Finite Group Databasebeta

← #10726751

Subgroups — #10726751

Order 768.

2662 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×D4×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#4994C211yesmaximal, characteristic, complemented
5C2×#4959C211yesmaximal, characteristic, complemented
6C2×#4958C211yesmaximal, characteristic, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8C2×#4942C211yesmaximal, characteristic, complemented
9#71564C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71548C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#14732—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C2×D4×Dic3—24no—
32C2×D4×Dic3—24no—
33C2×D4×Dic3—24no—
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C3×#394—24no—
44C2×C3×#95C2211yescharacteristic
45#5223—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
57#4994—24no—
58#4959—24no—
59#4958—24no—
60#4958—24no—
61#4942—24no—
62C22×C4×D4—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394D311yescharacteristic, complemented
66C2×#392—31no—
67C2×#386—31no—
68C2×#386—31no—
69C2×#380—31no—
70#1441—31no—
71#1440—31no—
72#1439—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—22no—
86C22×C3×D4D414yes—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C23×Dic3—22no—
107C23×Dic3—22no—
108C23×Dic3—22no—
109C23×Dic3—22no—
110C23×Dic3—22no—
111C23×Dic3—22no—
112C23×Dic3—22no—
113C23×Dic3—22no—
114C23×Dic3—22no—
115C23×Dic3—41no—
116C23×Dic3—41no—
117C23×Dic3—41no—
118C23×Dic3—41no—
119C23×Dic3D414yescomplemented
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C22⋊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⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—41no—
141C2×C3×C22⋊C4—41no—
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—41no—
152C2×#217—41no—
153C2×#217D414yescomplemented
154D4×Dic3—232no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
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—41no—
169C2×(C2×D3)⋊C4—41no—
170C2×C4⋊Dic3—22no—
171C2×C4⋊Dic3—22no—
172C2×C4⋊Dic3D414yescomplemented
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—41no—
178C2×Dic3⋊C4—41no—
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
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×D4—31no—
195C23×D4—31no—
196C23×D4C2×D311yescharacteristic
197C24×C4—31no—
198C24×C4—31no—
199C2×C4×D4—64no—
200C2×C4×D4—64no—
201C2×C4×D4—64no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4C2×D311yescharacteristic
206C22×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
216C22×C22⋊C4C2×D311yescharacteristic
217C22×C22⋊C4C2×D311yescharacteristic
218C22×C22⋊C4C2×D311yescharacteristic
219C22×C42—31no—
220#396—64no—
221#394—24no—
222#394—64no—
223#392—64no—
224#386—64no—
225#386—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×#95C2×D311yescharacteristic
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×C3C2×D412yes—
264C24×C3C2×D412yes—
265C24×C3C2×D412yes—
266C24×C3C2×D412yes—
267C24×C3#4112yes—
268C24×C3#4112yes—
269C24×C3C2411yescharacteristic
270C23×D3—21no—
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×D3—21no—
284C23×D3#4112yes—
285C2×C3×D4—28no—
286C2×C3×D4—28no—
287C2×C3×D4—28no—
288C2×C3×D4—28no—
289C2×C3×D4—28no—
290C2×C3×D4—28no—
291C2×C3×D4—28no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—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—21no—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4#4112yes—
327C2×#67—28no—
328C2×#67—28no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—44no—
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—28no—
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—28no—
375C22×Dic3—28no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—44no—
384C22×Dic3—44no—
385C22×Dic3—44no—
386C22×Dic3—44no—
387C22×Dic3—44no—
388C22×Dic3—44no—
389C22×Dic3—44no—
390C22×Dic3—44no—
391C22×Dic3—44no—
392C22×Dic3—44no—
393C22×Dic3—44no—
394C22×Dic3C2×D412yes—
395C22×Dic3C2×D412yes—
396C22×Dic3C2×D412yes—
397C22×Dic3C2×D412yes—
398C22×Dic3C2×D412yes—
399C22×Dic3C2×D412yes—
400C22×Dic3C2×D412yes—
401C22×Dic3C2×D412yes—
402C22×Dic3#4112yes—
403C22×Dic3#4112yes—
404C3×C4⋊C4—44no—
405C3×C22⋊C4—44no—
406C3×C22⋊C4—44no—
407C3×C22⋊C4—44no—
408C3×C22⋊C4—44no—
409#217—28no—
410#217—28no—
411#217—44no—
412#217—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416(C2×D3)⋊C4—44no—
417(C2×D3)⋊C4—44no—
418C4⋊Dic3—28no—
419Dic3⋊C4—44no—
420Dic3⋊C4—44no—
421C4×Dic3—28no—
422C25—31no—
423C25C22×D311yescharacteristic
424C25C22×D311yescharacteristic
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—121no—
442C22×D4—121no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4#6714yes—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—34no—
453C23×C4—31no—
454C23×C4—62no—
