Finite Group Databasebeta

← C2×#10595102 #11918814

Subgroups — C2×#10595102 #11918814

Order 1152.

3473 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C2×C3×#932C211yesmaximal, characteristic, complemented
4C22×C3×#213C211yesmaximal, characteristic, complemented
5C2×#63937C212yesmaximal, complemented
6C2×#63936C212yesmaximal, complemented
7#10595102C2116yesmaximal, direct product factor
8C2×#63927C212yesmaximal, complemented
9C2×#63926C212yesmaximal, complemented
10C2×#63830C211yesmaximal, characteristic, complemented
11C2×#63829C211yesmaximal, characteristic, complemented
12C2×#63817C211yesmaximal, characteristic, complemented
13C2×#5774—31nomaximal
14C2×#5757—31nomaximal
15C22×C32×D4C2211yescharacteristic, complemented
16C22×#638—22no—
17#64361—24no—
18#64361C2218yescomplemented
19C2×#3830—21no—
20C2×#3830C2212yescomplemented
21C2×D4×C3⋊D3—21no—
22C2×D4×C3⋊D3C2212yescomplemented
23C2×#3828C2211yescharacteristic
24C2×#3828C2211yescharacteristic, complemented
25C2×C3×#235C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C2×D3×#67—22no—
28#64307—24no—
29#64307C2218yescomplemented
30C2×#3802C2212yescomplemented
31C2×D3×D12—21no—
32C2×#3796C2212yescomplemented
33C2×#3795—21no—
34C2×C3×#214C2212yescomplemented
35C3×#932C2218yescomplemented
36C2×C3×#213C2212yescomplemented
37C2×C3×#213C2212yescomplemented
38C2×C3×#213C2212yescomplemented
39C2×C3×#213C2218yescomplemented
40C2×C3×#208C2211yescharacteristic, complemented
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42#63937C22116yescomplemented
43#63936C22116yescomplemented
44#63927C22116yescomplemented
45#63926C22116yescomplemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48#63830C2218yescomplemented
49#63829C2218yescomplemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3716C2212yescomplemented
52C2×#3714C2211yescharacteristic, complemented
53C2×#3714C2212yescomplemented
54C2×#3712C2212yescomplemented
55#63817C2218yescomplemented
56C2×#3710C2212yescomplemented
57C2×#1009—31no—
58C2×#1004—31no—
59C2×#1004—31no—
60C2×#1004—31no—
61C2×#1004—61no—
62C2×C3×AGL(1,ℤ/8)—31no—
63C22×C3×D8—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#932D311yescharacteristic, complemented
67C22×#213D311yescharacteristic, complemented
68#5774—316no—
69C2×#916—32no—
70C2×#914—32no—
71#5757—316no—
72C2×#912—32no—
73C2×#911—32no—
74C2×#911—32no—
75C2×#911—32no—
76C2×D3×D8—32no—
77C2×D3×D8—32no—
78C2×#908—31no—
79C2×#907—31no—
80C2×#904—31no—
81C2×#901—31no—
82C24×C32—21no—
83C23×C3⋊D3—22no—
84C23×C3×D3—21no—
85C22×D32—22no—
86C2×C32×D4—21no—
87C2×C32×D4—22no—
88C2×C32×D4C2312yes—
89C2×C32×D4C2314yescomplemented
90C22×C32×C4C2311yescharacteristic
91C2×#638—21no—
92C2×#638—22no—
93C2×#638—216no—
94C2×#638—22no—
95C2×#638D412yes—
96C22×C3⋊Dic3—22no—
97#3830—24no—
98#3830—28no—
99#3830C2318yescomplemented
100D4×C3⋊D3—28no—
101D4×C3⋊D3—24no—
102D4×C3⋊D3C2318yescomplemented
103#3828—22no—
104#3828D414yes—
