Finite Group Databasebeta

← #10733073

Subgroups — #10733073

Order 768.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1362 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×#5220C211yesmaximal, characteristic, complemented
6C2×#5220C211yesmaximal, characteristic, complemented
7C2×#5210C211yesmaximal, characteristic, complemented
8C2×#4942C211yesmaximal, characteristic, complemented
9#72131C211yesmaximal, characteristic, complemented
10#72127C211yesmaximal, characteristic, complemented
11#71568C211yesmaximal, characteristic, complemented
12#71566C211yesmaximal, characteristic, complemented
13#71548C211yesmaximal, characteristic, complemented
14#71547C211yesmaximal, characteristic, complemented
15#71547C211yesmaximal, characteristic, complemented
16#15274—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C2×C3×#121—24no—
23C2×C3×#121—24no—
24C2×C3×#121—24no—
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43#5222—24no—
44#5222—24no—
45#5222—24no—
46#5220—24no—
47#5220—24no—
48#5210—24no—
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
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4942—24no—
62C22×#121D311yescharacteristic
63C2×#394—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#386—31no—
67C2×#386—31no—
68C2×#385—31no—
69C2×#380—31no—
70#1444—31no—
71#1441—31no—
72#1440—31no—
73#1439—31no—
74#1439—31no—
75#1438—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—41no—
94C22×C3×D4—41no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4D414yes—
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×Dic3—22no—
113C23×Dic3—22no—
114C23×Dic3—22no—
115C23×Dic3—22no—
116C23×Dic3—22no—
117C23×Dic3—41no—
118C23×Dic3—41no—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C3×#121—232no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4D414yes—
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—22no—
156C2×#217—22no—
157C2×#217—22no—
158C2×#217—22no—
159C2×#217—22no—
160C2×#217—22no—
161C2×#217—41no—
162C2×#217—41no—
163C2×#217—41no—
164C2×#217—41no—
165C2×#217—41no—
166C2×#217—41no—
167C2×#217—41no—
168C2×#217—41no—
169C2×#217D414yescomplemented
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⋊C4—41no—
181C2×Dic3⋊C4—41no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—41no—
192C3⋊#95—41no—
193C3⋊#95D414yescomplemented
194C23×D4C2×D311yescharacteristic
195C23×D4C2×D311yescharacteristic
196C23×D4C2×D311yescharacteristic
197C24×C4—31no—
198C24×C4C2×D311yescharacteristic
199C2×#121—24no—
200C2×#121—24no—
201C2×#121—24no—
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⋊C4C2×D311yescharacteristic
219C22×C22⋊C4C2×D311yescharacteristic
220#394—64no—
221#394—64no—
222#394—64no—
223#386—64no—
224#386—64no—
225#385—64no—
226#380—64no—
227C2×#95—31no—
228C2×#95—31no—
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×C3C2×D412yes—
278C24×C3C2×D412yes—
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—28no—
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—28no—
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—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—21no—
328C22×C3×C4—21no—
329C22×C3×C4—44no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4—44no—
334C22×C3×C4—44no—
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—28no—
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×Dic3—21no—
392C22×Dic3—44no—
393C22×Dic3—44no—
394C22×Dic3—44no—
395C22×Dic3—44no—
396C22×Dic3—44no—
397C22×Dic3—44no—
398C22×Dic3C2×D412yes—
399C22×Dic3C2×D412yes—
400C22×Dic3C2×D412yes—
401C22×Dic3C2×D412yes—
402C22×Dic3#4112yes—
403C22×Dic3#4112yes—
404C3×C4⋊C4—28no—
405C3×C22⋊C4—28no—
406C3×C22⋊C4—28no—
407#217—28no—
408#217—44no—
409#217—44no—
410#217—44no—
411#217—44no—
412#217—44no—
413#217—44no—
414#217—44no—
415#217—44no—
416#217—44no—
417#217—44no—
418Dic3⋊C4—44no—
419Dic3⋊C4—44no—
420Dic3⋊C4—44no—
421Dic3⋊C4—44no—
422C25C22×D311yescharacteristic
423C25C22×D311yescharacteristic
424C25C22×D311yescharacteristic
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—22no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—41no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4—41no—
442C22×D4—41no—
443C22×D4—41no—
444C22×D4#6714yes—
445C22×D4#6714yes—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—31no—
456C23×C4—31no—
457C23×C4—31no—
458C23×C4—31no—
459C23×C4—41no—
460C23×C4—41no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—62no—
464C23×C4—62no—
465C23×C4—62no—
466C23×C4—121no—
467C23×C4—121no—
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472#121—232no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—121no—
