Finite Group Databasebeta

← #10718646

Subgroups — #10718646

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×#884C211yesmaximal, characteristic
2C22×C4×D12C211yesmaximal, characteristic, complemented
3C2×#4956C211yesmaximal, characteristic, complemented
4C2×#4956C211yesmaximal, characteristic, complemented
5C2×#4956C211yesmaximal, characteristic, complemented
6C2×#4665C211yesmaximal, characteristic, complemented
7C2×D3×#95C211yesmaximal, characteristic, complemented
8C3×#1437C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71536C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69410C211yesmaximal, characteristic, complemented
16#14023—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C23×C4×D3C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C2×#884—24no—
39C2×#884—24no—
40C2×#884C418yescomplemented
41C2×C4×D12—24no—
42C2×C4×D12—24no—
43C2×C4×D12—24no—
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
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
57C2×C3⋊#95C2211yescharacteristic
58#4956—24no—
59#4956—24no—
60#4956—24no—
61#4665—24no—
62D3×#95—24no—
63C22×#121—31no—
64C22×C4×D4—31no—
65C2×#386—31no—
66C2×#386—31no—
67C2×#386—31no—
68C2×#386—31no—
69C22×#95—31no—
70#1441—31no—
71#1440—31no—
72#1439—31no—
73#1438—31no—
74#1437D311yescharacteristic, complemented
75#1436—31no—
76C22⋊#95—31no—
77C22⋊#95—31no—
78C25×C3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67C2×C414yescomplemented
100C22×#67C2×C414yescomplemented
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12C2×C414yes—
112C22×D12D414yes—
113C22×D12D414yes—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—22no—
124C22×C4×D3—22no—
125C22×C4×D3—22no—
126C22×C4×D3—22no—
127C22×C4×D3—22no—
128C22×C4×D3—22no—
129C22×C4×D3—22no—
130C22×C4×D3—22no—
131C22×C4×D3—22no—
132C22×C4×D3—41no—
133C22×C4×D3—41no—
134C22×C4×D3—41no—
135C22×C4×D3—41no—
136C22×C4×D3—41no—
137C22×C4×D3—41no—
138C22×C4×D3—41no—
139C22×C4×D3—41no—
140C22×C4×D3C2×C414yescomplemented
141C22×C4×D3D414yescomplemented
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⋊C4C2×C414yescomplemented
151C2×C3×C42—22no—
152C2×C3×C42—22no—
153C2×C3×C42—22no—
154C2×#217—22no—
155C2×#217—22no—
156C2×#217—22no—
157C2×#217—41no—
158C2×#217—41no—
159C2×#217—41no—
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—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—22no—
171C2×(C2×D3)⋊C4—22no—
172C2×(C2×D3)⋊C4—22no—
173C2×(C2×D3)⋊C4—22no—
174C2×(C2×D3)⋊C4—41no—
175C2×(C2×D3)⋊C4—41no—
176C2×(C2×D3)⋊C4C2×C414yescomplemented
177C2×(C2×D3)⋊C4D414yescomplemented
178C2×C4⋊Dic3—22no—
179C2×C4⋊Dic3—22no—
180C2×C4⋊Dic3—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4—22no—
183C2×Dic3⋊C4C2×C414yescomplemented
184#884—232no—
185C4×D12—232no—
186C3×#95—22no—
187C3×#95—22no—
188C3×#95—41no—
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—22no—
198C3⋊#95—41no—
199C3⋊#95D414yescomplemented
200C23×D4—31no—
201C23×D4—31no—
202C23×D4—31no—
203C24×C4—31no—
204C24×C4—31no—
205C24×C4—31no—
206C24×C4—31no—
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×C42C2×D311yescharacteristic
227#386—64no—
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—64no—
243C2×#95C2×D311yescharacteristic
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×C3C22×C412yes—
261C24×C3C2411yescharacteristic
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
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×D3C22×C412yes—
283C23×D3C22×C412yes—
284C23×D3C2×D412yes—
285C23×D3C2×D412yes—
286C23×D3C2×D412yes—
287C23×D3C2×D412yes—
288C23×D3C2×D412yes—
289C23×D3C2×D412yes—
