Finite Group Databasebeta

← #10943826

Subgroups — #10943826

Order 768.

4004 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3C2×#5172C211yesmaximal, characteristic, complemented
4C2×#5170C211yesmaximal, characteristic, complemented
5C2×#5158C211yesmaximal, characteristic, complemented
6C2×#5156C211yesmaximal, characteristic, complemented
7#82723C211yesmaximal, characteristic, complemented
8C2×#5037C211yesmaximal, characteristic, complemented
9#72135C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70266C211yesmaximal, characteristic, complemented
12#70199C211yesmaximal, characteristic, complemented
13#70198C211yesmaximal, characteristic, complemented
14#69960C211yesmaximal, characteristic, complemented
15#69955C211yesmaximal, characteristic, complemented
16#32880—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×D3×#41—24no—
19C2×D3×#41—24no—
20C2×D3×#41—24no—
21C2×D3×#41—24no—
22C2×D3×#41—24no—
23C2×D3×#41—24no—
24C22×#239C2211yescharacteristic
25C22×D3×Q8C2211yescharacteristic
26C22×#237—21no—
27C22×#237C2211yescharacteristic
28C22×D3×D4—21no—
29C22×D3×D4C2211yescharacteristic
30C22×#235—21no—
31C22×#235C2211yescharacteristic
32C23×C4×D3—21no—
33C23×C4×D3C2211yescharacteristic
34C22×C3×SD16C2211yescharacteristic, complemented
35C22×C3×D8C2211yescharacteristic, complemented
36C2×C3×#121C2211yescharacteristic, complemented
37C2×#938C2211yescharacteristic
38C2×#938C2211yescharacteristic, complemented
39C2×#937—21no—
40C22×#214C2211yescharacteristic, complemented
41C22×#213C2211yescharacteristic, complemented
42C3×#449—24no—
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×C22⋊C8C2211yescharacteristic, complemented
46C2×#835C2211yescharacteristic, complemented
47C2×#835C2211yescharacteristic, complemented
48#5220—21no—
49C2×#832C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51#5212C2211yescharacteristic, complemented
52C2×#830C2211yescharacteristic, complemented
53#5172—24no—
54#5170—24no—
55#5158—24no—
56#5156—24no—
57C2×#821C2211yescharacteristic, complemented
58C2×#821C2211yescharacteristic, complemented
59C2×(C2×D3)⋊C8C2211yescharacteristic
60C2×(C2×D3)⋊C8C2211yescharacteristic
61C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
62C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
63C2×#816C2211yescharacteristic, complemented
64C2×#816C2211yescharacteristic, complemented
65#5037—24no—
66#4987C2211yescharacteristic
67#4987C2211yescharacteristic, complemented
68C2×#810C2211yescharacteristic, complemented
69C2×#809C2211yescharacteristic, complemented
70#4956—21no—
71#4956—21no—
72C23×#41—31no—
73C2×#449—31no—
74C2×#449—31no—
75C2×#449—31no—
76C2×#449D311yescharacteristic, complemented
77C2×#448—31no—
78C2×#447—31no—
79#2847—31no—
80#1788—31no—
81#1788—31no—
82#1788—31no—
83#1788—31no—
84#1787—31no—
85#1786—31no—
86#1779—31no—
87C24×D3—21no—
88C24×D3D411yescharacteristic
89C2×C3×#41—22no—
90C2×C3×#41—22no—
91C2×C3×#41—22no—
92C2×C3×#41—22no—
