Finite Group Databasebeta

← #10826293

Subgroups — #10826293

Order 768.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#950C211yesmaximal, characteristic, complemented
2C2×#5553C211yesmaximal, characteristic, complemented
3C3×#2407C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5047C211yesmaximal, characteristic, complemented
6C2×#5037C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71610C211yesmaximal, characteristic, complemented
10#69690C211yesmaximal, characteristic, complemented
11#69688C211yesmaximal, characteristic, complemented
12#69660C211yesmaximal, characteristic, complemented
13#69658C211yesmaximal, characteristic, complemented
14#69522C211yesmaximal, characteristic, complemented
15#69515C211yesmaximal, characteristic, complemented
16#23857—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×#950—24no—
24C2×#950—24no—
25C2×#950—24no—
26C22×#216C2211yescharacteristic
27C22×#215C2211yescharacteristic
28C22×#215C2211yescharacteristic
29C2×#940—21no—
30C22×#214C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C22×#213C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C23×C3⋊C8C2211yescharacteristic
36#5553—24no—
37#5553—24no—
38C2×#893—21no—
39C2×#884—21no—
40C2×#884—21no—
41C2×#874C2211yescharacteristic
42C2×C4×Dic6C2211yescharacteristic
43C3×#394—21no—
44C3×#392—21no—
45C3×#391C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#386—21no—
48C3×#385—21no—
49C3×#380C2211yescharacteristic
50#5238—24no—
51C2×#835C2211yescharacteristic
52C2×#832C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#830C2211yescharacteristic
55C2×#830C2211yescharacteristic
56#5047—24no—
57#5037—24no—
58C2×#810C2211yescharacteristic
59C2×#810C2211yescharacteristic
60C2×#809C2211yescharacteristic
61C2×#809C2211yescharacteristic
62C2×#809C2211yescharacteristic
63C2×#809C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66#4524C2211yescharacteristic
67#4524C2211yescharacteristic
68C22×#135—31no—
69C2×#550—31no—
70C2×#452—31no—
71C2×#449—31no—
72C2×#449—31no—
73#2407D311yescharacteristic, complemented
74#2014—31no—
75#2011—31no—
76#2000—31no—
77#1999—31no—
78#1893—31no—
79#1880—31no—
80#1878—31no—
81#1869—31no—
82#1788—31no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—41no—
88C2×C3×#41—41no—
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4D411yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C22×#67—21no—
101C2×#235—22no—
102C2×#235—22no—
103C2×#235—22no—
104C2×#235—22no—
105C2×#235—22no—
106C2×#235—22no—
107C2×#235—22no—
108C2×#235—41no—
109C2×#235—41no—
110C2×#235—41no—
111C2×#235—41no—
112C2×#235D414yescomplemented
113C22×D12—21no—
114C22×D12—21no—
115C22×D12C2311yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×C4×D3—21no—
119C22×Dic6C2311yescharacteristic
120C3×C22⋊Q8—22no—
121C3×C22⋊Q8—41no—
122C3×#121—22no—
123C3×#121—41no—
124C3×C4×D4—22no—
125C3×C4×D4—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4D411yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4D411yescharacteristic
136C2×C3×C22⋊C4D411yescharacteristic
137C2×C3×C42C2311yescharacteristic
138#950—232no—
139C2×#216—22no—
140C2×#216—22no—
141C2×#216D414yescomplemented
142C2×#215—22no—
143C2×#215—22no—
144C2×#215—22no—
145C2×#215—22no—
146C2×#215—22no—
147C2×#215—41no—
148#940—28no—
