Finite Group Databasebeta

← C2×#10590407 #11865264

Subgroups — C2×#10590407 #11865264

Order 1152.

2141 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic, complemented
3C2×#63977C211yesmaximal, characteristic, complemented
4C2×#63976C211yesmaximal, characteristic, complemented
5C2×#63633C211yesmaximal, characteristic, complemented
6C2×C3×#806C211yesmaximal, characteristic, complemented
7C2×#63580C211yesmaximal, characteristic, complemented
8#10590407C218yesmaximal, direct product factor
9C2×#5032—31nomaximal
10C2×#4741—31nomaximal
11C24×C3×D3C2211yescharacteristic, complemented
12C22×#638C2211yescharacteristic
13C22×C3×#67C2211yescharacteristic
14C22×C3×#67C2211yescharacteristic
15C22×C3×D12—21no—
16#64330—22no—
17#64330—22no—
18#64330—22no—
19#64330C2214yescomplemented
20C2×#3811—21no—
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23C22×#626—21no—
24C22×#625—21no—
25C2×#3805—21no—
26C2×#3804—21no—
27C2×#3804—21no—
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×#3757C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic, complemented
31C2×C3×(C2×D3)⋊C4—21no—
32C3×#882—22no—
33C3×#882C2214yescomplemented
34#63977—22no—
35#63977C2214yescomplemented
36#63976—22no—
37#63976C2214yescomplemented
38C2×(C2×D3)⋊Dic3—21no—
39C2×(C2×D3)⋊Dic3—21no—
40#63633C2214yescomplemented
41C3×#806C2214yescomplemented
42#63580C2214yescomplemented
43C2×#1004—31no—
44C2×#1004—31no—
45C2×C3×#120—31no—
46C2×#953—31no—
47C2×#953—31no—
48C2×#937—31no—
49C2×#882—31no—
50C2×#882D311yescharacteristic, complemented
51C2×C3×#99—31no—
52C2×#834—31no—
53#5032—38no—
54C2×#806—31no—
55C2×#806—31no—
56C2×#806—31no—
57C2×#806—61no—
58C2×#806D311yescharacteristic, complemented
59#4741—38no—
60C24×C32C2311yescharacteristic
61C23×C3⋊D3D411yescharacteristic, complemented
62C23×C3×D3—21no—
63C23×C3×D3—21no—
64C23×C3×D3—21no—
65C23×C3×D3—21no—
66C23×C3×D3—21no—
67C23×C3×D3—21no—
68C23×C3×D3—44no—
69C23×C3×D3D411yescharacteristic, complemented
70C23×C3×D3D411yescharacteristic, complemented
71C23×C3×D3C2312yescomplemented
72C22×D32—21no—
73C22×C32×C4—21no—
74C2×#638—21no—
75C2×#638—21no—
76C2×#638—21no—
77C2×#638—21no—
78C2×#638D412yescomplemented
79C2×#638C2312yes—
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3D411yescharacteristic, complemented
82C2×C3×#67—21no—
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C2×C3×#67—21no—
86C2×C3×#67—21no—
87C2×C3×#67—21no—
88C2×C3×#67—21no—
89C2×C3×#67—21no—
90C2×C3×#67D412yescomplemented
91C2×C3×#67D412yescomplemented
92C2×C3×#67C2312yes—
93C2×C3×#67C2312yes—
94C22×C3×Dic3—21no—
95C22×C3×Dic3D411yescharacteristic, complemented
96C22×C3×Dic3D411yescharacteristic, complemented
97C2×C3×D12—24no—
98C2×C3×D12—44no—
99#3811—24no—
100#3811—24no—
101D3×#67—24no—
102D3×#67—24no—
103D3×#67—24no—
104D3×#67—24no—
105C2×#627—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—24no—
109C2×#626—44no—
110C2×#625—21no—
111C2×#625—24no—
112C2×#625—44no—
113C2×#624—21no—
114#3805—24no—
115#3805—24no—
116#3804—24no—
117#3804—24no—
118#3804—24no—
119#3804—24no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122C32×C22⋊C4—21no—
123C32×C22⋊C4C2312yescomplemented
124#3757—21no—
125#3757C2312yescomplemented
126C3×#217—21no—
127C3×#217C2312yescomplemented
128C3×(C2×D3)⋊C4—24no—
129(C2×D3)⋊Dic3—24no—
130(C2×D3)⋊Dic3—24no—
131C2×B(4,𝔽2)—91noSylow
132C25×C3—31no—
133C24×D3C2×D311yescharacteristic, complemented
