Finite Group Databasebeta

← #10804992

Subgroups — #10804992

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×#5627C211yesmaximal, characteristic
2D3×#380C211yesmaximal, characteristic, complemented
3#73561C211yesmaximal, characteristic, complemented
4C3×#1996C211yesmaximal, characteristic, complemented
5#71701C211yesmaximal, characteristic, complemented
6#69528C211yesmaximal, characteristic, complemented
7#69456C211yesmaximal, characteristic, complemented
8#68970C214yesmaximal, complemented
9#68959C214yesmaximal, complemented
10#21874—31nomaximal, Sylow
11C22×#239C411yescharacteristic, complemented
12C23×C4×D3C2211yescharacteristic
13C2×C3×C22⋊Q8C2211yescharacteristic
14C2×#946C411yescharacteristic, complemented
15C2×#930C2211yescharacteristic
16#5627—21no—
17#5627—21no—
18#5627—21no—
19#5627—21no—
20#5627—21no—
21#5627—21no—
22#5627—21no—
23#5627—21no—
24C2×#895C411yescharacteristic, complemented
25C2×#894C412yescomplemented
26C2×#893C412yescomplemented
27C2×#892C411yescharacteristic, complemented
28C2×D3×C4⋊C4—21no—
29C2×#882C2212yes—
30C2×#67⋊C4C2212yes—
31C2×D3×C22⋊C4C2212yes—
32C2×#872—21no—
33C3×#380C2211yescharacteristic
34C3×C4×C22⋊C4C2211yescharacteristic
35#5212C2211yescharacteristic
36C4×#217C2211yescharacteristic
37#4987—21no—
38#4955C2212yes—
39C2×#806C2214yes—
40C2×#806C2214yes—
41#4942C2212yes—
42#4942C2212yes—
43C4×(C2×D3)⋊C4—21no—
44#4667—21no—
45#4667—21no—
46#4664—21no—
47D3×#95—21no—
48C3×#342C2214yes—
49#4526C2214yes—
50C2×#525—31no—
51#2280—31no—
52C2×#380—31no—
53#1996—31no—
54#1996D311yescharacteristic, complemented
55#1964—31no—
56#1964—31no—
57#1898—34no—
58#1799—34no—
59C24×D3C2311yescharacteristic
60C22×C3×Q8C2×C411yescharacteristic, complemented
61C23×C3×C4C2311yescharacteristic
62C22×#67C2312yes—
63C23×Dic3C2311yescharacteristic
64C2×#239—21no—
65C2×#239—21no—
66C2×#239—21no—
67C2×#239—21no—
68C2×#239—44no—
69C22×D12C2×C412yes—
70C22×D12C2×C412yes—
71C22×D12C2×C411yescharacteristic, complemented
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×D3C2×C412yescomplemented
79C22×C4×D3D411yescharacteristic
80C22×C4×D3D411yescharacteristic
81C22×C4×D3D411yescharacteristic
82C22×C4×D3D411yescharacteristic
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
93C2×C3×C4⋊C4C2×C412yescomplemented
94C2×C3×C22⋊C4C2312yes—
95C2×C3×C22⋊C4C2312yes—
96C2×C3×C22⋊C4C2312yes—
97C2×C3×C42—21no—
98C2×#217C2312yes—
99C2×#217C2312yes—
100#946—21no—
101#946—21no—
102#946—21no—
103#946—21no—
104#930—21no—
105#930—21no—
106#930—21no—
107#930—21no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4C2×C412yes—
112C2×(C2×D3)⋊C4C2×C412yes—
113C2×(C2×D3)⋊C4C2×C412yescomplemented
114C2×(C2×D3)⋊C4C2×C412yescomplemented
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3C2×C411yescharacteristic, complemented
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4C2×C412yescomplemented
120C2×C4×Dic3—21no—
121C2×C4×Dic3C2×C412yescomplemented
122#895—21no—
123#895—21no—
124#895—21no—
125#895—21no—
126#894—22no—
127#894—22no—
128#894—22no—
129#894—22no—
130#893—22no—
131#893—22no—
132#893—22no—
133#893—22no—
134#892—21no—
135#892—21no—
136#892—21no—
137#892—21no—
138D3×C4⋊C4—44no—
139#882—22no—
140#882—22no—
141#882—22no—
142#882—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×#95—21no—
150C3×#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155#806—44no—
156#806—44no—
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⋊Q8C2×D311yescharacteristic
170C2×#121—31no—
171C2×#121—31no—
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×#99—34no—
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#342C2×D314yes—
196C24×C3C2411yescharacteristic
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—42no—
200C23×D3—42no—
201C23×D3C22×C411yescharacteristic
202C23×D3C22×C411yescharacteristic
203C23×D3C22×C412yes—
204C23×D3C2×D411yescharacteristic
205C23×D3C2×D411yescharacteristic
206C23×D3C2×D411yescharacteristic
207C23×D3C2×D411yescharacteristic
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—42no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—42no—
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C22×C412yes—
216C22×C3×C4C22×C412yes—
217C22×C3×C4C22×C411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C2×#67—22no—