105#3828C2314yes—
106#3828C2314yescomplemented
107C2×C4⋊(C3⋊D3)D411yescharacteristic
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2312yes—
111C2×#634D411yescharacteristic
112C2×#634C2311yescharacteristic
113C2×C3×#67—21no—
114C3×#235—22no—
115C3×#235C2314yescomplemented
116C2×C3×D12—21no—
117C2×C3×D12—22no—
118C2×C3×D12C2312yes—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2314yescomplemented
121C2×C3×C4×D3—21no—
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—216no—
124C2×#626—22no—
125C2×#625—22no—
126C2×D3×Dic3—22no—
127#3802—24no—
128#3802C2318yescomplemented
129D3×D12—28no—
130#3796—24no—
131#3796C2318yescomplemented
132#3795—28no—
133C3×#214C2318yescomplemented
134C3×#213C2318yescomplemented
135C3×#213C2318yescomplemented
136C3×#213C2318yescomplemented
137C3×#208C2314yescomplemented
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2312yes—
141C2×C3×C3⋊C8C2314yescomplemented
142#3719C2314yescomplemented
143#3717C2314yescomplemented
144#3716C2314yescomplemented
145#3716C2318yescomplemented
146#3714C2314yescomplemented
147#3714C2318yescomplemented
148#3712C2318yescomplemented
149#3710C2318yescomplemented
150C2×#576—91noSylow
151C2×C3×#41—31no—
152C22×C3×D4—21no—
153C22×C3×D4—31no—
154C22×C3×D4C2×D311yescharacteristic, complemented
155C22×C3×D4C2×D311yescharacteristic, complemented
156C22×#67—62no—
157C22×#67—62no—
158C22×#67—62no—
159C22×#67—64no—
160#1009—38no—
161#1009—64no—
162C2×#239—32no—
163#1004—38no—
164#1004—38no—
165#1004—38no—
166#1004—68no—
167#1004—64no—
168#1004—64no—
169#1004—64no—
170#1004—68no—
171C2×#237—32no—
172C2×#237—32no—
173C2×#237—32no—
174C2×#237—62no—
175C2×#237—61no—
176C2×#237—61no—
177C2×#237—61no—
178C2×#237—62no—
179C2×D3×D4—32no—
180C2×D3×D4—32no—
181C2×D3×D4—32no—
182C2×D3×D4—32no—
183C2×D3×D4—62no—
184C2×D3×D4—61no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×D3×D4—62no—
188C2×D3×D4—62no—
189C2×#235—31no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C2×#235—61no—
196C2×#235C2×D311yescharacteristic, complemented
197C22×D12—61no—
198C22×D12C2×D311yescharacteristic, complemented
199C3×AGL(1,ℤ/8)—38no—
200C2×C3×SD16—32no—
201C2×C3×D8—32no—
202C2×C3×D8—32no—
203C2×C3×D8—32no—
204C2×C3×D8—38no—
205C2×C3×M16—31no—
206C22×C3×C8—31no—
207#950—38no—
208C2×#216—31no—
209C2×#215—31no—
210C2×#214—31no—
211C2×#214—32no—
212C2×#214C2×D312yescomplemented
213#932—38no—
214#932C2×D318yescomplemented
215C2×#213—31no—
216C2×#213—32no—
217C2×#213C2×D312yescomplemented
218C2×#213C2×D312yescomplemented
219C2×#213C2×D312yescomplemented
220C2×#213C2×D318yescomplemented
221C2×#208C2×D311yescharacteristic, complemented
222C22×C3⋊C8C2×D311yescharacteristic, complemented
223#916—316no—
224#914—316no—
225#912—316no—
226#911—316no—
227#911—316no—
228#911—316no—
229D3×D8—316no—
230D3×D8—316no—
231#908—38no—
232#907—38no—
233C2×Dic12—31no—
234#904—38no—
235C2×D24—31no—
236C2×D24—32no—
237C2×#204—31no—
