Finite Group Databasebeta

← #10718645

Subgroups — #10718645

Order 768.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C22×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4958C211yesmaximal, characteristic, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71549C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69410C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#14023—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C24×Dic3C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C2×#939—24no—
31C2×#939—24no—
32C2×#939C418yescomplemented
33C2×D4×Dic3—24no—
34C2×D4×Dic3—24no—
35C2×D4×Dic3—24no—
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×C4⋊Dic3C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C3×#386—24no—
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47#5213—24no—
48C2×C3⋊#95—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#4958—24no—
62#4958—24no—
63C22×#121—31no—
64C22×C4×D4—31no—
65C2×#386—31no—
66C2×#386—31no—
67C2×#386—31no—
68C2×#386D311yescharacteristic, complemented
69C22×#95—31no—
70#1441—31no—
71#1440—31no—
72#1439—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95—31no—
77C22⋊#95—31no—
78C25×C3C2311yescharacteristic
79C25×C3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4C2×C414yes—
86C22×C3×D4D414yes—
87C22×C3×D4D414yes—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—22no—
93C23×C3×C4—41no—
94C23×C3×C4—41no—
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
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×#67C2×C414yescomplemented
113C22×#67C2×C414yescomplemented
114C23×Dic3—22no—
115C23×Dic3—22no—
116C23×Dic3—22no—
117C23×Dic3—22no—
118C23×Dic3—22no—
119C23×Dic3—22no—
120C23×Dic3—22no—
121C23×Dic3—22no—
122C23×Dic3—22no—
123C23×Dic3—22no—
124C23×Dic3—22no—
125C23×Dic3—22no—
126C23×Dic3—22no—
127C23×Dic3—41no—
128C23×Dic3—41no—
129C23×Dic3—41no—
130C23×Dic3—41no—
131C23×Dic3—41no—
132C23×Dic3—41no—
133C23×Dic3C2×C414yescomplemented
134C23×Dic3D414yescomplemented
135C23×Dic3C2311yescharacteristic
136C23×Dic3C2311yescharacteristic
137C23×Dic3C2311yescharacteristic
138C23×Dic3C2311yescharacteristic
139C23×Dic3C2311yescharacteristic
140C23×Dic3C2311yescharacteristic
141C23×Dic3C2311yescharacteristic
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—22no—
145C2×C3×C22⋊C4—22no—
146C2×C3×C22⋊C4—22no—
147C2×C3×C22⋊C4—22no—
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—41no—
150C2×C3×C22⋊C4—41no—
151C2×#217—22no—
152C2×#217—22no—
153C2×#217—22no—
154C2×#217—22no—
155C2×#217—22no—
156C2×#217—22no—
157C2×#217—22no—
158C2×#217C2×C414yescomplemented
159C2×#217D414yescomplemented
160#939—232no—
161D4×Dic3—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×(C2×D3)⋊C4—41no—
175C2×(C2×D3)⋊C4—41no—
176C2×(C2×D3)⋊C4C2×C414yescomplemented
177C2×C4⋊Dic3—22no—
178C2×C4⋊Dic3—22no—
179C2×C4⋊Dic3—22no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4C2×C414yescomplemented
183C2×C4×Dic3—22no—
184C2×C4×Dic3—22no—
185C2×C4×Dic3—22no—
186C3×#95—22no—
187C3×#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—41no—
198C3⋊#95—41no—
199C3⋊#95D414yescomplemented
200C23×D4—31no—
201C23×D4—31no—
202C23×D4C2×D311yescharacteristic
203C24×C4—31no—
204C24×C4—31no—
205C24×C4—31no—
206C24×C4C2×D311yescharacteristic
207C2×#121—38no—
208C2×#121—64no—
209C2×#121—64no—
210C2×C4×D4—64no—
211C2×C4×D4—64no—
212C2×C4×D4—64no—
213C22×C4⋊C4—31no—
