Finite Group Databasebeta

← #10804991

Subgroups — #10804991

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5606C211yesmaximal, characteristic
2D3×#380C211yesmaximal, characteristic, complemented
3#73561C211yesmaximal, characteristic, complemented
4C3×#1964C211yesmaximal, characteristic, complemented
5#71686C211yesmaximal, characteristic, complemented
6#70036C214yesmaximal, complemented
7#70028C214yesmaximal, complemented
8#69529C211yesmaximal, characteristic, complemented
9#69457C211yesmaximal, characteristic, complemented
10#21874—31nomaximal, Sylow
11C22×#237C411yescharacteristic, complemented
12C23×C4×D3C2211yescharacteristic
13C2×C3×#121C2211yescharacteristic
14C2×#938C411yescharacteristic, complemented
15C2×#937C2212yes—
16C2×D4×Dic3C2212yes—
17C2×#924C2211yescharacteristic
18#5606—21no—
19#5606—21no—
20#5606—21no—
21#5606—21no—
22#5606—21no—
23#5606—21no—
24#5606—21no—
25#5606—21no—
26C2×#897C411yescharacteristic, complemented
27C2×#892C411yescharacteristic, complemented
28C2×D3×C4⋊C4—21no—
29C2×#883C412yescomplemented
30C2×#67⋊C4C412yescomplemented
31C2×D3×C22⋊C4C2212yes—
32C2×#872—21no—
33C2×C3×#99C2214yes—
34C3×#380C2211yescharacteristic
35C3×C4×C22⋊C4C2211yescharacteristic
36C2×#834C2214yes—
37#5212C2211yescharacteristic
38C4×#217C2211yescharacteristic
39#4987—21no—
40#4955C2212yes—
41#4942C2212yes—
42#4942C2212yes—
43C4×(C2×D3)⋊C4—21no—
44#4667—21no—
45#4667—21no—
46#4664—21no—
47D3×#95—21no—
48#4527C2214yes—
49#4527C2214yes—
50C2×#525—31no—
51#2280—31no—
52C2×#380—31no—
53#1996—31no—
54#1996—31no—
55#1964—31no—
56#1964D311yescharacteristic, complemented
57#1898—34no—
58#1799—34no—
59C24×D3C2311yescharacteristic
60C22×C3×D4C2×C411yescharacteristic, complemented
61C22×C3×D4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C22×#67C2×C412yes—
64C22×#67C2×C412yes—
65C23×Dic3C2×C412yescomplemented
66C23×Dic3C2311yescharacteristic
67C2×#237—21no—
68C2×#237—21no—
69C2×#237—21no—
70C2×#237—21no—
71C2×#237—44no—
72C22×C4×D3—22no—
73C22×C4×D3—44no—
74C22×C4×D3C2×C411yescharacteristic
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3C2×C411yescharacteristic
77C22×C4×D3C2×C411yescharacteristic
78C22×C4×D3D411yescharacteristic
79C22×C4×D3D411yescharacteristic
80C22×C4×D3D411yescharacteristic
81C22×C4×D3D411yescharacteristic
82C22×C4×D3D411yescharacteristic
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×Dic6C2×C411yescharacteristic, complemented
87C3×#121—21no—
88C3×#121—21no—
89C3×#121—21no—
90C3×#121—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
93C2×C3×C22⋊C4C2×C412yescomplemented
94C2×C3×C22⋊C4C2312yes—
95C2×C3×C22⋊C4C2312yes—
96C2×C3×C42—21no—
97C2×#217C2×C412yescomplemented
98C2×#217C2312yes—
99C2×#217C2312yes—
100C2×#217C2312yes—
101#938—21no—
102#938—21no—
103#938—21no—
104#938—21no—
105#937—22no—
106#937—22no—
107#937—22no—
108#937—22no—
109D4×Dic3—22no—
110D4×Dic3—22no—
111D4×Dic3—22no—
112D4×Dic3—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4C2×C412yes—
117C2×(C2×D3)⋊C4C2×C412yes—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3C2×C412yescomplemented
120C2×C4⋊Dic3C2×C411yescharacteristic, complemented
121#924—21no—
122#924—21no—
123#924—21no—
124#924—21no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4C2×C412yescomplemented
128C2×C4×Dic3—21no—
129C2×C4×Dic3C2×C412yescomplemented
130#897—21no—
131#897—21no—
132#897—21no—
133#897—21no—
134#892—21no—
135#892—21no—
136#892—21no—
137#892—21no—
138D3×C4⋊C4—44no—
139#883—22no—
140#883—22no—
141#883—22no—
142#883—22no—
143#67⋊C4—22no—
144#67⋊C4—22no—
145#67⋊C4—22no—
146#67⋊C4—22no—
147D3×C22⋊C4—44no—
148#872—44no—
149C3×#99—44no—
150C3×#95—21no—
151C3×#95—21no—
