Finite Group Databasebeta

← #11857550

Subgroups — #11857550

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic
2C3×#5486C211yesmaximal, characteristic, complemented
3#10595506C211yesmaximal, characteristic, complemented
4C2×#63633C211yesmaximal, characteristic, complemented
5C2×C3×#806C211yesmaximal, characteristic, complemented
6C2×#63581C211yesmaximal, characteristic, complemented
7C2×#63580C211yesmaximal, characteristic, complemented
8#10590405C214yesmaximal, complemented
9D3×#806C214yesmaximal, complemented
10#82546—31nomaximal
11#78688—31nomaximal
12C22×#638C2211yescharacteristic
13C22×C3×#67C2211yescharacteristic
14C22×C3×#67C2211yescharacteristic
15#64330—22no—
16#64330—22no—
17#64330—22no—
18#64330—22no—
19C2×#3811C412yescomplemented
20C2×D3×#67C412yescomplemented
21C2×D3×#67C2212yes—
22C2×#3805C412yescomplemented
23C2×#3804C412yescomplemented
24C2×#3804C2212yes—
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×#3757C2211yescharacteristic, complemented
27C2×C3×#217C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic, complemented
29C3×C4×#67—22no—
30C3×#67⋊C4—22no—
31C3×D3×C22⋊C4C2212yescomplemented
32C3×#877C2212yescomplemented
33#67⋊Dic3—22no—
34Dic3×#67—22no—
35D3×#217C2212yescomplemented
36#63955C2212yescomplemented
37#63633C2214yescomplemented
38C3×#806C2214yescomplemented
39#63581C2214yescomplemented
40#63580C2214yescomplemented
41C2×#1004—31no—
42C2×#1004—31no—
43C3×#518—31no—
44#5798—31no—
45#5486—31no—
46#5486D311yescharacteristic, complemented
47C2×C3×#99—31no—
48C2×#834—31no—
49#5006—34no—
50C2×#806—31no—
51C2×#806—31no—
52C2×#806—31no—
53C2×#806—31no—
54C2×#806—31no—
55C2×#806—34no—
56C2×#806—61no—
57C2×#806D311yescharacteristic, complemented
58D3×#99—34no—
59#4740—34no—
60C24×C32C2311yescharacteristic
61C23×C3⋊D3C2×C411yescharacteristic, complemented
62C23×C3×D3C2×C411yescharacteristic, complemented
63C23×C3×D3C2311yescharacteristic
64C22×D32C2×C412yescomplemented
65C22×C32×C4—21no—
66C2×#638—21no—
67C2×#638—21no—
68C2×#638—21no—
69C2×#638—21no—
70C2×#638C2×C412yescomplemented
71C2×#638C2312yes—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3C2×C411yescharacteristic, complemented
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C2×C3×#67C2×C412yes—
79C2×C3×#67C2×C412yes—
80C2×C3×#67C2×C412yescomplemented
81C2×C3×#67D412yes—
82C2×C3×#67D412yes—
83C2×C3×#67D412yes—
84C2×C3×#67D412yes—
85C2×C3×#67C2312yes—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3C2×C411yescharacteristic, complemented
89C22×C3×Dic3C2311yescharacteristic
90C2×C3×C4×D3—22no—
91#3811—24no—
92#3811—24no—
93D3×#67—24no—
94D3×#67—24no—
95D3×#67—24no—
96D3×#67—24no—
97C2×#627C2×C412yescomplemented
98C2×#626C2×C412yescomplemented
99C2×#626C2×C412yescomplemented
100C2×#625C2×C412yescomplemented
101C2×#624C2×C412yescomplemented
102#3805—24no—
103#3805—24no—
104#3804—24no—
105#3804—24no—
106#3804—24no—
107#3804—24no—
108C2×D3×Dic3—22no—
109C2×D3×Dic3C2×C412yescomplemented
110C2×D3×Dic3C2×C412yescomplemented
111C32×C22⋊C4—21no—
112C32×C22⋊C4C2312yes—
113#3757—21no—