290C23×D3#4112yes—
291C23×D3#4112yes—
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×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4C22×C412yes—
326C22×C3×C4C22×C412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C2×#67—28no—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—44no—
340C2×#67—44no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
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×Dic3C22×C412yes—
384C22×Dic3C22×C412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3#4112yes—
390C2×D12—28no—
391C2×D12—28no—
392C2×D12—28no—
393C2×D12—28no—
394C2×D12—28no—
395C2×D12—28no—
396C2×D12C22⋊C4116yescomplemented
397C2×C4×D3—28no—
398C2×C4×D3—28no—
399C2×C4×D3—28no—
400C2×C4×D3—28no—
401C2×C4×D3—28no—
402C2×C4×D3—28no—
403C2×C4×D3—44no—
404C2×C4×D3—44no—
405C2×C4×D3—44no—
406C2×C4×D3—44no—
407C2×C4×D3—44no—
408C2×C4×D3—44no—
409C2×C4×D3—44no—
410C2×C4×D3—44no—
411C2×C4×D3—44no—
412C2×C4×D3—44no—
413C2×C4×D3—44no—
414C2×C4×D3—44no—
415C2×C4×D3—44no—
416C2×C4×D3—44no—
417C2×C4×D3—44no—
418C2×C4×D3—44no—
419C2×C4×D3—44no—
420C2×C4×D3—44no—
421C2×C4×D3—44no—
422C2×C4×D3—44no—
423C2×C4×D3—44no—
424C2×C4×D3—44no—
425C3×C22⋊C4—28no—
426C3×C22⋊C4—44no—
427C3×C22⋊C4—44no—
428C3×C42—28no—
429#217—44no—
430#217—44no—
431(C2×D3)⋊C4—28no—
432(C2×D3)⋊C4—28no—
433(C2×D3)⋊C4—28no—
434(C2×D3)⋊C4—44no—
435(C2×D3)⋊C4—44no—
436(C2×D3)⋊C4—44no—
437C4⋊Dic3—28no—
438Dic3⋊C4—28no—
439C25—31no—
440C25—31no—
441C25C22×D311yescharacteristic
442C22×D4—34no—
443C22×D4—34no—
444C22×D4—34no—
445C22×D4—34no—
446C22×D4—34no—
447C22×D4—62no—
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—62no—
459C22×D4—62no—
460C22×D4—62no—
461C22×D4—121no—
462C22×D4—121no—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—31no—
468C23×C4—34no—
469C23×C4—34no—
470C23×C4—31no—
471C23×C4—62no—
472C23×C4—62no—
473C23×C4—62no—
474C23×C4—62no—
475C23×C4—62no—
476C23×C4—62no—
477C23×C4—62no—
478C23×C4—62no—
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—121no—
490C23×C4—121no—
491C23×C4—121no—
492C23×C4—121no—
493C23×C4—121no—
494C23×C4—121no—
495C23×C4—121no—
496C23×C4—121no—
497C23×C4C22×D311yescharacteristic
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—41no—
521C2×C22⋊C4—62no—
522C2×C22⋊C4—62no—
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—121no—
539C2×C22⋊C4—121no—
540C2×C22⋊C4—121no—
541C2×C22⋊C4—121no—
542C2×C22⋊C4—121no—
543C2×C22⋊C4C4×D314yescomplemented
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547#95—22no—
548#95—22no—
549#95—34no—
550#95—41no—
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—62no—
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—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×C3C23×C411yescharacteristic
597C23×C3C22×D411yescharacteristic
598C23×C3C22×D411yescharacteristic
599C23×C3C22×D411yescharacteristic
600C23×C3C22×D411yescharacteristic
601C23×C3C22×D411yescharacteristic
602C23×C3C2×#4111yescharacteristic
603C23×C3C2×#4111yescharacteristic
604C23×C3C2×#4111yescharacteristic
605C23×C3C2×#4111yescharacteristic
606C23×C3C2×#4111yescharacteristic
607C23×C3H(5,𝔽2)11yescharacteristic
608C23×C3H(5,𝔽2)11yescharacteristic
609C23×C3H(5,𝔽2)11yescharacteristic
610C23×C32−1+411yescharacteristic
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
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—22no—
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
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×D3C2×C22⋊C414yes—
674C22×D3C2×C22⋊C414yes—
675C22×D3C4×D414yes—
676C22×D3C4×D414yes—
677C22×D3#12014yes—
678C22×D3#12114yes—
679C22×D3#12114yes—