149C2×#214—22no—
150C2×#214—22no—
151C2×#214D414yescomplemented
152C2×#213—22no—
153C2×#213—22no—
154C2×#213—22no—
155C2×#213—22no—
156C2×#213—22no—
157C2×#213—41no—
158#930—22no—
159#930—22no—
160#930—22no—
161#930D414yescomplemented
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×Dic3⋊C4—21no—
166C2×C4×Dic3—21no—
167C22×C3⋊C8—22no—
168C22×C3⋊C8—22no—
169C22×C3⋊C8—22no—
170C22×C3⋊C8C2311yescharacteristic
171C22×C3⋊C8C2311yescharacteristic
172C22×C3⋊C8C2311yescharacteristic
173C22×C3⋊C8C2311yescharacteristic
174#893—28no—
175#884—28no—
176#884—28no—
177#874—22no—
178#874—22no—
179C4×Dic6—22no—
180C4×Dic6—22no—
181C3×#95—21no—
182C3×#95—21no—
183C3×#95—21no—
184#835—22no—
185#832—22no—
186#830—22no—
187#830—22no—
188#830—22no—
189#810—22no—
190#810—22no—
191#809—22no—
192#809—22no—
193#809—41no—
194#809—41no—
195C22×#41—31no—
196C22×#41—31no—
197C22×#41C2×D311yescharacteristic
198C2×#135—64no—
199C2×#135—64no—
200C2×#135—64no—
201C22×Q16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×SD16—31no—
205C22×D8—31no—
206C22×D8—31no—
207C23×C8—31no—
208#550—64no—
209#550—64no—
210C2×#127—31no—
211C2×#127—61no—
212C2×C22⋊Q8C2×D311yescharacteristic
213C2×#121—31no—
214C2×#121—31no—
215C2×#121—61no—
216C2×#121—61no—
217C2×#121C2×D311yescharacteristic
218C2×C4×Q8—31no—
219C2×C4×D4—61no—
220C2×C4×D4C2×D311yescharacteristic
221#452—64no—
222#449—64no—
223#449—64no—
224C2×#103—31no—
225C2×#103—31no—
226C2×#103—31no—
227C2×#102—31no—
228C2×#102—31no—
229C2×#102—31no—
230C2×#102—31no—
231C2×#102—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—31no—
234C2×C22⋊C8—31no—
235#394—21no—
236#392—21no—
237#391C2×D311yescharacteristic
238#390C2×D311yescharacteristic
239#386—21no—
240#385—21no—
241#380C2×D311yescharacteristic
242#340—31no—
243#340—31no—
244#336—31no—
245#336—31no—
246C24×C3—21no—
247C24×C3C2×D411yescharacteristic
248C24×C3C2×D411yescharacteristic
249C23×D3—21no—
250C23×D3—21no—
251C3×#41—28no—
252C3×#41—44no—
253C3×#41—44no—
254C3×#41—44no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8C2×D412yes—
261C2×C3×D4—22no—
262C2×C3×D4—22no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—41no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—81no—
275C2×C3×D4C2×D412yes—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—42no—
290C22×C3×C4—42no—
291C22×C3×C4—42no—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—42no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—81no—
308C2×#67—81no—
309C2×#67—81no—
310C2×#67—81no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313#235—28no—
314#235—44no—
315#235—44no—
316#235—44no—
317#235—44no—
318#235—44no—
319#235—44no—
320#235—44no—
321C2×D12—21no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—24no—
330C2×D12—21no—
331C2×D12—21no—
332C2×D12—24no—
333C2×D12—42no—
334C2×D12—42no—
335C2×D12—81no—
336C2×D12—81no—
337C2×D12C2×D412yes—
338C2×D12C2×D412yes—
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—42no—
342C2×C4×D3—42no—
343C2×C4×D3—42no—
344C2×C4×D3—42no—
345C2×Dic6—21no—
346C2×Dic6—21no—
347C2×Dic6—21no—
348C2×Dic6C2×D412yes—
349C2×Dic6C2×D412yes—
350C2×Dic6C2×D412yes—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—42no—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—42no—
360C3×C22⋊C4—42no—