134C22×C3×D4—31no—
135C22×C3×D4—31no—
136C22×C3×D4—61no—
137C22×#67—31no—
138C22×#67—31no—
139C22×#67—61no—
140C22×#67—61no—
141C22×#67—61no—
142C22×#67—61no—
143C22×#67—61no—
144C22×#67—61no—
145C22×#67C2×D311yescharacteristic
146C22×#67C2×D311yescharacteristic
147#1004—34no—
148#1004—34no—
149#1004—62no—
150#1004—62no—
151#1004—62no—
152#1004—62no—
153#1004—62no—
154#1004—62no—
155C2×#237—61no—
156C2×#237—61no—
157C2×#237—61no—
158C2×#237—61no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C2×D3×D4—61no—
163C2×#235—61no—
164C2×#235—61no—
165C22×D12—21no—
166C22×D12—61no—
167C3×#120—34no—
168C3×#120—62no—
169C2×C3×C22⋊C4—21no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—61no—
172C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
173C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
174#953—34no—
175#953—34no—
176#953—62no—
177#953—62no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—61no—
181C2×#217—61no—
182C2×#217—61no—
183C2×#217C2×D311yescharacteristic, complemented
184#937—34no—
185#937—62no—
186C2×(C2×D3)⋊C4—21no—
187C2×(C2×D3)⋊C4—61no—
188C2×(C2×D3)⋊C4—61no—
189#882—22no—
190#882—34no—
191#882—62no—
192#882C2×D314yescomplemented
193C3×#99—34no—
194#834—34no—
195#806—34no—
196#806—34no—
197#806—34no—
198#806—64no—
199#806C2×D314yescomplemented
200C23×C32—42no—
201C23×C32C2×D411yescharacteristic
202C23×C32C2×D411yescharacteristic
203C23×C32C2×D411yescharacteristic
204C23×C32C2×D411yescharacteristic
205C23×C32C2×D411yescharacteristic
206C23×C32C2×D411yescharacteristic
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—42no—
211C22×C3⋊D3C2×D412yescomplemented
212C22×C3×D3—24no—
213C22×C3×D3—24no—
214C22×C3×D3—24no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3—22no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—44no—
223C22×C3×D3—44no—
224C22×C3×D3—44no—
225C22×C3×D3—44no—
226C22×C3×D3—42no—
227C22×C3×D3—42no—
228C22×C3×D3—42no—
229C22×C3×D3—41no—
230C22×C3×D3—41no—
231C22×C3×D3—41no—
232C22×C3×D3—41no—
233C22×C3×D3—42no—
234C22×C3×D3—42no—
235C22×C3×D3C2×D412yescomplemented
236C22×C3×D3C2×D412yescomplemented
237C2×D32—24no—
238C2×D32—82no—
239C2×C32×C4—22no—
240C2×C32×C4—42no—
241#638—22no—
242#638—22no—
243#638—22no—
244#638—22no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—22no—
248C2×C3⋊Dic3—42no—
249C2×C3⋊Dic3C2×D412yescomplemented
250C3×#67—22no—
251C3×#67—22no—
252C3×#67—22no—
253C3×#67—22no—
254C3×#67—22no—
255C3×#67—22no—
256C3×#67—22no—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D412yescomplemented
265C2×C3×Dic3C2×D412yescomplemented
266C3×D12—48no—
267#627—24no—
268#626—24no—
269#626—24no—
270#626—48no—
271#625—24no—
272#625—48no—
273#624—24no—
274D3×Dic3—24no—
275D3×Dic3—24no—
276C2×H(5,𝔽2)—91no—
277C2×#120—31no—
278C2×#120—91no—
279C2×#120—91no—
280B(4,𝔽2)—98no—
281C2×#99—31no—
282C2×#99—91no—
283C2×#99—91no—
284C24×C3—21no—
285C24×C3—31no—
286C24×C3—31no—
287C24×C3—32no—
288C24×C3—61no—
289C24×C3—61no—
290C24×C3—61no—
291C24×C3—61no—
292C24×C3—61no—
293C24×C3—61no—
294C24×C3—124no—
295C24×C3C22×D311yescharacteristic
296C24×C3C22×D311yescharacteristic
297C23×D3—21no—
298C23×D3—21no—
299C23×D3—21no—
300C23×D3—21no—
301C23×D3—21no—
302C23×D3—21no—
303C23×D3—31no—
304C23×D3—31no—
305C23×D3—44no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3D1211yescharacteristic, complemented
310C23×D3#6711yescharacteristic, complemented
311C23×D3C22×D312yescomplemented