214C22×C4⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226C22×C42—31no—
227#386—24no—
228#386—64no—
229#386—64no—
230#386—64no—
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—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C2×#95—64no—
244C2×#95C2×D311yescharacteristic
245C2×#95C2×D311yescharacteristic
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×C3C22×C412yes—
267C24×C3C22×C412yes—
268C24×C3C2×D412yes—
269C24×C3C2×D412yes—
270C24×C3C2×D412yes—
271C24×C3C2×D412yes—
272C24×C3C2×D412yes—
273C24×C3C2×D412yes—
274C24×C3#4112yes—
275C24×C3#4112yes—
276C24×C3C2411yescharacteristic
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3—21no—
288C23×D3—21no—
289C23×D3—21no—
290C23×D3—21no—
291C23×D3C22×C412yes—
292C2×C3×D4—28no—
293C2×C3×D4—28no—
294C2×C3×D4—28no—
295C2×C3×D4—28no—
296C2×C3×D4—28no—
297C2×C3×D4—28no—
298C2×C3×D4C22⋊C4116yescomplemented
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—28no—
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×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—21no—
330C22×C3×C4—44no—
331C22×C3×C4—44no—
332C22×C3×C4—44no—
333C22×C3×C4—44no—
334C22×C3×C4—44no—
335C22×C3×C4—44no—
336C22×C3×C4C22×C412yes—
337C22×C3×C4C2×D412yes—
338C22×C3×C4C2×D412yes—
339C22×C3×C4C2×D412yes—
340C22×C3×C4#4112yes—
341C2×#67—28no—
342C2×#67—28no—
343C2×#67—28no—
344C2×#67—28no—
345C2×#67—28no—
346C2×#67—44no—
347C2×#67—44no—
348C2×#67—44no—
349C2×#67—44no—
350C2×#67—44no—
351C2×#67—44no—
352C2×#67—44no—
353C2×#67—44no—
354C2×#67—44no—
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—28no—
364C22×Dic3—28no—
365C22×Dic3—28no—
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—21no—
393C22×Dic3—21no—
394C22×Dic3—21no—
395C22×Dic3—21no—
396C22×Dic3—28no—
397C22×Dic3—28no—
398C22×Dic3—44no—
399C22×Dic3—44no—
400C22×Dic3—44no—
401C22×Dic3—44no—
402C22×Dic3—44no—
403C22×Dic3—44no—
404C22×Dic3—44no—
405C22×Dic3—44no—
406C22×Dic3—44no—
407C22×Dic3—44no—
408C22×Dic3—44no—
409C22×Dic3—44no—
410C22×Dic3—44no—
411C22×Dic3—44no—
412C22×Dic3—44no—
413C22×Dic3—44no—
414C22×Dic3C22×C412yes—
415C22×Dic3C22×C412yes—
416C22×Dic3C22×C412yes—
417C22×Dic3C2×D412yes—
418C22×Dic3C2×D412yes—
419C22×Dic3C2×D412yes—
420C22×Dic3C2×D412yes—
421C22×Dic3C2×D412yes—
422C22×Dic3C2×D412yes—
423C22×Dic3#4112yes—
424C22×Dic3#4112yes—
425C3×C22⋊C4—44no—
426C3×C22⋊C4—44no—
427C3×C22⋊C4—44no—
428#217—28no—
429#217—28no—
430#217—28no—
431(C2×D3)⋊C4—28no—
432(C2×D3)⋊C4—44no—
433(C2×D3)⋊C4—44no—
434(C2×D3)⋊C4—44no—
435(C2×D3)⋊C4—44no—
436C4⋊Dic3—28no—
437Dic3⋊C4—28no—
438C4×Dic3—28no—
439C25—31no—
440C25C22×D311yescharacteristic
441C25C22×D311yescharacteristic
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—34no—
447C22×D4—34no—
448C22×D4—62no—
449C22×D4—62no—
450C22×D4—62no—
451C22×D4—62no—
452C22×D4—62no—
453C22×D4—62no—
454C22×D4—62no—
455C22×D4—62no—
456C22×D4—62no—
457C22×D4—62no—
458C22×D4—121no—
459C22×D4—121no—
460C22×D4C4×D314yes—
461C22×D4D1214yes—
462C22×D4#6714yes—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—31no—
469C23×C4—31no—
470C23×C4—31no—
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—31no—
474C23×C4—31no—
475C23×C4—34no—
476C23×C4—34no—
477C23×C4—41no—
478C23×C4—41no—
479C23×C4—62no—
480C23×C4—62no—
481C23×C4—62no—
482C23×C4—62no—
483C23×C4—62no—
484C23×C4—62no—
485C23×C4—62no—
486C23×C4—62no—
487C23×C4—62no—
488C23×C4—62no—
489C23×C4—62no—
490C23×C4—62no—
491C23×C4—62no—
492C23×C4—121no—
493C23×C4—121no—
