Finite Group Databasebeta

← C2×#10594734 #11918807

Subgroups — C2×#10594734 #11918807

Order 1152.

3193 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C212yesmaximal, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#912C211yesmaximal, characteristic, complemented
4C2×C3×D3×D8C211yesmaximal, characteristic, complemented
5C2×#63937C212yesmaximal, complemented
6C2×#63934C212yesmaximal, complemented
7C2×#63925C212yesmaximal, complemented
8#10594734C2116yesmaximal, direct product factor
9C2×#63810C211yesmaximal, characteristic, complemented
10C2×#63808C211yesmaximal, characteristic, complemented
11C2×#63803C211yesmaximal, characteristic, complemented
12C2×D3×D24C211yesmaximal, characteristic, complemented
13C2×#5769—31nomaximal
14C2×#5757—31nomaximal
15C2×D4×C3⋊D3C2212yescomplemented
16C2×C3×#237C2212yescomplemented
17C2×C3×D3×D4C2212yescomplemented
18C2×#3811—22no—
19C2×D3×#67—22no—
20C22×#626—22no—
21C2×#3804—22no—
22#64314—28no—
23#64314C22116yescomplemented
24C2×D3×D12C2212yescomplemented
25C2×#3799C2212yescomplemented
26C2×#3798C2211yescharacteristic
27C2×#3796C2212yescomplemented
28C2×C32×D8C2211yescharacteristic, complemented
29C2×#3753C2212yescomplemented
30D8×C3⋊D3C2218yescomplemented
31C2×#3745C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#214C2212yescomplemented
34C2×C3×#213C2212yescomplemented
35C3×#912C2218yescomplemented
36C3×D3×D8C2218yescomplemented
37C2×C3×Dic12C2211yescharacteristic, complemented
38C2×C3×D24C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic, complemented
40C2×C3×D3×C8C2211yescharacteristic, complemented
41#63937C22116yescomplemented
42#63934C22116yescomplemented
43#63925C22116yescomplemented
44C2×#3717C2212yescomplemented
45C2×#3715C2212yescomplemented
46C2×#3714C2212yescomplemented
47C2×#3712C2211yescharacteristic, complemented
48C2×#3711C2211yescharacteristic, complemented
49C2×#3711C2211yescharacteristic, complemented
50#63810C2218yescomplemented
51#63808C2218yescomplemented
52#63803C2218yescomplemented
53D3×D24C2218yescomplemented
54C2×#1009—32no—
55C2×#1004—32no—
56C2×C3×#135—31no—
57C22×C3×D8—31no—
58C2×#949—32no—
59C2×#932—32no—
60#5769—316no—
61C2×#919—31no—
62C2×#919—31no—
63C2×#914—32no—
64C2×#914—32no—
65#5757—316no—
66C2×#912—31no—
67C2×#912D311yescharacteristic, complemented
68C2×#911—32no—
69C2×#911—32no—
70C2×D3×D8—31no—
71C2×D3×D8—31no—
72C2×D3×D8—31no—
73C2×D3×D8—61no—
74C2×D3×D8D311yescharacteristic, complemented
75C2×#904—31no—
76C22×D24—31no—
77C2×#901—31no—
78C2×#901—31no—
79C23×C3⋊D3—22no—
80C23×C3×D3—22no—
81C22×D32—22no—
82C2×C32×D4C2312yes—
83C2×#638—22no—
84D4×C3⋊D3—24no—
85D4×C3⋊D3C2318yescomplemented
86C2×C4⋊(C3⋊D3)C2312yes—
87C2×C4×C3⋊D3C2311yescharacteristic
88C2×C3×#67—22no—
89C2×C3×#67—22no—
90C22×C3×Dic3—22no—
91C3×#237—24no—
92C3×#237C2318yescomplemented
93C3×D3×D4—24no—
94C3×D3×D4C2318yescomplemented
95C2×C3×D12C2312yes—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2312yes—
99#3811—216no—
100D3×#67—216no—