312C2×C3×D4—32no—
313C2×C3×D4—32no—
314C2×C3×D4—32no—
315C2×C3×D4—32no—
316C2×C3×D4—64no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—124no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—41no—
331C22×C3×C4—61no—
332C2×#67—21no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—32no—
341C2×#67—32no—
342C2×#67—32no—
343C2×#67—32no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—64no—
349C2×#67—64no—
350C2×#67—64no—
351C2×#67—64no—
352C2×#67—64no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—64no—
364C2×#67—64no—
365C2×#67—121no—
366C2×#67—121no—
367C2×#67—121no—
368C2×#67—121no—
369C2×#67—124no—
370C2×#67—124no—
371C2×#67—124no—
372C2×#67D1212yescomplemented
373C2×#67#6712yescomplemented
374C2×#67C22×D312yes—
375C2×#67C22×D312yes—
376C22×Dic3—21no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—121no—
385C22×Dic3D1211yescharacteristic, complemented
386C22×Dic3#6711yescharacteristic, complemented
387#237—64no—
388#237—64no—
389#237—64no—
390#237—64no—
391#237—64no—
392#237—64no—
393#237—64no—
394#237—64no—
395D3×D4—64no—
396D3×D4—64no—
397D3×D4—64no—
398D3×D4—64no—
399D3×D4—64no—
400D3×D4—64no—
401D3×D4—64no—
402D3×D4—64no—
403#235—64no—
404#235—64no—
405#235—64no—
406#235—64no—
407C2×D12—24no—
408C2×D12—44no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12—64no—
412C2×D12—124no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3—61no—
416C2×C4×D3—61no—
417C2×Dic6—61no—
418C2×Dic6—61no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—21no—
421C3×C22⋊C4—22no—
422C3×C22⋊C4—32no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—64no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4C22×D312yescomplemented
427C3×C22⋊C4C22×D312yescomplemented
428#217—21no—
429#217—32no—
430#217—32no—
431#217—62no—
432#217—64no—
433#217—61no—
434#217—61no—
435#217—64no—
436#217—121no—
437#217C22×D312yescomplemented
438(C2×D3)⋊C4—24no—
439(C2×D3)⋊C4—64no—
440(C2×D3)⋊C4—64no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32#12011yescharacteristic
449C22×C32#12011yescharacteristic
450C22×C32#12011yescharacteristic
451C22×C32#12011yescharacteristic
452C22×C32C22×D411yescharacteristic
453C22×C32C22×D411yescharacteristic
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—22no—
456C2×C3⋊D3—42no—
457C2×C3⋊D3—42no—
458C2×C3⋊D3—81no—
459C2×C3×D3—24no—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—42no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3—44no—
468C2×C3×D3—44no—
469C2×C3×D3—44no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3—42no—
473C2×C3×D3—44no—
474C2×C3×D3—42no—
475C2×C3×D3—42no—
476C2×C3×D3—81no—
477C2×C3×D3—81no—
478D32—84no—
479C32×C4—42no—
480C3⋊Dic3—22no—
481C3⋊Dic3—42no—
482C3×Dic3—22no—
483C3×Dic3—22no—
484C3×Dic3—42no—
485C25—31no—
486H(5,𝔽2)—94no—
487H(5,𝔽2)—182no—
488H(5,𝔽2)—182no—
489H(5,𝔽2)—182no—
490C2×#41—181no—
491C2×#41—181no—
492C2×#41—181no—
493C22×D4—31no—
494C22×D4—31no—
495C22×D4—61no—
496C22×D4—91no—
497C22×D4—181no—
498C22×D4—181no—
499C22×D4—181no—
500C22×D4—181no—
501C22×D4—181no—
502#120—34no—
503#120—62no—
504#120—94no—
505#120—94no—
506#120—182no—
507#120—182no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—181no—
512C2×C22⋊C4—181no—
513C2×C22⋊C4D3211yescharacteristic, complemented
514#99—34no—
515#99—94no—
516#99—94no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—32no—
525C23×C3—32no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—64no—