93C2×C3×#41—22no—
94C2×C3×#41D414yescomplemented
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4C2311yescharacteristic
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C22×#67—21no—
106C22×#67—21no—
107C23×Dic3—21no—
108C23×Dic3D411yescharacteristic
109D3×#41—232no—
110D3×#41—232no—
111D3×#41—232no—
112D3×#41—232no—
113C2×#239—22no—
114C2×#239—22no—
115C2×#239—22no—
116C2×#239—22no—
117C2×#239—22no—
118C2×#239D414yescomplemented
119C2×D3×Q8—22no—
120C2×D3×Q8—22no—
121C2×D3×Q8—22no—
122C2×D3×Q8—22no—
123C2×D3×Q8—22no—
124C2×D3×Q8D414yescomplemented
125C2×#237—28no—
126C2×#237—28no—
127C2×#237—28no—
128C2×#237—22no—
129C2×#237—22no—
130C2×#237—22no—
131C2×#237—22no—
132C2×#237—22no—
133C2×#237D414yescomplemented
134C2×D3×D4—28no—
135C2×D3×D4—28no—
136C2×D3×D4—28no—
137C2×D3×D4—22no—
138C2×D3×D4—22no—
139C2×D3×D4—22no—
140C2×D3×D4—22no—
141C2×D3×D4—22no—
142C2×D3×D4D414yescomplemented
143C2×#235—28no—
144C2×#235—28no—
145C2×#235—28no—
146C2×#235—22no—
147C2×#235—22no—
148C2×#235—22no—
149C2×#235—22no—
150C2×#235—22no—
151C2×#235D414yescomplemented
152C22×D12—21no—
153C22×D12C2311yescharacteristic
154C22×C4×D3—28no—
155C22×C4×D3—28no—
156C22×C4×D3—28no—
157C22×C4×D3—21no—
158C22×C4×D3—21no—
159C22×C4×D3—22no—
160C22×C4×D3—22no—
161C22×C4×D3—21no—
162C22×C4×D3—22no—
163C22×C4×D3—22no—
164C22×C4×D3—22no—
165C22×C4×D3—22no—
166C22×C4×D3D411yescharacteristic
167C22×C4×D3D411yescharacteristic
168C22×C4×D3C2311yescharacteristic
169C22×C4×D3C2311yescharacteristic
170C22×Dic6—21no—
171C22×Dic6C2311yescharacteristic
172C2×C3×SD16—22no—
173C2×C3×SD16—22no—
174C2×C3×SD16—22no—
175C2×C3×D8—22no—
176C2×C3×D8—22no—
177C2×C3×D8—22no—
178C22×C3×C8C2311yescharacteristic
179C22×C3×C8C2311yescharacteristic
180C3×#121—22no—
181C3×#121—22no—
182C2×C3×C4⋊C4C2311yescharacteristic
183C2×C3×C22⋊C4—21no—
184C2×#217—21no—
185C2×#217—21no—
186C2×#217—21no—
187#938—22no—
188#938—22no—
189#938—22no—
190#938—22no—
191#937—44no—
192C2×#214—22no—
193C2×#214—22no—
194C2×#214—22no—
195C2×#213—22no—
196C2×#213—22no—
197C2×#213—22no—
198C2×(C2×D3)⋊C4—21no—
199C2×(C2×D3)⋊C4—21no—
200C2×C4⋊Dic3C2311yescharacteristic
201C2×C4⋊Dic3C2311yescharacteristic
202C22×C3⋊C8C2311yescharacteristic
203C22×C3⋊C8C2311yescharacteristic
204C3×#103—22no—
205C3×#102—22no—
206C3×C22⋊C8—22no—
207#835—22no—
208#835—22no—
209#832—22no—
210#832—22no—
211C3⋊#95—21no—
212C3⋊#95—21no—
213C3⋊#95—21no—
214#830—22no—
215#821—22no—
216#821—22no—
217(C2×D3)⋊C8—22no—
218(C2×D3)⋊C8—22no—
219(C2×D3)⋊C8—22no—
220(C2×D3)⋊C8—22no—
221#816—22no—
222#816—22no—
223#810—22no—
224#809—22no—
225C22×#41—31no—
226C22×#41—31no—
227C22×#41—31no—
228C22×#41—61no—
229C22×#41—61no—
230C22×#41—64no—
231C22×#41—64no—
232C22×#41—64no—
233C22×#41—64no—
234C22×#41—64no—
235C22×#41—64no—
236C22×#41C2×D311yescharacteristic
237C23×Q8—31no—
238C23×D4—31no—
239C23×D4—61no—
240C24×C4—31no—
241C24×C4—61no—
242C22×SD16—31no—
243C22×SD16C2×D311yescharacteristic, complemented