223C2×#67—22no—
224C2×#67—24no—
225C2×#67—24no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—42no—
229C22×Dic3C22×C412yes—
230C22×Dic3C22×C411yescharacteristic
231C22×Dic3C22×C411yescharacteristic
232C22×Dic3C2×D411yescharacteristic
233C22×Dic3C2×D411yescharacteristic
234C22×Dic3C2×D411yescharacteristic
235C22×Dic3C2×D411yescharacteristic
236#239—44no—
237#239—44no—
238#239—44no—
239#239—44no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—22no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—42no—
247C2×D12—44no—
248C2×D12—44no—
249C2×C4×D3—24no—
250C2×C4×D3—24no—
251C2×C4×D3—24no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
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×D3—44no—
266C2×C4×D3—44no—
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×C4×D3C22⋊C411yescharacteristic
282C2×C4×D3C22⋊C411yescharacteristic
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—42no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—22no—
293C3×C42—42no—
294#217—22no—
295#217—24no—
296#217—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—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—22no—
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—44no—
306(C2×D3)⋊C4—44no—
307(C2×D3)⋊C4—44no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
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×Q8C4×D311yescharacteristic, complemented
325C22×D4—32no—
326C22×D4—32no—
327C22×D4—32no—
328C22×D4—31no—
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—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—61no—
355C22⋊Q8—61no—
356C22⋊Q8—61no—
357C22⋊Q8—61no—
358#121—61no—
359#121—61no—
360#121—61no—
361#121—61no—
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—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—124no—
390C2×C4⋊C4C4×D311yescharacteristic, complemented
391C2×C4⋊C4C4×D312yescomplemented
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⋊C4C22×D312yes—
403C2×C22⋊C4C22×D312yes—
404C2×C22⋊C4C22×D312yes—
405C2×C42—21no—
406C2×C42—32no—
407C2×C42—61no—
408#99—124no—
409#99—124no—
410#95—21no—
411#95—21no—
412#95—62no—
413#95—62no—
414#95—61no—
415#95—61no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3C23×C411yescharacteristic
419C23×C3C22×D411yescharacteristic
420C23×C3C22×D411yescharacteristic
421C23×C3H(5,𝔽2)12yes—
422C23×C32−1+412yes—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—24no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—48no—
446C22×D3—48no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3C2×C22⋊C411yescharacteristic
450C22×D3C2×C22⋊C411yescharacteristic
451C22×D3C2×C22⋊C411yescharacteristic
452C22×D3C2×C22⋊C411yescharacteristic
453C3×Q8—42no—
454C3×Q8—42no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4C2×C22⋊C411yescharacteristic
472C2×C3×C4C2×C22⋊C411yescharacteristic
473C2×C3×C4C2×C22⋊C411yescharacteristic
474C2×C3×C4C2×C22⋊C411yescharacteristic
475#67—42no—
476#67—42no—
477#67—44no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—24no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—42no—
487C2×Dic3—42no—
488C2×Dic3—42no—
489C2×Dic3—42no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3C2×C22⋊C411yescharacteristic
493C2×Dic3C2×C22⋊C411yescharacteristic
494C2×Dic3C2×C22⋊C411yescharacteristic
495C2×Dic3C2×C22⋊C411yescharacteristic
496D12—42no—
497D12—44no—
498D12—44no—
499D12—44no—
500D12—44no—
501D12—42no—
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—44no—
518C4×D3—44no—
519C4×D3—88no—
520C4×D3#9914yescomplemented
521C24—31no—
522C24—31no—
523C24—31no—
524C24—31no—
525C24—31no—
526C24—31no—
527C24—32no—
528C24—62no—
529C24—62no—
530C24—122no—
531C24—122no—
532C24C23×D311yescharacteristic
533#41—124no—
534#41—124no—
535#41—124no—
536#41—124no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—42no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—64no—
547C2×D4—64no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—122no—
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—42no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—64no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—122no—
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—124no—
596C22×C4—124no—
597C22×C4—124no—