238C2×#204—32no—
239C2×#204—31no—
240#901—38no—
241C2×ΓL(1,𝔽25)—32no—
242C2×ΓL(1,𝔽25)—32no—
243C2×D3×C8—32no—
244C2×D3×C8—32no—
245C23×C32—22no—
246C23×C32—24no—
247C23×C32—82no—
248C23×C32C2×D411yescharacteristic
249C22×C3⋊D3—21no—
250C22×C3⋊D3—28no—
251C22×C3⋊D3—84no—
252C22×C3⋊D3C2×D412yes—
253C22×C3×D3—21no—
254C22×C3×D3—22no—
255C22×C3×D3—24no—
256C22×C3×D3—82no—
257C2×D32—28no—
258C2×D32—84no—
259C32×D4—22no—
260C32×D4—24no—
261C32×D4C2414yes—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D412yes—
264C2×C32×C4C2411yescharacteristic
265C2×C32×C4C2412yes—
266#638—24no—
267#638—28no—
268#638—28no—
269#638C2×D418yes—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—28no—
272C2×C3⋊Dic3C2×D412yes—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D414yes—
275C4⋊(C3⋊D3)C2412yes—
276C4×C3⋊D3—24no—
277C4×C3⋊D3C2×D414yes—
278C4×C3⋊D3C2414yes—
279#634—21no—
280#634C2×D414yes—
281#634C2412yes—
282C3×#67—24no—
283C2×C3×Dic3—21no—
284C3×D12—24no—
285C3×D12—22no—
286C3×D12—21no—
287C3×D12C2414yes—
288C3×D12C2412yes—
289C3×C4×D3—24no—
290C3×Dic6—21no—
291C3×Dic6C2412yes—
292#626—28no—
293#625—28no—
294D3×Dic3—28no—
295C3×C3⋊C8C2412yes—
296C3×C3⋊C8C2414yes—
297C3×C3⋊C8C2412yes—
298C2×H(5,𝔽2)—91no—
299C2×H(5,𝔽2)—91no—
300#576—916no—
301C2×AGL(1,ℤ/8)—31no—
302C2×AGL(1,ℤ/8)—91no—
303C2×AGL(1,ℤ/8)—92no—
304C2×AGL(1,ℤ/8)—92no—
305C2×#135—91no—
306C2×#135—92no—
307C22×D8—31no—
308C22×D8—92no—
309C2×#131—91no—
310C24×C3—22no—
311C24×C3—21no—
312C24×C3—21no—
313C24×C3—61no—
314C23×D3—21no—
315C23×D3—62no—
316C23×D3—62no—
317C23×D3—62no—
318C23×D3—62no—
319C23×D3—64no—
320C3×#41—34no—
321C3×#41—62no—
322C2×C3×Q8—31no—
323C2×C3×D4—22no—
324C2×C3×D4—24no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—22no—
328C2×C3×D4—22no—
329C2×C3×D4—22no—
330C2×C3×D4—24no—
331C2×C3×D4—31no—
332C2×C3×D4—32no—
333C2×C3×D4—34no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—62no—
337C2×C3×D4C22×D312yes—
338C2×C3×D4C22×D312yes—
339C2×C3×D4C22×D314yescomplemented
340C2×C3×D4C22×D314yescomplemented
341C22×C3×C4—21no—
342C22×C3×C4—61no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—21no—
346C2×#67—32no—
347C2×#67—32no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—616no—
355C2×#67—616no—
356C2×#67—616no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—64no—
361C2×#67—64no—
362C2×#67—632no—
363C2×#67—61no—
364C2×#67—61no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—62no—
368C22×Dic3—64no—
369#239—38no—
370#239—64no—
371#237—38no—
372#237—38no—
373#237—38no—
374#237—68no—
375#237—64no—
376#237—68no—
377#237—68no—
378#237—68no—
379#237—64no—
380#237—64no—
381#237—68no—
382#237—616no—
383D3×D4—38no—
384D3×D4—38no—
385D3×D4—38no—
386D3×D4—38no—
387D3×D4—68no—
388D3×D4—68no—
389D3×D4—64no—
390D3×D4—64no—
391D3×D4—64no—
392D3×D4—64no—
393D3×D4—68no—
394D3×D4—68no—
395D3×D4—616no—
396D3×D4—68no—
397D3×D4—616no—
398#235—22no—
399#235—34no—
400#235—34no—
401#235—34no—