244C22×D8—31no—
245C22×D8C2×D311yescharacteristic, complemented
246C2×#121—31no—
247C2×#121—31no—
248C2×#121C2×D311yescharacteristic, complemented
249C2×#120—61no—
250#449—24no—
251#449—64no—
252#449—64no—
253#449—64no—
254#448—64no—
255#447—64no—
256C2×#103—31no—
257C2×#103—31no—
258C2×#103—31no—
259C2×#103—31no—
260C2×#103—31no—
261C2×#103C2×D311yescharacteristic, complemented
262C2×#102—31no—
263C2×#102—31no—
264C2×#102—31no—
265C2×#102—31no—
266C2×#102—31no—
267C2×#102C2×D311yescharacteristic, complemented
268C2×C22⋊C8—31no—
269C2×C22⋊C8—31no—
270C2×C22⋊C8—31no—
271C2×C22⋊C8—31no—
272C2×C22⋊C8—31no—
273C2×C22⋊C8C2×D311yescharacteristic, complemented
274#386—61no—
275#386—61no—
276#386—61no—
277#380—31no—
278#380—31no—
279#380—31no—
280C24×C3—21no—
281C24×C3—21no—
282C24×C3C2×D411yescharacteristic
283C23×D3—24no—
284C23×D3—24no—
285C23×D3—22no—
286C23×D3—21no—
287C23×D3—22no—
288C23×D3—22no—
289C23×D3—24no—
290C23×D3—22no—
291C23×D3—22no—
292C23×D3—41no—
293C23×D3—41no—
294C23×D3—42no—
295C23×D3—42no—
296C23×D3—42no—
297C23×D3—42no—
298C23×D3C2×D411yescharacteristic
299C23×D3C2×D411yescharacteristic
300C3×#41—28no—
301C3×#41—28no—
302C3×#41—28no—
303C3×#41—28no—
304C2×C3×Q8—21no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8C2×D412yes—
308C2×C3×Q8C2×D412yes—
309C2×C3×Q8C2×D412yes—
310C2×C3×D4—24no—
311C2×C3×D4—24no—
312C2×C3×D4—24no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—42no—
323C2×C3×D4—42no—
324C2×C3×D4—42no—
325C2×C3×D4C2×D412yes—
326C2×C3×D4C2×D412yes—
327C2×C3×D4C2×D412yes—
328C22×C3×C4—24no—
329C22×C3×C4—24no—
330C22×C3×C4—21no—
331C22×C3×C4—24no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2×D412yes—
339C22×C3×C4C2×D412yes—
340C22×C3×C4C2411yescharacteristic
341C2×#67—24no—
342C2×#67—24no—
343C2×#67—24no—
344C2×#67—24no—
345C2×#67—24no—
346C2×#67—24no—
347C2×#67—24no—
348C2×#67—24no—
349C2×#67—24no—
350C2×#67—42no—
351C2×#67—42no—
352C2×#67—42no—
353C2×#67—42no—
354C2×#67—42no—
355C2×#67—42no—
356C22×Dic3—24no—
357C22×Dic3—24no—
358C22×Dic3—22no—
359C22×Dic3—21no—
360C22×Dic3—22no—
361C22×Dic3—22no—
362C22×Dic3—24no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3C2×D411yescharacteristic
366C22×Dic3C2×D411yescharacteristic
367#239—28no—
368#239—28no—
369#239—28no—
370#239—28no—
371D3×Q8—28no—
372D3×Q8—28no—
373D3×Q8—28no—
374D3×Q8—28no—
375#237—264no—
376#237—28no—
377#237—28no—
378#237—28no—
379#237—28no—
380D3×D4—264no—
381D3×D4—28no—
382D3×D4—28no—
383D3×D4—28no—
384D3×D4—28no—
385#235—264no—
386#235—28no—
387#235—28no—
388#235—28no—
389#235—28no—
390C2×D12—24no—
391C2×D12—24no—
392C2×D12—24no—
393C2×D12—21no—
394C2×D12—21no—
395C2×D12—21no—
396C2×D12C2×D412yes—
397C2×D12C2×D412yes—
398C2×D12C2×D412yes—
399C2×C4×D3—24no—
400C2×C4×D3—24no—
401C2×C4×D3—24no—
402C2×C4×D3—24no—
403C2×C4×D3—24no—
404C2×C4×D3—24no—
405C2×C4×D3—264no—
406C2×C4×D3—28no—
407C2×C4×D3—28no—
408C2×C4×D3—28no—
409C2×C4×D3—28no—
410C2×C4×D3—22no—
