Finite Group Databasebeta

← #10800527

Subgroups — #10800527

Order 768.

1678 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5606C211yesmaximal, characteristic
2#73862C211yesmaximal, characteristic, complemented
3C4×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#1964C211yesmaximal, characteristic, complemented
5#71686C211yesmaximal, characteristic, complemented
6#70036C214yesmaximal, complemented
7Dic3×#99C214yesmaximal, complemented
8#69529C211yesmaximal, characteristic, complemented
9#69457C211yesmaximal, characteristic, complemented
10#21420—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×#892—21no—
28C2×#892C411yescharacteristic, complemented
29C2×#883C412yescomplemented
30C2×#67⋊C4C412yescomplemented
31C2×D3×C22⋊C4C2212yes—
32C2×C42×D3—21no—
33C2×C3×#99C2214yes—
34C3×#380C2211yescharacteristic
35C3×C4×C22⋊C4C2211yescharacteristic
36C2×#834C2214yes—
37#5212C2211yescharacteristic
38C4×#217C2211yescharacteristic
39#4987—21no—
40#4955C2212yes—
41Dic3×C22⋊C4C2212yes—
42Dic3×C22⋊C4C2212yes—
43C4×(C2×D3)⋊C4—21no—
44#4666—21no—
45#4666—21no—
46#4664—21no—
47D3×#95—21no—
48#4527C2214yes—
49#4527C2214yes—
50C2×#525—31no—
51#2280—31no—
52C2×C4×C22⋊C4—31no—
53#1996—31no—
54#1996—31no—
55#1964—31no—
56#1964D311yescharacteristic, complemented
57#1898—34no—
58C4×#99—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⋊C4C2×C412yescomplemented
126C2×C4×Dic3—21no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—22no—
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—
138#892—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—24no—
148D3×C22⋊C4—24no—
149C42×D3—44no—
150C3×#99—28no—
151C3×#95—21no—
152C3×#95—21no—
153#834—28no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C22×#41—31no—
159C24×C4—31no—
160#525—61no—
161#525—61no—
162#525—61no—
163#525—61no—
164#525—61no—
165#525—61no—
166#525—61no—
167#525—61no—
168C2×#123—32no—
169C2×C22⋊Q8—31no—
170C2×C22⋊Q8—31no—
171C2×#121—31no—
172C2×#121C2×D311yescharacteristic
173C2×#120—32no—
174C2×C4×D4—32no—
175C2×C4×D4—32no—
176C2×#117—31no—
177C2×#117—61no—
178C22×C22⋊C4—32no—
179C22×C42—61no—
180C2×#99—34no—
181C2×#99C2×D314yes—
182#381—61no—
183#380—31no—
184#380—61no—
185#380C2×D311yescharacteristic
186#379—32no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—32no—
189C4×C22⋊C4—32no—
190C4×C22⋊C4—61no—
191C4×C22⋊C4—61no—
192C4×C22⋊C4—61no—
193C4×C22⋊C4C2×D311yescharacteristic
194C2×#95—61no—
195#342—34no—
196#342—34no—
197C24×C3C22×C412yes—
198C24×C3C2411yescharacteristic
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—42no—
202C23×D3—42no—
203C23×D3C22×C411yescharacteristic
204C23×D3C22×C411yescharacteristic
205C23×D3C2×D411yescharacteristic
206C23×D3C2×D411yescharacteristic
207C23×D3C2×D411yescharacteristic
208C23×D3C2×D411yescharacteristic
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—24no—
212C2×C3×D4—24no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—42no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—42no—
219C22×C3×C4C22×C412yes—
220C22×C3×C4C22×C411yescharacteristic
221C22×C3×C4C22×C411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C2×#67—22no—
227C2×#67—22no—
228C2×#67—22no—
229C2×#67—22no—
230C2×#67—44no—
231C2×#67—44no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—42no—
237C22×Dic3—44no—
238C22×Dic3C22×C411yescharacteristic
239C22×Dic3C22×C412yes—
240C22×Dic3C22×C412yes—
241C22×Dic3C22×C411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246#237—44no—
247#237—44no—
248#237—44no—
249#237—44no—
250C2×C4×D3—24no—
251C2×C4×D3—24no—
252C2×C4×D3—24no—
253C2×C4×D3—28no—
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—42no—
262C2×C4×D3—42no—
263C2×C4×D3—44no—
264C2×C4×D3—44no—
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×C4×D3C22⋊C411yescharacteristic
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—42no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—42no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—24no—
291C3×C22⋊C4#4114yescomplemented
292C3×C42—42no—
293#217—22no—
294#217—22no—
295#217—22no—
296#217—22no—
297#217—22no—
298#217—24no—
299#217#4114yescomplemented
300(C2×D3)⋊C4—28no—
