Finite Group Databasebeta

← #10733665

Subgroups — #10733665

Order 768.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 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×#5222C211yesmaximal, characteristic, complemented
5C2×#5221C211yesmaximal, characteristic, complemented
6C2×#5210C211yesmaximal, characteristic, complemented
7C2×#4976C211yesmaximal, characteristic, complemented
8C2×#4948C211yesmaximal, characteristic, complemented
9#72131C211yesmaximal, characteristic, complemented
10#72131C211yesmaximal, characteristic, complemented
11#72127C211yesmaximal, characteristic, complemented
12#71565C211yesmaximal, characteristic, complemented
13#71547C211yesmaximal, characteristic, complemented
14#71547C211yesmaximal, characteristic, complemented
15#71545C211yesmaximal, characteristic, complemented
16#15316—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×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45#5222—24no—
46#5222—24no—
47#5222—24no—
48#5221—24no—
49#5210—24no—
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60#4976—24no—
61#4948—24no—
62C22×#121D311yescharacteristic
63C2×#396—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#394—31no—
67C2×#390—31no—
68C2×#389—31no—
69C2×#385—31no—
70#1441—31no—
71#1439—31no—
72#1439—31no—
73#1438—31no—
74#1438—31no—
75#1437—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C25×C3C2311yescharacteristic
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—22no—
93C22×C3×D4—22no—
94C22×C3×D4—41no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4—41no—
100C22×C3×D4D414yes—
101C23×C3×C4—22no—
102C23×C3×C4—22no—
103C23×C3×C4—22no—
104C23×C3×C4—22no—
105C23×C3×C4—22no—
106C23×C3×C4—41no—
107C23×C3×C4—41no—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C3×#121—232no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4D414yes—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4D414yes—
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—22no—
148C2×#217—22no—
149C2×#217—22no—
150C2×#217—22no—
151C2×#217—22no—
152C2×#217—22no—
153C2×#217—22no—
154C2×#217—22no—
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×#217—41no—
164C2×#217—41no—
165C2×#217D414yescomplemented
166C2×C4⋊Dic3—22no—
167C2×C4⋊Dic3—22no—
168C2×C4⋊Dic3—41no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—41no—
179C2×Dic3⋊C4—41no—
180C2×Dic3⋊C4D414yescomplemented
181C2×C4×Dic3—22no—
182C2×C4×Dic3—22no—
183C2×C4×Dic3—41no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C23×D4C2×D311yescharacteristic
195C23×D4C2×D311yescharacteristic
196C23×D4C2×D311yescharacteristic
197C24×C4C2×D311yescharacteristic
198C2×#121—24no—
199C2×#121—24no—
200C2×#121—24no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4—31no—
206C22×C4⋊C4C2×D311yescharacteristic
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4C2×D311yescharacteristic
220C22×C22⋊C4C2×D311yescharacteristic
221C22×C42—31no—
222#396—64no—
223#394—64no—
224#394—64no—
225#394—64no—
226#390—64no—
227#389—64no—
228#385—64no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95—31no—
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×C3—21no—
272C24×C3—21no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3—21no—
276C24×C3—21no—
277C24×C3—21no—
278C24×C3—21no—
279C24×C3C2×D412yes—
280C24×C3C2×D412yes—
281C24×C3C2×D412yes—
282C24×C3C2×D412yes—
283C24×C3#4112yes—
284C24×C3C2411yescharacteristic
285C2×C3×D4—28no—
286C2×C3×D4—28no—
287C2×C3×D4—28no—
288C2×C3×D4—28no—
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—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—44no—
303C2×C3×D4—44no—
304C2×C3×D4—44no—
305C2×C3×D4—44no—
306C22×C3×C4—21no—
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—28no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—44no—
328C22×C3×C4—44no—
329C22×C3×C4—44no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4C2×D412yes—
337C22×C3×C4C2×D412yes—
338C22×C3×C4C2×D412yes—
339C22×C3×C4C2×D412yes—
340C22×C3×C4#4112yes—
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×Dic3—21no—
386C22×Dic3—21no—
387C22×Dic3—21no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3—21no—
391C22×Dic3C2×D412yes—
392C22×Dic3C2×D412yes—
393C22×Dic3C2×D412yes—
394C22×Dic3C2×D412yes—
395C22×Dic3#4112yes—
396C22×Dic3#4112yes—
397C3×C4⋊C4—28no—
398C3×C22⋊C4—28no—
399C3×C22⋊C4—28no—
400#217—28no—
401#217—44no—
402#217—44no—
403#217—44no—
404#217—44no—
405#217—44no—
406#217—44no—
407#217—44no—
408#217—44no—
409#217—44no—
410#217—44no—
411#217—44no—
412C4⋊Dic3—44no—
413Dic3⋊C4—28no—
414Dic3⋊C4—44no—
415Dic3⋊C4—44no—
416Dic3⋊C4—44no—
417C4×Dic3—44no—
418C25C22×D311yescharacteristic
419C25C22×D311yescharacteristic
420C25C22×D311yescharacteristic