402#235—34no—
403#235—34no—
404#235—34no—
405#235—64no—
406#235—64no—
407#235—64no—
408#235—68no—
409#235—64no—
410#235—62no—
411#235—62no—
412#235C22×D314yescomplemented
413C2×D12—21no—
414C2×D12—22no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—68no—
422C2×D12—62no—
423C2×D12C22×D312yes—
424C2×D12C22×D311yescharacteristic
425C2×D12C22×D314yescomplemented
426C2×C4×D3—21no—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C2×Dic6C22×D311yescharacteristic
441C3×SD16—38no—
442C3×D8—38no—
443C3×D8—38no—
444C3×D8—38no—
445C3×M16—34no—
446C2×C3×C8—31no—
447C2×C3×C8—32no—
448C2×C3×C8—31no—
449C2×C3×C8—34no—
450#216—34no—
451#215—34no—
452#214—34no—
453#214—38no—
454#214C22×D318yescomplemented
455#213—34no—
456#213—38no—
457#213C22×D318yescomplemented
458#213C22×D318yescomplemented
459#213C22×D318yescomplemented
460#208C22×D314yescomplemented
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D312yes—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D314yescomplemented
465Dic12—34no—
466D24—34no—
467D24—38no—
468#204—34no—
469#204—38no—
470#204—34no—
471ΓL(1,𝔽25)—38no—
472ΓL(1,𝔽25)—38no—
473D3×C8—38no—
474D3×C8—38no—
475C22×C32—24no—
476C22×C32—22no—
477C22×C32—44no—
478C22×C32—84no—
479C22×C32C22×D412yes—
480C22×C32C22×D411yescharacteristic
481C2×C3⋊D3—22no—
482C2×C3⋊D3—24no—
483C2×C3⋊D3—42no—
484C2×C3⋊D3—88no—
485C2×C3⋊D3C22×D414yes—
486C2×C3×D3—24no—
487C2×C3×D3—22no—
488C2×C3×D3—42no—
489C2×C3×D3—44no—
490C2×C3×D3—84no—
491D32—88no—
492C32×C4C22×D411yescharacteristic
493C32×C4C22×D412yes—
494C32×C4C2511yescharacteristic
495C3⋊Dic3—22no—
496C3⋊Dic3C22×D414yes—
497C3×Dic3—22no—
498H(5,𝔽2)—98no—
499H(5,𝔽2)—98no—
500H(5,𝔽2)—184no—
501H(5,𝔽2)—184no—
502C2×#41—31no—
503C2×#41—91no—
504C2×#41—92no—
505C2×#41—92no—
506C2×#41—91no—
507C2×#41—181no—
508C2×#41—181no—
509C22×D4—31no—
510C22×D4—92no—
511C22×D4—92no—
512C22×D4—181no—
513C22×D4—181no—
514C22×D4—182no—
515C22×D4—182no—
516C22×D4D3211yescharacteristic, complemented
517AGL(1,ℤ/8)—38no—
518AGL(1,ℤ/8)—98no—
519AGL(1,ℤ/8)—916no—
520AGL(1,ℤ/8)—916no—
521#135—98no—
522#135—916no—
523C2×Q16—91no—
524C2×SD16—32no—
525C2×SD16—91no—
526C2×SD16—92no—
527C2×SD16—91no—
528C2×D8—32no—
529C2×D8—32no—
530C2×D8—32no—
531C2×D8—38no—
532C2×D8—91no—
533C2×D8—92no—
534C2×D8—916no—
535#131—98no—
536C2×M16—31no—
537C2×M16—92no—
538C22×C8—31no—
539C22×C8—92no—
540C23×C3—24no—
541C23×C3—28no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—24no—
545C23×C3—24no—
546C23×C3—21no—
547C23×C3—62no—
548C23×C3—61no—
549C23×C3—64no—
550C23×C3—82no—
551C23×C3—82no—
552C23×C3—84no—
553C23×C3—242no—
554C23×C3D3×D411yescharacteristic
555C23×C3D3×D411yescharacteristic
556C22×D3—21no—
557C22×D3—22no—
558C22×D3—24no—
559C22×D3—32no—
560C22×D3—32no—
561C22×D3—62no—
562C22×D3—68no—
563C22×D3—68no—
564C22×D3—68no—
565C22×D3—68no—
566C22×D3—62no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—616no—
570C22×D3—82no—