411C2×C4×D3—24no—
412C2×C4×D3—22no—
413C2×C4×D3—22no—
414C2×C4×D3—24no—
415C2×C4×D3—22no—
416C2×C4×D3—21no—
417C2×C4×D3—21no—
418C2×C4×D3—21no—
419C2×C4×D3—21no—
420C2×C4×D3—21no—
421C2×C4×D3—21no—
422C2×C4×D3—21no—
423C2×C4×D3—21no—
424C2×C4×D3—22no—
425C2×C4×D3—24no—
426C2×C4×D3—22no—
427C2×C4×D3C2×D412yes—
428C2×C4×D3C2×D412yes—
429C2×C4×D3C2×D412yes—
430C2×C4×D3C2×D412yes—
431C2×Dic6—24no—
432C2×Dic6—24no—
433C2×Dic6—21no—
434C2×Dic6—21no—
435C2×Dic6—21no—
436C2×Dic6—24no—
437C2×Dic6C2×D412yes—
438C2×Dic6C2×D412yes—
439C2×Dic6C2×D412yes—
440C3×SD16—44no—
441C3×D8—44no—
442C2×C3×C8—21no—
443C2×C3×C8—21no—
444C2×C3×C8—21no—
445C2×C3×C8—21no—
446C2×C3×C8—21no—
447C2×C3×C8—21no—
448C3×C4⋊C4—21no—
449C3×C4⋊C4—21no—
450C3×C22⋊C4—42no—
451#217—42no—
452#217—42no—
453#217—42no—
454#214—44no—
455#213—44no—
456(C2×D3)⋊C4—42no—
457(C2×D3)⋊C4—42no—
458C4⋊Dic3—21no—
459C4⋊Dic3—21no—
460C4⋊Dic3—21no—
461C4⋊Dic3—21no—
462C2×C3⋊C8—21no—
463C2×C3⋊C8—21no—
464C2×C3⋊C8—21no—
465C2×C3⋊C8—21no—
466C2×C3⋊C8—21no—
467C2×C3⋊C8—21no—
468C25—31no—
469C25—61no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—34no—
476C2×#41—34no—
477C2×#41—34no—
478C2×#41—62no—
479C2×#41—62no—
480C2×#41—62no—
481C2×#41—62no—
482C2×#41—68no—
483C2×#41—68no—
484C2×#41—68no—
485C2×#41—62no—
486C2×#41—62no—
487C2×#41—62no—
488C2×#41—62no—
489C2×#41—68no—
490C2×#41—68no—
491C2×#41—68no—
492C2×#41—62no—
493C2×#41—62no—
494C2×#41—632no—
495C2×#41—632no—
496C2×#41—632no—
497C2×#41—632no—
498C2×#41—62no—
499C2×#41—62no—
500C2×#41—62no—
501C2×#41—62no—
502C2×#41—62no—
503C2×#41#6714yescomplemented
504C22×Q8—34no—
505C22×Q8—31no—
506C22×Q8—61no—
507C22×Q8—62no—
508C22×Q8—62no—
509C22×Q8—62no—
510C22×Q8—62no—
511C22×Q8—62no—
512C22×Q8C22×D311yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—34no—
516C22×D4—31no—
517C22×D4—61no—
518C22×D4—62no—
519C22×D4—61no—
520C22×D4—62no—
521C22×D4—62no—
522C22×D4—68no—
523C22×D4—68no—
524C22×D4—68no—
525C22×D4—61no—
526C22×D4—61no—
527C22×D4—62no—
528C22×D4—62no—
529C22×D4—61no—
530C22×D4—61no—
531C22×D4C22×D311yescharacteristic
532C22×D4C22×D311yescharacteristic
533C23×C4—21no—
534C23×C4—31no—
535C23×C4—31no—
536C23×C4—31no—
537C23×C4—31no—
538C23×C4—31no—
539C23×C4—62no—
540C23×C4—62no—
541C23×C4—62no—
542C23×C4—62no—
543C23×C4—61no—
544C23×C4—61no—
545C23×C4—68no—
546C23×C4—68no—
547C23×C4—68no—
548C23×C4—61no—
549C23×C4—62no—
550C23×C4—61no—
551C23×C4—62no—
552C23×C4C22×D311yescharacteristic
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—62no—
557C2×SD16—62no—
558C2×SD16—62no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—62no—
563C2×D8—62no—
564C2×D8—62no—
565C22×C8—31no—
566C22×C8—31no—
567C22×C8C22×D311yescharacteristic
568C22×C8C22×D311yescharacteristic
569#121—22no—
570#121—22no—
571#121—62no—
572#121—62no—
573#121—62no—
574#121—62no—
575#120—124no—
576C2×C4⋊C4—31no—
577C2×C4⋊C4—31no—
578C2×C4⋊C4C22×D311yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—61no—
