Finite Group Databasebeta

← #10795119

Subgroups — #10795119

Order 768.

1866 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic
2#73561C212yesmaximal, complemented
3C3×C4×#99C211yesmaximal, characteristic, complemented
4C4×#834C211yesmaximal, characteristic, complemented
5#70035C212yesmaximal
6#70028C212yesmaximal, complemented
7C4×#806C212yesmaximal, complemented
8#68969C212yesmaximal, complemented
9#68959C212yesmaximal, complemented
10#20722—31nomaximal, Sylow
11C22×D3×D4C2211yescharacteristic
12C23×C4×D3C411yescharacteristic, complemented
13C23×C4×D3C2211yescharacteristic
14C2×C3×C4×D4C2211yescharacteristic
15C2×D4×Dic3C2211yescharacteristic
16C2×C4×#67C411yescharacteristic, complemented
17C2×C4×#67C2211yescharacteristic
18C4×D3×D4—22no—
19C4×D3×D4—22no—
20C4×D3×D4—22no—
21C4×D3×D4—22no—
22C2×#893C411yescharacteristic, complemented
23C2×D3×C4⋊C4C411yescharacteristic, complemented
24C2×#67⋊C4C411yescharacteristic, complemented
25C2×#67⋊C4C2211yescharacteristic
26C2×D3×C22⋊C4C411yescharacteristic, complemented
27C2×D3×C22⋊C4C2211yescharacteristic
28C2×C4×D12C411yescharacteristic, complemented
29C2×#872—22no—
30C2×C42×D3C411yescharacteristic, complemented
31C2×C3×#99C2212yes—
32C3×C4×C22⋊C4C2212yescomplemented
33C2×#834C2212yes—
34C4×#217C2212yescomplemented
35#4955C2214yes—
36C2×#806C2214yes—
37#4942C2214yescomplemented
38C4×(C2×D3)⋊C4—22no—
39#4667—22no—
40#4664—22no—
41C3×#342C2212yescomplemented
42#4527C2214yescomplemented
43#4526C2212yescomplemented
44C22×C4×D4—31no—
45#2280—32no—
46#1819—32no—
47#1799—32no—
48#1799—32no—
49#1781—32no—
50C4×#99—32no—
51C4×#99—31no—
52C4×#99D311yescharacteristic, complemented
53C24×D3C2×C411yescharacteristic
54C24×D3C2311yescharacteristic
55C22×C3×D4C2311yescharacteristic
56C23×C3×C4C2×C411yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C22×#67C2×C411yescharacteristic
59C22×#67C2311yescharacteristic
60C23×Dic3C2×C411yescharacteristic
61C23×Dic3C2311yescharacteristic
62C2×D3×D4—22no—
63C2×D3×D4—22no—
64C2×D3×D4—24no—
65C2×D3×D4—24no—
66C22×D12C2×C411yescharacteristic
67C22×C4×D3—21no—
68C22×C4×D3—21no—
69C22×C4×D3—21no—
70C22×C4×D3—21no—
71C22×C4×D3—44no—
72C22×C4×D3—44no—
73C22×C4×D3C2×C411yescharacteristic
74C22×C4×D3C2×C411yescharacteristic
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3C2×C411yescharacteristic
77C22×C4×D3C2×C411yescharacteristic
78C22×C4×D3C2×C411yescharacteristic
79C22×C4×D3C2×C411yescharacteristic
80C22×C4×D3C2×C411yescharacteristic
81C22×C4×D3C2×C411yescharacteristic
82C22×C4×D3D412yes—
83C22×C4×D3D412yes—
84C22×C4×D3D412yes—
85C22×C4×D3D412yes—
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C2×C3×C4⋊C4C2×C411yescharacteristic
89C2×C3×C22⋊C4C2×C411yescharacteristic
90C2×C3×C22⋊C4C2314yes—
91C2×C3×C22⋊C4C2311yescharacteristic
92C2×C3×C42—22no—
93C2×C3×C42C2×C411yescharacteristic
94C2×#217C2×C411yescharacteristic
95C2×#217C2314yes—
96C2×#217C2311yescharacteristic
97D4×Dic3—22no—
98D4×Dic3—22no—
99C4×#67—22no—
100C4×#67—22no—
101C4×#67—22no—
102C4×#67—22no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4C2×C411yescharacteristic
106C2×(C2×D3)⋊C4C2×C411yescharacteristic
