Finite Group Databasebeta

← #10826970

Subgroups — #10826970

Order 768.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5828C211yesmaximal, characteristic, complemented
2C2×#5627C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5187C211yesmaximal, characteristic, complemented
6C2×#5172C211yesmaximal, characteristic, complemented
7#72071C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71693C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#70269C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70201C211yesmaximal, characteristic, complemented
14#69955C211yesmaximal, characteristic, complemented
15#69933C211yesmaximal, characteristic, complemented
16#23923—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×#239C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic, complemented
21C22×C3×SD16C2211yescharacteristic, complemented
22C2×C3×C22⋊Q8C2211yescharacteristic
23#5828—24no—
24#5828—24no—
25C2×#946C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C2×#946C2211yescharacteristic
28C22×#215C2211yescharacteristic, complemented
29C2×#938C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×#937—21no—
32C2×#935—21no—
33C22×#213C2211yescharacteristic, complemented
34C2×#930C2211yescharacteristic
35C2×C4×#67—21no—
36C2×C4×#67—21no—
37C2×#926C2211yescharacteristic
38#5627—24no—
39#5627—24no—
40C2×#895C2211yescharacteristic
41C2×#894—21no—
42C2×#893—21no—
43C2×#892C2211yescharacteristic
44C2×#882—21no—
45C2×#67⋊C4—21no—
46C3×#452—24no—
47C2×C3×#103C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×C22⋊C8C2211yescharacteristic
50#5238—24no—
51C2×#835C2211yescharacteristic, complemented
52C2×#835C2211yescharacteristic, complemented
53C2×#835C2211yescharacteristic, complemented
54C2×#832C2211yescharacteristic, complemented
55C2×#830C2211yescharacteristic
56#5187—24no—
57#5172—24no—
58C2×#821C2211yescharacteristic, complemented
59C2×#821C2211yescharacteristic, complemented
60C2×(C2×D3)⋊C8C2211yescharacteristic
61C2×(C2×D3)⋊C8C2211yescharacteristic
62C2×(C2×D3)⋊C8C2211yescharacteristic
63C2×(C2×D3)⋊C8C2211yescharacteristic
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C2×#525—31no—
69C2×#525—31no—
70C2×#452—31no—
71C2×#452D311yescharacteristic, complemented
72C2×#449—31no—
73C2×#449—31no—
74#2001—31no—
75#2000—31no—
76#2000—31no—
77#1999—31no—
78#1875—31no—
79#1875—31no—
80#1873—31no—
81#1873—31no—
82#1779—31no—
83C24×D3D411yescharacteristic
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×Q8C2311yescharacteristic
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C22×#67—21no—
97C22×#67—21no—
98C22×#67—21no—
99C23×Dic3D411yescharacteristic
100C2×#239—22no—
101C2×#239—22no—
102C2×#239—22no—
103C2×#239—22no—
104C2×#239—41no—
105C2×#239—41no—
106C22×D12—21no—
107C22×D12—21no—
108C22×D12C2311yescharacteristic
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—21no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3D411yescharacteristic
117C22×C4×D3D411yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2311yescharacteristic
120C2×C3×Q16—22no—
121C2×C3×Q16—22no—
122C2×C3×Q16—41no—
123C2×C3×SD16—22no—
124C2×C3×SD16—22no—
125C2×C3×SD16—41no—
126C22×C3×C8C2311yescharacteristic
127C22×C3×C8C2311yescharacteristic
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8D414yescomplemented
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217—21no—
136#946—22no—
137#946—22no—
138#946—22no—
139#946—22no—
140#946—22no—
141#946D414yescomplemented
142C2×#215—22no—
143C2×#215—22no—
144C2×#215—41no—