114#3757C2312yes—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217C2312yes—
118C3×#217C2312yes—
119C3×(C2×D3)⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×C4×Dic3—22no—
122Dic3⋊Dic3—22no—
123(C2×D3)⋊Dic3—22no—
124Dic32—22no—
125#2883—91noSylow
126C22×C3×D4—31no—
127C22×C3×D4—31no—
128C22×#67—31no—
129C22×#67—31no—
130C22×#67—32no—
131C22×#67—32no—
132C22×#67—61no—
133C22×#67C2×D311yescharacteristic
134C22×#67C2×D311yescharacteristic
135#1004—62no—
136#1004—62no—
137#1004—62no—
138#1004—62no—
139#1004—62no—
140#1004—62no—
141#1004—62no—
142#1004—62no—
143C2×#237—32no—
144C2×#237—32no—
145C2×#237—32no—
146C2×#237—32no—
147C2×D3×D4—32no—
148C2×D3×D4—32no—
149C2×D3×D4—32no—
150C2×D3×D4—32no—
151C2×#235—32no—
152C2×#235—32no—
153C3×C4×D4—62no—
154C3×C4×D4—62no—
155C3×#117—32no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
161C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—32no—
165C2×#217—61no—
166C2×#217C2×D311yescharacteristic, complemented
167C2×#217C2×D311yescharacteristic, complemented
168D4×Dic3—62no—
169D4×Dic3—62no—
170C4×#67—22no—
171C4×#67—62no—
172#926—32no—
173#67⋊C4—22no—
174#67⋊C4—62no—
175D3×C22⋊C4—32no—
176D3×C22⋊C4C2×D312yescomplemented
177#877—32no—
178#877C2×D312yescomplemented
179C3×#99—34no—
180#834—34no—
181#806—34no—
182#806—34no—
183#806—34no—
184#806—34no—
185#806—34no—
186#806—64no—
187#806C2×D314yescomplemented
188C23×C32—81no—
189C23×C32C22×C411yescharacteristic
190C23×C32C22×C411yescharacteristic
191C23×C32C2×D411yescharacteristic
192C23×C32C2×D411yescharacteristic
193C23×C32C2×D411yescharacteristic
194C23×C32C2×D411yescharacteristic
195C23×C32C2411yescharacteristic
196C22×C3⋊D3—21no—
197C22×C3⋊D3—21no—
198C22×C3⋊D3—81no—
199C22×C3⋊D3C22×C412yes—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—81no—
203C22×C3×D3—81no—
204C22×C3×D3C22×C412yes—
205C22×C3×D3C22×C412yes—
206C22×C3×D3C2×D412yes—
207C22×C3×D3C2×D412yes—
208C2×D32—24no—
209C2×D32—82no—
210C2×C32×C4—22no—
211C2×C32×C4—81no—
212#638—22no—
213#638—22no—
214#638—22no—
215#638—22no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—81no—
220C2×C3⋊Dic3C22×C412yes—
221C3×#67—22no—
222C3×#67—22no—
223C3×#67—22no—
224C3×#67—22no—
225C3×#67C22⋊C414yes—
226C3×#67C22⋊C414yes—
227C3×#67C22⋊C414yes—
228C3×#67C22⋊C414yes—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—81no—
234C2×C3×Dic3—81no—
235C2×C3×Dic3C22×C412yes—
236C2×C3×Dic3C22×C412yes—
237C2×C3×Dic3C2×D412yes—
238C2×C3×Dic3C2×D412yes—
239C3×C4×D3—82no—
240#627—24no—
241#626—24no—
242#626—24no—
243#625—24no—
244#624—24no—
245D3×Dic3—24no—
246D3×Dic3—24no—
247D3×Dic3—82no—
248C2×H(5,𝔽2)—91no—
249#518—31no—
250#518—91no—
251#410—94no—
252C2×#99—31no—
253C2×#99—94no—
254C2×#99—91no—
255C2×#99—91no—
256C2×#99—91no—
257C24×C3—21no—
258C24×C3—31no—
259C24×C3—31no—
260C24×C3C22×D311yescharacteristic
261C24×C3C22×D311yescharacteristic
262C23×D3—31no—
263C23×D3—31no—
264C23×D3—32no—
265C23×D3—32no—
266C23×D3—61no—
267C23×D3C4×D311yescharacteristic, complemented
268C23×D3C22×D311yescharacteristic
269C2×C3×D4—32no—
