Finite Group Databasebeta

← C2×#10590408 #11865291

Subgroups — C2×#10590408 #11865291

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×#63966C211yesmaximal, characteristic, complemented
4C2×#63961C211yesmaximal, characteristic, complemented
5C2×#63633C211yesmaximal, characteristic, complemented
6C2×C3×#806C211yesmaximal, characteristic, complemented
7C2×#63580C211yesmaximal, characteristic, complemented
8#10590408C218yesmaximal, direct product factor
9C2×#5053—31nomaximal
10C2×#4742—31nomaximal
11C22×#638C2211yescharacteristic
12C22×C3×#67C2211yescharacteristic
13C22×C3×#67C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic, complemented
15#64330—22no—
16#64330—22no—
17#64330—22no—
18#64330C2214yes—
19C2×#3811—21no—
20C2×D3×#67—21no—
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C2×#3804—21no—
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×#3757C2211yescharacteristic, complemented
27C2×C3×#217C2211yescharacteristic, complemented
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×C4⋊Dic3—21no—
30C3×#886—22no—
31C3×#886C2214yescomplemented
32C2×#3724—21no—
33#63966—22no—
34#63966C2214yescomplemented
35C2×Dic3⋊Dic3—21no—
36C2×#3722—21no—
37#63961—22no—
38#63961C2214yescomplemented
39C2×(C2×D3)⋊Dic3—21no—
40#63633C2214yescomplemented
41C3×#806C2214yescomplemented
42#63580C2214yescomplemented
43C2×#1004—31no—
44C2×#1004—31no—
45C2×C3×#123—31no—
46C2×#935—31no—
47C2×#929—31no—
48C2×#929—31no—
49C2×#886—31no—
50C2×#886D311yescharacteristic, complemented
51C2×C3×#99—31no—
52C2×#834—31no—
53#5053—38no—
54C2×#806—31no—
55C2×#806—31no—
56C2×#806—31no—
57C2×#806—61no—
58C2×#806D311yescharacteristic, complemented
59#4742—38no—
60C24×C32C2311yescharacteristic
61C23×C3⋊D3D411yescharacteristic
62C23×C3×D3D411yescharacteristic
63C23×C3×D3D411yescharacteristic
64C22×D32—21no—
65C22×C32×C4—21no—
66C2×#638—21no—
67C2×#638—21no—
68C2×#638—21no—
69C2×#638—21no—
70C2×#638D412yes—
71C2×#638C2312yes—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3D411yescharacteristic
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C2×C3×#67—21no—
79C2×C3×#67—21no—
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C2×C3×#67D412yes—
83C2×C3×#67D412yes—
84C2×C3×#67C2312yes—
85C2×C3×#67C2312yes—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3D411yescharacteristic
94C22×C3×Dic3D411yescharacteristic
95C22×C3×Dic3C2312yescomplemented
96#3811—24no—
97#3811—24no—
98D3×#67—24no—
99D3×#67—24no—
100D3×#67—24no—
101D3×#67—24no—
102C2×#627—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#625—21no—
106C2×#624—21no—
107#3805—24no—
108#3805—24no—
109#3804—24no—
110#3804—24no—
111#3804—24no—
112#3804—24no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115C32×C22⋊C4—21no—
116C32×C22⋊C4C2312yescomplemented
117#3757—21no—
118#3757C2312yescomplemented
119C3×#217—21no—
120C3×#217C2312yescomplemented
121C3×(C2×D3)⋊C4—24no—
122C3×C4⋊Dic3—24no—
123#3724—24no—
124Dic3⋊Dic3—24no—
125#3722—24no—
126(C2×D3)⋊Dic3—24no—
127C2×#458—91noSylow
128C22×C3×D4—31no—
129C22×C3×D4—31no—
130C23×C3×C4—31no—
131C22×#67—31no—
132C22×#67—31no—
133C22×#67—61no—
134C22×#67—61no—
135C22×#67—61no—
136C22×#67C2×D311yescharacteristic
137C22×#67C2×D311yescharacteristic
138C23×Dic3C2×D311yescharacteristic, complemented
139#1004—34no—
140#1004—34no—
141#1004—62no—
142#1004—62no—
143#1004—62no—
144#1004—62no—
145#1004—62no—
146#1004—62no—