145#938—22no—
146#938—22no—
147#938—22no—
148#938D414yescomplemented
149#937—28no—
150#935—28no—
151C2×#213—22no—
152C2×#213—22no—
153C2×#213—41no—
154#930—22no—
155#930D414yescomplemented
156C4×#67—28no—
157C4×#67—28no—
158C2×(C2×D3)⋊C4—21no—
159C2×(C2×D3)⋊C4—21no—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164#926—22no—
165#926—22no—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2311yescharacteristic
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4—21no—
171C2×Dic3⋊C4—21no—
172C2×C4×Dic3—21no—
173C2×C4×Dic3—21no—
174C22×C3⋊C8C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176#895—22no—
177#895—22no—
178#894—28no—
179#893—28no—
180#892—22no—
181#892—22no—
182#882—28no—
183#67⋊C4—28no—
184C3×#103—22no—
185C3×#102—22no—
186C3×C22⋊C8—22no—
187#835—22no—
188#835—22no—
189#835—22no—
190#832—22no—
191#830—22no—
192#821—22no—
193#821—22no—
194(C2×D3)⋊C8—22no—
195(C2×D3)⋊C8—22no—
196(C2×D3)⋊C8—41no—
197(C2×D3)⋊C8—41no—
198C22×#41—31no—
199C22×#41C2×D311yescharacteristic
200C24×C4—31no—
201C22×Q16C2×D311yescharacteristic, complemented
202C22×SD16—31no—
203C22×SD16C2×D311yescharacteristic, complemented
204C22×D8—31no—
205#525—64no—
206#525—64no—
207#525—64no—
208#525—64no—
209C2×#123—61no—
210C2×#123—61no—
211C2×C22⋊Q8—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8C2×D311yescharacteristic
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—31no—
218C2×#121—31no—
219C2×#120—61no—
220C2×#120—61no—
221C2×C4×D4—61no—
222C2×C4×D4—61no—
223C2×C4×D4—61no—
224C2×C4×D4—61no—
225C2×#117—31no—
226C2×#117—31no—
227#452—24no—
228#452—64no—
229#449—64no—
230#449—64no—
231C2×#103—31no—
232C2×#103—31no—
233C2×#103—31no—
234C2×#103C2×D311yescharacteristic, complemented
235C2×#102—31no—
236C2×#102—31no—
237C2×#102—31no—
238C2×#102C2×D311yescharacteristic, complemented
239C2×C22⋊C8—31no—
240C2×C22⋊C8—31no—
241C2×C22⋊C8—31no—
242C2×C22⋊C8—31no—
243C2×C22⋊C8—31no—
244C2×C22⋊C8C2×D311yescharacteristic
245#340—31no—
246#340—31no—
247#340—31no—
248#340—31no—
249C24×C3—21no—
250C24×C3C2×D411yescharacteristic
251C23×D3—22no—
252C23×D3—21no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—41no—
256C23×D3—41no—
257C23×D3—41no—
258C23×D3—41no—
259C23×D3C2×D411yescharacteristic
260C23×D3C2×D411yescharacteristic
261C3×#41—44no—
262C3×#41—44no—
263C3×#41—44no—
264C3×#41—44no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8C2×D412yes—
276C2×C3×Q8C2×D412yes—
277C2×C3×D4—24no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4C2×D412yes—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—24no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2411yescharacteristic
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—42no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—42no—
308C2×#67—42no—
309C22×Dic3—22no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—22no—
314C22×Dic3—41no—
315C22×Dic3C2×D411yescharacteristic
316C22×Dic3C2×D411yescharacteristic
317#239—44no—
318#239—44no—
319#239—44no—
320#239—44no—
321C2×D12—21no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—24no—
326C2×D12—24no—
327C2×D12—21no—
328C2×D12—42no—
329C2×D12—42no—
330C2×D12—42no—
331C2×D12—42no—
332C2×D12C2×D412yes—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—24no—
338C2×C4×D3—22no—
339C2×C4×D3—22no—
340C2×C4×D3—22no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—21no—
346C2×C4×D3—21no—
347C2×C4×D3—22no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—41no—
353C2×C4×D3—41no—
354C2×C4×D3—42no—
355C2×C4×D3—42no—