361C3×C22⋊C4—42no—
362C3×C22⋊C4—81no—
363C3×C22⋊C4—81no—
364C3×C42—21no—
365C3×C42—21no—
366#216—28no—
367#215—28no—
368#215—44no—
369#214—28no—
370#213—28no—
371#213—44no—
372(C2×D3)⋊C4—24no—
373(C2×D3)⋊C4—24no—
374C4⋊Dic3—21no—
375C4⋊Dic3C2×D412yes—
376Dic3⋊C4—24no—
377C4×Dic3—24no—
378C2×C3⋊C8—28no—
379C2×C3⋊C8—21no—
380C2×C3⋊C8—21no—
381C2×C3⋊C8—21no—
382C2×C3⋊C8—21no—
383C2×C3⋊C8—21no—
384C2×C3⋊C8—21no—
385C2×C3⋊C8—21no—
386C2×C3⋊C8—21no—
387C2×C3⋊C8—21no—
388C2×C3⋊C8—21no—
389C2×C3⋊C8C2×D412yes—
390C2×C3⋊C8C2×D412yes—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41—34no—
396C2×#41—41no—
397C2×#41—41no—
398C2×#41—62no—
399C2×#41—62no—
400C2×#41—62no—
401C2×#41—62no—
402C2×#41—62no—
403C2×#41—62no—
404C2×#41—62no—
405C2×#41—121no—
406C2×#41—121no—
407C2×#41—121no—
408C2×#41—121no—
409C22×Q8—31no—
410C22×Q8C22×D311yescharacteristic
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—31no—
414C22×D4—31no—
415C22×D4—61no—
416C22×D4—61no—
417C22×D4—61no—
418C22×D4—61no—
419C22×D4—61no—
420C22×D4—61no—
421C22×D4#6711yescharacteristic
422C22×D4C22×D311yescharacteristic
423C23×C4—21no—
424C23×C4—61no—
425C23×C4—61no—
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428#135—632no—
429C2×Q16—34no—
430C2×Q16—62no—
431C2×Q16—62no—
432C2×SD16—34no—
433C2×SD16—62no—
434C2×SD16—62no—
435C2×SD16—62no—
436C2×SD16—62no—
437C2×SD16—62no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—121no—
441C2×D8—62no—
442C2×D8—62no—
443C2×D8—62no—
444C2×D8—62no—
445C2×D8—62no—
446C2×D8—121no—
447C22×C8—31no—
448C22×C8—31no—
449C22×C8—31no—
450C22×C8—31no—
451C22×C8—62no—
452C22×C8—62no—
453C22×C8—62no—
454#127—62no—
455#127—62no—
456#127—68no—
457C22⋊Q8—22no—
458C22⋊Q8—41no—
459#121—22no—
460#121—34no—
461#121—41no—
462#121—68no—
463#121—68no—
464#121—62no—
465#121—62no—
466#121—62no—
467C4×Q8—62no—
468C4×Q8—62no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—68no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—61no—
475C2×C4⋊C4#6711yescharacteristic
476C2×C4⋊C4C22×D311yescharacteristic
477C2×C4⋊C4C22×D311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—61no—
484C2×C22⋊C4—61no—
485C2×C22⋊C4#6711yescharacteristic
486C2×C22⋊C4#6711yescharacteristic
487C2×C42—61no—
488C2×C42C22×D311yescharacteristic
489#103—62no—
490#103—62no—
491#103—62no—
492#102—62no—
493#102—62no—
494#102—62no—
495#102—121no—
496#102—121no—
497C22⋊C8—62no—
498C22⋊C8—62no—
499C22⋊C8—62no—
500#95—21no—
501#95—21no—
502#95—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3#12012yes—
524C23×C3C22×D411yescharacteristic
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—41no—
542C3×Q8—41no—
543C3×D4—22no—
544C3×D4—22no—
545C3×D4—44no—
546C3×D4—48no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—84no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—22no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—48no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4#12012yes—
579C2×C3×C4#13512yescomplemented
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4H(5,𝔽2)11yescharacteristic
585C2×C3×C4H(5,𝔽2)11yescharacteristic
586#67—48no—
587#67—48no—
588#67—84no—
589#67—84no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596D12—22no—
597D12—22no—
598D12—22no—
599D12—22no—
600D12—48no—
601D12—41no—