147C2×#237—61no—
148C2×#237—61no—
149C2×#237—61no—
150C2×#237—61no—
151C2×D3×D4—61no—
152C2×D3×D4—61no—
153C2×D3×D4—61no—
154C2×D3×D4—61no—
155C2×#235—61no—
156C2×#235—61no—
157C3×#123—34no—
158C3×#123—62no—
159C2×C3×C4⋊C4—61no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—61no—
163C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
164C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—61no—
168C2×#217—61no—
169C2×#217C2×D311yescharacteristic, complemented
170#935—34no—
171#935—62no—
172#929—34no—
173#929—34no—
174#929—62no—
175#929—62no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4—61no—
178C2×(C2×D3)⋊C4—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×C4⋊Dic3—21no—
181C2×C4⋊Dic3—61no—
182C2×Dic3⋊C4—61no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4—61no—
185#886—22no—
186#886—34no—
187#886—62no—
188#886C2×D314yescomplemented
189C3×#99—34no—
190#834—34no—
191#806—34no—
192#806—34no—
193#806—34no—
194#806—64no—
195#806C2×D314yescomplemented
196C23×C32—42no—
197C23×C32C2×D411yescharacteristic
198C23×C32C2×D411yescharacteristic
199C23×C32C2×D411yescharacteristic
200C23×C32C2×D411yescharacteristic
201C23×C32C2×D411yescharacteristic
202C23×C32C2×D411yescharacteristic
203C23×C32C2411yescharacteristic
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—42no—
207C22×C3⋊D3C2×D412yes—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3—42no—
213C22×C3×D3—42no—
214C22×C3×D3C2×D412yes—
215C22×C3×D3C2×D412yes—
216C2×D32—24no—
217C2×D32—82no—
218C2×C32×C4—22no—
219C2×C32×C4—42no—
220#638—22no—
221#638—22no—
222#638—22no—
223#638—22no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3—42no—
228C2×C3⋊Dic3C2×D412yes—
229C3×#67—22no—
230C3×#67—22no—
231C3×#67—22no—
232C3×#67—22no—
233C3×#67—22no—
234C3×#67—22no—
235C3×#67—22no—
236C3×#67—22no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—42no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3—41no—
250C2×C3×Dic3C2×D412yes—
251C2×C3×Dic3C2×D412yes—
252#627—24no—
253#626—24no—
254#626—24no—
255#625—24no—
256#624—24no—
257D3×Dic3—24no—
258D3×Dic3—24no—
259C2×H(5,𝔽2)—91no—
260C2×#123—31no—
261C2×#123—91no—
262C2×#123—91no—
263#458—98no—
264C2×#99—31no—
265C2×#99—91no—
266C2×#99—91no—
267C24×C3—21no—
268C24×C3—31no—
269C24×C3—31no—
270C24×C3C22×D311yescharacteristic
271C24×C3C22×D311yescharacteristic
272C23×D3—31no—
273C23×D3—31no—
274C23×D3—61no—
275C23×D3—61no—
276C23×D3—61no—
277C23×D3D1211yescharacteristic
278C23×D3#6711yescharacteristic
279C2×C3×D4—32no—
280C2×C3×D4—32no—
281C2×C3×D4—32no—
282C2×C3×D4—32no—
283C2×C3×D4—61no—
284C2×C3×D4—61no—
285C2×C3×D4—61no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4—61no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—32no—
296C22×C3×C4—41no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—32no—
313C2×#67—32no—
314C2×#67—32no—
315C2×#67—32no—
316C2×#67—62no—
317C2×#67—62no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—64no—
321C2×#67—64no—
322C2×#67—64no—
323C2×#67—64no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—121no—
335C2×#67—121no—
336C2×#67—121no—
337C2×#67—121no—
338C2×#67D1212yes—
339C2×#67#6712yes—
340C2×#67C22×D312yes—
341C2×#67C22×D312yes—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—121no—
357C22×Dic3D1211yescharacteristic
358C22×Dic3#6711yescharacteristic
359C22×Dic3C22×D312yescomplemented
360#237—64no—
361#237—64no—