485C2×C4⋊C4—121no—
486C2×C4⋊C4—121no—
487C2×C4⋊C4—121no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—34no—
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—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—62no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C22⋊C4—121no—
525C2×C22⋊C4—121no—
526C2×C22⋊C4#6714yes—
527#95—34no—
528#95—62no—
529#95—62no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—121no—
538#95—121no—
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—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
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—41no—
640C23×C3—41no—
641C23×C3—41no—
642C23×C3#12014yes—
643C23×C3#12114yes—
644C23×C3C22×D411yescharacteristic
645C23×C3C22×D411yescharacteristic
646C23×C3C22×D411yescharacteristic
647C23×C3C22×D411yescharacteristic
648C23×C3C22×D411yescharacteristic
649C23×C3C2×#4111yescharacteristic
650C23×C3C2×#4111yescharacteristic
651C23×C3C2×#4111yescharacteristic
652C23×C3C2×#4111yescharacteristic
653C23×C3H(5,𝔽2)11yescharacteristic
654C23×C3H(5,𝔽2)11yescharacteristic
655C23×C3H(5,𝔽2)11yescharacteristic
656C23×C3H(5,𝔽2)11yescharacteristic
657C23×C32−1+411yescharacteristic
658C23×C32−1+411yescharacteristic
659C3×D4—416no—
660C3×D4—416no—
661C3×D4—416no—
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—22no—
677C2×C3×C4—416no—
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—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4#12114yes—
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—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—416no—
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—41no—
743C2×Dic3—41no—
744C2×Dic3—41no—
745C2×Dic3—41no—
746C2×Dic3—41no—
747C2×Dic3#12114yescomplemented
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—
783C24—21no—
784C24—21no—
785C24—21no—
786C24D3×D412yes—
787C24#23712yes—
788C24C2×#6712yes—
789C24C2×#6712yes—
790C24C2×#6712yes—
791C24C2×#6712yes—
792C24C2×#6712yes—
793C24C23×D311yescharacteristic
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
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—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—28no—
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—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—32no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—32no—
843C22×C4—32no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—68no—
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×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4D3×D412yes—
908C22×C4#23712yes—
909C22×C4C2×#6712yes—
910C22×C4C2×#6712yes—
911C22×C4C2×#6712yes—
912C22×C4C2×#6712yes—
913C4⋊C4—28no—
914C4⋊C4—124no—
915C4⋊C4—124no—
916C4⋊C4—124no—
917C4⋊C4—124no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—68no—
921C22⋊C4—124no—
922C22⋊C4—124no—
923C22⋊C4—124no—
924C22⋊C4—124no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22×C3—24no—
932C22×C3—24no—
933C22×C3—24no—
934C22×C3—24no—
935C22×C3—24no—
936C22×C3—24no—
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—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3—42no—
959C22×C3—42no—
960C22×C3—42no—
961C22×C3—42no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—42no—
966C22×C3—42no—
967C22×C3—42no—
968C22×C3—81no—
969C22×C3—81no—
970C22×C3—81no—
971C22×C3—81no—
972C22×C3—81no—
973C22×C3—81no—
974C22×C3—81no—
975C22×C3—81no—
976C22×C3C2×#12011yescharacteristic
977C22×C3C2×#12111yescharacteristic
978C22×C3C2×#12111yescharacteristic
979C22×C3C2×#12111yescharacteristic
980C22×C3#52511yescharacteristic
981C22×C3#52911yescharacteristic
982C22×C3#53411yescharacteristic
983C22×C3#53411yescharacteristic
984C22×C3#53611yescharacteristic
985C22×C3#53711yescharacteristic
986C22×C3#53711yescharacteristic
987C22×C3#53811yescharacteristic
988C22×C3#53911yescharacteristic
989C22×C3#54011yescharacteristic
990C22×C3#54211yescharacteristic
991C22×C3D4211yescharacteristic
992C22×C3D4211yescharacteristic
993C22×C3D4211yescharacteristic
994C22×C3D4211yescharacteristic
995C22×C3#54611yescharacteristic
996C22×C3#54611yescharacteristic
997C22×C3#54611yescharacteristic
998C22×C3#54611yescharacteristic
999C22×C3#54611yescharacteristic
1000C22×C3#54611yescharacteristic
1001C22×C3#54711yescharacteristic
1002C22×C3#54711yescharacteristic
1003C22×C3#54711yescharacteristic
1004C22×C3#54711yescharacteristic
1005C22×C3#54711yescharacteristic
1006C22×C3#54811yescharacteristic
1007C22×C3#55311yescharacteristic
1008C22×C3#55511yescharacteristic
1009C22×C3#56211yescharacteristic