602D12—41no—
603D12—41no—
604D12—41no—
605D12—84no—
606C4×D3—48no—
607C4×D3—48no—
608Dic6—22no—
609Dic6—22no—
610Dic6—22no—
611Dic6#12014yes—
612C3⋊C8—22no—
613C3⋊C8—22no—
614C3⋊C8—41no—
615C3⋊C8—41no—
616C24—21no—
617C24—61no—
618C24—61no—
619C24C2×#6711yescharacteristic
620C24C2×#6711yescharacteristic
621#41—28no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—68no—
626#41—124no—
627#41—124no—
628#41—124no—
629#41—124no—
630#41—124no—
631#41—124no—
632#41—124no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—32no—
639C2×Q8—32no—
640C2×Q8—32no—
641C2×Q8—61no—
642C2×Q8—61no—
643C2×Q8—61no—
644C2×Q8D3×D412yes—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—32no—
653C2×D4—32no—
654C2×D4—41no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—64no—
661C2×D4—64no—
662C2×D4—64no—
663C2×D4—64no—
664C2×D4—64no—
665C2×D4—64no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—81no—
677C2×D4—122no—
678C2×D4—122no—
679C2×D4—122no—
680C2×D4—122no—
681C2×D4—122no—
682C2×D4—122no—
683C2×D4—241no—
684C2×D4—241no—
685C2×D4—241no—
686C2×D4—241no—
687C2×D4—241no—
688C2×D4—241no—
689C2×D4D3×D412yes—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—64no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—64no—
710C22×C4—122no—
711C22×C4—122no—
712C22×C4—122no—
713C22×C4—122no—
714C22×C4D3×D412yes—
715C22×C4D3×D412yes—
716C22×C4C2×#6711yescharacteristic
717C22×C4C2×#6711yescharacteristic
718C22×C4C2×#6711yescharacteristic
719C22×C4C2×#6711yescharacteristic
720C22×C4C23×D311yescharacteristic
721Q16—68no—
722SD16—68no—
723SD16—68no—
724SD16—124no—
725D8—68no—
726D8—124no—
727C2×C8—32no—
728C2×C8—32no—
729C2×C8—68no—
730C2×C8—61no—
731C2×C8—61no—
732C2×C8—61no—
733C2×C8—61no—
734C2×C8—61no—
735C2×C8—61no—
736C2×C8—61no—
737C2×C8—61no—
738C2×C8—61no—
739C2×C8—61no—
740C4⋊C4—22no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—32no—
746C4⋊C4—42no—
747C4⋊C4—64no—
748C4⋊C4—61no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—42no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—64no—
755C22⋊C4—64no—
756C22⋊C4—81no—
757C22⋊C4—81no—
758C42—21no—
759C42—21no—
760C42—64no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—42no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—42no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—42no—
777C22×C3—41no—
778C22×C3—81no—
779C22×C3—81no—
780C22×C3—81no—
781C22×C3—81no—
782C22×C3C2×#12011yescharacteristic
783C22×C3D4211yescharacteristic
784C22×C3D4211yescharacteristic
785C22×C3C2×#13511yescharacteristic
786C22×C3#57511yescharacteristic
787C22×C3#57611yescharacteristic
788C22×C3#57711yescharacteristic
789C2×D3—42no—
790C2×D3—42no—
791C2×D3—42no—
792C2×D3—42no—
793C2×D3—42no—
794C2×D3—42no—
795C2×D3—81no—
796C2×D3—81no—
797C2×D3—81no—
798C2×D3—81no—
799C2×D3—81no—
800C2×D3—81no—
801C2×D3—81no—
802C2×D3—81no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—41no—
806C3×C4—42no—
807C3×C4—41no—
808C3×C4—81no—
809C3×C4—81no—
810C3×C4C2×#12011yescharacteristic
811C3×C4#53411yescharacteristic
812C3×C4D4211yescharacteristic
813C3×C4D4211yescharacteristic
814Dic3—24no—
815Dic3—42no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—22no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—62no—
837C23—62no—
838C23—121no—
839C23—121no—