680C22×D3#12314yes—
681C2×C3×C4—22no—
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—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
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×C4—41no—
718C2×C3×C4—41no—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4C2×C22⋊C414yes—
722C2×C3×C4#12114yescomplemented
723#67—416no—
724#67—416no—
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—41no—
744C2×Dic3—41no—
745C2×Dic3—41no—
746C2×Dic3—41no—
747C2×Dic3—41no—
748C2×Dic3—41no—
749C2×Dic3—41no—
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×Dic3C4×D414yescomplemented
767D12—232no—
768C4×D3—416no—
769C4×D3—416no—
770C4×D3—416no—
771C4×D3—416no—
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—32no—
787C24—32no—
788C24—32no—
789C24—32no—
790C24—32no—
791C24—32no—
792C24—32no—
793C24—32no—
794C24—32no—
795C24—32no—
796C24—61no—
797C24—61no—
798C24—61no—
799C24—61no—
800C24—61no—
801C24—61no—
802C24—61no—
803C24—61no—
804C24—61no—
805C24—61no—
806C24—61no—
807C24—61no—
808C24—61no—
809C24—61no—
810C24—61no—
811C24—61no—
812C24—61no—
813C24—61no—
814C24—61no—
815C24—61no—
816C24C2×C4×D312yes—
817C24C23×D311yescharacteristic
818C2×D4—316no—
819C2×D4—68no—
820C2×D4—68no—
821C2×D4—68no—
822C2×D4—68no—
823C2×D4—68no—
824C2×D4—68no—
825C2×D4—68no—
826C2×D4—68no—
827C2×D4—68no—
828C2×D4—68no—
829C2×D4—68no—
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—124no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
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—21no—
871C22×C4—21no—
872C22×C4—32no—
873C22×C4—32no—
874C22×C4—32no—
875C22×C4—32no—
876C22×C4—32no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—68no—
880C22×C4—68no—
881C22×C4—68no—
882C22×C4—68no—
883C22×C4—68no—
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—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—68no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—61no—
919C22×C4—61no—
920C22×C4—124no—
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×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×C4C2×C4×D312yes—
943C22×C4C2×C4×D312yes—
944C22×C4#23512yes—
945C22×C4#23512yes—
946C22×C4D3×D412yes—
947C22×C4D3×D412yes—
948C22×C4D3×D412yes—
949C22×C4D3×D412yes—
950C22×C4D3×D412yes—
951C4⋊C4—68no—
952C4⋊C4—68no—
953C22⋊C4—28no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—68no—
957C22⋊C4—68no—
958C22⋊C4—68no—
959C22⋊C4—124no—
960C22⋊C4—124no—
961C22⋊C4—124no—
962C22⋊C4—124no—
963C22⋊C4—124no—
964C42—28no—
965C22×C3—42no—
966C22×C3—42no—
967C22×C3—42no—
968C22×C3—42no—
969C22×C3—42no—
970C22×C3—42no—
971C22×C3—42no—
972C22×C3—81no—
973C22×C3—81no—
974C22×C3—81no—
975C22×C3—81no—
976C22×C3—81no—
977C22×C3—81no—
978C22×C3—81no—
979C22×C3—81no—
980C22×C3C22×C22⋊C411yescharacteristic
981C22×C3C2×C4×D411yescharacteristic
982C22×C3C2×C4×D411yescharacteristic
983C22×C3C2×C4×D411yescharacteristic
984C22×C3C4×#4111yescharacteristic
985C22×C3#51811yescharacteristic
986C22×C3#52011yescharacteristic
987C22×C3C2×#12011yescharacteristic
988C22×C3C2×#12111yescharacteristic
989C22×C3C2×#12111yescharacteristic
990C22×C3C2×#12111yescharacteristic
991C22×C3C2×#12311yescharacteristic
992C22×C3#52511yescharacteristic
993C22×C3#52911yescharacteristic
994C22×C3#53211yescharacteristic
995C22×C3#53411yescharacteristic
996C22×C3#53711yescharacteristic
997C22×C3#53811yescharacteristic
998C22×C3#53911yescharacteristic
999C22×C3D4211yescharacteristic
1000C22×C3D4211yescharacteristic
1001C22×C3D4211yescharacteristic
1002C22×C3#54611yescharacteristic
1003C22×C3#54611yescharacteristic
1004C22×C3#54611yescharacteristic