270C2×C3×D4—32no—
271C2×C3×D4—32no—
272C2×C3×D4—32no—
273C2×C3×D4—32no—
274C2×C3×D4—32no—
275C2×C3×D4—32no—
276C2×C3×D4—32no—
277C2×C3×D4—61no—
278C2×C3×D4—61no—
279C2×C3×D4—61no—
280C2×C3×D4—61no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—41no—
286C22×C3×C4—62no—
287C22×C3×C4—61no—
288C22×C3×C4—61no—
289C2×#67—21no—
290C2×#67—21no—
291C2×#67—21no—
292C2×#67—21no—
293C2×#67—32no—
294C2×#67—32no—
295C2×#67—32no—
296C2×#67—32no—
297C2×#67—32no—
298C2×#67—32no—
299C2×#67—32no—
300C2×#67—32no—
301C2×#67—62no—
302C2×#67—62no—
303C2×#67—64no—
304C2×#67—64no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—64no—
314C2×#67—64no—
315C2×#67—121no—
316C2×#67—121no—
317C2×#67—121no—
318C2×#67—121no—
319C2×#67C4×D312yes—
320C2×#67C4×D312yes—
321C2×#67C4×D312yescomplemented
322C2×#67D1212yes—
323C2×#67D1212yes—
324C2×#67#6712yes—
325C2×#67#6712yes—
326C2×#67C22×D312yes—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—32no—
332C22×Dic3—32no—
333C22×Dic3—61no—
334C22×Dic3—62no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—121no—
338C22×Dic3C4×D311yescharacteristic, complemented
339C22×Dic3C22×D311yescharacteristic
340#237—64no—
341#237—64no—
342#237—64no—
343#237—64no—
344#237—64no—
345#237—64no—
346#237—64no—
347#237—64no—
348D3×D4—64no—
349D3×D4—64no—
350D3×D4—64no—
351D3×D4—64no—
352D3×D4—64no—
353D3×D4—64no—
354D3×D4—64no—
355D3×D4—64no—
356#235—64no—
357#235—64no—
358#235—64no—
359#235—64no—
360C2×D12—32no—
361C2×D12—32no—
362C2×C4×D3—22no—
363C2×C4×D3—32no—
364C2×C4×D3—32no—
365C2×C4×D3—32no—
366C2×C4×D3—32no—
367C2×C4×D3—62no—
368C2×Dic6—32no—
369C2×Dic6—32no—
370C3×C4⋊C4—62no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—22no—
374C3×C22⋊C4—32no—
375C3×C22⋊C4—32no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—62no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4C22×D312yes—
381C3×C22⋊C4C22×D312yes—
382C3×C42—62no—
383#217—21no—
384#217—21no—
385#217—32no—
386#217—32no—
387#217—62no—
388#217—62no—
389#217—61no—
390#217—61no—
391#217—121no—
392#217C22×D312yes—
393#217C22×D312yes—
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—62no—
396C4⋊Dic3—62no—
397Dic3⋊C4—22no—
398Dic3⋊C4—62no—
399C4×Dic3—22no—
400C4×Dic3—62no—
401C4×Dic3—62no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C2×C22⋊C411yescharacteristic
410C22×C32C2×C22⋊C411yescharacteristic
411C22×C32C2×C22⋊C411yescharacteristic
412C22×C32C2×C22⋊C411yescharacteristic
413C22×C32C23×C411yescharacteristic
414C22×C32C22×D411yescharacteristic
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—42no—
418C2×C3⋊D3—81no—
419C2×C3⋊D3—81no—
420C2×C3×D3—22no—
421C2×C3×D3—42no—
422C2×C3×D3—42no—
423C2×C3×D3—42no—
424C2×C3×D3—42no—
425C2×C3×D3—81no—
426C2×C3×D3—81no—
427C2×C3×D3C2×C22⋊C414yes—
428D32—84no—
429C32×C4—42no—
430C3⋊Dic3—22no—
431C3⋊Dic3—42no—
432C3×Dic3—22no—
433C3×Dic3—42no—
434C3×Dic3—42no—
435C3×Dic3C2×C22⋊C414yes—
436H(5,𝔽2)—182no—
437H(5,𝔽2)—182no—
438H(5,𝔽2)—182no—
439H(5,𝔽2)—182no—
440C2×#41—92no—
441C2×#41—92no—
442C2×#41—92no—
443C22×D4—31no—
444C22×D4—31no—