529C23×C3—64no—
530C23×C3—64no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—62no—
534C23×C3—62no—
535C23×C3—62no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—82no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—122no—
544C23×C3—124no—
545C23×C3—124no—
546C23×C3—124no—
547C23×C3—124no—
548C23×C3—121no—
549C23×C3—121no—
550C23×C3—121no—
551C23×C3—121no—
552C23×C3C2×D1211yescharacteristic
553C23×C3C2×D1211yescharacteristic
554C23×C3D3×D411yescharacteristic
555C23×C3D3×D411yescharacteristic
556C23×C3D3×D411yescharacteristic
557C23×C3D3×D411yescharacteristic
558C23×C3D3×D411yescharacteristic
559C23×C3D3×D411yescharacteristic
560C23×C3D3×D411yescharacteristic
561C23×C3D3×D411yescharacteristic
562C23×C3C2×#6711yescharacteristic
563C23×C3C2×#6711yescharacteristic
564C23×C3C23×D311yescharacteristic
565C23×C3C23×D311yescharacteristic
566C22×D3—24no—
567C22×D3—24no—
568C22×D3—24no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—44no—
579C22×D3—44no—
580C22×D3—44no—
581C22×D3—44no—
582C22×D3—42no—
583C22×D3—42no—
584C22×D3—42no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—42no—
590C22×D3—42no—
591C22×D3—62no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—121no—
599C22×D3—121no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3—242no—
603C22×D3—242no—
604C22×D3—242no—
605C22×D3C2×D1212yescomplemented
606C22×D3C2×#6712yescomplemented
607C3×D4—62no—
608C3×D4—62no—
609C3×D4—62no—
610C3×D4—62no—
611C3×D4—62no—
612C3×D4—62no—
613C3×D4—62no—
614C3×D4—62no—
615C3×D4—128no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—42no—
621C2×C3×C4—42no—
622C2×C3×C4—42no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—62no—
628C2×C3×C4—82no—
629C2×C3×C4—122no—
630#67—22no—
631#67—22no—
632#67—22no—
633#67—22no—
634#67—22no—
635#67—22no—
636#67—22no—
637#67—22no—
638#67—64no—
639#67—64no—
640#67—64no—
641#67—64no—
642#67—62no—
643#67—62no—
644#67—62no—
645#67—62no—
646#67—62no—
647#67—62no—
648#67—62no—
649#67—62no—
650#67—122no—
651#67—122no—
652#67—122no—
653#67—122no—
654#67—128no—
655#67—128no—
656#67—128no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—22no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—42no—
665C2×Dic3—62no—
666C2×Dic3—64no—
667C2×Dic3—64no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3—122no—
677C2×Dic3—122no—
678C2×Dic3—122no—
679C2×Dic3—242no—
680C2×Dic3C2×D1212yescomplemented
681C2×Dic3C2×#6712yescomplemented
682D12—48no—
683D12—64no—
684D12—64no—
685D12—128no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—64no—
689C4×D3—64no—
690Dic6—64no—
691Dic6—64no—
692C2×C32—21no—
693C2×C32—21no—
694C2×C32—21no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32B(4,𝔽2)12yescomplemented
699C2×C32C2×#12011yescharacteristic
700C3⋊D3—42no—
701C3×D3—42no—
702C3×D3—42no—
703C3×D3—44no—
704C24—31no—
705C24—31no—
706C24—32no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—91no—
714C24—124no—
715C24—181no—
716C24C2×D3211yescharacteristic
717#41—184no—
718#41—184no—
719#41—184no—
720#41—184no—
721#41—184no—
722#41—184no—
723C2×Q8—181no—
724C2×D4—32no—
725C2×D4—32no—
726C2×D4—32no—
727C2×D4—32no—
728C2×D4—64no—
729C2×D4—61no—
730C2×D4—61no—
731C2×D4—61no—
732C2×D4—61no—
733C2×D4—61no—
734C2×D4—61no—
735C2×D4—61no—
736C2×D4—61no—
737C2×D4—92no—
738C2×D4—92no—
739C2×D4—124no—
740C2×D4—181no—
741C2×D4—181no—
742C2×D4—184no—
