Finite Group Databasebeta

← #10726611

Subgroups — #10726611

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×C4×#67C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#4989C211yesmaximal, characteristic, complemented
6C2×#4956C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10#71564C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic, complemented
12#71550C211yesmaximal, characteristic, complemented
13#71549C211yesmaximal, characteristic, complemented
14#71547C211yesmaximal, characteristic, complemented
15#71545C211yesmaximal, characteristic, complemented
16#14721—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C2×C3×#123—24no—
23C2×C3×#123—24no—
24C2×C3×#123—24no—
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C2×C4×#67—24no—
37C2×C4×#67—24no—
38C2×C4×#67—24no—
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×C4×Dic3C2211yescharacteristic
46#5223—24no—
47#5222—24no—
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
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60#4989—24no—
61#4956—24no—
62C22×#123D311yescharacteristic, complemented
63C22×C4×D4—31no—
64C2×#394—31no—
65C2×#392—31no—
66C2×#386—31no—
67C2×#385—31no—
68#1444—31no—
69#1440—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—41no—
86C22×C3×D4—41no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—41no—
92C23×C3×C4—41no—
93C23×C3×C4D414yescomplemented
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—22no—
103C22×#67—22no—
104C22×#67—22no—
105C22×#67—22no—
106C22×#67—22no—
107C22×#67—22no—
108C22×#67—22no—
109C22×#67—22no—
110C22×#67—41no—
111C22×#67—41no—
112C22×#67D414yes—
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—22no—
124C22×C4×D3—22no—
125C22×C4×D3—41no—
126C22×C4×D3—41no—
127C3×#123—232no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4D414yescomplemented
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4D414yescomplemented
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—41no—
157C2×#217—41no—
158C2×#217—41no—
159C2×#217—41no—
160C2×#217D414yescomplemented
161C4×#67—232no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—22no—
171C2×(C2×D3)⋊C4—22no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4—41no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—22no—
179C2×Dic3⋊C4—41no—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182C2×C4×Dic3—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—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C3⋊#95—41no—
195C23×D4—31no—
196C23×D4—31no—
197C23×D4C2×D311yescharacteristic
198C24×C4—31no—
199C24×C4C2×D311yescharacteristic
200C2×#123—24no—
201C2×#123—24no—
202C2×#123—24no—
203C2×C4×D4—64no—
204C2×C4×D4—64no—
205C2×C4×D4—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4C2×D311yescharacteristic
209C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
220C22×C22⋊C4C2×D311yescharacteristic
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C42—31no—
224#394—64no—
225#392—64no—
226#386—64no—
227#385—64no—
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—
239C2×#95—31no—
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×C3C2×D412yes—
267C24×C3C2×D412yes—
268C24×C3C2×D412yes—
269C24×C3C2×D412yes—
270C24×C3C2411yescharacteristic
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3C2×D412yes—
284C23×D3#4112yes—
285C23×D3#4112yes—
286C2×C3×D4—28no—
287C2×C3×D4—44no—
288C2×C3×D4—44no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
291C2×C3×D4—44no—
292C2×C3×D4—44no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—28no—
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—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—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—28no—
323C22×C3×C4—44no—
324C22×C3×C4—44no—
325C22×C3×C4—44no—
326C22×C3×C4—44no—
327C22×C3×C4—44no—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—28no—
341C2×#67—28no—
342C2×#67—28no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
348C2×#67—44no—
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×Dic3#4112yes—
395C22×Dic3#4112yes—
396C22×Dic3#4112yes—
397C22×Dic3#4112yes—
398C2×C4×D3—28no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C2×C4×D3—44no—
404C2×C4×D3—44no—
405C3×C4⋊C4—28no—
406C3×C4⋊C4—28no—
407C3×C22⋊C4—28no—
408C3×C22⋊C4—28no—
409C3×C22⋊C4—28no—
410#217—28no—
411#217—44no—
412#217—44no—
413#217—44no—
414#217—44no—
415#217—44no—
416(C2×D3)⋊C4—28no—
417(C2×D3)⋊C4—28no—
418(C2×D3)⋊C4—44no—
419(C2×D3)⋊C4—44no—
420Dic3⋊C4—28no—
421Dic3⋊C4—44no—
422C4×Dic3—28no—
423C25—31no—
424C25C22×D311yescharacteristic
425C25C22×D311yescharacteristic
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—34no—
432C22×D4—41no—
433C22×D4—41no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—62no—
442C22×D4—62no—
443C22×D4—62no—
444C22×D4—62no—
445C22×D4—121no—
446C22×D4—121no—
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—41no—