494C23×C4—121no—
495C23×C4—121no—
496C23×C4—121no—
497C23×C4—121no—
498C23×C4C22×D311yescharacteristic
499C23×C4C22×D311yescharacteristic
500C23×C4C22×D311yescharacteristic
501C23×C4C22×D311yescharacteristic
502C23×C4C22×D311yescharacteristic
503#121—632no—
504C4×D4—632no—
505C2×C4⋊C4—34no—
506C2×C4⋊C4—62no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—62no—
509C2×C4⋊C4—62no—
510C2×C4⋊C4—62no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—34no—
519C2×C22⋊C4—34no—
520C2×C22⋊C4—34no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—62no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531C2×C22⋊C4—62no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—121no—
541C2×C22⋊C4—121no—
542C2×C22⋊C4—121no—
543C2×C22⋊C4—121no—
544C2×C42—62no—
545C2×C42—62no—
546C2×C42—62no—
547#95—22no—
548#95—22no—
549#95—34no—
550#95—62no—
551#95—62no—
552#95—62no—
553#95—62no—
554#95—62no—
555#95—62no—
556#95—62no—
557#95—62no—
558#95—62no—
559#95—121no—
560#95—121no—
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—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
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×C3C2×C22⋊C414yes—
624C23×C3C2×C22⋊C414yes—
625C23×C3C4×D414yes—
626C23×C3C4×D414yes—
627C23×C3#12014yes—
628C23×C3#12114yes—
629C23×C3#12114yes—
630C23×C3#12314yes—
631C23×C3C23×C411yescharacteristic
632C23×C3C22×D411yescharacteristic
633C23×C3C22×D411yescharacteristic
634C23×C3C22×D411yescharacteristic
635C23×C3C22×D411yescharacteristic
636C23×C3C22×D411yescharacteristic
637C23×C3C2×#4111yescharacteristic
638C23×C3C2×#4111yescharacteristic
639C23×C3C2×#4111yescharacteristic
640C23×C3C2×#4111yescharacteristic
641C23×C3C2×#4111yescharacteristic
642C23×C3H(5,𝔽2)11yescharacteristic
643C23×C3H(5,𝔽2)11yescharacteristic
644C23×C3H(5,𝔽2)11yescharacteristic
645C23×C32−1+411yescharacteristic
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3—41no—
660C22×D3—41no—
661C22×D3—41no—
662C22×D3—41no—
663C22×D3—41no—
664C22×D3—41no—
665C22×D3—41no—
666C22×D3—41no—
667C22×D3—41no—
668C22×D3—41no—
669C22×D3—41no—
670C22×D3—41no—
671C22×D3—41no—
672C22×D3—41no—
673C22×D3—41no—
674C22×D3—41no—
675C22×D3—41no—
676C22×D3—41no—
677C22×D3—41no—
678C22×D3—41no—
679C22×D3—41no—
680C22×D3—41no—
681C3×D4—232no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—22no—
694C2×C3×C4—416no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4C2×C22⋊C414yes—
718#67—416no—
719#67—416no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—22no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—22no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—22no—
742C2×Dic3—22no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—416no—
748C2×Dic3—416no—
749C2×Dic3—416no—
750C2×Dic3—41no—
751C2×Dic3—41no—
752C2×Dic3—41no—
753C2×Dic3—41no—
754C2×Dic3—41no—
755C2×Dic3—41no—
756C2×Dic3—41no—
757C2×Dic3—41no—
758C2×Dic3—41no—
759C2×Dic3—41no—
760C2×Dic3—41no—
761C2×Dic3—41no—
762C2×Dic3—41no—
763C2×Dic3—41no—
764C2×Dic3—41no—
765C2×Dic3—41no—
766C2×Dic3—41no—
767C2×Dic3—41no—
768C2×Dic3—41no—
769C2×Dic3—41no—
770C2×Dic3C4×D414yescomplemented
771C2×Dic3#12114yescomplemented
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—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—32no—
793C24—61no—
794C24—61no—
795C24—61no—
796C24—61no—
797C24—61no—
798C24—61no—
799C24—61no—
800C24—61no—
801C24—61no—
802C24—61no—
803C24—61no—
804C24—61no—
805C24—61no—
806C24—61no—