1010C22×C3#56211yescharacteristic
1011C3×C4—24no—
1012C3×C4—42no—
1013C3×C4—42no—
1014C3×C4—42no—
1015Dic3—24no—
1016Dic3—42no—
1017Dic3—42no—
1018Dic3—42no—
1019Dic3—81no—
1020Dic3—81no—
1021Dic3—81no—
1022Dic3—81no—
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—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
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—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23#93914yes—
1127C23#95314yes—
1128C23C2×D3×D411yescharacteristic
1129C23C2×D3×D411yescharacteristic
1130C23C2×#23711yescharacteristic
1131C23C2×#23711yescharacteristic
1132C23#100411yescharacteristic
1133C23#100411yescharacteristic
1134C23#100411yescharacteristic
1135C23#100411yescharacteristic
1136C23D3×#4111yescharacteristic
1137C23D3×#4111yescharacteristic
1138C23#101011yescharacteristic
1139C23#101011yescharacteristic
1140C23C22×#6711yescharacteristic
1141C23C22×#6711yescharacteristic
1142C23C22×#6711yescharacteristic
1143D4—416no—
1144D4—416no—
1145D4—416no—
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—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—34no—
1162C2×C4—416no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—1216no—
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—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4#93914yes—
1232C2×C3—44no—
1233C2×C3—44no—
1234C2×C3—82no—
1235C2×C3#240611yescharacteristic
1236C2×C3#241011yescharacteristic
1237C2×C3#241011yescharacteristic
1238C2×C3#241611yescharacteristic
1239C2×C3#242411yescharacteristic
1240C2×C3#242511yescharacteristic
1241C2×C3#242711yescharacteristic
1242C2×C3#247611yescharacteristic
1243C2×C3#253711yescharacteristic
1244C2×C3#267111yescharacteristic
1245C2×C3#267111yescharacteristic
1246C2×C3#267211yescharacteristic
1247C2×C3#268111yescharacteristic
1248C2×C3#268611yescharacteristic
1249C2×C3#270811yescharacteristic
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
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—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22#559711yescharacteristic
1296C22#559811yescharacteristic
1297C22#560011yescharacteristic
1298C22#560111yescharacteristic
1299C22#560211yescharacteristic
1300C22#560311yescharacteristic
1301C22D3×#12111yescharacteristic
1302C22#560811yescharacteristic
1303C22#561011yescharacteristic
1304C22#561111yescharacteristic
1305C22#561211yescharacteristic
1306C22#561311yescharacteristic
1307C22#561511yescharacteristic
1308C22#561611yescharacteristic
1309C22#562111yescharacteristic
1310C22#562111yescharacteristic
1311C22D4×#6711yescharacteristic
1312C22D4×#6711yescharacteristic
1313C22D4×#6711yescharacteristic
1314C22D4×#6711yescharacteristic
1315C22C2×#93911yescharacteristic
1316C22C2×#93911yescharacteristic
1317C22#580411yescharacteristic
1318C22#580411yescharacteristic
1319C22#580611yescharacteristic
1320C22#580611yescharacteristic
1321C22#580611yescharacteristic
1322C22#580611yescharacteristic
1323C22#582411yescharacteristic
1324C22#582411yescharacteristic
1325C22#582411yescharacteristic
1326C22#582411yescharacteristic
1327C22#582511yescharacteristic
1328C22#582811yescharacteristic
1329C22C2×#95311yescharacteristic
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—64no—
1335C4—122no—
1336C4—122no—
1337C4—122no—
1338C4—241no—
1339C4—241no—
1340C4—241no—
1341C4—241no—
1342C3#1527411yescharacteristic, complemented, Sylow
1343C2—44no—
1344C2—44no—
1345C2—82no—
1346C2#8264211yescharacteristic
1347C2#8264511yescharacteristic
1348C2#8264711yescharacteristic
1349C2#8266011yescharacteristic
1350C2#8266711yescharacteristic
1351C2#8268111yescharacteristic
1352C2#8268211yescharacteristic
1353C2#8268511yescharacteristic
1354C2#8268711yescharacteristic
1355C2#8269411yescharacteristic
1356C2#8270711yescharacteristic
1357C2#8271511yescharacteristic
1358C2#8404811yescharacteristic
1359C2#8404811yescharacteristic
1360C2#8409011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
Fitting, prime radicalC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#15274
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×#5220C2semidirect
6. C2×#5220C2semidirect
7. C2×#5210C2semidirect
8. C2×#4942C2semidirect
9. #72131C2semidirect
10. #72127C2semidirect
11. #71568C2semidirect
12. #71566C2semidirect
13. #71548C2semidirect
14. #71547C2semidirect
15. #71547C2semidirect
169. C2×#217D4semidirect
193. C3⋊#95D4semidirect
747. C2×Dic3#121semidirect
1342. C3#15274semidirect

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×#52202
C2×#52102
C2×#49422
#721312
#721272
#715682
#715662
#715482
#715472
#152743