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—22no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—41no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4#6714yes—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—41no—
456C23×C4—41no—
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461#121—232no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—34no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—62no—
470C2×C4⋊C4—62no—
471C2×C4⋊C4—62no—
472C2×C4⋊C4—62no—
473C2×C4⋊C4—62no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—121no—
477C2×C4⋊C4—121no—
478C2×C4⋊C4—121no—
479C2×C4⋊C4#6714yes—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—34no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—121no—
512C2×C22⋊C4—121no—
513C2×C22⋊C4—121no—
514C2×C22⋊C4—121no—
515C2×C22⋊C4—121no—
516C2×C22⋊C4—121no—
517C2×C22⋊C4—121no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4#6714yes—
522C2×C42—62no—
523C2×C42—62no—
524C2×C42—121no—
525#95—62no—
526#95—62no—
527#95—62no—
528#95—62no—
529#95—62no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—121no—
534#95—121no—
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—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
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—41no—
626C23×C3—41no—
627C23×C3—41no—
628C23×C3—41no—
629C23×C3—41no—
630C23×C3—41no—
631C23×C3—41no—
632C23×C3—41no—
633C23×C3—41no—
634C23×C3—41no—
635C23×C3—41no—
636C23×C3—41no—
637C23×C3—41no—
638C23×C3—41no—
639C23×C3#12114yes—
640C23×C3C22×D411yescharacteristic
641C23×C3C22×D411yescharacteristic
642C23×C3C22×D411yescharacteristic
643C23×C3C22×D411yescharacteristic
644C23×C3C22×D411yescharacteristic
645C23×C3C2×#4111yescharacteristic
646C23×C3C2×#4111yescharacteristic
647C23×C3C2×#4111yescharacteristic
648C23×C3C2×#4111yescharacteristic
649C23×C3H(5,𝔽2)11yescharacteristic
650C23×C3H(5,𝔽2)11yescharacteristic
651C23×C3H(5,𝔽2)11yescharacteristic
652C23×C3H(5,𝔽2)11yescharacteristic
653C23×C32−1+411yescharacteristic
654C23×C32−1+411yescharacteristic
655C3×D4—416no—
656C3×D4—416no—
657C3×D4—416no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—416no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4#12014yes—
686C2×C3×C4#12114yes—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
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—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3—41no—
742C2×Dic3#12114yescomplemented
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—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24D3×D412yes—
784C24#23712yes—
785C24C2×#6712yes—
786C24C2×#6712yes—
787C24C2×#6712yes—
788C24C23×D311yescharacteristic
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—32no—
832C22×C4—32no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—32no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
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—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4D3×D412yes—
894C22×C4#23712yes—
895C22×C4C2×#6712yes—
896C22×C4C2×#6712yes—
897C22×C4C2×#6712yes—
898C22×C4C2×#6712yes—
899C22×C4C2×#6712yes—
900C22×C4C2×#6712yes—
901C4⋊C4—28no—
902C4⋊C4—68no—
903C4⋊C4—124no—
904C4⋊C4—124no—
905C4⋊C4—124no—
906C4⋊C4—124no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—68no—
910C22⋊C4—124no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22⋊C4—124no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C22⋊C4—124no—
920C22⋊C4—124no—
921C42—124no—
922C22×C3—24no—
923C22×C3—24no—
924C22×C3—24no—
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—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—42no—
949C22×C3—42no—
950C22×C3—42no—
951C22×C3—81no—
952C22×C3—81no—
953C22×C3—81no—
954C22×C3—81no—
955C22×C3—81no—
956C22×C3—81no—
957C22×C3—81no—
958C22×C3—81no—
959C22×C3—81no—
960C22×C3—81no—
961C22×C3—81no—
962C22×C3—81no—
963C22×C3—81no—
964C22×C3—81no—
965C22×C3—81no—
966C22×C3—81no—
967C22×C3C2×#12011yescharacteristic
968C22×C3C2×#12111yescharacteristic
969C22×C3C2×#12111yescharacteristic
970C22×C3C2×#12111yescharacteristic
971C22×C3#52911yescharacteristic
972C22×C3#53211yescharacteristic
973C22×C3#53411yescharacteristic
974C22×C3#53511yescharacteristic
975C22×C3#53611yescharacteristic
976C22×C3#53711yescharacteristic
977C22×C3#53711yescharacteristic
978C22×C3#53811yescharacteristic
979C22×C3#53911yescharacteristic
980C22×C3#54011yescharacteristic
981C22×C3#54211yescharacteristic
982C22×C3D4211yescharacteristic
983C22×C3D4211yescharacteristic
984C22×C3D4211yescharacteristic
985C22×C3D4211yescharacteristic
986C22×C3#54611yescharacteristic
987C22×C3#54611yescharacteristic
988C22×C3#54611yescharacteristic
989C22×C3#54611yescharacteristic
990C22×C3#54611yescharacteristic