107C2×(C2×D3)⋊C4C2×C411yescharacteristic
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×C4⋊Dic3C2×C411yescharacteristic
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4C2×C411yescharacteristic
112C2×Dic3⋊C4C2×C411yescharacteristic
113C2×C4×Dic3—22no—
114C2×C4×Dic3C2×C411yescharacteristic
115C2×C4×Dic3C2×C411yescharacteristic
116C2×C4×Dic3C2×C411yescharacteristic
117#893—22no—
118#893—22no—
119D3×C4⋊C4—22no—
120D3×C4⋊C4—22no—
121#67⋊C4—22no—
122#67⋊C4—22no—
123#67⋊C4—22no—
124#67⋊C4—22no—
125D3×C22⋊C4—22no—
126D3×C22⋊C4—22no—
127D3×C22⋊C4—22no—
128D3×C22⋊C4—22no—
129C4×D12—22no—
130C4×D12—22no—
131#872—48no—
132C42×D3—21no—
133C42×D3—21no—
134C42×D3—21no—
135C42×D3—21no—
136C3×#99—24no—
137C3×#95—22no—
138#834—24no—
139C3⋊#95—22no—
140C3⋊#95—24no—
141#806—28no—
142C23×D4—31no—
143C24×C4—31no—
144C24×C4—31no—
145C2×C4×D4—31no—
146C2×C4×D4—31no—
147C2×C4×D4—31no—
148C2×C4×D4—31no—
149C2×C4×D4—31no—
150C2×C4×D4—31no—
151C2×C4×D4—31no—
152C2×C4×D4—62no—
153C2×C4×D4—62no—
154C2×C4×D4—62no—
155C2×C4×D4—62no—
156C2×C4×D4C2×D311yescharacteristic
157C2×#117—62no—
158C22×C4⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C42—31no—
162C2×#99—32no—
163C2×#99—34no—
164C2×#99C2×D312yes—
165#381—62no—
166#380—34no—
167#380—62no—
168#379—34no—
169C4×C22⋊C4—32no—
170C4×C22⋊C4—62no—
171C4×C22⋊C4C2×D312yescomplemented
172#342—32no—
173#342—34no—
174#342C2×D312yescomplemented
175C24×C3C22×C411yescharacteristic
176C24×C3C2411yescharacteristic
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—21no—
181C23×D3—21no—
182C23×D3—22no—
183C23×D3—42no—
184C23×D3—42no—
185C23×D3—42no—
186C23×D3—42no—
187C23×D3C22×C411yescharacteristic
188C23×D3C22×C411yescharacteristic
189C23×D3C22×C411yescharacteristic
190C23×D3C2×D412yes—
191C23×D3C2×D412yes—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4#4114yes—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—24no—
198C22×C3×C4—42no—
199C22×C3×C4—42no—
200C22×C3×C4C22×C411yescharacteristic
201C22×C3×C4C22×C411yescharacteristic
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C22×C411yescharacteristic
204C22×C3×C4C22×C411yescharacteristic
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C2×#67—22no—
208C2×#67—22no—
209C2×#67—22no—
210C2×#67—22no—
211C2×#67—22no—
212C2×#67#4114yes—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—24no—
216C22×Dic3—42no—
217C22×Dic3—42no—
218C22×Dic3C22×C411yescharacteristic
219C22×Dic3C22×C411yescharacteristic
220C22×Dic3C22×C411yescharacteristic
221C22×Dic3C22×C411yescharacteristic
222C22×Dic3C22×C411yescharacteristic
223C22×Dic3C2×D412yes—
224C22×Dic3C2×D412yes—
225D3×D4—216no—
226D3×D4—216no—
227C2×D12—22no—
228C2×D12—22no—
229C2×D12—22no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—28no—
235C2×C4×D3—24no—
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—42no—
245C2×C4×D3—44no—
246C2×C4×D3—42no—
247C2×C4×D3—44no—
248C2×C4×D3—42no—
249C2×C4×D3—44no—
250C2×C4×D3—44no—
251C2×C4×D3—44no—
252C2×C4×D3—44no—
253C2×C4×D3—44no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3C22⋊C411yescharacteristic
259C2×C4×D3C22⋊C411yescharacteristic
260C2×C4×D3C22⋊C411yescharacteristic