1005C22×C3#54611yescharacteristic
1006C22×C3#54611yescharacteristic
1007C22×C3#54611yescharacteristic
1008C22×C3#54711yescharacteristic
1009C22×C3#54711yescharacteristic
1010C22×C3#54711yescharacteristic
1011C22×C3#54811yescharacteristic
1012C22×C3#55311yescharacteristic
1013C22×C3#55311yescharacteristic
1014C22×C3#55311yescharacteristic
1015C2×D3—24no—
1016C2×D3—24no—
1017C2×D3—24no—
1018C2×D3—24no—
1019C2×D3—24no—
1020C2×D3—24no—
1021C2×D3—24no—
1022C2×D3—24no—
1023C2×D3—24no—
1024C2×D3—24no—
1025C2×D3—24no—
1026C2×D3—24no—
1027C2×D3—24no—
1028C2×D3—24no—
1029C2×D3—24no—
1030C2×D3—24no—
1031C2×D3—24no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—42no—
1036C2×D3—42no—
1037C2×D3—42no—
1038C2×D3—42no—
1039C2×D3—42no—
1040C2×D3—42no—
1041C2×D3—42no—
1042C2×D3—42no—
1043C2×D3—42no—
1044C2×D3#38618yescomplemented
1045C3×C4—24no—
1046C3×C4—24no—
1047C3×C4—42no—
1048C3×C4—42no—
1049C3×C4—42no—
1050C3×C4—81no—
1051Dic3—24no—
1052Dic3—42no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—42no—
1056Dic3—81no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—34no—
1065C23—34no—
1066C23—34no—
1067C23—34no—
1068C23—34no—
1069C23—34no—
1070C23—34no—
1071C23—34no—
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—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—62no—
1114C23—62no—
1115C23—62no—
1116C23—62no—
1117C23—62no—
1118C23—62no—
1119C23—62no—
1120C23—62no—
1121C23—62no—
1122C23—62no—
1123C23—62no—
1124C23—62no—
1125C23—62no—
1126C23—62no—
1127C23—62no—
1128C23—62no—
1129C23—62no—
1130C23—62no—
1131C23—62no—
1132C23—62no—
1133C23—62no—
1134C23—62no—
1135C23—62no—
1136C23—62no—
1137C23—62no—
1138C23—62no—
1139C23—62no—
1140C23—62no—
1141C23—62no—
1142C23—62no—
1143C23—62no—
1144C23—62no—
1145C23—62no—
1146C23—121no—
1147C23—121no—
1148C23—121no—
1149C23—121no—
1150C23—121no—
1151C23—121no—
1152C23—121no—
1153C23—121no—
1154C23—121no—
1155C23—121no—
1156C23—121no—
1157C23—121no—
1158C23—121no—
1159C23—121no—
1160C23—121no—
1161C23—121no—
1162C23C22×C4×D311yescharacteristic
1163C23C2×#23511yescharacteristic
1164C23C2×#23511yescharacteristic
1165C23C2×D3×D411yescharacteristic
1166C23C2×D3×D411yescharacteristic
1167C23C2×D3×D411yescharacteristic
1168C23C2×D3×D411yescharacteristic
1169C23C2×D3×D411yescharacteristic
1170C23#100411yescharacteristic
1171C23D3×#4111yescharacteristic
1172C23D3×#4111yescharacteristic
1173C23D3×#4111yescharacteristic
1174C23#100911yescharacteristic
1175C23#100911yescharacteristic
1176C23#101011yescharacteristic
1177D4—632no—
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—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—34no—
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—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
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—1216no—
1240C2×C4—1216no—
1241C2×C4—1216no—
1242C2×C4—1216no—
1243C2×C4—121no—
1244C2×C4—121no—
1245C2×C4—121no—
1246C2×C4—121no—
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×C4D3×C22⋊C414yes—
1267C2×C4#88414yescomplemented
1268C2×C3—82no—
1269C2×C3C2×#38611yescharacteristic
1270C2×C3C4×#12111yescharacteristic
1271C2×C3#232511yescharacteristic
1272C2×C3D4×C22⋊C411yescharacteristic
1273C2×C3#233911yescharacteristic
1274C2×C3#236111yescharacteristic
1275C2×C3#236411yescharacteristic
1276C2×C3#241011yescharacteristic
1277C2×C3#241611yescharacteristic
1278C2×C3#242411yescharacteristic
1279C2×C3#242511yescharacteristic
1280C2×C3#243011yescharacteristic
1281C2×C3#244311yescharacteristic
1282C2×C3#244411yescharacteristic
1283C2×C3#254311yescharacteristic
1284D3—28no—