581C2×C22⋊C4—61no—
582C2×C22⋊C4—61no—
583C2×C22⋊C4—61no—
584C2×C22⋊C4—61no—
585#103—22no—
586#103—62no—
587#103—62no—
588#103—62no—
589#103—62no—
590#103—62no—
591#102—22no—
592#102—62no—
593#102—62no—
594#102—62no—
595#102—62no—
596#102—62no—
597C22⋊C8—22no—
598C22⋊C8—62no—
599C22⋊C8—62no—
600C22⋊C8—62no—
601C22⋊C8—62no—
602C22⋊C8—62no—
603#95—61no—
604#95—61no—
605#95—61no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
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×C3—41no—
624C23×C3—41no—
625C23×C3—41no—
626C23×C3#12012yes—
627C23×C3C22×D411yescharacteristic
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—28no—
633C22×D3—216no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—21no—
640C22×D3—21no—
641C22×D3—21no—
642C22×D3—21no—
643C22×D3—44no—
644C22×D3—44no—
645C22×D3—44no—
646C22×D3—44no—
647C22×D3—48no—
648C22×D3—48no—
649C22×D3—44no—
650C22×D3—48no—
651C22×D3—48no—
652C22×D3—48no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—44no—
658C22×D3—48no—
659C22×D3#12012yes—
660C22×D3#12012yes—
661C22×D3#13512yes—
662C22×D3AGL(1,ℤ/8)12yes—
663C3×Q8—22no—
664C3×Q8—22no—
665C3×Q8—22no—
666C3×Q8#12014yescomplemented
667C3×D4—216no—
668C3×D4—22no—
669C3×D4—22no—
670C3×D4—22no—
671C3×D4—41no—
672C3×D4—41no—
673C3×D4—41no—
674C3×D4—41no—
675C3×D4—84no—
676C3×D4#12014yescomplemented
677C2×C3×C4—216no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4#12012yes—
691C2×C3×C4C22×D411yescharacteristic
692C2×C3×C4C22×D411yescharacteristic
693C2×C3×C4C22×D411yescharacteristic
694C2×C3×C4C22×D411yescharacteristic
695C2×C3×C4C22×D411yescharacteristic
696C2×C3×C4C22×D411yescharacteristic
697#67—216no—
698#67—216no—
699#67—216no—
700#67—84no—
701#67—84no—
702C2×Dic3—28no—
703C2×Dic3—216no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3#12012yes—
718C2×Dic3#12012yes—
719D12—216no—
720D12—22no—
721D12—22no—
722D12—22no—
723D12#12014yescomplemented
724C4×D3—28no—
725C4×D3—28no—
726C4×D3—216no—
727C4×D3—216no—
728C4×D3—216no—
729C4×D3—22no—
730C4×D3—22no—
731C4×D3—22no—
732C4×D3—22no—
733C4×D3—22no—
734C4×D3—22no—
735C4×D3—22no—
736C4×D3—22no—
737Dic6—216no—
738Dic6—22no—
739Dic6—22no—
740Dic6—22no—
741Dic6#12014yescomplemented
742C3×C8—41no—
743C3×C8—41no—
744C3⋊C8—41no—
745C3⋊C8—41no—
746C24—21no—
747C24—21no—
748C24—31no—
749C24—31no—
750C24—64no—
751C24—62no—
752C24—62no—
753C24—62no—
754C24—62no—
755C24—64no—
756C24—64no—
757C24—62no—
758C24—61no—
759C24—121no—
760C24—121no—
761C24—122no—
762C24—122no—
763C24—122no—
764C24—122no—
765C24D3×D411yescharacteristic
766#41—28no—
767#41—28no—
768#41—28no—
769#41—28no—
770#41—68no—
771#41—68no—
772#41—664no—
773#41—68no—
774#41—68no—
775#41—68no—
776#41—664no—
777#41—68no—
778#41—68no—
779#41—68no—
780#41—68no—
781#41—68no—
782#41—68no—
783#41—68no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—32no—
788C2×Q8—32no—
789C2×Q8—32no—
790C2×Q8—64no—
791C2×Q8—64no—
792C2×Q8—64no—
793C2×Q8—68no—
794C2×Q8—68no—