807C24C2×C4×D312yes—
808C24C2×C4×D312yes—
809C24C2×D1212yes—
810C24C2×D1212yes—
811C24D3×D412yes—
812C24D3×D412yes—
813C24#23712yes—
814C24#23712yes—
815C24C2×#6712yes—
816C24C2×#6712yes—
817C24C23×D311yescharacteristic
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—68no—
825C2×D4—68no—
826C2×D4—68no—
827C2×D4—68no—
828C2×D4—68no—
829C2×D4—124no—
830C2×D4—124no—
831C2×D4—124no—
832C2×D4—124no—
833C2×D4—124no—
834C2×D4—124no—
835C2×D4—124no—
836C2×D4—124no—
837C2×D4—124no—
838C2×D4(C2×D3)⋊C4116yescomplemented
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—28no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—32no—
871C22×C4—32no—
872C22×C4—32no—
873C22×C4—32no—
874C22×C4—32no—
875C22×C4—32no—
876C22×C4—32no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—32no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—68no—
888C22×C4—68no—
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—68no—
898C22×C4—68no—
899C22×C4—68no—
900C22×C4—61no—
901C22×C4—61no—
902C22×C4—61no—
903C22×C4—61no—
904C22×C4—61no—
905C22×C4—61no—
906C22×C4—61no—
907C22×C4—61no—
908C22×C4—61no—
909C22×C4—61no—
910C22×C4—61no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—61no—
919C22×C4—61no—
920C22×C4—61no—
921C22×C4—61no—
922C22×C4—61no—
923C22×C4—61no—
924C22×C4—61no—
925C22×C4—61no—
926C22×C4—61no—
927C22×C4—61no—
928C22×C4—61no—
929C22×C4—61no—
930C22×C4—124no—
931C22×C4—124no—
932C22×C4—124no—
933C22×C4—124no—
934C22×C4—124no—
935C22×C4—124no—
936C22×C4—124no—
937C22×C4—124no—
938C22×C4—124no—
939C22×C4—124no—
940C22×C4—124no—
941C22×C4—124no—
942C22×C4—124no—
943C22×C4—124no—
944C22×C4—124no—
945C22×C4—124no—
946C22×C4C2×C4×D312yes—
947C22×C4C2×D1212yes—
948C22×C4D3×D412yes—
949C22×C4#23712yes—
950C22×C4C2×#6712yes—
951C4⋊C4—68no—
952C4⋊C4—68no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—68no—
957C22⋊C4—68no—
958C22⋊C4—68no—
959C22⋊C4—68no—
960C22⋊C4—124no—
961C22⋊C4—124no—
962C22⋊C4—124no—
963C22⋊C4—124no—
964C42—68no—
965C22×C3—24no—
966C22×C3—24no—
967C22×C3—24no—
968C22×C3—24no—
969C22×C3—24no—
970C22×C3—24no—
971C22×C3—24no—
972C22×C3—24no—
973C22×C3—24no—
974C22×C3—24no—
975C22×C3—24no—
976C22×C3—24no—
977C22×C3—24no—
978C22×C3—24no—
979C22×C3—24no—
980C22×C3—24no—
981C22×C3—24no—
982C22×C3—42no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—42no—
989C22×C3—42no—
990C22×C3—42no—
991C22×C3—42no—
992C22×C3—42no—
993C22×C3—42no—
994C22×C3#38618yescomplemented
995C22×C3C22×C22⋊C411yescharacteristic
996C22×C3C2×C4×D411yescharacteristic
997C22×C3C2×C4×D411yescharacteristic
998C22×C3C2×C4×D411yescharacteristic
999C22×C3C4×#4111yescharacteristic
1000C22×C3#51811yescharacteristic
1001C22×C3#52011yescharacteristic
1002C22×C3C2×#12011yescharacteristic
1003C22×C3C2×#12111yescharacteristic
1004C22×C3C2×#12111yescharacteristic
1005C22×C3C2×#12111yescharacteristic
1006C22×C3C2×#12311yescharacteristic
1007C22×C3#52511yescharacteristic
1008C22×C3#52911yescharacteristic
1009C22×C3#53211yescharacteristic
1010C22×C3#53411yescharacteristic
1011C22×C3#53711yescharacteristic
1012C22×C3#53811yescharacteristic
1013C22×C3#53911yescharacteristic
1014C22×C3D4211yescharacteristic
1015C22×C3D4211yescharacteristic
1016C22×C3D4211yescharacteristic
1017C22×C3#54611yescharacteristic
1018C22×C3#54611yescharacteristic
1019C22×C3#54611yescharacteristic
1020C22×C3#54611yescharacteristic
1021C22×C3#54611yescharacteristic
1022C22×C3#54611yescharacteristic