743C2×D4—184no—
744C2×D4—184no—
745C2×D4—184no—
746C2×D4—184no—
747C2×D4—184no—
748C2×D4—184no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C2×D4—181no—
754C2×D4—184no—
755C2×D4—364no—
756C2×D4—364no—
757C22×C4—21no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—61no—
761C22×C4—91no—
762C22×C4—181no—
763C22×C4—181no—
764C22×C4—181no—
765C22×C4—181no—
766C22⋊C4—21no—
767C22⋊C4—32no—
768C22⋊C4—64no—
769C22⋊C4—61no—
770C22⋊C4—92no—
771C22⋊C4—184no—
772C22⋊C4—184no—
773C22⋊C4—181no—
774C22⋊C4C2×D3212yescomplemented
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—64no—
800C22×C3—64no—
801C22×C3—64no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—122no—
809C22×C3—122no—
810C22×C3—122no—
811C22×C3—122no—
812C22×C3—122no—
813C22×C3—124no—
814C22×C3—124no—
815C22×C3—124no—
816C22×C3—122no—
817C22×C3—122no—
818C22×C3—124no—
819C22×C3—122no—
820C22×C3—241no—
821C22×C3—241no—
822C22×C3#88211yescharacteristic
823C22×C3#88211yescharacteristic
824C22×C3#88211yescharacteristic
825C22×C3#88211yescharacteristic
826C22×C3#93711yescharacteristic
827C22×C3#93711yescharacteristic
828C22×C3#93711yescharacteristic
829C22×C3#93711yescharacteristic
830C22×C3C22×D1211yescharacteristic
831C22×C3C2×D3×D411yescharacteristic
832C22×C3C2×D3×D411yescharacteristic
833C22×C3C2×D3×D411yescharacteristic
834C22×C3C2×D3×D411yescharacteristic
835C22×C3C22×#6711yescharacteristic
836C2×D3—24no—
837C2×D3—24no—
838C2×D3—24no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—44no—
845C2×D3—44no—
846C2×D3—44no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—44no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—81no—
856C2×D3—81no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—242no—
863C2×D3—242no—
864C2×D3—244no—
865C2×D3—244no—
866C2×D3—241no—
867C2×D3—241no—
868C2×D3—242no—
869C3×C4—42no—
870C3×C4—42no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—82no—
874C3×C4—122no—
875Dic3—22no—
876Dic3—22no—
877Dic3—42no—
878Dic3—62no—
879Dic3—62no—
880Dic3—122no—
881Dic3—122no—
882Dic3—122no—
883Dic3—242no—
884C32C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
885C23—32no—
886C23—32no—
887C23—42no—
888C23—64no—
889C23—64no—
890C23—64no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—92no—
899C23—122no—
900C23—122no—
901C23—122no—
902C23—122no—
903C23—122no—
904C23—124no—
905C23—124no—
906C23—124no—
907C23—124no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—184no—
913C23—181no—
914C23—181no—
915C23—362no—
916C23—722no—
917C23D3×D1211yescharacteristic
918C23D3×D1211yescharacteristic
919C23#380211yescharacteristic
920C23#380211yescharacteristic
921C23D3×#6711yescharacteristic
922C23D3×#6711yescharacteristic
923C23C22×D3211yescharacteristic
924Q8—184no—
925D4—62no—
926D4—62no—
927D4—62no—
928D4—62no—
929D4—62no—
930D4—62no—
931D4—62no—
932D4—62no—
933D4—128no—
934D4—184no—
935D4—184no—
936D4—184no—
937D4—182no—
938D4—182no—
939D4—182no—
940D4—182no—
941D4—368no—
942D4—368no—
943C2×C4—22no—
944C2×C4—32no—
945C2×C4—32no—
946C2×C4—42no—
947C2×C4—61no—
948C2×C4—61no—
949C2×C4—61no—
950C2×C4—61no—
951C2×C4—62no—
952C2×C4—92no—
953C2×C4—122no—
954C2×C4—184no—
955C2×C4—184no—
956C2×C4—184no—
957C2×C4—181no—
958C2×C4—181no—
959C2×C4—182no—
960C2×C4—362no—
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—22no—
974C2×C3—21no—
975C2×C3—41no—
976C2×C3—41no—
977C2×C3—41no—
978C2×C3—41no—
979C2×C3—41no—
980C2×C3—41no—