795C2×Q8—68no—
796C2×Q8—68no—
797C2×Q8—61no—
798C2×Q8—61no—
799C2×Q8—61no—
800C2×Q8D3×D412yes—
801C2×Q8D3×D412yes—
802C2×Q8C2×#6712yes—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—32no—
816C2×D4—32no—
817C2×D4—32no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—64no—
822C2×D4—64no—
823C2×D4—64no—
824C2×D4—64no—
825C2×D4—68no—
826C2×D4—664no—
827C2×D4—68no—
828C2×D4—68no—
829C2×D4—64no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—64no—
833C2×D4—64no—
834C2×D4—64no—
835C2×D4—64no—
836C2×D4—64no—
837C2×D4—68no—
838C2×D4—61no—
839C2×D4—61no—
840C2×D4—61no—
841C2×D4—122no—
842C2×D4—122no—
843C2×D4—122no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—122no—
847C2×D4D3×D412yes—
848C2×D4D3×D412yes—
849C2×D4C2×#6712yes—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—21no—
853C22×C4—24no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—32no—
862C22×C4—32no—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—62no—
866C22×C4—62no—
867C22×C4—64no—
868C22×C4—62no—
869C22×C4—62no—
870C22×C4—64no—
871C22×C4—64no—
872C22×C4—64no—
873C22×C4—664no—
874C22×C4—64no—
875C22×C4—64no—
876C22×C4—64no—
877C22×C4—64no—
878C22×C4—68no—
879C22×C4—68no—
880C22×C4—68no—
881C22×C4—68no—
882C22×C4—62no—
883C22×C4—62no—
884C22×C4—64no—
885C22×C4—64no—
886C22×C4—64no—
887C22×C4—62no—
888C22×C4—61no—
889C22×C4—62no—
890C22×C4—62no—
891C22×C4—64no—
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×C4D3×D411yescharacteristic
903C22×C4D3×D412yes—
904C22×C4C2×#6712yes—
905C22×C4C23×D311yescharacteristic
906SD16—44no—
907SD16—124no—
908D8—44no—
909D8—124no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—61no—
917C2×C8—61no—
918C2×C8—61no—
919C2×C8—61no—
920C2×C8—61no—
921C2×C8—61no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—61no—
925C4⋊C4—61no—
926C4⋊C4—61no—
927C4⋊C4—61no—
928C22⋊C4—42no—
929C22⋊C4—122no—
930C22⋊C4—122no—
931C22⋊C4—122no—
932C22⋊C4—122no—
933C22⋊C4—122no—
934C22×C3—22no—
935C22×C3—24no—
936C22×C3—22no—
937C22×C3—22no—
938C22×C3—41no—
939C22×C3—42no—
940C22×C3—41no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—41no—
944C22×C3—42no—
945C22×C3—41no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3—81no—
949C22×C3—81no—
950C22×C3—81no—
951C22×C3—81no—
952C22×C3—81no—
953C22×C3—81no—
954C22×C3—81no—
955C22×C3C2×#12011yescharacteristic
956C22×C3C2×#12011yescharacteristic
957C22×C3C2×#12011yescharacteristic
958C22×C3C2×#13511yescharacteristic
959C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
960C22×C3#57511yescharacteristic
961C22×C3#57511yescharacteristic
962C2×D3—22no—
963C2×D3—22no—
964C2×D3—22no—
965C2×D3—22no—
966C2×D3—22no—
967C2×D3—22no—
968C2×D3—22no—
969C2×D3—24no—
970C2×D3—22no—
971C2×D3—22no—
972C2×D3—416no—
973C2×D3—432no—
974C2×D3—41no—
975C2×D3—42no—
976C2×D3—41no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—41no—
980C2×D3—42no—
981C2×D3—41no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3#44914yescomplemented