356C2×C4×D3C2×D412yes—
357C2×C4×D3C2×D412yes—
358C3×Q16—44no—
359C3×SD16—44no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C2×C3×C8—21no—
365C2×C3×C8—21no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4C2×D412yes—
369C3×C22⋊C4—24no—
370#217—24no—
371#217—24no—
372#217—24no—
373#215—44no—
374#213—44no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C2×D412yes—
385C4⋊Dic3C2×D412yes—
386C4⋊Dic3C2×D412yes—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390C4×Dic3—24no—
391C4×Dic3—24no—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—21no—
394C2×C3⋊C8—21no—
395C2×C3⋊C8—21no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8—21no—
398C25—31no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—41no—
404C2×#41—41no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—62no—
408C2×#41—62no—
409C2×#41—121no—
410C2×#41—121no—
411C22×Q8C22×D311yescharacteristic
412C22×Q8C22×D311yescharacteristic
413C22×D4—21no—
414C22×D4—31no—
415C22×D4—61no—
416C22×D4—61no—
417C22×D4—61no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4C22×D311yescharacteristic
421C23×C4—21no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—61no—
428C23×C4—62no—
429C23×C4—62no—
430C23×C4—62no—
431C23×C4—62no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4C22×D311yescharacteristic
435C2×Q16—22no—
436C2×Q16—22no—
437C2×Q16—41no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—41no—
441C2×SD16—62no—
442C2×SD16—62no—
443C2×SD16—121no—
444C2×D8—62no—
445C2×D8—62no—
446C2×D8—121no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8C22×D311yescharacteristic
450C22×C8C22×D311yescharacteristic
451#123—68no—
452#123—68no—
453C22⋊Q8—22no—
454C22⋊Q8—34no—
455C22⋊Q8—62no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8#6714yescomplemented
461#121—34no—
462#121—34no—
463#121—62no—
464#121—62no—
465#121—62no—
466#121—62no—
467#121—62no—
468#121—62no—
469#120—68no—
470#120—68no—
471C4×D4—68no—
472C4×D4—68no—
473C4×D4—68no—
474C4×D4—68no—
475#117—62no—
476#117—62no—
477#117—62no—
478#117—62no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—61no—
484C2×C4⋊C4—61no—
485C2×C4⋊C4—61no—
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—61no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—61no—
492C2×C22⋊C4—61no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C22⋊C4—61no—
496C2×C22⋊C4—61no—
497C2×C42—61no—
498C2×C42—61no—
499#103—22no—
500#103—62no—
501#103—62no—
502#103—62no—
503#102—22no—
504#102—62no—
505#102—62no—
506#102—62no—
507C22⋊C8—22no—
508C22⋊C8—62no—
509C22⋊C8—62no—
510C22⋊C8—62no—
511C22⋊C8—121no—
512C22⋊C8—121no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3#12012yes—
527C23×C3C22×D411yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—22no—
541C22×D3—44no—
542C22×D3—44no—
543C22×D3—44no—
544C22×D3—44no—
545C22×D3—44no—
546C22×D3—44no—
547C22×D3—44no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3#12012yes—
555C22×D3#13512yes—
556C3×Q8—22no—
557C3×Q8—22no—
558C3×Q8—22no—
559C3×Q8—22no—
560C3×Q8—41no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—41no—
564C3×D4—22no—
565C3×D4—22no—
566C3×D4—48no—
567C3×D4—41no—
568C3×D4—41no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—48no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4#12012yes—
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4H(5,𝔽2)11yescharacteristic
591C2×C3×C4H(5,𝔽2)11yescharacteristic
592#67—48no—
593#67—48no—
594#67—48no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—44no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3#12012yes—