571C22×D3—244no—
572C22×D3—244no—
573C22×D3—244no—
574C22×D3—244no—
575C22×D3—248no—
576C3×Q8—32no—
577C3×Q8—61no—
578C3×D4—24no—
579C3×D4—28no—
580C3×D4—22no—
581C3×D4—22no—
582C3×D4—24no—
583C3×D4—24no—
584C3×D4—24no—
585C3×D4—32no—
586C3×D4—34no—
587C3×D4—64no—
588C3×D4—61no—
589C3×D4—62no—
590C3×D4—64no—
591C3×D4C23×D314yes—
592C3×D4C23×D314yes—
593C2×C3×C4—21no—
594C2×C3×C4—22no—
595C2×C3×C4—21no—
596C2×C3×C4—22no—
597C2×C3×C4—61no—
598C2×C3×C4—64no—
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4D3×D412yes—
602C2×C3×C4D3×D412yes—
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607#67—24no—
608#67—38no—
609#67—38no—
610#67—68no—
611#67—68no—
612#67—68no—
613#67—68no—
614#67—68no—
615#67—68no—
616#67—68no—
617#67—68no—
618#67—68no—
619#67—616no—
620#67—616no—
621#67—64no—
622#67—64no—
623C2×Dic3—21no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—62no—
627C2×Dic3—68no—
628C2×Dic3—68no—
629C2×Dic3—68no—
630C2×Dic3—62no—
631C2×Dic3—616no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634D12—24no—
635D12—22no—
636D12—21no—
637D12—34no—
638D12—34no—
639D12—32no—
640D12—32no—
641D12—64no—
642D12—62no—
643D12—62no—
644D12—68no—
645D12—61no—
646D12—61no—
647D12C23×D314yes—
648D12C23×D312yes—
649C4×D3—24no—
650C4×D3—34no—
651C4×D3—34no—
652C4×D3—34no—
653C4×D3—34no—
654C4×D3—64no—
655C4×D3—64no—
656C4×D3—68no—
657C4×D3—68no—
658C4×D3—64no—
659C4×D3—64no—
660Dic6—21no—
661Dic6—34no—
662Dic6—34no—
663Dic6—32no—
664Dic6—32no—
665Dic6—64no—
666Dic6—62no—
667Dic6—62no—
668Dic6—61no—
669Dic6—61no—
670Dic6C23×D312yes—
671C3×C8—32no—
672C3×C8—34no—
673C3×C8—32no—
674C3⋊C8C23×D312yes—
675C3⋊C8C23×D314yes—
676C3⋊C8C23×D312yes—
677C2×C32—22no—
678C2×C32—44no—
679C2×C32#57612yescomplemented
680C2×C32C23×D411yescharacteristic
681C3⋊D3—24no—
682C3⋊D3—42no—
683C3×D3—42no—
684C3×D3—44no—
685C24—21no—
686C24—61no—
687C24—182no—
688C24—182no—
689#41—34no—
690#41—62no—
691#41—94no—
692#41—94no—
693#41—98no—
694#41—98no—
695#41—94no—
696#41—188no—
697#41—184no—
698#41—184no—
699#41—188no—
700#41—182no—
701C2×Q8—31no—
702C2×Q8—91no—
703C2×Q8—91no—
704C2×D4—21no—
705C2×D4—22no—
706C2×D4—32no—
707C2×D4—31no—
708C2×D4—34no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—62no—
712C2×D4—98no—
713C2×D4—92no—
714C2×D4—98no—
715C2×D4—91no—
716C2×D4—91no—
717C2×D4—188no—
718C2×D4—182no—
719C2×D4—184no—
720C2×D4—184no—
721C2×D4—182no—
722C2×D4—182no—
723C2×D4—188no—
724C2×D4—1816no—
725C2×D4—1816no—
726C2×D4—182no—
727C2×D4—181no—
728C2×D4C2×D3212yes—
729C2×D4C2×D3214yescomplemented
730C22×C4—61no—
731C22×C4—92no—
732C22×C4—182no—
733C22×C4—182no—
734C22×C4—181no—
735C22×C4C2×D3211yescharacteristic
736Q16—94no—
737SD16—38no—
738SD16—94no—
739SD16—98no—
740SD16—94no—
741D8—38no—
742D8—38no—
743D8—38no—
744D8—94no—
745D8—98no—
746M16—34no—
747M16—98no—
748C2×C8—31no—
749C2×C8—31no—
750C2×C8—34no—
751C2×C8—32no—
752C2×C8—98no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—28no—