152#834—44no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C22×#41—31no—
158C24×C4—31no—
159#525—61no—
160#525—61no—
161#525—61no—
162#525—61no—
163#525—61no—
164#525—61no—
165#525—61no—
166#525—61no—
167C2×#123—32no—
168C2×C22⋊Q8—31no—
169C2×C22⋊Q8—31no—
170C2×#121—31no—
171C2×#121C2×D311yescharacteristic
172C2×#120—32no—
173C2×C4×D4—32no—
174C2×C4×D4—32no—
175C2×#117—31no—
176C2×#117—61no—
177C22×C4⋊C4—61no—
178C22×C22⋊C4—32no—
179C2×#99—34no—
180C2×#99C2×D314yes—
181#381—61no—
182#380—31no—
183#380—32no—
184#380—32no—
185#380—61no—
186#380—61no—
187#380—61no—
188#380C2×D311yescharacteristic
189#379—32no—
190C4×C22⋊C4—31no—
191C4×C22⋊C4—61no—
192C4×C22⋊C4C2×D311yescharacteristic
193C2×#95—61no—
194#342—34no—
195#342—34no—
196C24×C3C22×C412yes—
197C24×C3C2411yescharacteristic
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—42no—
201C23×D3—42no—
202C23×D3C22×C411yescharacteristic
203C23×D3C22×C411yescharacteristic
204C23×D3C2×D411yescharacteristic
205C23×D3C2×D411yescharacteristic
206C23×D3C2×D411yescharacteristic
207C23×D3C2×D411yescharacteristic
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—42no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—42no—
218C22×C3×C4C22×C412yes—
219C22×C3×C4C22×C411yescharacteristic
220C22×C3×C4C22×C411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C2×#67—22no—
226C2×#67—22no—
227C2×#67—22no—
228C2×#67—22no—
229C2×#67—44no—
230C2×#67—44no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—42no—
236C22×Dic3—44no—
237C22×Dic3C22×C411yescharacteristic
238C22×Dic3C22×C412yes—
239C22×Dic3C22×C412yes—
240C22×Dic3C22×C411yescharacteristic
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245#237—44no—
246#237—44no—
247#237—44no—
248#237—44no—
249C2×C4×D3—24no—
250C2×C4×D3—24no—
251C2×C4×D3—24no—
252C2×C4×D3—42no—
253C2×C4×D3—42no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3—44no—
262C2×C4×D3—44no—
263C2×C4×D3—44no—
264C2×C4×D3C22⋊C411yescharacteristic
265C2×C4×D3C22⋊C411yescharacteristic
266C2×C4×D3C22⋊C411yescharacteristic
267C2×C4×D3C22⋊C411yescharacteristic
268C2×C4×D3C22⋊C411yescharacteristic
269C2×C4×D3C22⋊C411yescharacteristic
270C2×C4×D3C22⋊C411yescharacteristic
271C2×C4×D3C22⋊C411yescharacteristic
272C2×C4×D3C22⋊C411yescharacteristic
273C2×C4×D3C22⋊C411yescharacteristic
274C2×C4×D3C22⋊C411yescharacteristic
275C2×C4×D3C22⋊C411yescharacteristic
276C2×C4×D3C22⋊C411yescharacteristic
277C2×C4×D3C22⋊C411yescharacteristic
278C2×C4×D3C22⋊C411yescharacteristic
279C2×C4×D3C22⋊C411yescharacteristic
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—42no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—42no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—22no—
291C3×C42—42no—
292#217—22no—
293#217—22no—
294#217—22no—
295#217—22no—
296#217—22no—
297#217—24no—
298#217—22no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—44no—
304(C2×D3)⋊C4—44no—
305(C2×D3)⋊C4—44no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—22no—
309C4⋊Dic3—22no—
310C4⋊Dic3—42no—
311Dic3⋊C4—22no—
312Dic3⋊C4—22no—
313Dic3⋊C4—44no—
314Dic3⋊C4—44no—
315C4×Dic3—22no—
316C4×Dic3—22no—
317C4×Dic3—42no—
318C25—31no—
319C2×#41—61no—
320C2×#41—61no—
321C2×#41—61no—
322C2×#41—61no—
323C2×#41—124no—
324C22×Q8—31no—
325C22×D4—32no—
326C22×D4—32no—
327C22×D4C4×D311yescharacteristic, complemented
328C22×D4C22×D312yes—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—32no—
343C23×C4—62no—
344C23×C4—124no—
345C23×C4C22×D311yescharacteristic
346#123—62no—
347#123—62no—
348#123—62no—
349#123—62no—
350C22⋊Q8—61no—
351C22⋊Q8—61no—
352C22⋊Q8—61no—
353C22⋊Q8—61no—
354C22⋊Q8—61no—
355C22⋊Q8—61no—
356C22⋊Q8—61no—
357C22⋊Q8—61no—
358#121—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—61no—