101C2×#627D411yescharacteristic
102C2×#626—22no—
103C2×#626—22no—
104C2×#626—22no—
105C2×#626—216no—
106C2×#626D411yescharacteristic
107C2×#626D411yescharacteristic
108C2×#625D411yescharacteristic
109C2×#624—22no—
110#3804—216no—
111C2×D3×Dic3—22no—
112D3×D12—24no—
113D3×D12C2318yescomplemented
114#3799—24no—
115#3799C2318yescomplemented
116#3798D414yes—
117#3798C2314yes—
118#3796—24no—
119#3796C2318yescomplemented
120C32×D8C2314yescomplemented
121C2×C32×C8C2311yescharacteristic
122#3753C2318yescomplemented
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3745C2314yescomplemented
125C8×C3⋊D3C2314yescomplemented
126C3×#214C2318yescomplemented
127C3×#213C2318yescomplemented
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×Dic12C2314yescomplemented
131C3×D24C2314yescomplemented
132C3×D3×C8C2314yescomplemented
133C3×D3×C8C2314yescomplemented
134#3717C2318yescomplemented
135#3715C2318yescomplemented
136#3714C2318yescomplemented
137#3712C2314yescomplemented
138#3711C2314yescomplemented
139#3711C2314yescomplemented
140C2×#576—91noSylow
141C2×C3×#41—32no—
142C22×C3×D4—32no—
143C22×#67—62no—
144C22×#67—62no—
145#1009—316no—
146#1009—68no—
147C2×#239—32no—
148C2×#239—32no—
149#1004—316no—
150#1004—68no—
151C2×#237—32no—
152C2×#237—62no—
153C2×#237C2×D312yescomplemented
154C2×D3×D4—32no—
155C2×D3×D4—32no—
156C2×D3×D4—32no—
157C2×D3×D4—62no—
158C2×D3×D4—62no—
159C2×D3×D4—62no—
160C2×D3×D4—62no—
161C2×D3×D4C2×D312yescomplemented
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—32no—
165C2×#235—62no—
166C22×D12—32no—
167C22×D12—62no—
168C3×#135—38no—
169C2×C3×Q16—31no—
170C2×C3×SD16—32no—
171C2×C3×D8—21no—
172C2×C3×D8—32no—
173C2×C3×D8—38no—
174C2×C3×D8—31no—
175C2×C3×D8C2×D311yescharacteristic, complemented
176C2×C3×D8C2×D311yescharacteristic, complemented
177C22×C3×C8—31no—
178C22×C3×C8—31no—
179#949—316no—
180C2×#215—32no—
181C2×#215—32no—
182C2×#214—32no—
183C2×#214C2×D312yescomplemented
184#932—316no—
185C2×#213—32no—
186C2×#213—32no—
187C2×#213—32no—
188C2×#213—62no—
189C2×#213C2×D312yescomplemented
190C2×#208—31no—
191C2×#208—31no—
192#919—38no—
193#919—38no—
194#914—316no—
195#914—316no—
196#912—38no—
197#912C2×D318yescomplemented
198#911—316no—
199#911—316no—
200D3×D8—38no—
201D3×D8—38no—
202D3×D8—38no—
203D3×D8—68no—
204D3×D8C2×D318yescomplemented
205C2×Dic12C2×D311yescharacteristic, complemented
206#904—38no—
207C2×D24—32no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—38no—
211C2×D24—61no—
212C2×D24C2×D311yescharacteristic, complemented
213C2×#204—32no—
214#901—38no—
215#901—38no—
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—31no—
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—31no—
220C2×D3×C8—31no—
221C2×D3×C8—31no—
222C2×D3×C8—61no—
223C2×D3×C8C2×D311yescharacteristic, complemented
224C2×D3×C8C2×D311yescharacteristic, complemented
225C23×C32—22no—
226C22×C3⋊D3—22no—
227C22×C3⋊D3—28no—
228C22×C3⋊D3—84no—
229C22×C3⋊D3C2×D411yescharacteristic
230C22×C3×D3—22no—