756C22×C3—24no—
757C22×C3—24no—
758C22×C3—22no—
759C22×C3—21no—
760C22×C3—42no—
761C22×C3—48no—
762C22×C3—44no—
763C22×C3—44no—
764C22×C3—64no—
765C22×C3—62no—
766C22×C3—84no—
767C22×C3—84no—
768C22×C3—88no—
769C22×C3—122no—
770C22×C3—124no—
771C22×C3—244no—
772C22×C3C2×D3×D412yes—
773C22×C3C2×D3×D412yes—
774C22×C3C2×D3×D411yescharacteristic
775C22×C3C2×D3×D411yescharacteristic
776C2×D3—22no—
777C2×D3—24no—
778C2×D3—34no—
779C2×D3—34no—
780C2×D3—44no—
781C2×D3—42no—
782C2×D3—64no—
783C2×D3—64no—
784C2×D3—64no—
785C2×D3—64no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—84no—
789C2×D3—124no—
790C2×D3—124no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—248no—
794C2×D3—248no—
795C2×D3—248no—
796C2×D3—248no—
797C2×D3—2416no—
798C3×C4—22no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—62no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D412yes—
804C3×C4C2×D3×D412yes—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4C24×D311yescharacteristic
807C3×C4C24×D311yescharacteristic
808Dic3—22no—
809Dic3—34no—
810Dic3—34no—
811Dic3—64no—
812Dic3—64no—
813Dic3—62no—
814Dic3—62no—
815C32C2×#57611yescharacteristic, complemented, Sylow
816C23—22no—
817C23—24no—
818C23—61no—
819C23—62no—
820C23—64no—
821C23—82no—
822C23—92no—
823C23—188no—
824C23—188no—
825C23—181no—
826C23—242no—
827C23—724no—
828C23—724no—
829C23#381111yescharacteristic
830Q8—32no—
831Q8—61no—
832Q8—94no—
833Q8—92no—
834Q8—181no—
835D4—22no—
836D4—24no—
837D4—34no—
838D4—32no—
839D4—64no—
840D4—64no—
841D4—62no—
842D4—61no—
843D4—98no—
844D4—94no—
845D4—92no—
846D4—188no—
847D4—188no—
848D4—188no—
849D4—188no—
850D4—184no—
851D4—181no—
852D4C22×D3214yes—
853C2×C4—61no—
854C2×C4—64no—
855C2×C4—92no—
856C2×C4—94no—
857C2×C4—94no—
858C2×C4—188no—
859C2×C4—188no—
860C2×C4—181no—
861C2×C4—184no—
862C2×C4#381112yes—
863C2×C4#381111yescharacteristic
864C2×C4C22×D3212yes—
865C2×C4C22×D3211yescharacteristic
866C8—32no—
867C8—32no—
868C8—34no—
869C2×C3—22no—
870C2×C3—22no—
871C2×C3—22no—
872C2×C3—21no—
873C2×C3—42no—
874C2×C3—48no—
875C2×C3—44no—
876C2×C3—44no—
877C2×C3—122no—
878C2×C3—124no—
879C2×C3#575712yescomplemented
880C2×C3#577412yescomplemented
881C2×C3C22×D3×D411yescharacteristic
882C2×C3C22×D3×D411yescharacteristic
883D3—44no—
884D3—42no—
885D3—64no—
886D3—64no—
887D3—124no—
888D3—124no—
889D3—122no—
890D3—122no—
891C22—22no—
892C22—24no—
893C22—44no—
894C22—62no—
895C22—64no—
896C22—84no—
897C22—94no—
898C22—124no—
899C22—122no—
900C22—184no—
901C22—182no—
902C22—244no—
903C22—362no—
904C22—728no—
905C22—728no—
906C22C2×#381112yes—
907C22C2×#381111yescharacteristic
908C4—62no—
909C4—94no—
910C4—182no—
911C4C2×#381112yes—
912C4C2×#381111yescharacteristic
913C4C23×D3211yescharacteristic
914C3—21no—
915C3C2×#575711yescharacteristic, complemented
916C3C2×#577411yescharacteristic, complemented
917C2—22no—
918C2—44no—
919C2—124no—
920C2—122no—
921C2—184no—