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—44no—
306(C2×D3)⋊C4—44no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—22no—
310C4⋊Dic3—22no—
311C4⋊Dic3—42no—
312Dic3⋊C4—22no—
313Dic3⋊C4—22no—
314C4×Dic3—22no—
315C4×Dic3—22no—
316C4×Dic3—44no—
317C4×Dic3—44no—
318C4×Dic3—42no—
319C25—31no—
320C2×#41—61no—
321C2×#41—61no—
322C2×#41—61no—
323C2×#41—61no—
324C2×#41—124no—
325C22×Q8—31no—
326C22×D4—32no—
327C22×D4—32no—
328C22×D4C4×D311yescharacteristic, complemented
329C22×D4C22×D312yes—
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—31no—
343C23×C4—32no—
344C23×C4—62no—
345C23×C4—124no—
346C23×C4C22×D311yescharacteristic
347#123—62no—
348#123—62no—
349#123—62no—
350#123—62no—
351C22⋊Q8—61no—
352C22⋊Q8—61no—
353C22⋊Q8—61no—
354C22⋊Q8—61no—
355C22⋊Q8—61no—
356C22⋊Q8—61no—
357C22⋊Q8—61no—
358C22⋊Q8—61no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—61no—
364#121—61no—
365#121—61no—
366#121—61no—
367#120—62no—
368#120—62no—
369#120—62no—
370#120—62no—
371C4×D4—62no—
372C4×D4—62no—
373C4×D4—62no—
374C4×D4—62no—
375C4×D4—62no—
376C4×D4—62no—
377C4×D4—62no—
378C4×D4—62no—
379#117—61no—
380#117—61no—
381#117—61no—
382#117—61no—
383#117—124no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C4×D311yescharacteristic, complemented
390C2×C22⋊C4—32no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—64no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—64no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4C4×D312yescomplemented
402C2×C22⋊C4C22×D312yes—
403C2×C22⋊C4C22×D312yes—
404C2×C42—21no—
405C2×C42—32no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—61no—
409C2×C42—124no—
410#99—28no—
411#99—68no—
412#95—21no—
413#95—21no—
414#95—62no—
415#95—62no—
416#95—61no—
417#95—61no—
418C23×C3—22no—
419C23×C3—24no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3C23×C411yescharacteristic
425C23×C3C22×D411yescharacteristic
426C23×C3C22×D411yescharacteristic
427C23×C3C2×#4112yes—
428C23×C3C2×#4112yes—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—48no—
450C22×D3—48no—
451C22×D3C2×C22⋊C411yescharacteristic
452C22×D3C2×C22⋊C411yescharacteristic
453C22×D3C2×C22⋊C411yescharacteristic
454C22×D3C2×C22⋊C411yescharacteristic
455C3×D4—42no—
456C3×D4—44no—
457C3×D4—42no—
458C3×D4—42no—
459C3×D4—42no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4C2×C22⋊C411yescharacteristic
475C2×C3×C4C2×C22⋊C411yescharacteristic
476C2×C3×C4C2×C22⋊C411yescharacteristic
477C2×C3×C4C2×C22⋊C411yescharacteristic
478#67—44no—
479#67—44no—
480#67—44no—
481#67—44no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—44no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3—44no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3C2×C22⋊C411yescharacteristic
501C2×Dic3C2×C22⋊C411yescharacteristic
502C2×Dic3C2×C22⋊C411yescharacteristic
503C2×Dic3C2×C22⋊C411yescharacteristic
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—41no—
517C4×D3—41no—
518C4×D3—41no—
519C4×D3—416no—
520C4×D3#9914yescomplemented
521Dic6—42no—
522Dic6—42no—
523C24—31no—
524C24—31no—
525C24—31no—
526C24—31no—
527C24—31no—
528C24—31no—
529C24—62no—
530C24—62no—
531C24—122no—
532C24—122no—
533C24C2×C4×D312yes—
534C24C23×D311yescharacteristic
535#41—124no—
536#41—124no—
537#41—124no—
538#41—124no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—122no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—62no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—62no—
553C2×D4—124no—
554C2×D4—124no—
555C22×C4—22no—
556C22×C4—22no—
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—31no—
578C22×C4—31no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—42no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—68no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4—122no—
595C22×C4—122no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4—124no—
600C22×C4—124no—
601C22×C4—122no—
602C22×C4—124no—
603C22×C4C2×C4×D312yes—
604C22×C4C2×C4×D311yescharacteristic
605C22×C4C2×C4×D311yescharacteristic
606C22×C4D3×D411yescharacteristic
607C22×C4D3×D411yescharacteristic
608C22×C4D3×D411yescharacteristic
609C22×C4D3×D411yescharacteristic
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—62no—
618C4⋊C4—62no—