1023C22×C3#54711yescharacteristic
1024C22×C3#54711yescharacteristic
1025C22×C3#54711yescharacteristic
1026C22×C3#54811yescharacteristic
1027C22×C3#55311yescharacteristic
1028C22×C3#55311yescharacteristic
1029C22×C3#55311yescharacteristic
1030C2×D3—42no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—81no—
1038C2×D3—81no—
1039C2×D3—81no—
1040C2×D3—81no—
1041C2×D3—81no—
1042C2×D3—81no—
1043C2×D3—81no—
1044C2×D3—81no—
1045C3×C4—24no—
1046C3×C4—42no—
1047C3×C4—42no—
1048C3×C4—81no—
1049C3×C4—81no—
1050Dic3—24no—
1051Dic3—24no—
1052Dic3—42no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—42no—
1056Dic3—42no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
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—62no—
1120C23—62no—
1121C23—62no—
1122C23—62no—
1123C23—62no—
1124C23—62no—
1125C23—62no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23—121no—
1130C23—121no—
1131C23—121no—
1132C23—121no—
1133C23—121no—
1134C23—121no—
1135C23—121no—
1136C23—121no—
1137C23—121no—
1138C23—121no—
1139C23—121no—
1140C23—121no—
1141C23—121no—
1142C23—121no—
1143C23—121no—
1144C23—121no—
1145C23—121no—
1146C23—121no—
1147C23—121no—
1148C23—121no—
1149C23—121no—
1150C23—121no—
1151C23—121no—
1152C23—121no—
1153C23—121no—
1154C23#67⋊C414yes—
1155C23#67⋊C414yes—
1156C23#88214yes—
1157C23#88614yes—
1158C23C2×(C2×D3)⋊C414yes—
1159C23C2×(C2×D3)⋊C414yes—
1160C23#93914yes—
1161C23#93914yes—
1162C23C22×C4×D311yescharacteristic
1163C23C22×D1211yescharacteristic
1164C23C2×D3×D411yescharacteristic
1165C23C2×D3×D411yescharacteristic
1166C23C2×D3×D411yescharacteristic
1167C23C2×#23711yescharacteristic
1168C23C2×#23711yescharacteristic
1169C23C2×#23711yescharacteristic
1170C23#100411yescharacteristic
1171C23#100411yescharacteristic
1172C23D3×#4111yescharacteristic
1173C23D3×#4111yescharacteristic
1174C23#100911yescharacteristic
1175C23#101011yescharacteristic
1176C23C22×#6711yescharacteristic
1177D4—232no—
1178D4—1216no—
1179D4—1216no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—34no—
1193C2×C4—34no—
1194C2×C4—416no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—62no—
1218C2×C4—62no—
1219C2×C4—62no—
1220C2×C4—62no—
1221C2×C4—62no—
1222C2×C4—62no—
1223C2×C4—62no—
1224C2×C4—62no—
1225C2×C4—62no—
1226C2×C4—62no—
1227C2×C4—62no—
1228C2×C4—62no—
1229C2×C4—62no—
1230C2×C4—62no—
1231C2×C4—62no—
1232C2×C4—62no—
1233C2×C4—62no—
1234C2×C4—62no—
1235C2×C4—62no—
1236C2×C4—62no—
1237C2×C4—62no—
1238C2×C4—62no—
1239C2×C4—62no—
1240C2×C4—62no—
1241C2×C4—62no—
1242C2×C4—62no—
1243C2×C4—62no—
1244C2×C4—1216no—
1245C2×C4—1216no—
1246C2×C4—1216no—
1247C2×C4—121no—
1248C2×C4—121no—
1249C2×C4—121no—
1250C2×C4—121no—
1251C2×C4—121no—
1252C2×C4—121no—
1253C2×C4—121no—
1254C2×C4—121no—
1255C2×C4—121no—
1256C2×C4—121no—
1257C2×C4—121no—
1258C2×C4—121no—
1259C2×C4—121no—
1260C2×C4—121no—
1261C2×C4—121no—
1262C2×C4—121no—
1263C2×C4—121no—
1264C2×C4—121no—
1265C2×C4—121no—
1266C2×C4—121no—
1267C2×C4C2×(C2×D3)⋊C414yes—
1268C2×C3—28no—
1269C2×C3—44no—
1270C2×C3C2×#38611yescharacteristic
1271C2×C3C4×#12111yescharacteristic
1272C2×C3#232511yescharacteristic
1273C2×C3D4×C22⋊C411yescharacteristic
1274C2×C3#233911yescharacteristic
1275C2×C3#236111yescharacteristic
1276C2×C3#236411yescharacteristic
1277C2×C3#241011yescharacteristic
1278C2×C3#241611yescharacteristic
1279C2×C3#242411yescharacteristic
1280C2×C3#242511yescharacteristic
1281C2×C3#243011yescharacteristic