445C22×D4—92no—
446C22×D4—92no—
447C22×D4—92no—
448C22×D4—91no—
449C4×D4—62no—
450C4×D4—62no—
451C4×D4—182no—
452C4×D4—182no—
453#117—32no—
454#117—92no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—32no—
458C2×C22⋊C4—92no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4D3211yescharacteristic, complemented
461#99—34no—
462#99—94no—
463#99—94no—
464#99—94no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—32no—
473C23×C3—32no—
474C23×C3—32no—
475C23×C3—32no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—81no—
479C23×C3—81no—
480C23×C3—82no—
481C23×C3—241no—
482C23×C3—241no—
483C23×C3C2×C4×D311yescharacteristic
484C23×C3C2×C4×D311yescharacteristic
485C23×C3C2×C4×D311yescharacteristic
486C23×C3C2×C4×D311yescharacteristic
487C23×C3C2×D1211yescharacteristic
488C23×C3C2×D1211yescharacteristic
489C23×C3D3×D411yescharacteristic
490C23×C3D3×D411yescharacteristic
491C23×C3D3×D411yescharacteristic
492C23×C3D3×D411yescharacteristic
493C23×C3C2×#6711yescharacteristic
494C23×C3C2×#6711yescharacteristic
495C23×C3C23×D311yescharacteristic
496C23×C3C23×D311yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—62no—
502C22×D3—64no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—64no—
508C22×D3—81no—
509C22×D3—81no—
510C22×D3—121no—
511C22×D3—121no—
512C22×D3—242no—
513C22×D3—242no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3—242no—
517C22×D3C2×C4×D312yes—
518C22×D3C2×C4×D312yes—
519C22×D3C2×D1212yes—
520C22×D3C2×#6712yes—
521C3×D4—34no—
522C3×D4—34no—
523C3×D4—34no—
524C3×D4—34no—
525C3×D4—62no—
526C3×D4—62no—
527C3×D4—62no—
528C3×D4—62no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—42no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—81no—
541C2×C3×C4—81no—
542C2×C3×C4—82no—
543C2×C3×C4—242no—
544C2×C3×C4—241no—
545C2×C3×C4—241no—
546#67—22no—
547#67—22no—
548#67—22no—
549#67—22no—
550#67—64no—
551#67—64no—
552#67—62no—
553#67—62no—
554#67—62no—
555#67—62no—
556#67—62no—
557#67—62no—
558#67—62no—
559#67—62no—
560#67—64no—
561#67—64no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67(C2×D3)⋊C414yes—
567#67(C2×D3)⋊C414yes—
568#67(C2×D3)⋊C414yes—
569#67(C2×D3)⋊C414yes—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—62no—
577C2×Dic3—64no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—64no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—81no—
586C2×Dic3—81no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—122no—
590C2×Dic3—242no—
591C2×Dic3—241no—
592C2×Dic3—241no—
593C2×Dic3—242no—
594C2×Dic3C2×C4×D312yes—
595C2×Dic3C2×C4×D312yes—
596C2×Dic3C2×D1212yes—
597C2×Dic3C2×#6712yes—
598D12—64no—
599D12—64no—
600C4×D3—64no—
601C4×D3—64no—
602C4×D3—64no—
603C4×D3—64no—
604C4×D3—82no—
605C4×D3—242no—
606Dic6—64no—
607Dic6—64no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32C22×C22⋊C411yescharacteristic
616C3⋊D3—42no—
617C3×D3—24no—
618C3×D3—42no—
619C24—31no—
620C24—31no—
621C24—92no—
622C24—91no—
623C24C2×D3211yescharacteristic
624#41—184no—
625#41—184no—
626#41—184no—
627#41—184no—
628#41—184no—
629#41—184no—