991C22×C3#54711yescharacteristic
992C22×C3#54711yescharacteristic
993C22×C3#54711yescharacteristic
994C22×C3#54811yescharacteristic
995C22×C3#54811yescharacteristic
996C22×C3#54811yescharacteristic
997C22×C3#55011yescharacteristic
998C22×C3#55311yescharacteristic
999C22×C3#55311yescharacteristic
1000C22×C3#56211yescharacteristic
1001C22×C3#56211yescharacteristic
1002C3×C4—24no—
1003C3×C4—24no—
1004C3×C4—42no—
1005C3×C4—42no—
1006Dic3—24no—
1007Dic3—42no—
1008Dic3—42no—
1009Dic3—42no—
1010Dic3—81no—
1011Dic3—81no—
1012Dic3—81no—
1013Dic3—81no—
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—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
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—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23#93914yes—
1119C23C2×D3×D411yescharacteristic
1120C23C2×D3×D411yescharacteristic
1121C23C2×#23711yescharacteristic
1122C23C2×#23711yescharacteristic
1123C23#100411yescharacteristic
1124C23#100411yescharacteristic
1125C23#100411yescharacteristic
1126C23#100411yescharacteristic
1127C23D3×#4111yescharacteristic
1128C23D3×#4111yescharacteristic
1129C23#101011yescharacteristic
1130C23#101011yescharacteristic
1131C23C22×#6711yescharacteristic
1132C23C22×#6711yescharacteristic
1133C23C22×#6711yescharacteristic
1134D4—416no—
1135D4—416no—
1136D4—416no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—34no—
1156C2×C4—416no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
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—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4#93814yes—
1221C2×C4#95314yes—
1222C2×C3—44no—
1223C2×C3—82no—
1224C2×C3—82no—
1225C2×C3#240811yescharacteristic
1226C2×C3#241011yescharacteristic
1227C2×C3#241611yescharacteristic
1228C2×C3#241611yescharacteristic
1229C2×C3#242511yescharacteristic
1230C2×C3#242611yescharacteristic
1231C2×C3#242811yescharacteristic
1232C2×C3#243211yescharacteristic
1233C2×C3#255911yescharacteristic
1234C2×C3#267211yescharacteristic
1235C2×C3#267611yescharacteristic
1236C2×C3#268111yescharacteristic
1237C2×C3#268211yescharacteristic
1238C2×C3#270111yescharacteristic
1239C2×C3#271111yescharacteristic
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22#559711yescharacteristic
1286C22#559811yescharacteristic
1287C22#559911yescharacteristic
1288C22#560011yescharacteristic
1289C22#560111yescharacteristic
1290C22#560211yescharacteristic
1291C22#560311yescharacteristic
1292C22D3×#12111yescharacteristic
1293C22#560811yescharacteristic
1294C22#561011yescharacteristic
1295C22#561111yescharacteristic
1296C22#561311yescharacteristic
1297C22#561411yescharacteristic
1298C22#561511yescharacteristic
1299C22#562111yescharacteristic
1300C22#562111yescharacteristic
1301C22C2×#93811yescharacteristic
1302C22D4×#6711yescharacteristic
1303C22D4×#6711yescharacteristic
1304C22D4×#6711yescharacteristic
1305C22D4×#6711yescharacteristic
1306C22C2×#93911yescharacteristic
1307C22#580411yescharacteristic
1308C22#580511yescharacteristic
1309C22#580611yescharacteristic
1310C22#580611yescharacteristic
1311C22#580611yescharacteristic
1312C22#580611yescharacteristic
1313C22#582411yescharacteristic
1314C22#582411yescharacteristic
1315C22#582511yescharacteristic
1316C22#583111yescharacteristic
1317C22#583111yescharacteristic
1318C22#583211yescharacteristic
1319C22C2×#95311yescharacteristic
1320C4—24no—
1321C4—24no—
1322C4—42no—
1323C4—42no—
1324C4—64no—
1325C4—122no—
1326C4—122no—
1327C4—122no—
1328C4—241no—
1329C4—241no—
1330C4—241no—
1331C4—241no—
1332C3#1531611yescharacteristic, complemented, Sylow
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2#8264111yescharacteristic
1337C2#8264211yescharacteristic
1338C2#8264511yescharacteristic
1339C2#8264611yescharacteristic
1340C2#8265011yescharacteristic
1341C2#8267311yescharacteristic
1342C2#8268211yescharacteristic
1343C2#8268511yescharacteristic
1344C2#8268611yescharacteristic
1345C2#8269211yescharacteristic
1346C2#8269511yescharacteristic
1347C2#8271911yescharacteristic
1348C2#8404811yescharacteristic
1349C2#8405311yescharacteristic
1350C2#8409311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#15316
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×#5222C2semidirect
5. C2×#5221C2semidirect
6. C2×#5210C2semidirect
7. C2×#4976C2semidirect
8. C2×#4948C2semidirect
9. #72131C2semidirect
10. #72131C2semidirect
11. #72127C2semidirect
12. #71565C2semidirect
13. #71547C2semidirect
14. #71547C2semidirect
15. #71545C2semidirect
165. C2×#217D4semidirect
180. C2×Dic3⋊C4D4semidirect
742. C2×Dic3#121semidirect
1332. C3#15316semidirect

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×#52102
C2×#49762
C2×#49482
#721312
#721272
#715652
#715472
#715452
#153163