362#237—64no—
363#237—64no—
364#237—64no—
365#237—64no—
366#237—64no—
367#237—64no—
368D3×D4—64no—
369D3×D4—64no—
370D3×D4—64no—
371D3×D4—64no—
372D3×D4—64no—
373D3×D4—64no—
374D3×D4—64no—
375D3×D4—64no—
376#235—64no—
377#235—64no—
378#235—64no—
379#235—64no—
380C2×D12—61no—
381C2×D12—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×Dic6—61no—
387C2×Dic6—61no—
388C3×C4⋊C4—64no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—32no—
393C3×C22⋊C4—41no—
394C3×C22⋊C4—64no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4C22×D312yescomplemented
397C3×C22⋊C4C22×D312yescomplemented
398#217—21no—
399#217—32no—
400#217—32no—
401#217—62no—
402#217—64no—
403#217—61no—
404#217—61no—
405#217—121no—
406#217C22×D312yescomplemented
407(C2×D3)⋊C4—24no—
408(C2×D3)⋊C4—64no—
409(C2×D3)⋊C4—64no—
410(C2×D3)⋊C4—64no—
411C4⋊Dic3—24no—
412C4⋊Dic3—64no—
413Dic3⋊C4—64no—
414Dic3⋊C4—64no—
415Dic3⋊C4—64no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32#12011yescharacteristic
424C22×C32#12011yescharacteristic
425C22×C32#12011yescharacteristic
426C22×C32#12011yescharacteristic
427C22×C32C22×D411yescharacteristic
428C22×C32C22×D411yescharacteristic
429C22×C32C22×D411yescharacteristic
430C2×C3⋊D3—22no—
431C2×C3⋊D3—42no—
432C2×C3⋊D3—42no—
433C2×C3⋊D3—81no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—42no—
437C2×C3×D3—42no—
438C2×C3×D3—42no—
439C2×C3×D3—42no—
440C2×C3×D3—81no—
441C2×C3×D3—81no—
442D32—84no—
443C32×C4—42no—
444C3⋊Dic3—22no—
445C3⋊Dic3—42no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—42no—
449C3×Dic3—42no—
450H(5,𝔽2)—94no—
451H(5,𝔽2)—182no—
452H(5,𝔽2)—182no—
453H(5,𝔽2)—182no—
454C2×#41—181no—
455C2×#41—181no—
456C2×#41—181no—
457C22×D4—31no—
458C22×D4—31no—
459C22×D4—91no—
460C22×D4—181no—
461C22×D4—181no—
462C22×D4—181no—
463C23×C4—31no—
464#123—34no—
465#123—62no—
466#123—94no—
467#123—94no—
468#123—182no—
469#123—182no—
470C2×C4⋊C4—61no—
471C2×C4⋊C4—181no—
472C2×C4⋊C4—181no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—61no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—181no—
477C2×C22⋊C4—181no—
478C2×C22⋊C4D3211yescharacteristic, complemented
479#99—34no—
480#99—94no—
481#99—94no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—32no—
490C23×C3—32no—
491C23×C3—42no—
492C23×C3—42no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—82no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3C2×D1211yescharacteristic
501C23×C3C2×D1211yescharacteristic
502C23×C3D3×D411yescharacteristic
503C23×C3D3×D411yescharacteristic
504C23×C3D3×D411yescharacteristic
505C23×C3D3×D411yescharacteristic
506C23×C3D3×D411yescharacteristic
507C23×C3D3×D411yescharacteristic
508C23×C3D3×D411yescharacteristic
509C23×C3D3×D411yescharacteristic
510C23×C3C2×#6711yescharacteristic
511C23×C3C2×#6711yescharacteristic
512C23×C3C23×D311yescharacteristic
513C23×C3C23×D311yescharacteristic
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—32no—
519C22×D3—32no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—62no—
523C22×D3—64no—
524C22×D3—64no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—121no—
530C22×D3—121no—
531C22×D3—122no—
532C22×D3—122no—
533C22×D3—242no—
534C22×D3—242no—
535C22×D3—242no—
536C22×D3C2×D1212yes—
537C22×D3C2×#6712yes—
538C3×D4—62no—
539C3×D4—62no—
540C3×D4—62no—
541C3×D4—62no—
542C3×D4—62no—
543C3×D4—62no—
544C3×D4—62no—