1282C2×C3#244311yescharacteristic
1283C2×C3#244411yescharacteristic
1284C2×C3#254311yescharacteristic
1285D3—82no—
1286C22—24no—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—122no—
1316C22—122no—
1317C22—122no—
1318C22—122no—
1319C22—122no—
1320C22—122no—
1321C22—122no—
1322C22—241no—
1323C22—241no—
1324C22—241no—
1325C22—241no—
1326C22—241no—
1327C22—241no—
1328C22—241no—
1329C22—241no—
1330C22#495818yescomplemented
1331C22C2×#67⋊C411yescharacteristic
1332C22C2×#67⋊C411yescharacteristic
1333C22C2×#88211yescharacteristic
1334C22C2×#88611yescharacteristic
1335C22C4×#23711yescharacteristic
1336C22C4×D3×D411yescharacteristic
1337C22#554511yescharacteristic
1338C22#554611yescharacteristic
1339C22D4×D1211yescharacteristic
1340C22#555411yescharacteristic
1341C22#555411yescharacteristic
1342C22#555511yescharacteristic
1343C22#558611yescharacteristic
1344C22#559011yescharacteristic
1345C22#559111yescharacteristic
1346C22#559311yescharacteristic
1347C22#559611yescharacteristic
1348C22#559711yescharacteristic
1349C22#559811yescharacteristic
1350C22#560111yescharacteristic
1351C22#560111yescharacteristic
1352C22D3×#12111yescharacteristic
1353C22#560511yescharacteristic
1354C22#561811yescharacteristic
1355C22#564911yescharacteristic
1356C22#565411yescharacteristic
1357C22#565511yescharacteristic
1358C22#566511yescharacteristic
1359C22C22×(C2×D3)⋊C411yescharacteristic
1360C22D4×#6711yescharacteristic
1361C22C2×#93911yescharacteristic
1362C22C2×#93911yescharacteristic
1363C22#580611yescharacteristic
1364C22#582411yescharacteristic
1365C22#582911yescharacteristic
1366C4—24no—
1367C4—42no—
1368C4—42no—
1369C4—64no—
1370C4—64no—
1371C4—81no—
1372C4—81no—
1373C4—122no—
1374C4—122no—
1375C4—122no—
1376C4—122no—
1377C4—122no—
1378C3#1402311yescharacteristic, complemented, Sylow
1379C2—28no—
1380C2—44no—
1381C2—242no—
1382C2#7466011yescharacteristic
1383C2#7466611yescharacteristic
1384C2#7467611yescharacteristic
1385C2#7467811yescharacteristic
1386C2#7469911yescharacteristic
1387C2#7470311yescharacteristic
1388C2#7470611yescharacteristic
1389C2#7488811yescharacteristic
1390C2C2×#495811yescharacteristic
1391C2#8233011yescharacteristic
1392C2D4×(C2×D3)⋊C411yescharacteristic
1393C2#8258711yescharacteristic
1394C2#8264211yescharacteristic
1395C2#8267011yescharacteristic
1396C2#8284711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3#14023
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic3C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5213C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4958C2semidirect
7. C2×#4958C2semidirect
8. #71550C2semidirect
9. #71549C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
12. #69427C2semidirect
13. #69410C2semidirect
14. #69408C2semidirect
15. #69405C2semidirect
32. C2×#939C4semidirect
68. C2×#386D3semidirect
112. C22×#67C2×C4semidirect
113. C22×#67C2×C4semidirect
133. C23×Dic3C2×C4semidirect
134. C23×Dic3D4semidirect
158. C2×#217C2×C4semidirect
159. C2×#217D4semidirect
176. C2×(C2×D3)⋊C4C2×C4semidirect
182. C2×Dic3⋊C4C2×C4semidirect
199. C3⋊#95D4semidirect
298. C2×C3×D4C22⋊C4semidirect
770. C2×Dic3C4×D4semidirect
771. C2×Dic3#121semidirect
838. C2×D4(C2×D3)⋊C4semidirect
994. C22×C3#386semidirect
1330. C22#4958semidirect
1378. C3#14023semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C22×D4×Dic32
C2×C3×#3862
C2×#52132
C22×C3⋊#952
C2×#49582
#715502
#715492
#715442
#694272
#694102
#694082
#694052
#140233