455C23×C4—62no—
456C23×C4—62no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—121no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4—121no—
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C4×D4—632no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—34no—
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—121no—
484C2×C4⋊C4—121no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
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—41no—
497C2×C22⋊C4—41no—
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—62no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C42—62no—
525C2×C42—62no—
526C2×C42—62no—
527#95—22no—
528#95—34no—
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—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#12114yes—
608C23×C3#12114yes—
609C23×C3C22×D411yescharacteristic
610C23×C3C22×D411yescharacteristic
611C23×C3C22×D411yescharacteristic
612C23×C3C22×D411yescharacteristic
613C23×C3C22×D411yescharacteristic
614C23×C3C2×#4111yescharacteristic
615C23×C3C2×#4111yescharacteristic
616C23×C3C2×#4111yescharacteristic
617C23×C3C2×#4111yescharacteristic
618C23×C3C2×#4111yescharacteristic
619C23×C3C2×#4111yescharacteristic
620C23×C3H(5,𝔽2)11yescharacteristic
621C23×C3H(5,𝔽2)11yescharacteristic
622C23×C3H(5,𝔽2)11yescharacteristic
623C23×C32−1+411yescharacteristic
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
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—
659C3×D4—232no—
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—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
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—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#12114yes—
695#67—416no—
696#67—416no—
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—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—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—416no—
722C2×Dic3—416no—
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#12014yes—
747C2×Dic3#12114yes—
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—32no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24D3×D412yes—
788C24D3×D412yes—
789C24#23712yes—
790C24#23712yes—
791C24C2×#6712yes—
792C24C2×#6712yes—
793C24C23×D311yescharacteristic
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
810C2×D4—124no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
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—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—32no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—32no—
850C22×C4—32no—
851C22×C4—32no—
852C22×C4—32no—
853C22×C4—32no—
854C22×C4—32no—
855C22×C4—32no—
856C22×C4—68no—
857C22×C4—68no—
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—68no—
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—124no—
899C22×C4—124no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4—124no—
908C22×C4—124no—
909C22×C4D3×D412yes—
910C22×C4D3×D412yes—
911C22×C4#23712yes—
912C22×C4C2×#6712yes—
913C4⋊C4—44no—
914C4⋊C4—68no—
915C4⋊C4—124no—
916C4⋊C4—124no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—68no—
922C22⋊C4—68no—
923C22⋊C4—124no—
924C22⋊C4—124no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C42—68no—
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×C3C2×#12011yescharacteristic
962C22×C3C2×#12111yescharacteristic
963C22×C3C2×#12111yescharacteristic
964C22×C3C2×#12111yescharacteristic
965C22×C3C2×#12111yescharacteristic
966C22×C3#52511yescharacteristic
967C22×C3#52511yescharacteristic
968C22×C3#52511yescharacteristic
969C22×C3#52511yescharacteristic
970C22×C3#52511yescharacteristic
971C22×C3#52911yescharacteristic
972C22×C3#52911yescharacteristic
973C22×C3#53211yescharacteristic
974C22×C3#53411yescharacteristic
975C22×C3#53711yescharacteristic
976C22×C3#53811yescharacteristic
977C22×C3#53911yescharacteristic
978C22×C3#54011yescharacteristic
979C22×C3#54211yescharacteristic
980C22×C3D4211yescharacteristic
981C22×C3D4211yescharacteristic
982C22×C3D4211yescharacteristic
983C22×C3#54611yescharacteristic
984C22×C3#54611yescharacteristic
985C22×C3#54611yescharacteristic
986C22×C3#54611yescharacteristic
987C22×C3#54611yescharacteristic
988C22×C3#54711yescharacteristic
989C22×C3#54711yescharacteristic
990C22×C3#54811yescharacteristic
991C22×C3#54811yescharacteristic
992C22×C3#55011yescharacteristic
993C22×C3#55111yescharacteristic
994C22×C3#55111yescharacteristic
995C22×C3#55311yescharacteristic
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—81no—
1004C2×D3—81no—
1005C2×D3—81no—
1006C2×D3—81no—
1007C2×D3—81no—
1008C2×D3—81no—
1009C2×D3—81no—
1010C2×D3—81no—
1011C3×C4—24no—
1012C3×C4—42no—
1013C3×C4—81no—
1014C3×C4—81no—
1015C3×C4—81no—
1016Dic3—24no—
1017Dic3—24no—