231C22×C3×D3—28no—
232C22×C3×D3—84no—
233C22×C3×D3C2×D411yescharacteristic
234C22×C3×D3C2×D411yescharacteristic
235C2×D32—28no—
236C2×D32—84no—
237C32×D4—22no—
238C32×D4C2414yes—
239C2×C32×C4C2411yescharacteristic
240#638—28no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—22no—
243C4⋊(C3⋊D3)C2414yes—
244C4×C3⋊D3C2×D412yes—
245C4×C3⋊D3C2412yes—
246C3×#67—28no—
247C3×#67—28no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—28no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—22no—
253C3×D12C2414yes—
254C3×C4×D3C2×D412yes—
255C3×C4×D3C2×D412yes—
256C3×C4×D3C2412yes—
257C3×C4×D3C2412yes—
258C3×Dic6—22no—
259C3×Dic6C2414yes—
260#627C2×D414yes—
261#626—28no—
262#626—28no—
263#626—28no—
264#626C2×D414yes—
265#626C2×D414yes—
266#625C2×D414yes—
267#624—28no—
268D3×Dic3—28no—
269C32×C8C2412yes—
270C3⋊(C3⋊C8)C2412yes—
271C3×C3⋊C8C2412yes—
272C3×C3⋊C8C2412yes—
273C2×H(5,𝔽2)—92no—
274#576—916no—
275C2×AGL(1,ℤ/8)—92no—
276C2×AGL(1,ℤ/8)—92no—
277C2×AGL(1,ℤ/8)—92no—
278C2×#135—31no—
279C2×#135—91no—
280C2×#135—91no—
281C22×D8—31no—
282C22×D8—91no—
283C22×D8—91no—
284C2×#131—91no—
285C24×C3—62no—
286C23×D3—22no—
287C23×D3—62no—
288C23×D3—62no—
289C23×D3—62no—
290C23×D3—62no—
291C23×D3—122no—
292C3×#41—38no—
293C3×#41—64no—
294C2×C3×Q8—32no—
295C2×C3×D4—22no—
296C2×C3×D4—38no—
297C2×C3×D4—32no—
298C2×C3×D4—64no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4C22×D312yes—
302C2×C3×D4C22×D312yes—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—62no—
306C2×#67—22no—
307C2×#67—22no—
308C2×#67—31no—
309C2×#67—31no—
310C2×#67—31no—
311C2×#67—31no—
312C2×#67—616no—
313C2×#67—62no—
314C2×#67—62no—
315C2×#67—62no—
316C2×#67—62no—
317C2×#67—616no—
318C2×#67—62no—
319C2×#67—122no—
320C22×Dic3—22no—
321C22×Dic3—62no—
322#239—38no—
323#239—38no—
324#239—64no—
325#239—64no—
326#237—24no—
327#237—38no—
328#237—64no—
329#237—616no—
330#237C22×D318yescomplemented
331D3×D4—24no—
332D3×D4—38no—
333D3×D4—38no—
334D3×D4—38no—
335D3×D4—68no—
336D3×D4—64no—
337D3×D4—64no—
338D3×D4—616no—
339D3×D4—616no—
340D3×D4—616no—
341D3×D4—64no—
342D3×D4—124no—
343D3×D4C22×D318yescomplemented
344#235—34no—
345#235—34no—
346#235—34no—
347#235—34no—
348#235—38no—
349#235—64no—
350#235—616no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—32no—
354C2×D12—32no—
355C2×D12—38no—
356C2×D12—62no—
357C2×D12—64no—
358C2×D12—616no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12C22×D312yes—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—61no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3C22×D311yescharacteristic
370C2×C4×D3C22×D311yescharacteristic
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6C22×D312yes—
374C3×Q16—34no—
375C3×SD16—38no—
376C3×D8—24no—
377C3×D8—38no—
378C3×D8—34no—
379C3×D8C22×D314yescomplemented
380C3×D8C22×D314yescomplemented
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—34no—
385C2×C3×C8—34no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388#215—38no—
389#215—38no—
390#214—38no—