619C4⋊C4—122no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—34no—
625C22⋊C4—62no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—62no—
629C22⋊C4—68no—
630C22⋊C4—62no—
631C22⋊C4—62no—
632C22⋊C4—62no—
633C22⋊C4—62no—
634C22⋊C4—62no—
635C22⋊C4—64no—
636C22⋊C4—124no—
637C22⋊C4—124no—
638C22⋊C4#23714yescomplemented
639C42—42no—
640C42—62no—
641C42—62no—
642C42—122no—
643C42—124no—
644C42—124no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—84no—
657C22×C3C22×C22⋊C411yescharacteristic
658C22×C3C4×#4112yes—
659C22×C3#52512yes—
660C22×C3#53211yescharacteristic
661C22×C3#53211yescharacteristic
662C2×D3—28no—
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—21no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—44no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—44no—
679C2×D3—44no—
680C2×D3C2×#9912yes—
681C2×D3#41012yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—44no—
686C3×C4—42no—
687C3×C4—82no—
688C3×C4C2×#9912yes—
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—44no—
693Dic3—42no—
694Dic3—42no—
695Dic3—82no—
696Dic3C2×#9912yes—
697C23—22no—
698C23—24no—
699C23—31no—
700C23—31no—
701C23—31no—
702C23—31no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23—62no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—128no—
728C23—128no—
729C23C22×C4×D311yescharacteristic
730C23C2×D3×D411yescharacteristic
731C23C2×D3×D411yescharacteristic
732C23C2×#23712yes—
733C23D3×#4112yes—
734Q8—122no—
735Q8—122no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—44no—
740D4—42no—
741D4—124no—
742D4—124no—
743D4—124no—
744D4—124no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—31no—
752C2×C4—34no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
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—62no—
777C2×C4—62no—
778C2×C4—64no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—124no—
786C2×C4—1216no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—124no—
791C2×C4—122no—
792C2×C4—122no—
793C2×C4—122no—
794C2×C4—122no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4D3×C22⋊C411yescharacteristic
799C2×C4D3×C22⋊C411yescharacteristic
800C2×C4D3×C22⋊C411yescharacteristic
801C2×C4D3×C22⋊C411yescharacteristic
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—22no—
806C2×C3—82no—
807C2×C3#229711yescharacteristic
808C2×C3C22×#9911yescharacteristic
809C2×C3C2×#41011yescharacteristic
810D3—22no—
811D3—22no—
812D3—41no—
813D3—41no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—32no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—68no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—84no—
839C22—122no—
840C22—122no—
841C22—122no—
842C22—122no—
843C22—124no—
844C22—124no—
845C22—124no—
846C22C2×D3×C22⋊C411yescharacteristic
847C22C4×#23712yes—
848C22#560612yes—
849C22#566811yescharacteristic
850C22#571611yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—32no—
855C4—44no—
856C4—42no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—82no—
861C4—124no—
862C4—122no—
863C4—122no—
864C4—242no—
865C4D3×#9912yes—
866C3#2142011yescharacteristic, complemented, Sylow
867C2—22no—
868C2—21no—
869C2—21no—
870C2—22no—
871C2—62no—
872C2—62no—
873C2—82no—
874C2—121no—
875C2—121no—
876C2#7629011yescharacteristic
877C2C2×D3×#9911yescharacteristic
878C2D3×#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#21420
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. #73862C2semidirect
3. C4×D3×C22⋊C4C2semidirect
4. C3×#1964C2semidirect
5. #71686C2semidirect
6. #70036C2semidirect
7. Dic3×#99C2semidirect
8. #69529C2semidirect
9. #69457C2semidirect
11. C22×#237C4semidirect
14. C2×#938C4semidirect
26. C2×#897C4semidirect
28. 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
125. C2×Dic3⋊C4C2×C4semidirect
129. C2×C4×Dic3C2×C4semidirect
291. C3×C22⋊C4#41semidirect
299. #217#41semidirect
328. C22×D4C4×D3semidirect
389. C2×C4⋊C4C4×D3semidirect
401. C2×C22⋊C4C4×D3semidirect
520. C4×D3#99semidirect
638. C22⋊C4#237semidirect
866. C3#21420semidirect

Maximal subgroups

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

subgroupindex
C2×#56062
#738622
C4×D3×C22⋊C42
C3×#19642
#716862
#700362
Dic3×#992
#695292
#694572
#214203