598C22×C4—124no—
599C22×C4—122no—
600C22×C4C2×C4×D311yescharacteristic
601C22×C4C2×C4×D312yes—
602C22×C4C2×C4×D312yes—
603C22×C4C2×C4×D311yescharacteristic
604C22×C4D3×D411yescharacteristic
605C22×C4D3×D411yescharacteristic
606C22×C4D3×D411yescharacteristic
607C22×C4D3×D411yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—42no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—122no—
618C4⋊C4—124no—
619C4⋊C4—124no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
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—62no—
635C22⋊C4—64no—
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×C3C22×C22⋊C411yescharacteristic
652C22×C3#52012yes—
653C22×C3#53511yescharacteristic
654C22×C3#53611yescharacteristic
655C22×C3#53712yes—
656C2×D3—24no—
657C2×D3—24no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—44no—
669C2×D3—44no—
670C2×D3—44no—
671C2×D3—44no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—84no—
678C2×D3C2×#9912yes—
679C2×D3#41012yes—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—82no—
686C3×C4—82no—
687C3×C4C2×#9912yes—
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—42no—
692Dic3—82no—
693Dic3—82no—
694Dic3C2×#9912yes—
695C23—31no—
696C23—31no—
697C23—31no—
698C23—31no—
699C23—41no—
700C23—41no—
701C23—62no—
702C23—62no—
703C23—62no—
704C23—62no—
705C23—62no—
706C23—62no—
707C23—61no—
708C23—61no—
709C23—61no—
710C23—61no—
711C23—62no—
712C23—62no—
713C23—62no—
714C23—62no—
715C23—62no—
716C23—64no—
717C23—121no—
718C23—121no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23—122no—
724C23—122no—
725C23—128no—
726C23—128no—
727C23C22×C4×D311yescharacteristic
728C23C2×D3×D411yescharacteristic
729C23C2×D3×D411yescharacteristic
730C23#100712yes—
731C23#100912yes—
732Q8—42no—
733Q8—42no—
734D4—122no—
735D4—124no—
736D4—124no—
737D4—124no—
738D4—124no—
739D4—122no—
740D4—122no—
741D4—124no—
742D4—122no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
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—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—64no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—124no—
785C2×C4—124no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
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#231111yescharacteristic
805C2×C3C22×#9911yescharacteristic
806C2×C3C2×#41011yescharacteristic
807D3—22no—
808D3—22no—
809D3—41no—
810D3—41no—
811D3—82no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—32no—
819C22—32no—
820C22—42no—
821C22—42no—
822C22—64no—
823C22—64no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—124no—
835C22—124no—
836C22—124no—
837C22—124no—
838C22—122no—
839C22—122no—
840C22—122no—
841C22—122no—
842C22—122no—
843C22—244no—
844C22C2×D3×C22⋊C411yescharacteristic
845C22#557412yes—
846C22#562912yes—
847C22#567411yescharacteristic
848C22#572411yescharacteristic
849C4—21no—
850C4—21no—
851C4—21no—
852C4—32no—
853C4—42no—
854C4—42no—
855C4—61no—
856C4—61no—
857C4—61no—
858C4—82no—
859C4—82no—
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—121no—
872C2—121no—
873C2—242no—
874C2#7648211yescharacteristic
875C2C2×D3×#9911yescharacteristic
876C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1996C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5627C2
cosocleC24×C3C24
hypercenter#1996D3
hypocenterC3#21874
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. D3×#380C2semidirect
3. #73561C2semidirect
4. C3×#1996C2semidirect
5. #71701C2semidirect
6. #69528C2semidirect
7. #69456C2semidirect
8. #68970C2semidirect
9. #68959C2semidirect
11. C22×#239C4semidirect
14. C2×#946C4semidirect
24. C2×#895C4semidirect
25. C2×#894C4semidirect
26. C2×#893C4semidirect
27. C2×#892C4semidirect
54. #1996D3semidirect
60. C22×C3×Q8C2×C4semidirect
71. C22×D12C2×C4semidirect
78. C22×C4×D3C2×C4semidirect
92. C2×C3×C4⋊C4C2×C4semidirect
93. C2×C3×C4⋊C4C2×C4semidirect
113. C2×(C2×D3)⋊C4C2×C4semidirect
114. C2×(C2×D3)⋊C4C2×C4semidirect
116. C2×C4⋊Dic3C2×C4semidirect
119. C2×Dic3⋊C4C2×C4semidirect
121. C2×C4×Dic3C2×C4semidirect
324. C22×Q8C4×D3semidirect
390. C2×C4⋊C4C4×D3semidirect
391. C2×C4⋊C4C4×D3semidirect
520. 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×#56272
D3×#3802
#735612
C3×#19962
#717012
#695282
#694562
#689702
#689592
#218743