922C2—362no—
923C2#1059510212yesdirect product factor
924C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C2×#64307C2semidirect
3. C2×C3×#932C2semidirect
4. C22×C3×#213C2semidirect
5. C2×#63937C2semidirect
6. C2×#63936C2semidirect
7. #10595102C2direct (N × H)
8. C2×#63927C2semidirect
9. C2×#63926C2semidirect
10. C2×#63830C2semidirect
11. C2×#63829C2semidirect
12. C2×#63817C2semidirect
15. C22×C32×D4C22semidirect
18. #64361C22semidirect
20. C2×#3830C22semidirect
22. C2×D4×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
25. C2×C3×#235C22semidirect
26. C22×C3×D12C22semidirect
29. #64307C22semidirect
30. C2×#3802C22semidirect
32. C2×#3796C22semidirect
34. C2×C3×#214C22semidirect
35. C3×#932C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×#213C22semidirect
38. C2×C3×#213C22semidirect
39. C2×C3×#213C22semidirect
40. C2×C3×#208C22semidirect
41. C22×C3×C3⋊C8C22semidirect
42. #63937C22semidirect
43. #63936C22semidirect
44. #63927C22semidirect
45. #63926C22semidirect
46. C2×#3719C22semidirect
47. C2×#3717C22semidirect
48. #63830C22semidirect
49. #63829C22semidirect
50. C2×#3716C22semidirect
51. C2×#3716C22semidirect
52. C2×#3714C22semidirect
53. C2×#3714C22semidirect
54. C2×#3712C22semidirect
55. #63817C22semidirect
56. C2×#3710C22semidirect
66. C2×#932D3semidirect
67. C22×#213D3semidirect
89. C2×C32×D4C23semidirect
99. #3830C23semidirect
102. D4×C3⋊D3C23semidirect
106. #3828C23semidirect
115. C3×#235C23semidirect
120. C2×C3×D12C23semidirect
128. #3802C23semidirect
131. #3796C23semidirect
133. C3×#214C23semidirect
134. C3×#213C23semidirect
135. C3×#213C23semidirect
136. C3×#213C23semidirect
137. C3×#208C23semidirect
141. C2×C3×C3⋊C8C23semidirect
142. #3719C23semidirect
143. #3717C23semidirect
144. #3716C23semidirect
145. #3716C23semidirect
146. #3714C23semidirect
147. #3714C23semidirect
148. #3712C23semidirect
149. #3710C23semidirect
154. C22×C3×D4C2×D3semidirect
155. C22×C3×D4C2×D3semidirect
196. C2×#235C2×D3semidirect
198. C22×D12C2×D3semidirect
212. C2×#214C2×D3semidirect
214. #932C2×D3semidirect
217. C2×#213C2×D3semidirect
218. C2×#213C2×D3semidirect
219. C2×#213C2×D3semidirect
220. C2×#213C2×D3semidirect
221. C2×#208C2×D3semidirect
222. C22×C3⋊C8C2×D3semidirect
339. C2×C3×D4C22×D3semidirect
340. C2×C3×D4C22×D3semidirect
412. #235C22×D3semidirect
425. C2×D12C22×D3semidirect
454. #214C22×D3semidirect
457. #213C22×D3semidirect
458. #213C22×D3semidirect
459. #213C22×D3semidirect
460. #208C22×D3semidirect
464. C2×C3⋊C8C22×D3semidirect
516. C22×D4D32semidirect
679. C2×C32#576semidirect
729. C2×D4C2×D32semidirect
815. C32C2×#576semidirect
879. C2×C3#5757semidirect
880. C2×C3#5774semidirect
915. C3C2×#5757semidirect
916. C3C2×#5774semidirect
923. C2#10595102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#643072
C2×C3×#9322
C22×C3×#2132
C2×#639372
C2×#639362
#105951022
C2×#639272
C2×#639262
C2×#638302
C2×#638292
C2×#638172
C2×#57743
C2×#57573