840C23—121no—
841C23—121no—
842C23—121no—
843C23—121no—
844C23—121no—
845C23—121no—
846C23—121no—
847C23—121no—
848C23—121no—
849C23—121no—
850C23#93712yes—
851C23C22×#6711yescharacteristic
852Q8—22no—
853Q8—22no—
854Q8—34no—
855Q8—41no—
856Q8—41no—
857Q8—62no—
858Q8—62no—
859Q8—62no—
860D4—22no—
861D4—22no—
862D4—44no—
863D4—48no—
864D4—41no—
865D4—41no—
866D4—62no—
867D4—62no—
868D4—62no—
869D4—62no—
870D4—84no—
871D4—128no—
872D4—128no—
873D4—128no—
874D4—121no—
875D4—121no—
876D4—121no—
877D4—121no—
878D4—244no—
879D4—244no—
880D4—244no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—48no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—128no—
914C2×C4—128no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4#93712yes—
918C2×C4#95012yescomplemented
919C2×C4C2×D3×D411yescharacteristic
920C2×C4C2×D3×D411yescharacteristic
921C2×C4C2×D3×D411yescharacteristic
922C2×C4C2×D3×D411yescharacteristic
923C2×C4#100411yescharacteristic
924C2×C4#100411yescharacteristic
925C8—62no—
926C8—62no—
927C8—121no—
928C8—121no—
929C2×C3—42no—
930C2×C3—81no—
931C2×C3—82no—
932C2×C3#240311yescharacteristic
933C2×C3#300211yescharacteristic
934C2×C3#301211yescharacteristic
935C2×C3#326811yescharacteristic
936C2×C3#327111yescharacteristic
937C2×C3#328411yescharacteristic
938C2×C3#328711yescharacteristic
939D3—82no—
940D3—82no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—122no—
963C22—122no—
964C22—122no—
965C22—122no—
966C22—122no—
967C22—122no—
968C22—241no—
969C22—241no—
970C22—241no—
971C22—241no—
972C22—241no—
973C22—241no—
974C22—241no—
975C22—241no—
976C22C2×#93711yescharacteristic
977C22D4×#6711yescharacteristic
978C22D4×#6711yescharacteristic
979C22C2×#95011yescharacteristic
980C22#582211yescharacteristic
981C22#583511yescharacteristic
982C22#583711yescharacteristic
983C4—22no—
984C4—22no—
985C4—41no—
986C4—42no—
987C4—41no—
988C4—64no—
989C4—81no—
990C4—81no—
991C4—122no—
992C4D3×#12011yescharacteristic
993C4#558911yescharacteristic
994C4#559011yescharacteristic
995C4#559011yescharacteristic
996C3#2385711yescharacteristic, complemented, Sylow
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—242no—
1001C2—242no—
1002C2#8260411yescharacteristic
1003C2#8292611yescharacteristic
1004C2#8342411yescharacteristic
1005C2#8350711yescharacteristic
1006C2#8353011yescharacteristic
1007C2#8354711yescharacteristic
1008C2#8358511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#23857
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C22×#950C2semidirect
2. C2×#5553C2semidirect
3. C3×#2407C2semidirect
4. C2×#5238C2semidirect
5. C2×#5047C2semidirect
6. C2×#5037C2semidirect
7. #71699C2semidirect
8. #71684C2semidirect
9. #71610C2semidirect
10. #69690C2semidirect
11. #69688C2semidirect
12. #69660C2semidirect
13. #69658C2semidirect
14. #69522C2semidirect
15. #69515C2semidirect
73. #2407D3semidirect
112. C2×#235D4semidirect
141. C2×#216D4semidirect
151. C2×#214D4semidirect
161. #930D4semidirect
579. C2×C3×C4#135semidirect
918. C2×C4#950semidirect
996. C3#23857semidirect

Maximal subgroups

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

subgroupindex
C22×#9502
C2×#55532
C3×#24072
C2×#52382
C2×#50472
C2×#50372
#716992
#716842
#716102
#696902
#696882
#696602
#696582
#695222
#695152
#238573