261C2×C4×D3C22⋊C412yes—
262C2×C4×D3C22⋊C412yes—
263C2×C4×D3C22⋊C412yes—
264C2×C4×D3C22⋊C412yes—
265C2×C4×D3C22⋊C412yes—
266C2×C4×D3C22⋊C412yes—
267C2×C4×D3C22⋊C411yescharacteristic
268C3×C4⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—44no—
276#217—22no—
277#217—22no—
278#217—24no—
279#217—24no—
280(C2×D3)⋊C4—22no—
281(C2×D3)⋊C4—22no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—48no—
285(C2×D3)⋊C4—48no—
286C4⋊Dic3—22no—
287Dic3⋊C4—22no—
288Dic3⋊C4—22no—
289Dic3⋊C4—48no—
290C4×Dic3—21no—
291C4×Dic3—21no—
292C4×Dic3—21no—
293C4×Dic3—21no—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C4×Dic3—44no—
297C25—31no—
298C25—31no—
299C22×D4—31no—
300C22×D4—31no—
301C22×D4—31no—
302C22×D4—64no—
303C22×D4—62no—
304C22×D4—62no—
305C22×D4—64no—
306C22×D4C22×D311yescharacteristic
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—32no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—32no—
314C23×C4—32no—
315C23×C4—32no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—61no—
323C23×C4—61no—
324C23×C4—61no—
325C23×C4—61no—
326C23×C4—124no—
327C23×C4—124no—
328C23×C4C4×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—62no—
333C4×D4—62no—
334C4×D4—62no—
335C4×D4—62no—
336C4×D4—62no—
337C4×D4—62no—
338C4×D4—62no—
339C4×D4—62no—
340C4×D4—62no—
341C4×D4—62no—
342C4×D4—62no—
343C4×D4—62no—
344C4×D4—62no—
345C4×D4—62no—
346#117—128no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—62no—
351C2×C4⋊C4—62no—
352C2×C4⋊C4—64no—
353C2×C4⋊C4C4×D311yescharacteristic
354C2×C22⋊C4—31no—
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—31no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—34no—
361C2×C22⋊C4—62no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4C4×D311yescharacteristic
368C2×C22⋊C4C22×D314yes—
369C2×C22⋊C4C22×D311yescharacteristic
370C2×C42—22no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—31no—
374C2×C42—61no—
375C2×C42—61no—
376C2×C42—61no—
377C2×C42—61no—
378C2×C42—62no—
379C2×C42C4×D311yescharacteristic
380#99—24no—
381#99—68no—
382#99—64no—
383#95—22no—
384#95—64no—
385#95—62no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3#11712yescomplemented
393C23×C3C23×C411yescharacteristic
394C23×C3C22×D412yes—
395C23×C3C2×#4112yes—
396C23×C3C2×#4112yes—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—41no—
412C22×D3—42no—
413C22×D3—41no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—48no—
417C22×D3—48no—
418C22×D3—48no—
419C22×D3—48no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3—42no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3C2×C22⋊C412yes—
426C22×D3C2×C22⋊C411yescharacteristic
427C22×D3C2×C22⋊C411yescharacteristic
428C22×D3#11712yescomplemented
429C3×D4—28no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—24no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445C2×C3×C4C2×C22⋊C411yescharacteristic
446C2×C3×C4C2×C22⋊C412yes—
447C2×C3×C4C2×C22⋊C411yescharacteristic
448C2×C3×C4#11712yescomplemented
449#67—28no—
450#67—28no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—24no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—41no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—44no—