391#214C22×D318yescomplemented
392#213—38no—
393#213—38no—
394#213—38no—
395#213—68no—
396#213C22×D318yescomplemented
397#208—34no—
398#208—34no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12C22×D314yescomplemented
405D24—38no—
406D24—34no—
407D24—34no—
408D24—64no—
409D24C22×D314yescomplemented
410#204—38no—
411ΓL(1,𝔽25)—34no—
412ΓL(1,𝔽25)—34no—
413ΓL(1,𝔽25)—34no—
414ΓL(1,𝔽25)—34no—
415D3×C8—34no—
416D3×C8—34no—
417D3×C8—64no—
418D3×C8C22×D314yescomplemented
419D3×C8C22×D314yescomplemented
420C22×C32—24no—
421C22×C32—44no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—24no—
425C2×C3⋊D3—44no—
426C2×C3⋊D3—88no—
427C2×C3⋊D3C22×D412yes—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—24no—
431C2×C3×D3—44no—
432C2×C3×D3—88no—
433C2×C3×D3C22×D412yes—
434C2×C3×D3C22×D412yes—
435D32—88no—
436C32×C4C22×D411yescharacteristic
437C32×C4C2511yescharacteristic
438C3⋊Dic3C22×D412yes—
439C3×Dic3—24no—
440C3×Dic3C22×D412yes—
441C3×Dic3C22×D412yes—
442H(5,𝔽2)—916no—
443H(5,𝔽2)—188no—
444C2×#41—32no—
445C2×#41—91no—
446C2×#41—92no—
447C2×#41—92no—
448C2×#41—182no—
449C22×D4—32no—
450C22×D4—92no—
451C22×D4—92no—
452C22×D4—182no—
453C22×D4—182no—
454C22×D4—182no—
455AGL(1,ℤ/8)—916no—
456AGL(1,ℤ/8)—916no—
457AGL(1,ℤ/8)—916no—
458#135—38no—
459#135—98no—
460#135—98no—
461C2×Q16—31no—
462C2×SD16—32no—
463C2×SD16—92no—
464C2×SD16—92no—
465C2×D8—32no—
466C2×D8—38no—
467C2×D8—31no—
468C2×D8—98no—
469C2×D8—92no—
470C2×D8—92no—
471C2×D8—98no—
472C2×D8—91no—
473C2×D8D3211yescharacteristic, complemented
474#131—98no—
475C2×M16—91no—
476C2×M16—91no—
477C2×M16—91no—
478C22×C8—31no—
479C22×C8—31no—
480C22×C8—91no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—42no—
486C23×C3—68no—
487C23×C3—62no—
488C23×C3—244no—
489C22×D3—22no—
490C22×D3—28no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—61no—
494C22×D3—68no—
495C22×D3—68no—
496C22×D3—68no—
497C22×D3—62no—
498C22×D3—62no—
499C22×D3—68no—
500C22×D3—84no—
501C22×D3—128no—
502C22×D3—122no—
503C22×D3—244no—
504C22×D3—244no—
505C22×D3—244no—
506C22×D3—244no—
507C22×D3—248no—
508C22×D3D3×D411yescharacteristic
509C22×D3D3×D411yescharacteristic
510C3×Q8—34no—
511C3×Q8—62no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—24no—
515C3×D4—34no—
516C3×D4—42no—
517C3×D4—68no—
518C3×D4—68no—
519C3×D4—62no—
520C3×D4C23×D314yes—
521C3×D4C23×D314yes—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—68no—
530C2×C3×C4—62no—
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—28no—
534#67—28no—
535#67—34no—
536#67—34no—
537#67—34no—
538#67—34no—
539#67—68no—
540#67—68no—
541#67—68no—
542#67—68no—
543#67—68no—
544#67—128no—
545C2×Dic3—22no—
546C2×Dic3—28no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—61no—
550C2×Dic3—68no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—22no—
554D12—34no—
555D12—34no—
556D12—34no—
557D12—34no—
558D12—64no—
559D12—68no—
560D12—68no—
561D12—68no—
562D12—62no—
563D12—62no—
564D12—122no—