611D12—22no—
612D12—22no—
613D12—48no—
614D12—48no—
615D12—41no—
616D12—41no—
617C4×D3—22no—
618C4×D3—22no—
619C4×D3—22no—
620C4×D3—22no—
621C4×D3—44no—
622C4×D3—48no—
623C4×D3—44no—
624C4×D3—41no—
625C4×D3—41no—
626C4×D3—41no—
627C4×D3—41no—
628C3×C8—41no—
629C3×C8—41no—
630C3⋊C8—41no—
631C3⋊C8—41no—
632C24—21no—
633C24—31no—
634C24—31no—
635C24—62no—
636C24—62no—
637C24—62no—
638C24—61no—
639C24—121no—
640C24—121no—
641C24—121no—
642C24—121no—
643C24D3×D411yescharacteristic
644#41—44no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—124no—
649#41—124no—
650#41—124no—
651#41—124no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8D3×D412yes—
663C2×Q8C2×#6712yes—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—32no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—64no—
674C2×D4—64no—
675C2×D4—64no—
676C2×D4—64no—
677C2×D4—64no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—122no—
684C2×D4—122no—
685C2×D4—122no—
686C2×D4—122no—
687C2×D4—122no—
688C2×D4—122no—
689C2×D4—122no—
690C2×D4—122no—
691C2×D4—122no—
692C2×D4—122no—
693C2×D4D3×D412yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—31no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—31no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—64no—
711C22×C4—62no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—62no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—62no—
721C22×C4—62no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—121no—
729C22×C4—121no—
730C22×C4—124no—
731C22×C4—124no—
732C22×C4—124no—
733C22×C4—124no—
734C22×C4—122no—
735C22×C4—122no—
736C22×C4—121no—
737C22×C4D3×D411yescharacteristic
738C22×C4D3×D412yes—
739C22×C4C2×#6712yes—
740C22×C4C23×D311yescharacteristic
741Q16—44no—
742SD16—44no—
743SD16—124no—
744D8—124no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—61no—
752C2×C8—61no—
753C2×C8—61no—
754C2×C8—61no—
755C2×C8—61no—
756C2×C8—61no—
757C4⋊C4—24no—
758C4⋊C4—21no—
759C4⋊C4—32no—
760C4⋊C4—32no—
761C4⋊C4—32no—
762C4⋊C4—64no—
763C4⋊C4—64no—
764C4⋊C4—64no—
765C4⋊C4—61no—
766C4⋊C4—61no—
767C4⋊C4—61no—
768C4⋊C4C2×#6712yes—
769C22⋊C4—24no—
770C22⋊C4—64no—
771C22⋊C4—64no—
772C22⋊C4—64no—
773C22⋊C4—64no—
774C22⋊C4—64no—
775C22⋊C4—64no—
776C22⋊C4—64no—
777C22⋊C4—64no—
778C22⋊C4—64no—
779C42—64no—
780C42—64no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—81no—
794C22×C3—81no—
795C22×C3C2×#12011yescharacteristic
796C22×C3C2×#12011yescharacteristic
797C22×C3#53411yescharacteristic
798C22×C3C2×#13511yescharacteristic
799C22×C3#57511yescharacteristic
800C22×C3#57511yescharacteristic
801C22×C3#57511yescharacteristic
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—416no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—81no—
821C2×D3—81no—
822C2×D3—81no—
823C2×D3—81no—
824C3×C4—22no—
825C3×C4—42no—
826C3×C4—42no—
827C3×C4—42no—
828C3×C4D4211yescharacteristic
829C3×C4D4211yescharacteristic
830C3×C4D4211yescharacteristic
831C3×C4D4211yescharacteristic
832Dic3—22no—
833Dic3—41no—
834Dic3—42no—
835Dic3—42no—
836Dic3—42no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—32no—
845C23—32no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—62no—
865C23—124no—
866C23—124no—
867C23—124no—
868C23—124no—
869C23—124no—
870C23—124no—
871C23—124no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23#93712yes—
879C23C2×D3×D411yescharacteristic
880Q8—22no—
881Q8—22no—
882Q8—22no—
883Q8—22no—
884Q8—41no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888D4—22no—