630C2×Q8—92no—
631C2×D4—32no—
632C2×D4—32no—
633C2×D4—32no—
634C2×D4—32no—
635C2×D4—32no—
636C2×D4—32no—
637C2×D4—32no—
638C2×D4—32no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—92no—
644C2×D4—92no—
645C2×D4—92no—
646C2×D4—92no—
647C2×D4—92no—
648C2×D4—184no—
649C2×D4—184no—
650C2×D4—184no—
651C2×D4—184no—
652C2×D4—184no—
653C2×D4—184no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4—181no—
657C2×D4—181no—
658C22×C4—21no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—62no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—92no—
665C22×C4—92no—
666C22×C4—92no—
667C22×C4—91no—
668C22×C4—182no—
669C22×C4—181no—
670C4⋊C4—62no—
671C4⋊C4—182no—
672C22⋊C4—21no—
673C22⋊C4—32no—
674C22⋊C4—32no—
675C22⋊C4—62no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—92no—
679C22⋊C4—182no—
680C22⋊C4—181no—
681C22⋊C4C2×D3212yes—
682C42—62no—
683C42—182no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—34no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—62no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—122no—
715C22×C3—122no—
716C22×C3—122no—
717C22×C3—122no—
718C22×C3—241no—
719C22×C3—241no—
720C22×C3D3×C22⋊C411yescharacteristic
721C22×C3D3×C22⋊C411yescharacteristic
722C22×C3D3×C22⋊C411yescharacteristic
723C22×C3D3×C22⋊C411yescharacteristic
724C22×C3C2×(C2×D3)⋊C411yescharacteristic
725C22×C3C2×(C2×D3)⋊C411yescharacteristic
726C22×C3C2×(C2×D3)⋊C411yescharacteristic
727C22×C3C2×(C2×D3)⋊C411yescharacteristic
728C22×C3C22×C4×D311yescharacteristic
729C22×C3C22×C4×D311yescharacteristic
730C22×C3C22×D1211yescharacteristic
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C22×C3C22×#6711yescharacteristic
734C2×D3—22no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—122no—
744C2×D3—122no—
745C2×D3—122no—
746C2×D3—242no—
747C2×D3—244no—
748C2×D3—244no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—242no—
754C2×D3—242no—
755C2×D3C2×(C2×D3)⋊C414yes—
756C3×C4—34no—
757C3×C4—42no—
758C3×C4—42no—
759C3×C4—62no—
760C3×C4—82no—
761C3×C4—122no—
762C3×C4—122no—
763Dic3—22no—
764Dic3—42no—
765Dic3—42no—
766Dic3—62no—
767Dic3—62no—
768Dic3—122no—
769Dic3—122no—
770Dic3—122no—
771Dic3—242no—
772Dic3C2×(C2×D3)⋊C414yes—
773C32#288311yescharacteristic, complemented, Sylow
774C23—32no—
775C23—32no—
776C23—32no—
777C23—32no—
778C23—61no—
779C23—61no—
780C23—81no—
781C23—92no—
782C23—184no—
783C23—181no—
784C23—181no—
785C23—241no—
786C23—241no—
787C23—721no—
788C23—722no—
789C23C4×D3211yescharacteristic
790C23C4×D3211yescharacteristic
791C23D3×D1211yescharacteristic
792C23D3×D1211yescharacteristic
793C23D3×#6711yescharacteristic
794C23D3×#6711yescharacteristic
795C23C22×D3211yescharacteristic
796Q8—184no—
797D4—34no—
798D4—34no—
799D4—34no—
800D4—34no—
801D4—62no—
802D4—62no—
803D4—62no—
804D4—62no—
805D4—184no—
806D4—184no—
807D4—184no—
808D4—182no—
809D4—182no—
810D4—182no—
811D4—182no—
812C2×C4—22no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—81no—
822C2×C4—92no—
823C2×C4—184no—
824C2×C4—184no—
825C2×C4—184no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—182no—