459C23×C4—41no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—62no—
464C23×C4—62no—
465C23×C4—121no—
466C23×C4—121no—
467C23×C4#6714yescomplemented
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C23×C4C22×D311yescharacteristic
473#123—232no—
474C4×D4—632no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4—121no—
486C2×C4⋊C4#6714yescomplemented
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—34no—
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—62no—
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#6714yescomplemented
526C2×C42—62no—
527C2×C42—62no—
528C2×C42—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—62no—
538#95—121no—
539#95—121no—
540#95—121no—
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—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#12014yes—
611C23×C3C22×D411yescharacteristic
612C23×C3C22×D411yescharacteristic
613C23×C3C22×D411yescharacteristic
614C23×C3C22×D411yescharacteristic
615C23×C3C22×D411yescharacteristic
616C23×C3C2×#4111yescharacteristic
617C23×C3C2×#4111yescharacteristic
618C23×C3C2×#4111yescharacteristic
619C23×C3C2×#4111yescharacteristic
620C23×C3C2×#4111yescharacteristic
621C23×C3C2×#4111yescharacteristic
622C23×C3H(5,𝔽2)11yescharacteristic
623C23×C3H(5,𝔽2)11yescharacteristic
624C23×C3H(5,𝔽2)11yescharacteristic
625C23×C32−1+411yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3—41no—
660C22×D3#12314yescomplemented
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—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—416no—
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—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4#12014yes—
698#67—232no—
699#67—416no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
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—41no—
748C2×Dic3#12314yescomplemented
749C4×D3—416no—
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—32no—
777C24—32no—
778C24—32no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24—61no—
791C24D3×D412yes—
792C24D3×D412yes—
793C24C2×#6712yes—
794C24C2×#6712yes—
795C24C23×D311yescharacteristic
796C2×D4—28no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—68no—
804C2×D4—68no—
805C2×D4—68no—
806C2×D4—68no—
807C2×D4—68no—
808C2×D4—68no—
809C2×D4—68no—
810C2×D4—68no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C2×D4—124no—
816C2×D4—124no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
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—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—28no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—32no—
850C22×C4—32no—
851C22×C4—32no—
852C22×C4—32no—
853C22×C4—32no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—68no—
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—61no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4—124no—
908C22×C4C2×#6712yes—
909C22×C4C2×#6712yes—
910C22×C4C2×#6712yes—
911C22×C4C2×#6712yes—
912C22×C4C2×#6712yes—
913C22×C4C2×#6712yes—
914C22×C4C2×#6712yes—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—68no—
918C4⋊C4—124no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—68no—
923C22⋊C4—68no—
924C22⋊C4—68no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22⋊C4—124no—
932C42—68no—
933C22×C3—24no—
934C22×C3—24no—
935C22×C3—24no—
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—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
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×C3C2×#12011yescharacteristic
964C22×C3C2×#12011yescharacteristic
965C22×C3C2×#12311yescharacteristic
966C22×C3C2×#12311yescharacteristic
967C22×C3#52511yescharacteristic
968C22×C3#52511yescharacteristic
969C22×C3#52511yescharacteristic
970C22×C3#52511yescharacteristic
971C22×C3#52511yescharacteristic
972C22×C3#52511yescharacteristic
973C22×C3#53211yescharacteristic
974C22×C3#53211yescharacteristic
975C22×C3#53211yescharacteristic
976C22×C3#53411yescharacteristic
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#54711yescharacteristic
990C22×C3#54711yescharacteristic
991C22×C3#54711yescharacteristic
992C22×C3#54811yescharacteristic
993C22×C3#55011yescharacteristic
994C22×C3#55111yescharacteristic
995C22×C3#55311yescharacteristic
996C22×C3#55311yescharacteristic
997C22×C3#55911yescharacteristic
998C2×D3—24no—
999C2×D3—24no—
1000C2×D3—24no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—42no—
1004C2×D3—42no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—42no—
1010C2×D3—42no—
1011C2×D3—42no—
1012C2×D3—42no—
1013C3×C4—24no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—42no—
1017C3×C4—42no—
1018Dic3—24no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—42no—
1023Dic3—81no—
1024Dic3—81no—
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—34no—
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—62no—
1096C23—62no—
1097C23—62no—