889D4—22no—
890D4—48no—
891D4—41no—
892D4—41no—
893D4—62no—
894D4—62no—
895D4—128no—
896D4—128no—
897D4—128no—
898D4—128no—
899D4—128no—
900D4—121no—
901D4—121no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—32no—
912C2×C4—48no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—61no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—124no—
932C2×C4—124no—
933C2×C4—128no—
934C2×C4—124no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4#93712yes—
946C2×C4C2×D3×D411yescharacteristic
947C2×C4C2×D3×D411yescharacteristic
948C2×C4C2×D3×D411yescharacteristic
949C2×C4#100411yescharacteristic
950C2×C4#100411yescharacteristic
951C2×C4C22×#6711yescharacteristic
952C8—41no—
953C8—41no—
954C8—121no—
955C8—121no—
956C2×C3—42no—
957C2×C3—82no—
958C2×C3#240311yescharacteristic
959C2×C3#300211yescharacteristic
960C2×C3#300211yescharacteristic
961C2×C3#300511yescharacteristic
962C2×C3#300511yescharacteristic
963C2×C3#319111yescharacteristic
964C2×C3#319711yescharacteristic
965D3—42no—
966D3—42no—
967D3—82no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—1216no—
989C22—121no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—121no—
996C22—121no—
997C22—122no—
998C22—122no—
999C22—122no—
1000C22—241no—
1001C22—241no—
1002C22—241no—
1003C22—241no—
1004C22D3×#12011yescharacteristic
1005C22#558911yescharacteristic
1006C22D3×#13511yescharacteristic
1007C22#576811yescharacteristic
1008C22#577711yescharacteristic
1009C22#577711yescharacteristic
1010C22C2×#93711yescharacteristic
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—62no—
1016C4—122no—
1017C4—122no—
1018C4—122no—
1019C4—121no—
1020C4#559011yescharacteristic
1021C4#559011yescharacteristic
1022C4D4×#6711yescharacteristic
1023C4D4×#6711yescharacteristic
1024C3#2392311yescharacteristic, complemented, Sylow
1025C2—42no—
1026C2—82no—
1027C2—122no—
1028C2—122no—
1029C2—242no—
1030C2#8022611yescharacteristic
1031C2#8022711yescharacteristic
1032C2#8023411yescharacteristic
1033C2#8023611yescharacteristic
1034C2#8260411yescharacteristic
1035C2#8391111yescharacteristic
1036C2#8398011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
hypercenterC2×#452D3
hypocenterC3#23923
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#5828C2semidirect
2. C2×#5627C2semidirect
3. C2×C3×#452C2semidirect
4. C2×#5238C2semidirect
5. C2×#5187C2semidirect
6. C2×#5172C2semidirect
7. #72071C2semidirect
8. #72054C2semidirect
9. #71693C2semidirect
10. #70272C2semidirect
11. #70269C2semidirect
12. #70204C2semidirect
13. #70201C2semidirect
14. #69955C2semidirect
15. #69933C2semidirect
20. C22×C3×Q16C22semidirect
21. C22×C3×SD16C22semidirect
28. C22×#215C22semidirect
33. C22×#213C22semidirect
47. C2×C3×#103C22semidirect
48. C2×C3×#102C22semidirect
51. C2×#835C22semidirect
52. C2×#835C22semidirect
53. C2×#835C22semidirect
54. C2×#832C22semidirect
58. C2×#821C22semidirect
59. C2×#821C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
66. #4529C22semidirect
67. #4529C22semidirect
71. C2×#452D3semidirect
129. C3×C22⋊Q8D4semidirect
141. #946D4semidirect
148. #938D4semidirect
155. #930D4semidirect
201. C22×Q16C2×D3semidirect
203. C22×SD16C2×D3semidirect
234. C2×#103C2×D3semidirect
238. C2×#102C2×D3semidirect
460. C22⋊Q8#67semidirect
1024. C3#23923semidirect

Maximal subgroups

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

subgroupindex
C2×#58282
C2×#56272
C2×C3×#4522
C2×#52382
C2×#51872
C2×#51722
#720712
#720542
#716932
#702722
#702692
#702042
#702012
#699552
#699332
#239233