1018Dic3—42no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—42no—
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—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—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
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#93914yes—
1127C23#93914yes—
1128C23C2×D3×D411yescharacteristic
1129C23C2×D3×D411yescharacteristic
1130C23C2×D3×D411yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23C2×#23711yescharacteristic
1133C23C2×#23711yescharacteristic
1134C23C2×#23711yescharacteristic
1135C23#100411yescharacteristic
1136C23D3×#4111yescharacteristic
1137C23D3×#4111yescharacteristic
1138C23D3×#4111yescharacteristic
1139C23#100911yescharacteristic
1140C23#100911yescharacteristic
1141C23#101011yescharacteristic
1142C23C22×#6711yescharacteristic
1143D4—232no—
1144D4—1216no—
1145D4—1216no—
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—34no—
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—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—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
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—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—62no—
1203C2×C4—62no—
1204C2×C4—62no—
1205C2×C4—62no—
1206C2×C4—1216no—
1207C2×C4—1216no—
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#239211yescharacteristic
1235C2×C3#240711yescharacteristic
1236C2×C3#241011yescharacteristic
1237C2×C3#241611yescharacteristic
1238C2×C3#242411yescharacteristic
1239C2×C3#242511yescharacteristic
1240C2×C3#242711yescharacteristic
1241C2×C3#242811yescharacteristic
1242C2×C3#245711yescharacteristic
1243C2×C3#246111yescharacteristic
1244C2×C3#246311yescharacteristic
1245C2×C3#246711yescharacteristic
1246C2×C3#253411yescharacteristic
1247C2×C3#263011yescharacteristic
1248C2×C3#284711yescharacteristic
1249D3—82no—
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—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—241no—
1288C22—241no—
1289C22—241no—
1290C22—241no—
1291C22—241no—
1292C22—241no—
1293C22—241no—
1294C22—241no—
1295C22#558611yescharacteristic
1296C22#558611yescharacteristic
1297C22#558611yescharacteristic
1298C22D3×#12011yescharacteristic
1299C22#559611yescharacteristic
1300C22#559711yescharacteristic
1301C22#559811yescharacteristic
1302C22#559911yescharacteristic
1303C22#560111yescharacteristic
1304C22D3×#12111yescharacteristic
1305C22#560611yescharacteristic
1306C22#560911yescharacteristic
1307C22#560911yescharacteristic
1308C22#561011yescharacteristic
1309C22#561711yescharacteristic
1310C22#561911yescharacteristic
1311C22#564911yescharacteristic
1312C22#565311yescharacteristic
1313C22#565411yescharacteristic
1314C22#565511yescharacteristic
1315C22#565611yescharacteristic
1316C22#565811yescharacteristic
1317C22#565811yescharacteristic
1318C22#566511yescharacteristic
1319C22#567611yescharacteristic
1320C22#567711yescharacteristic
1321C22#568011yescharacteristic
1322C22#568211yescharacteristic
1323C22D4×#6711yescharacteristic
1324C22C2×#93911yescharacteristic
1325C22C2×#93911yescharacteristic
1326C22C2×#93911yescharacteristic
1327C22#582411yescharacteristic
1328C22#582911yescharacteristic
1329C22#582911yescharacteristic
1330C4—24no—
1331C4—42no—
1332C4—64no—
1333C4—64no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—122no—
1338C4—122no—
1339C4—122no—
1340C4—122no—
1341C4—241no—
1342C3#1473211yescharacteristic, complemented, Sylow
1343C2—44no—
1344C2—44no—
1345C2—242no—
1346C2#7689011yescharacteristic
1347C2#7689411yescharacteristic
1348C2#7690911yescharacteristic
1349C2#7691511yescharacteristic
1350C2#7691611yescharacteristic
1351C2#7692011yescharacteristic
1352C2#7697611yescharacteristic
1353C2#7710811yescharacteristic
1354C2#8260111yescharacteristic
1355C2#8264211yescharacteristic
1356C2#8264911yescharacteristic
1357C2#8270611yescharacteristic
1358C2#8284711yescharacteristic
1359C2#8290011yescharacteristic
1360C2#8299611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC2×#5223C2
hypercenterC2×#394D3
hypocenterC3#14732
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic3C2semidirect
2. C2×C3×#394C2semidirect
4. C2×#4994C2semidirect
5. C2×#4959C2semidirect
6. C2×#4958C2semidirect
7. C2×#4958C2semidirect
8. C2×#4942C2semidirect
9. #71564C2semidirect
10. #71550C2semidirect
11. #71548C2semidirect
12. #71547C2semidirect
13. #71544C2semidirect
14. #69411C2semidirect
15. #69408C2semidirect
65. C2×#394D3semidirect
119. C23×Dic3D4semidirect
153. C2×#217D4semidirect
172. C2×C4⋊Dic3D4semidirect
193. C3⋊#95D4semidirect
1342. C3#14732semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic32
C2×C3×#3942
C2×#52232
C2×#49942
C2×#49592
C2×#49582
C2×#49422
#715642
#715502
#715482
#715472
#715442
#694112
#694082
#147323