985C3×C4—24no—
986C3×C4—22no—
987C3×C4—81no—
988C3×C4C2×#12011yescharacteristic
989C3×C4C2×#12011yescharacteristic
990C3×C4C2×#12011yescharacteristic
991C3×C4C2×#12011yescharacteristic
992Dic3—22no—
993Dic3—24no—
994Dic3—22no—
995Dic3—81no—
996Dic3—81no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—22no—
1002C23—21no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—32no—
1007C23—32no—
1008C23—32no—
1009C23—32no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—68no—
1022C23—616no—
1023C23—61no—
1024C23—61no—
1025C23—61no—
1026C23—61no—
1027C23—61no—
1028C23—61no—
1029C23—61no—
1030C23—61no—
1031C23—62no—
1032C23—61no—
1033C23—62no—
1034C23—62no—
1035C23—61no—
1036C23—124no—
1037C23—124no—
1038C23—124no—
1039C23—128no—
1040C23—124no—
1041C23—124no—
1042C23—128no—
1043C23—128no—
1044C23—124no—
1045C23—128no—
1046C23—128no—
1047C23—128no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23#93712yes—
1053C23C2×D3×D411yescharacteristic
1054Q8—22no—
1055Q8—22no—
1056Q8—22no—
1057Q8—34no—
1058Q8—616no—
1059Q8—62no—
1060Q8—62no—
1061Q8—62no—
1062Q8#93714yescomplemented
1063D4—216no—
1064D4—22no—
1065D4—22no—
1066D4—22no—
1067D4—34no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—616no—
1073D4—616no—
1074D4—616no—
1075D4—616no—
1076D4—62no—
1077D4—62no—
1078D4—62no—
1079D4—84no—
1080D4—244no—
1081D4—244no—
1082D4#93714yescomplemented
1083C2×C4—216no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—32no—
1094C2×C4—32no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—68no—
1099C2×C4—616no—
1100C2×C4—68no—
1101C2×C4—616no—
1102C2×C4—616no—
1103C2×C4—68no—
1104C2×C4—616no—
1105C2×C4—61no—
1106C2×C4—61no—
1107C2×C4—62no—
1108C2×C4—61no—
1109C2×C4—61no—
1110C2×C4—62no—
1111C2×C4—62no—
1112C2×C4—62no—
1113C2×C4—62no—
1114C2×C4—62no—
1115C2×C4—62no—
1116C2×C4—62no—
1117C2×C4—62no—
1118C2×C4—62no—
1119C2×C4—62no—
1120C2×C4—121no—
1121C2×C4—121no—
1122C2×C4—121no—
1123C2×C4—121no—
1124C2×C4—121no—
1125C2×C4—121no—
1126C2×C4#93712yes—
1127C2×C4C2×D3×D411yescharacteristic
1128C2×C4C2×D3×D411yescharacteristic
1129C2×C4C2×D3×D411yescharacteristic
1130C2×C4C2×D3×D411yescharacteristic
1131C2×C4C2×D3×D411yescharacteristic
1132C2×C4C22×#6711yescharacteristic
1133C8—41no—
1134C8—41no—
1135C8—121no—
1136C8—121no—
1137C2×C3—42no—
1138C2×C3—44no—
1139C2×C3—161no—
1140C2×C3#284611yescharacteristic
1141C2×C3C2×#44911yescharacteristic
1142C2×C3#300211yescharacteristic
1143C2×C3#300211yescharacteristic
1144C2×C3#300511yescharacteristic
1145C2×C3#300611yescharacteristic
1146C2×C3#300611yescharacteristic
1147D3—24no—
1148D3—42no—
1149D3—44no—
1150C22—22no—
1151C22—24no—
1152C22—22no—
1153C22—22no—
1154C22—34no—
1155C22—42no—
1156C22—41no—
1157C22—42no—
1158C22—41no—
1159C22—42no—
1160C22—41no—
1161C22—42no—
1162C22—41no—
1163C22—42no—
1164C22—42no—
1165C22—62no—
1166C22—62no—
1167C22—62no—
1168C22—62no—
1169C22—62no—
1170C22—62no—
1171C22—64no—
1172C22—62no—
1173C22—62no—