464C2×Dic3—44no—
465C2×Dic3—44no—
466C2×Dic3C2×C22⋊C411yescharacteristic
467C2×Dic3C2×C22⋊C412yes—
468C2×Dic3C2×C22⋊C411yescharacteristic
469C2×Dic3#11712yescomplemented
470D12—28no—
471C4×D3—24no—
472C4×D3—24no—
473C4×D3—22no—
474C4×D3—24no—
475C4×D3—22no—
476C4×D3—24no—
477C4×D3—22no—
478C4×D3—24no—
479C4×D3—42no—
480C4×D3—42no—
481C4×D3—42no—
482C4×D3—42no—
483C4×D3—42no—
484C4×D3—42no—
485C4×D3—42no—
486C4×D3—42no—
487C4×D3—42no—
488C4×D3—42no—
489C4×D3—42no—
490C4×D3#9914yescomplemented
491C24—31no—
492C24—32no—
493C24—32no—
494C24—31no—
495C24—31no—
496C24—61no—
497C24—61no—
498C24—62no—
499C24—62no—
500C24—62no—
501C24—62no—
502C24—122no—
503C24—122no—
504C24—122no—
505C24—122no—
506C24C2×C4×D311yescharacteristic
507C24C23×D311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—34no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—616no—
515C2×D4—616no—
516C2×D4—62no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4#23514yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—32no—
529C22×C4—31no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—31no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—68no—
545C22×C4—64no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—62no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—64no—
561C22×C4—124no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—124no—
565C22×C4—122no—
566C22×C4—124no—
567C22×C4—122no—
568C22×C4—124no—
569C22×C4—124no—
570C22×C4—124no—
571C22×C4—124no—
572C22×C4—122no—
573C22×C4—122no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4C2×C4×D311yescharacteristic
578C22×C4C2×C4×D311yescharacteristic
579C22×C4C2×C4×D311yescharacteristic
580C22×C4C2×C4×D311yescharacteristic
581C22×C4C2×C4×D311yescharacteristic
582C22×C4D3×D412yes—
583C22×C4D3×D412yes—
584C4⋊C4—22no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—62no—
588C4⋊C4—128no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—62no—
594C22⋊C4—62no—
595C22⋊C4—62no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C22⋊C4—62no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—128no—
602C22⋊C4—128no—
603C42—21no—
604C42—21no—
605C42—44no—
606C42—61no—
607C42—61no—
608C42—61no—
609C42—61no—
610C42—61no—
611C42—61no—
612C42—124no—
613C22×C3—22no—
614C22×C3—21no—
615C22×C3—22no—
616C22×C3—21no—
617C22×C3—22no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3C22×C22⋊C411yescharacteristic
625C22×C3C2×#11711yescharacteristic
626C22×C3C2×#11711yescharacteristic
627C22×C3#52514yes—
628C2×D3—24no—
629C2×D3—24no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—48no—
639C2×D3—48no—
640C2×D3—48no—
641C2×D3—48no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—42no—
648C2×D3C2×#9912yes—
649C2×D3#41012yes—
650C3×C4—21no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—84no—
656C3×C4C2×#9912yes—
657Dic3—21no—
658Dic3—22no—
659Dic3—22no—
660Dic3—41no—
661Dic3—41no—
662Dic3—84no—
663Dic3C2×#9912yes—
664C23—21no—
665C23—21no—
666C23—31no—
667C23—31no—
668C23—32no—
669C23—32no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—62no—
675C23—62no—