545C3×D4—62no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—42no—
551C2×C3×C4—42no—
552C2×C3×C4—42no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—62no—
558C2×C3×C4—62no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—82no—
562C2×C3×C4—122no—
563C2×C3×C4—121no—
564C2×C3×C4—121no—
565C2×C3×C4—121no—
566C2×C3×C4—121no—
567#67—22no—
568#67—22no—
569#67—22no—
570#67—22no—
571#67—22no—
572#67—22no—
573#67—22no—
574#67—22no—
575#67—64no—
576#67—64no—
577#67—64no—
578#67—64no—
579#67—62no—
580#67—62no—
581#67—62no—
582#67—62no—
583#67—62no—
584#67—62no—
585#67—62no—
586#67—62no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—42no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—62no—
607C2×Dic3—64no—
608C2×Dic3—64no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3—242no—
621C2×Dic3C2×D1212yes—
622C2×Dic3C2×#6712yes—
623D12—64no—
624D12—64no—
625C4×D3—64no—
626C4×D3—64no—
627C4×D3—64no—
628C4×D3—64no—
629Dic6—64no—
630Dic6—64no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32#45812yescomplemented
638C2×C32C2×#12011yescharacteristic
639C3⋊D3—42no—
640C3×D3—42no—
641C3×D3—42no—
642C24—31no—
643C24—31no—
644C24—91no—
645C24—181no—
646C24C2×D3211yescharacteristic
647#41—184no—
648#41—184no—
649#41—184no—
650#41—184no—
651#41—184no—
652#41—184no—
653C2×Q8—181no—
654C2×D4—32no—
655C2×D4—32no—
656C2×D4—32no—
657C2×D4—32no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—92no—
667C2×D4—92no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—184no—
671C2×D4—184no—
672C2×D4—184no—
673C2×D4—184no—
674C2×D4—184no—
675C2×D4—184no—
676C2×D4—181no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C22×C4—21no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—32no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—91no—
693C22×C4—181no—
694C22×C4—181no—
695C22×C4—181no—
696C22×C4—181no—
697C4⋊C4—64no—
698C4⋊C4—184no—
699C4⋊C4—184no—
700C22⋊C4—21no—
701C22⋊C4—32no—
702C22⋊C4—64no—
703C22⋊C4—61no—
704C22⋊C4—92no—
705C22⋊C4—184no—
706C22⋊C4—184no—
707C22⋊C4—181no—
708C22⋊C4C2×D3212yescomplemented
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—122no—
740C22×C3—122no—
741C22×C3—122no—
742C22×C3—122no—
743C22×C3—241no—
744C22×C3—241no—
745C22×C3#88211yescharacteristic
746C22×C3#88211yescharacteristic
747C22×C3#88211yescharacteristic
748C22×C3#88211yescharacteristic
749C22×C3#93711yescharacteristic
750C22×C3#93711yescharacteristic
751C22×C3#93711yescharacteristic
752C22×C3#93711yescharacteristic
753C22×C3C22×D1211yescharacteristic
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C22×#6711yescharacteristic
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—81no—
768C2×D3—81no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—122no—
772C2×D3—122no—
773C2×D3—122no—
774C2×D3—242no—
775C2×D3—242no—
776C2×D3—244no—
777C2×D3—244no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—242no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4—82no—
786C3×C4—122no—
787C3×C4—122no—
788Dic3—22no—
789Dic3—22no—
790Dic3—42no—
791Dic3—42no—
792Dic3—62no—
793Dic3—62no—
794Dic3—122no—
795Dic3—122no—
796Dic3—122no—
797Dic3—242no—
798C32C2×#45811yescharacteristic, complemented, Sylow
799C23—32no—
800C23—32no—
801C23—42no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—92no—
807C23—122no—
808C23—122no—
809C23—184no—
810C23—181no—
811C23—181no—
812C23—362no—
813C23—722no—
814C23D3×D1211yescharacteristic
