—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24D3×D412yes—
770C24#23712yes—
771C24C2×#6712yes—
772C24C2×#6712yes—
773C24C2×#6712yes—
774C24C23×D311yescharacteristic
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
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—28no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—32no—
818C22×C4—32no—
819C22×C4—32no—
820C22×C4—32no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
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×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4#23712yes—
880C22×C4#23712yes—
881C22×C4C2×#6712yes—
882C22×C4C2×#6712yes—
883C22×C4C2×#6712yes—
884C22×C4C2×#6712yes—
885C22×C4C2×#6712yes—
886C22×C4C2×#6712yes—
887C4⋊C4—28no—
888C4⋊C4—124no—
889C4⋊C4—124no—
890C4⋊C4—124no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—68no—
894C22⋊C4—124no—
895C22⋊C4—124no—
896C22⋊C4—124no—
897C22⋊C4—124no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C42—124no—
906C22×C3—24no—
907C22×C3—24no—
908C22×C3—24no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—42no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—81no—
936C22×C3—81no—
937C22×C3—81no—
938C22×C3—81no—
939C22×C3—81no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—81no—
943C22×C3—81no—
944C22×C3—81no—
945C22×C3—81no—
946C22×C3—81no—
947C22×C3—81no—
948C22×C3—81no—
949C22×C3—81no—
950C22×C3—81no—
951C22×C3C2×#12011yescharacteristic
952C22×C3C2×#12111yescharacteristic
953C22×C3#52511yescharacteristic
954C22×C3C2×#12411yescharacteristic
955C22×C3#52911yescharacteristic
956C22×C3#53211yescharacteristic
957C22×C3#53411yescharacteristic
958C22×C3#53411yescharacteristic
959C22×C3#53511yescharacteristic
960C22×C3#53711yescharacteristic
961C22×C3#53911yescharacteristic
962C22×C3#54011yescharacteristic
963C22×C3#54011yescharacteristic
964C22×C3#54011yescharacteristic
965C22×C3#54211yescharacteristic
966C22×C3D4211yescharacteristic
967C22×C3D4211yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54611yescharacteristic
972C22×C3#54611yescharacteristic
973C22×C3#54611yescharacteristic
974C22×C3#54611yescharacteristic
975C22×C3#54611yescharacteristic
976C22×C3#54711yescharacteristic
977C22×C3#54711yescharacteristic
978C22×C3#54811yescharacteristic
979C22×C3#55011yescharacteristic
980C22×C3#55311yescharacteristic
981C22×C3#55311yescharacteristic
982C22×C3#55311yescharacteristic
983C22×C3#55511yescharacteristic
984C22×C3#56011yescharacteristic
985C22×C3#56211yescharacteristic
986C3×C4—24no—
987C3×C4—24no—
988C3×C4—42no—
989C3×C4—42no—
990Dic3—42no—
991Dic3—42no—
992Dic3—42no—
993Dic3—42no—
994Dic3—81no—
995Dic3—81no—
996Dic3—81no—
997Dic3—81no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
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—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23#93914yes—
1103C23C2×D3×D411yescharacteristic
1104C23C2×#23711yescharacteristic
1105C23C2×#23711yescharacteristic
1106C23C2×#23711yescharacteristic
1107C23#100411yescharacteristic
1108C23#100411yescharacteristic
1109C23#100411yescharacteristic
1110C23#100411yescharacteristic
1111C23D3×#4111yescharacteristic
1112C23D3×#4111yescharacteristic
1113C23#100911yescharacteristic
1114C23#101011yescharacteristic
1115C23C22×#6711yescharacteristic
1116C23C22×#6711yescharacteristic
1117C23C22×#6711yescharacteristic
1118D4—416no—
1119D4—416no—
1120D4—416no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—416no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—62no—
1152C2×C4—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
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×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4#93614yes—
1205C2×C4#95314yes—
1206C2×C3—44no—
1207C2×C3—82no—
1208C2×C3—82no—
1209C2×C3#240711yescharacteristic
1210C2×C3#241011yescharacteristic
1211C2×C3#242511yescharacteristic
1212C2×C3#243511yescharacteristic
1213C2×C3#246411yescharacteristic
1214C2×C3#247611yescharacteristic
1215C2×C3#249011yescharacteristic
1216C2×C3#249111yescharacteristic
1217C2×C3#254311yescharacteristic
1218C2×C3#267111yescharacteristic
1219C2×C3#267311yescharacteristic
1220C2×C3#269111yescharacteristic
1221C2×C3#269911yescharacteristic
1222C2×C3#270111yescharacteristic
1223C2×C3#271111yescharacteristic
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22#559611yescharacteristic
1270C22#560011yescharacteristic
1271C22#560111yescharacteristic
1272C22#560211yescharacteristic
1273C22#560311yescharacteristic
1274C22#560511yescharacteristic
1275C22#561011yescharacteristic
1276C22#561111yescharacteristic
1277C22#561411yescharacteristic
1278C22#561511yescharacteristic
1279C22#561511yescharacteristic
1280C22#561611yescharacteristic
1281C22#561811yescharacteristic
1282C22#561911yescharacteristic
1283C22#562011yescharacteristic
1284C22#562111yescharacteristic
1285C22C2×#93611yescharacteristic
1286C22D4×#6711yescharacteristic
1287C22D4×#6711yescharacteristic
1288C22C2×#93911yescharacteristic
1289C22#580411yescharacteristic
1290C22#580511yescharacteristic
1291C22#580611yescharacteristic
1292C22#580611yescharacteristic
1293C22#580611yescharacteristic
1294C22#580611yescharacteristic
1295C22#580611yescharacteristic
1296C22#580611yescharacteristic
1297C22#582411yescharacteristic
1298C22#582811yescharacteristic
1299C22#582911yescharacteristic
1300C22#583111yescharacteristic
1301C22#583311yescharacteristic
1302C22#583411yescharacteristic
1303C22C2×#95311yescharacteristic
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—42no—
1308C4—122no—
1309C4—122no—
1310C4—122no—
1311C4—122no—
1312C4—241no—
1313C4—241no—
1314C4—241no—
1315C4—241no—
1316C3#1531911yescharacteristic, complemented, Sylow
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2#8264511yescharacteristic
1321C2#8265811yescharacteristic
1322C2#8266011yescharacteristic
1323C2#8266111yescharacteristic
1324C2#8266211yescharacteristic
1325C2#8267011yescharacteristic
1326C2#8269011yescharacteristic
1327C2#8269111yescharacteristic
1328C2#8269211yescharacteristic
1329C2#8269511yescharacteristic
1330C2#8271611yescharacteristic
1331C2#8271711yescharacteristic
1332C2#8404811yescharacteristic
1333C2#8405011yescharacteristic
1334C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#15319
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C2×#5222C2semidirect
3. C2×#5222C2semidirect
4. C2×#5221C2semidirect
5. C2×#4982C2semidirect
6. C2×#4945C2semidirect
7. #72131C2semidirect
8. #72131C2semidirect
9. #72131C2semidirect
10. #72127C2semidirect
11. #72127C2semidirect
12. #71564C2semidirect
13. #71549C2semidirect
14. #71547C2semidirect
15. #71546C2semidirect
163. C2×#217D4semidirect
1316. C3#15319semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×#52222
C2×#52212
C2×#49822
C2×#49452
#721312
#721272
#715642
#715492
#715472
#715462
#153193