676C23—64no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—64no—
687C23—64no—
688C23—122no—
689C23—121no—
690C23—122no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—128no—
698C23—128no—
699C23—128no—
700C23—128no—
701C23—122no—
702C23#87212yescomplemented
703C23C22×C4×D311yescharacteristic
704C23C2×#23512yes—
705C23C2×D3×D412yes—
706C23D3×#4112yes—
707D4—28no—
708D4—68no—
709D4—68no—
710D4—68no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—34no—
719C2×C4—31no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—62no—
734C2×C4—64no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—64no—
738C2×C4—62no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—121no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—124no—
763C2×C4—124no—
764C2×C4—124no—
765C2×C4#87212yescomplemented
766C2×C4D3×C22⋊C411yescharacteristic
767C2×C4D3×C22⋊C412yes—
768C2×C4D3×C22⋊C411yescharacteristic
769C2×C3—24no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—42no—
773C2×C3#228011yescharacteristic
774C2×C3C22×#9911yescharacteristic
775C2×C3C2×#41011yescharacteristic
776D3—22no—
777D3—22no—
778D3—42no—
779D3—42no—
780C22—22no—
781C22—21no—
782C22—22no—
783C22—21no—
784C22—22no—
785C22—32no—
786C22—32no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—64no—
794C22—64no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—128no—
804C22—128no—
805C22—122no—
806C22—122no—
807C22—122no—
808C22—122no—
809C22—128no—
810C22—128no—
811C22—121no—
812C22—121no—
813C22C2×#87211yescharacteristic
814C22C2×D3×C22⋊C411yescharacteristic
815C22D3×#11711yescharacteristic
816C22#554714yes—
817C4—22no—
818C4—21no—
819C4—22no—
820C4—32no—
821C4—41no—
822C4—41no—
823C4—62no—
824C4—61no—
825C4—62no—
826C4—84no—
827C4—121no—
828C4—121no—
829C4—244no—
830C4D3×#9912yes—
831C3#2072211yescharacteristic, complemented, Sylow
832C2—24no—
833C2—21no—
834C2—21no—
835C2—42no—
836C2—62no—
837C2—62no—
838C2—122no—
839C2—122no—
840C2#7356111yescharacteristic
841C2C2×D3×#9911yescharacteristic
842C2D3×#41011yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×C4×#99C2
socleC22×C3C22×C22⋊C4
prime radicalC22×D3×D4C22
cosocleC24×C3C24
hypercenterC4×#99D3
hypocenterC3#20722
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #73561C2semidirect
3. C3×C4×#99C2semidirect
4. C4×#834C2semidirect
6. #70028C2semidirect
7. C4×#806C2semidirect
8. #68969C2semidirect
9. #68959C2semidirect
12. C23×C4×D3C4semidirect
16. C2×C4×#67C4semidirect
22. C2×#893C4semidirect
23. C2×D3×C4⋊C4C4semidirect
24. C2×#67⋊C4C4semidirect
26. C2×D3×C22⋊C4C4semidirect
28. C2×C4×D12C4semidirect
30. C2×C42×D3C4semidirect
32. C3×C4×C22⋊C4C22semidirect
34. C4×#217C22semidirect
37. #4942C22semidirect
41. C3×#342C22semidirect
42. #4527C22semidirect
43. #4526C22semidirect
52. C4×#99D3semidirect
171. C4×C22⋊C4C2×D3semidirect
174. #342C2×D3semidirect
392. C23×C3#117semidirect
428. C22×D3#117semidirect
448. C2×C3×C4#117semidirect
469. C2×Dic3#117semidirect
490. C4×D3#99semidirect
702. C23#872semidirect
765. C2×C4#872semidirect
831. C3#20722semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D42
#735612
C3×C4×#992
C4×#8342
#700352
#700282
C4×#8062
#689692
#689592
#207223