815C23D3×D1211yescharacteristic
816C23#380211yescharacteristic
817C23#380211yescharacteristic
818C23D3×#6711yescharacteristic
819C23D3×#6711yescharacteristic
820C23C22×D3211yescharacteristic
821Q8—184no—
822D4—62no—
823D4—62no—
824D4—62no—
825D4—62no—
826D4—62no—
827D4—62no—
828D4—62no—
829D4—62no—
830D4—184no—
831D4—184no—
832D4—184no—
833D4—182no—
834D4—182no—
835D4—182no—
836D4—182no—
837C2×C4—22no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—42no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—92no—
850C2×C4—122no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—184no—
856C2×C4—184no—
857C2×C4—184no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—182no—
861C2×C4—362no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—22no—
875C2×C3—21no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—41no—
879C2×C3—41no—
880C2×C3—41no—
881C2×C3—41no—
882C2×C3—122no—
883C2×C3—122no—
884C2×C3#474212yescomplemented
885C2×C3#505312yescomplemented
886C2×C3C2×#88211yescharacteristic
887C2×C3C2×#93711yescharacteristic
888D3—42no—
889D3—42no—
890D3—122no—
891D3—122no—
892D3—242no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—62no—
901C22—62no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—182no—
907C22—241no—
908C22—241no—
909C22—362no—
910C22—362no—
911C22—721no—
912C22—724no—
913C22#6392211yescharacteristic
914C22#6392211yescharacteristic
915C22#6392211yescharacteristic
916C22#6392211yescharacteristic
917C22C2×D3×D1211yescharacteristic
918C22C2×#380211yescharacteristic
919C22C2×D3×#6711yescharacteristic
920C4—42no—
921C4—62no—
922C4—62no—
923C4—122no—
924C4—122no—
925C4—182no—
926C4—362no—
927C3—21no—
928C3C2×#474211yescharacteristic, complemented
929C3C2×#505311yescharacteristic, complemented
930C2—21no—
931C2—21no—
932C2—21no—
933C2—21no—
934C2—21no—
935C2—21no—
936C2—122no—
937C2—122no—
938C2—362no—
939C2#1059040812yesdirect product factor
940C2C2×#6392211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC2×#64330C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#458
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
2. C2×C3×#886C2semidirect
3. C2×#63966C2semidirect
4. C2×#63961C2semidirect
5. C2×#63633C2semidirect
6. C2×C3×#806C2semidirect
7. C2×#63580C2semidirect
8. #10590408C2direct (N × H)
14. C23×C3×Dic3C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×#3757C22semidirect
27. C2×C3×#217C22semidirect
31. C3×#886C22semidirect
34. #63966C22semidirect
38. #63961C22semidirect
40. #63633C22semidirect
41. C3×#806C22semidirect
42. #63580C22semidirect
50. C2×#886D3semidirect
58. C2×#806D3semidirect
95. C22×C3×Dic3C23semidirect
116. C32×C22⋊C4C23semidirect
118. #3757C23semidirect
120. C3×#217C23semidirect
138. C23×Dic3C2×D3semidirect
163. C2×C3×C22⋊C4C2×D3semidirect
164. C2×C3×C22⋊C4C2×D3semidirect
169. C2×#217C2×D3semidirect
188. #886C2×D3semidirect
195. #806C2×D3semidirect
359. C22×Dic3C22×D3semidirect
396. C3×C22⋊C4C22×D3semidirect
397. C3×C22⋊C4C22×D3semidirect
406. #217C22×D3semidirect
478. C2×C22⋊C4D32semidirect
637. C2×C32#458semidirect
708. C22⋊C4C2×D32semidirect
798. C32C2×#458semidirect
884. C2×C3#4742semidirect
885. C2×C3#5053semidirect
928. C3C2×#4742semidirect
929. C3C2×#5053semidirect
939. C2#10590408direct (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×#8862
C2×#639662
C2×#639612
C2×#636332
C2×C3×#8062
C2×#635802
#105904082
C2×#50533
C2×#47423