981C2×C3—122no—
982C2×C3—124no—
983C2×C3—122no—
984C2×C3#474112yescomplemented
985C2×C3#503212yescomplemented
986C2×C3C2×#88211yescharacteristic
987C2×C3C2×#93711yescharacteristic
988D3—42no—
989D3—44no—
990D3—42no—
991D3—122no—
992D3—122no—
993D3—242no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—64no—
1002C22—64no—
1003C22—64no—
1004C22—62no—
1005C22—62no—
1006C22—122no—
1007C22—122no—
1008C22—122no—
1009C22—122no—
1010C22—122no—
1011C22—124no—
1012C22—124no—
1013C22—124no—
1014C22—124no—
1015C22—122no—
1016C22—122no—
1017C22—122no—
1018C22—182no—
1019C22—241no—
1020C22—241no—
1021C22—362no—
1022C22—362no—
1023C22—721no—
1024C22—724no—
1025C22#6392211yescharacteristic
1026C22#6392211yescharacteristic
1027C22#6392211yescharacteristic
1028C22#6392211yescharacteristic
1029C22C2×D3×D1211yescharacteristic
1030C22C2×#380211yescharacteristic
1031C22C2×D3×#6711yescharacteristic
1032C4—42no—
1033C4—62no—
1034C4—62no—
1035C4—122no—
1036C4—182no—
1037C4—362no—
1038C3—21no—
1039C3C2×#474111yescharacteristic, complemented
1040C3C2×#503211yescharacteristic, complemented
1041C2—21no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—21no—
1046C2—21no—
1047C2—124no—
1048C2—122no—
1049C2—122no—
1050C2—362no—
1051C2#1059040712yesdirect product factor
1052C2C2×#6392211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32C2×B(4,𝔽2)
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C2×C3×#882C2semidirect
3. C2×#63977C2semidirect
4. C2×#63976C2semidirect
5. C2×#63633C2semidirect
6. C2×C3×#806C2semidirect
7. C2×#63580C2semidirect
8. #10590407C2direct (N × H)
11. C24×C3×D3C22semidirect
19. #64330C22semidirect
28. C2×C32×C22⋊C4C22semidirect
29. C2×#3757C22semidirect
30. C2×C3×#217C22semidirect
33. C3×#882C22semidirect
35. #63977C22semidirect
37. #63976C22semidirect
40. #63633C22semidirect
41. C3×#806C22semidirect
42. #63580C22semidirect
50. C2×#882D3semidirect
58. C2×#806D3semidirect
61. C23×C3⋊D3D4semidirect
69. C23×C3×D3D4semidirect
70. C23×C3×D3D4semidirect
71. C23×C3×D3C23semidirect
78. C2×#638D4semidirect
81. C22×C3⋊Dic3D4semidirect
90. C2×C3×#67D4semidirect
91. C2×C3×#67D4semidirect
95. C22×C3×Dic3D4semidirect
96. C22×C3×Dic3D4semidirect
123. C32×C22⋊C4C23semidirect
125. #3757C23semidirect
127. C3×#217C23semidirect
133. C24×D3C2×D3semidirect
172. C2×C3×C22⋊C4C2×D3semidirect
173. C2×C3×C22⋊C4C2×D3semidirect
183. C2×#217C2×D3semidirect
192. #882C2×D3semidirect
199. #806C2×D3semidirect
211. C22×C3⋊D3C2×D4semidirect
235. C22×C3×D3C2×D4semidirect
236. C22×C3×D3C2×D4semidirect
249. C2×C3⋊Dic3C2×D4semidirect
264. C2×C3×Dic3C2×D4semidirect
265. C2×C3×Dic3C2×D4semidirect
309. C23×D3D12semidirect
310. C23×D3#67semidirect
311. C23×D3C22×D3semidirect
372. C2×#67D12semidirect
373. C2×#67#67semidirect
385. C22×Dic3D12semidirect
386. C22×Dic3#67semidirect
426. C3×C22⋊C4C22×D3semidirect
427. C3×C22⋊C4C22×D3semidirect
437. #217C22×D3semidirect
513. C2×C22⋊C4D32semidirect
605. C22×D3C2×D12semidirect
606. C22×D3C2×#67semidirect
680. C2×Dic3C2×D12semidirect
681. C2×Dic3C2×#67semidirect
698. C2×C32B(4,𝔽2)semidirect
774. C22⋊C4C2×D32semidirect
884. C32C2×B(4,𝔽2)semidirect
984. C2×C3#4741semidirect
985. C2×C3#5032semidirect
1039. C3C2×#4741semidirect
1040. C3C2×#5032semidirect
1051. C2#10590407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643302
C2×C3×#8822
C2×#639772
C2×#639762
C2×#636332
C2×C3×#8062
C2×#635802
#105904072
C2×#50323
C2×#47413