1098C23—62no—
1099C23—62no—
1100C23—62no—
1101C23—62no—
1102C23—62no—
1103C23—62no—
1104C23—62no—
1105C23—62no—
1106C23—62no—
1107C23—62no—
1108C23—62no—
1109C23—62no—
1110C23—62no—
1111C23—62no—
1112C23—62no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23#93714yes—
1130C23C2×D3×D411yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23#100411yescharacteristic
1133C23#100411yescharacteristic
1134C23D3×#4111yescharacteristic
1135C23D3×#4111yescharacteristic
1136C23D3×#4111yescharacteristic
1137C23D3×#4111yescharacteristic
1138C23D3×#4111yescharacteristic
1139C23D3×#4111yescharacteristic
1140C23#100911yescharacteristic
1141C23#101011yescharacteristic
1142C23C22×#6711yescharacteristic
1143C23C22×#6711yescharacteristic
1144C23C22×#6711yescharacteristic
1145D4—416no—
1146D4—632no—
1147D4—1216no—
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—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—34no—
1167C2×C4—416no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—1216no—
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—121no—
1232C2×C4—121no—
1233C2×C4#95314yes—
1234C2×C3—44no—
1235C2×C3—82no—
1236C2×C3#238811yescharacteristic
1237C2×C3#240311yescharacteristic
1238C2×C3#240711yescharacteristic
1239C2×C3#241811yescharacteristic
1240C2×C3#242211yescharacteristic
1241C2×C3#243011yescharacteristic
1242C2×C3#244311yescharacteristic
1243C2×C3#244511yescharacteristic
1244C2×C3#245511yescharacteristic
1245C2×C3#245611yescharacteristic
1246C2×C3#246111yescharacteristic
1247C2×C3#246411yescharacteristic
1248C2×C3#260211yescharacteristic
1249C2×C3#263011yescharacteristic
1250C2×C3#284911yescharacteristic
1251D3—44no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
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—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—64no—
1275C22—64no—
1276C22—64no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—122no—
1286C22—122no—
1287C22—122no—
1288C22—122no—
1289C22—122no—
1290C22—122no—
1291C22—122no—
1292C22—122no—
1293C22—122no—
1294C22—122no—
1295C22—122no—
1296C22—122no—
1297C22D3×#12311yescharacteristic
1298C22D3×#12311yescharacteristic
1299C22#565411yescharacteristic
1300C22#565411yescharacteristic
1301C22#565511yescharacteristic
1302C22#565511yescharacteristic
1303C22#565611yescharacteristic
1304C22#565611yescharacteristic
1305C22#565711yescharacteristic
1306C22#565911yescharacteristic
1307C22#566011yescharacteristic
1308C22#566111yescharacteristic
1309C22#566111yescharacteristic
1310C22#566211yescharacteristic
1311C22#566311yescharacteristic
1312C22#566411yescharacteristic
1313C22C2×#93711yescharacteristic
1314C22D4×#6711yescharacteristic
1315C22D4×#6711yescharacteristic
1316C22D4×#6711yescharacteristic
1317C22D4×#6711yescharacteristic
1318C22#580411yescharacteristic
1319C22#582411yescharacteristic
1320C22#582811yescharacteristic
1321C22#582811yescharacteristic
1322C22#582811yescharacteristic
1323C22#582811yescharacteristic
1324C22#582911yescharacteristic
1325C22#583111yescharacteristic
1326C22#583211yescharacteristic
1327C22#583211yescharacteristic
1328C22#583211yescharacteristic
1329C22#583311yescharacteristic
1330C22#583411yescharacteristic
1331C22C2×#95311yescharacteristic
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—64no—
1338C4—122no—
1339C4—122no—
1340C4—122no—
1341C4—122no—
1342C4—241no—
1343C4—241no—
1344C3#1472111yescharacteristic, complemented, Sylow
1345C2—44no—
1346C2—82no—
1347C2—124no—
1348C2#8284511yescharacteristic
1349C2#8284811yescharacteristic
1350C2#8284911yescharacteristic
1351C2#8285211yescharacteristic
1352C2#8285311yescharacteristic
1353C2#8289611yescharacteristic
1354C2#8289711yescharacteristic
1355C2#8289811yescharacteristic
1356C2#8289911yescharacteristic
1357C2#8290211yescharacteristic
1358C2#8290411yescharacteristic
1359C2#8291211yescharacteristic
1360C2#8405211yescharacteristic
1361C2#8409511yescharacteristic
1362C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#123C2
prime radicalC2×#5223C2
hypercenterC22×#123D3
hypocenterC3#14721
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×C4×#67C2semidirect
4. C2×#5222C2semidirect
5. C2×#4989C2semidirect
6. C2×#4956C2semidirect
7. #72127C2semidirect
8. #71570C2semidirect
9. #71568C2semidirect
10. #71564C2semidirect
11. #71550C2semidirect
12. #71550C2semidirect
13. #71549C2semidirect
14. #71547C2semidirect
15. #71545C2semidirect
62. C22×#123D3semidirect
93. C23×C3×C4D4semidirect
133. C2×C3×C4⋊C4D4semidirect
142. C2×C3×C22⋊C4D4semidirect
160. C2×#217D4semidirect
467. C23×C4#67semidirect
486. C2×C4⋊C4#67semidirect
525. C2×C22⋊C4#67semidirect
660. C22×D3#123semidirect
748. C2×Dic3#123semidirect
1344. C3#14721semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C4×#672
C2×#52232
C2×#52222
C2×#49892
C2×#49562
#721272
#715702
#715682
#715642
#715502
#715492
#715472
#715452
#147213