363#121—61no—
364#121—61no—
365#121—61no—
366#120—62no—
367#120—62no—
368#120—62no—
369#120—62no—
370C4×D4—62no—
371C4×D4—62no—
372C4×D4—62no—
373C4×D4—62no—
374C4×D4—62no—
375C4×D4—62no—
376C4×D4—62no—
377C4×D4—62no—
378#117—61no—
379#117—61no—
380#117—61no—
381#117—61no—
382#117—124no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—124no—
391C2×C4⋊C4C4×D311yescharacteristic, complemented
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—124no—
402C2×C22⋊C4C4×D312yescomplemented
403C2×C22⋊C4C22×D312yes—
404C2×C22⋊C4C22×D312yes—
405C2×C42—21no—
406C2×C42—32no—
407C2×C42—61no—
408#99—44no—
409#99—124no—
410#95—21no—
411#95—21no—
412#95—62no—
413#95—62no—
414#95—61no—
415#95—61no—
416C23×C3—22no—
417C23×C3—24no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3C23×C411yescharacteristic
423C23×C3C22×D411yescharacteristic
424C23×C3C22×D411yescharacteristic
425C23×C3H(5,𝔽2)12yes—
426C23×C32−1+412yes—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—48no—
448C22×D3—48no—
449C22×D3C2×C22⋊C411yescharacteristic
450C22×D3C2×C22⋊C411yescharacteristic
451C22×D3C2×C22⋊C411yescharacteristic
452C22×D3C2×C22⋊C411yescharacteristic
453C3×D4—42no—
454C3×D4—42no—
455C3×D4—42no—
456C3×D4—44no—
457C3×D4—42no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4C2×C22⋊C411yescharacteristic
473C2×C3×C4C2×C22⋊C411yescharacteristic
474C2×C3×C4C2×C22⋊C411yescharacteristic
475C2×C3×C4C2×C22⋊C411yescharacteristic
476#67—44no—
477#67—44no—
478#67—44no—
479#67—44no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—44no—
489C2×Dic3—44no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3—42no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3C2×C22⋊C411yescharacteristic
499C2×Dic3C2×C22⋊C411yescharacteristic
500C2×Dic3C2×C22⋊C411yescharacteristic
501C2×Dic3C2×C22⋊C411yescharacteristic
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—41no—
512C4×D3—41no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—41no—
517C4×D3—88no—
518C4×D3#9914yescomplemented
519Dic6—42no—
520Dic6—42no—
521C24—31no—
522C24—31no—
523C24—31no—
524C24—31no—
525C24—31no—
526C24—31no—
527C24—62no—
528C24—62no—
529C24—122no—
530C24—122no—
531C24C2×C4×D312yes—
532C24C23×D311yescharacteristic
533#41—124no—
534#41—124no—
535#41—124no—
536#41—124no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—122no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—62no—
550C2×D4—62no—
551C2×D4—124no—
552C2×D4—124no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—42no—
580C22×C4—64no—
581C22×C4—64no—
582C22×C4—64no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4—122no—
595C22×C4—122no—
596C22×C4—124no—
597C22×C4—124no—
598C22×C4—124no—
599C22×C4—122no—
600C22×C4—124no—
601C22×C4C2×C4×D312yes—
602C22×C4C2×C4×D311yescharacteristic
603C22×C4C2×C4×D311yescharacteristic
604C22×C4D3×D411yescharacteristic
605C22×C4D3×D411yescharacteristic
606C22×C4D3×D411yescharacteristic
607C22×C4D3×D411yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—62no—
616C4⋊C4—62no—
617C4⋊C4—122no—
618C4⋊C4—124no—
619C4⋊C4—124no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—62no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—62no—
629C22⋊C4—62no—
630C22⋊C4—62no—
631C22⋊C4—62no—
632C22⋊C4—62no—
633C22⋊C4—62no—
634C22⋊C4—64no—
635C22⋊C4—62no—
636C22⋊C4—124no—
637C22⋊C4—124no—
638C22⋊C4—124no—
639C42—42no—
640C42—62no—
641C42—62no—
642C42—122no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—84no—
655C22×C3C22×C22⋊C411yescharacteristic
656C22×C3#52012yes—
657C22×C3#53511yescharacteristic
658C22×C3#53611yescharacteristic
659C22×C3#53712yes—
660C2×D3—24no—
661C2×D3—24no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—44no—