829C2×C4—242no—
830C2×C4—241no—
831C2×C4—241no—
832C2×C4—722no—
833C2×C4—721no—
834C2×C3—22no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—41no—
851C2×C3—41no—
852C2×C3—41no—
853C2×C3—41no—
854C2×C3—41no—
855C2×C3—41no—
856C2×C3—64no—
857C2×C3—122no—
858C2×C3C2×D3×C22⋊C411yescharacteristic
859C2×C3C22×(C2×D3)⋊C411yescharacteristic
860D3—24no—
861D3—42no—
862D3—122no—
863D3—122no—
864D3—242no—
865C22—34no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—62no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—182no—
879C22—241no—
880C22—241no—
881C22—362no—
882C22—721no—
883C22—721no—
884C22—724no—
885C22D3×(C2×D3)⋊C411yescharacteristic
886C22D3×(C2×D3)⋊C411yescharacteristic
887C22D3×(C2×D3)⋊C411yescharacteristic
888C22D3×(C2×D3)⋊C411yescharacteristic
889C22C2×C4×D3211yescharacteristic
890C22C2×D3×D1211yescharacteristic
891C22C2×D3×#6711yescharacteristic
892C4—34no—
893C4—42no—
894C4—62no—
895C4—122no—
896C4—122no—
897C4—182no—
898C4—362no—
899C3—21no—
900C3#7868811yescharacteristic, complemented
901C3#8254611yescharacteristic, complemented
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—64no—
910C2—122no—
911C2—362no—
912C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2C2×D3×(C2×D3)⋊C4
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#64330C2
cosocleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32#2883
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#5486C2semidirect
3. #10595506C2semidirect
4. C2×#63633C2semidirect
5. C2×C3×#806C2semidirect
6. C2×#63581C2semidirect
7. C2×#63580C2semidirect
8. #10590405C2semidirect
9. D3×#806C2semidirect
19. C2×#3811C4semidirect
20. C2×D3×#67C4semidirect
22. C2×#3805C4semidirect
23. C2×#3804C4semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×#3757C22semidirect
27. C2×C3×#217C22semidirect
28. C2×C3×#217C22semidirect
31. C3×D3×C22⋊C4C22semidirect
32. C3×#877C22semidirect
35. D3×#217C22semidirect
36. #63955C22semidirect
37. #63633C22semidirect
38. C3×#806C22semidirect
39. #63581C22semidirect
40. #63580C22semidirect
46. #5486D3semidirect
57. C2×#806D3semidirect
61. C23×C3⋊D3C2×C4semidirect
62. C23×C3×D3C2×C4semidirect
64. C22×D32C2×C4semidirect
70. C2×#638C2×C4semidirect
73. C22×C3⋊Dic3C2×C4semidirect
80. C2×C3×#67C2×C4semidirect
88. C22×C3×Dic3C2×C4semidirect
97. C2×#627C2×C4semidirect
98. C2×#626C2×C4semidirect
99. C2×#626C2×C4semidirect
100. C2×#625C2×C4semidirect
101. C2×#624C2×C4semidirect
109. C2×D3×Dic3C2×C4semidirect
110. C2×D3×Dic3C2×C4semidirect
160. C2×C3×C22⋊C4C2×D3semidirect
161. C2×C3×C22⋊C4C2×D3semidirect
166. C2×#217C2×D3semidirect
167. C2×#217C2×D3semidirect
176. D3×C22⋊C4C2×D3semidirect
178. #877C2×D3semidirect
187. #806C2×D3semidirect
267. C23×D3C4×D3semidirect
321. C2×#67C4×D3semidirect
338. C22×Dic3C4×D3semidirect
460. C2×C22⋊C4D32semidirect
773. C32#2883semidirect
900. C3#78688semidirect
901. C3#82546semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C3×#54862
#105955062
C2×#636332
C2×C3×#8062
C2×#635812
C2×#635802
#105904052
D3×#8062
#825463
#786883