1285D3—44no—
1286C22—38no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—64no—
1295C22—64no—
1296C22—64no—
1297C22—64no—
1298C22—64no—
1299C22—64no—
1300C22—64no—
1301C22—64no—
1302C22—64no—
1303C22—64no—
1304C22—64no—
1305C22—64no—
1306C22—64no—
1307C22—64no—
1308C22—64no—
1309C22—64no—
1310C22—64no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—122no—
1320C22—122no—
1321C22—122no—
1322C22—122no—
1323C22—122no—
1324C22—122no—
1325C22—122no—
1326C22—122no—
1327C22—122no—
1328C22—122no—
1329C22—122no—
1330C22—122no—
1331C22C4×#23511yescharacteristic
1332C22C2×D3×C22⋊C411yescharacteristic
1333C22C2×#88411yescharacteristic
1334C22#549011yescharacteristic
1335C22#552311yescharacteristic
1336C22#552811yescharacteristic
1337C22#553011yescharacteristic
1338C22C4×D3×D411yescharacteristic
1339C22C4×D3×D411yescharacteristic
1340C22C4×D3×D411yescharacteristic
1341C22#554511yescharacteristic
1342C22#554711yescharacteristic
1343C22#554811yescharacteristic
1344C22#555011yescharacteristic
1345C22#555011yescharacteristic
1346C22#555011yescharacteristic
1347C22#555111yescharacteristic
1348C22#555111yescharacteristic
1349C22#555811yescharacteristic
1350C22D3×#12011yescharacteristic
1351C22D3×#12111yescharacteristic
1352C22D3×#12111yescharacteristic
1353C22#560811yescharacteristic
1354C22#560911yescharacteristic
1355C22#560911yescharacteristic
1356C22#561211yescharacteristic
1357C22D3×#12311yescharacteristic
1358C22#565311yescharacteristic
1359C22#565511yescharacteristic
1360C22#567611yescharacteristic
1361C22#567711yescharacteristic
1362C22#567811yescharacteristic
1363C22#570711yescharacteristic
1364C22#570911yescharacteristic
1365C22#571711yescharacteristic
1366C4—24no—
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—64no—
1372C4—81no—
1373C4—122no—
1374C4—122no—
1375C4—122no—
1376C4—122no—
1377C4—241no—
1378C3#1402311yescharacteristic, complemented, Sylow
1379C2—68no—
1380C2—82no—
1381C2—124no—
1382C2C4×#88411yescharacteristic
1383C2#7357311yescharacteristic
1384C2#7357911yescharacteristic
1385C2D3×#38611yescharacteristic
1386C2#7488711yescharacteristic
1387C2#7489611yescharacteristic
1388C2#7547711yescharacteristic
1389C2#7582911yescharacteristic
1390C2#7584711yescharacteristic
1391C2#7584811yescharacteristic
1392C2#7584911yescharacteristic
1393C2#7588211yescharacteristic
1394C2#7643111yescharacteristic
1395C2#7643911yescharacteristic
1396C2#7644211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC22×#884C2
hypercenter#1437D3
hypocenterC3#14023
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×D12C2semidirect
3. C2×#4956C2semidirect
4. C2×#4956C2semidirect
5. C2×#4956C2semidirect
6. C2×#4665C2semidirect
7. C2×D3×#95C2semidirect
8. C3×#1437C2semidirect
9. #71550C2semidirect
10. #71546C2semidirect
11. #71536C2semidirect
12. #69429C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69410C2semidirect
40. C2×#884C4semidirect
74. #1437D3semidirect
99. C22×#67C2×C4semidirect
100. C22×#67C2×C4semidirect
140. C22×C4×D3C2×C4semidirect
141. C22×C4×D3D4semidirect
150. C2×C3×C22⋊C4C2×C4semidirect
176. C2×(C2×D3)⋊C4C2×C4semidirect
177. C2×(C2×D3)⋊C4D4semidirect
183. C2×Dic3⋊C4C2×C4semidirect
199. C3⋊#95D4semidirect
396. C2×D12C22⋊C4semidirect
543. C2×C22⋊C4C4×D3semidirect
722. C2×C3×C4#121semidirect
766. C2×Dic3C4×D4semidirect
1044. C2×D3#386semidirect
1267. C2×C4#884semidirect
1378. C3#14023semidirect

Maximal subgroups

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

subgroupindex
C22×#8842
C22×C4×D122
C2×#49562
C2×#46652
C2×D3×#952
C3×#14372
#715502
#715462
#715362
#694292
(C2×D3)⋊#952
#694102
#140233