673C2×D3—44no—
674C2×D3—44no—
675C2×D3—44no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3C2×#9912yes—
679C2×D3#41012yes—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—42no—
684C3×C4—82no—
685C3×C4—82no—
686C3×C4C2×#9912yes—
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—42no—
691Dic3—42no—
692Dic3—82no—
693Dic3—82no—
694Dic3C2×#9912yes—
695C23—22no—
696C23—24no—
697C23—31no—
698C23—31no—
699C23—31no—
700C23—31no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—62no—
706C23—62no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—128no—
726C23—128no—
727C23C22×C4×D311yescharacteristic
728C23C2×D3×D411yescharacteristic
729C23C2×D3×D411yescharacteristic
730C23#100412yes—
731C23#101012yes—
732Q8—122no—
733Q8—122no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—44no—
738D4—42no—
739D4—124no—
740D4—124no—
741D4—124no—
742D4—124no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—31no—
749C2×C4—34no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—124no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—124no—
787C2×C4—122no—
788C2×C4—122no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4—122no—
792C2×C4—122no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—248no—
796C2×C4D3×C22⋊C411yescharacteristic
797C2×C4D3×C22⋊C411yescharacteristic
798C2×C4D3×C22⋊C411yescharacteristic
799C2×C4D3×C22⋊C411yescharacteristic
800C2×C3—21no—
801C2×C3—22no—
802C2×C3—21no—
803C2×C3—22no—
804C2×C3—82no—
805C2×C3#231111yescharacteristic
806C2×C3C22×#9911yescharacteristic
807C2×C3C2×#41011yescharacteristic
808D3—22no—
809D3—22no—
810D3—41no—
811D3—41no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—32no—
819C22—32no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—64no—
826C22—64no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—84no—
838C22—124no—
839C22—124no—
840C22—124no—
841C22—124no—
842C22—122no—
843C22—122no—
844C22C2×D3×C22⋊C411yescharacteristic
845C22#554612yes—
846C22#560812yes—
847C22#567511yescharacteristic
848C22#571511yescharacteristic
849C4—21no—
850C4—21no—
851C4—21no—
852C4—32no—
853C4—42no—
854C4—61no—
855C4—61no—
856C4—61no—
857C4—82no—
858C4—82no—
859C4—122no—
860C4—122no—
861C4—242no—
862C4—242no—
863C4D3×#9912yes—
864C3#2187411yescharacteristic, complemented, Sylow
865C2—21no—
866C2—22no—
867C2—21no—
868C2—22no—
869C2—62no—
870C2—62no—
871C2—82no—
872C2—121no—
873C2—121no—
874C2#7629411yescharacteristic
875C2C2×D3×#9911yescharacteristic
876C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1964C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5606C2
cosocleC24×C3C24
hypercenter#1964D3
hypocenterC3#21874
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. D3×#380C2semidirect
3. #73561C2semidirect
4. C3×#1964C2semidirect
5. #71686C2semidirect
6. #70036C2semidirect
7. #70028C2semidirect
8. #69529C2semidirect
9. #69457C2semidirect
11. C22×#237C4semidirect
14. C2×#938C4semidirect
26. C2×#897C4semidirect
27. C2×#892C4semidirect
29. C2×#883C4semidirect
30. C2×#67⋊C4C4semidirect
56. #1964D3semidirect
60. C22×C3×D4C2×C4semidirect
65. C23×Dic3C2×C4semidirect
86. C22×Dic6C2×C4semidirect
92. C2×C3×C4⋊C4C2×C4semidirect
93. C2×C3×C22⋊C4C2×C4semidirect
97. C2×#217C2×C4semidirect
119. C2×C4⋊Dic3C2×C4semidirect
120. C2×C4⋊Dic3C2×C4semidirect
127. C2×Dic3⋊C4C2×C4semidirect
129. C2×C4×Dic3C2×C4semidirect
327. C22×D4C4×D3semidirect
391. C2×C4⋊C4C4×D3semidirect
402. C2×C22⋊C4C4×D3semidirect
518. C4×D3#99semidirect
864. C3#21874semidirect

Maximal subgroups

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

subgroupindex
C2×#56062
D3×#3802
#735612
C3×#19642
#716862
#700362
#700282
#695292
#694572
#218743