1174C22—62no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—1216no—
1183C22—1232no—
1184C22—121no—
1185C22—122no—
1186C22—121no—
1187C22—122no—
1188C22—122no—
1189C22—121no—
1190C22—122no—
1191C22—122no—
1192C22—121no—
1193C22—122no—
1194C22D3×#12011yescharacteristic
1195C22D3×#12011yescharacteristic
1196C22D3×#13511yescharacteristic
1197C22#576811yescharacteristic
1198C22D3×AGL(1,ℤ/8)11yescharacteristic
1199C22#577311yescharacteristic
1200C22C2×#93711yescharacteristic
1201C4—22no—
1202C4—24no—
1203C4—62no—
1204C4—62no—
1205C4—64no—
1206C4—81no—
1207C4—241no—
1208C4—241no—
1209C4D3×#12011yescharacteristic
1210C4D3×#12011yescharacteristic
1211C4C2×#93711yescharacteristic
1212C4C2×#93711yescharacteristic
1213C3#3288011yescharacteristic, complemented, Sylow
1214C2—42no—
1215C2—44no—
1216C2—64no—
1217C2—122no—
1218C2—124no—
1219C2—161no—
1220C2D3×#44911yescharacteristic
1221C2#8008211yescharacteristic
1222C2#8008311yescharacteristic
1223C2#8008411yescharacteristic
1224C2#8261211yescharacteristic
1225C2#8391111yescharacteristic
1226C2#8394611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#32880
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C22×D3×#41C2semidirect
2. C2×C3×#449C2semidirect
3. C2×#5172C2semidirect
4. C2×#5170C2semidirect
5. C2×#5158C2semidirect
6. C2×#5156C2semidirect
7. #82723C2semidirect
8. C2×#5037C2semidirect
9. #72135C2semidirect
10. #70267C2semidirect
11. #70266C2semidirect
12. #70199C2semidirect
13. #70198C2semidirect
14. #69960C2semidirect
15. #69955C2semidirect
34. C22×C3×SD16C22semidirect
35. C22×C3×D8C22semidirect
36. C2×C3×#121C22semidirect
38. C2×#938C22semidirect
40. C22×#214C22semidirect
41. C22×#213C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×C22⋊C8C22semidirect
46. C2×#835C22semidirect
47. C2×#835C22semidirect
49. C2×#832C22semidirect
50. C2×#832C22semidirect
51. #5212C22semidirect
52. C2×#830C22semidirect
57. C2×#821C22semidirect
58. C2×#821C22semidirect
61. C2×(C2×D3)⋊C8C22semidirect
62. C2×(C2×D3)⋊C8C22semidirect
63. C2×#816C22semidirect
64. C2×#816C22semidirect
67. #4987C22semidirect
68. C2×#810C22semidirect
69. C2×#809C22semidirect
76. C2×#449D3semidirect
94. C2×C3×#41D4semidirect
118. C2×#239D4semidirect
124. C2×D3×Q8D4semidirect
133. C2×#237D4semidirect
142. C2×D3×D4D4semidirect
151. C2×#235D4semidirect
243. C22×SD16C2×D3semidirect
245. C22×D8C2×D3semidirect
248. C2×#121C2×D3semidirect
261. C2×#103C2×D3semidirect
267. C2×#102C2×D3semidirect
273. C2×C22⋊C8C2×D3semidirect
503. C2×#41#67semidirect
666. C3×Q8#120semidirect
676. C3×D4#120semidirect
723. D12#120semidirect
741. Dic6#120semidirect
984. C2×D3#449semidirect
1062. Q8#937semidirect
1082. D4#937semidirect
1213. C3#32880semidirect

Maximal subgroups

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

subgroupindex
C22×D3×#412
C2×C3×#4492
C2×#51722
C2×#51702
C2×#51582
C2×#51562
#827232
C2×#50372
#721352
#702672
#702662
#701992
#701982
#699602
#699552
#328803