565D12C23×D314yes—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—32no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—68no—
573C4×D3—68no—
574C4×D3—68no—
575C4×D3D3×D412yes—
576C4×D3D3×D412yes—
577C4×D3C23×D312yes—
578C4×D3C23×D312yes—
579Dic6—22no—
580Dic6—34no—
581Dic6—34no—
582Dic6C23×D314yes—
583C3×C8—22no—
584C3×C8—32no—
585C3×C8—32no—
586C3×C8C23×D312yes—
587C3×C8C23×D312yes—
588C3⋊C8—32no—
589C3⋊C8—32no—
590C3⋊C8—62no—
591C3⋊C8C23×D312yes—
592C3⋊C8C23×D312yes—
593C2×C32—44no—
594C2×C32#57612yescomplemented
595C2×C32C23×D411yescharacteristic
596C3⋊D3—22no—
597C3⋊D3—44no—
598C3×D3—22no—
599C3×D3—22no—
600C3×D3—44no—
601C24—62no—
602C24—182no—
603C24—182no—
604#41—38no—
605#41—64no—
606#41—94no—
607#41—94no—
608#41—98no—
609#41—98no—
610#41—184no—
611#41—1816no—
612#41—184no—
613C2×Q8—32no—
614C2×Q8—91no—
615C2×D4—38no—
616C2×D4—32no—
617C2×D4—64no—
618C2×D4—62no—
619C2×D4—62no—
620C2×D4—98no—
621C2×D4—91no—
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—98no—
625C2×D4—92no—
626C2×D4—184no—
627C2×D4—182no—
628C2×D4—1816no—
629C2×D4—182no—
630C2×D4—182no—
631C2×D4—184no—
632C2×D4—182no—
633C2×D4—1816no—
634C2×D4—1816no—
635C2×D4C2×D3212yes—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—62no—
639C22×C4—91no—
640C22×C4—182no—
641C22×C4—182no—
642Q16—34no—
643SD16—38no—
644SD16—98no—
645SD16—98no—
646D8—38no—
647D8—34no—
648D8—98no—
649D8—98no—
650D8—94no—
651D8C2×D3214yescomplemented
652M16—94no—
653M16—94no—
654M16—94no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—34no—
658C2×C8—34no—
659C2×C8—91no—
660C2×C8—94no—
661C2×C8C2×D3211yescharacteristic
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—21no—
665C22×C3—32no—
666C22×C3—32no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—64no—
673C22×C3—84no—
674C22×C3—124no—
675C22×C3—248no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—24no—
681C2×D3—32no—
682C2×D3—32no—
683C2×D3—44no—
684C2×D3—62no—
685C2×D3—64no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—64no—
689C2×D3—64no—
690C2×D3—88no—
691C2×D3—124no—
692C2×D3—124no—
693C2×D3—124no—
694C2×D3—244no—
695C2×D3—248no—
696C2×D3—248no—
697C2×D3—248no—
698C2×D3—248no—
699C2×D3—2416no—
700C2×D3C2×D3×D412yes—
701C2×D3C2×D3×D412yes—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—32no—
705C3×C4—32no—
706C3×C4—64no—
707C3×C4C2×D3×D411yescharacteristic
708C3×C4C2×D3×D411yescharacteristic
709C3×C4C24×D311yescharacteristic
710C3×C4C24×D311yescharacteristic
711Dic3—24no—
712Dic3—32no—
713Dic3—32no—
714Dic3—62no—
715Dic3C2×D3×D412yes—
716Dic3C2×D3×D412yes—
717C32C2×#57611yescharacteristic, complemented, Sylow
718C23—22no—
719C23—31no—
720C23—31no—
721C23—68no—
722C23—62no—
723C23—91no—
724C23—188no—
725C23—188no—
726C23—182no—
727C23—244no—
728C23—724no—
729C23—724no—
730Q8—34no—
731Q8—62no—
732Q8—94no—
733D4—22no—
734D4—34no—
735D4—68no—
736D4—68no—
737D4—62no—
738D4—94no—
739D4—94no—
740D4—94no—
741D4—94no—
742D4—188no—
743D4—188no—
744D4—188no—
745D4—188no—
746D4—182no—
747D4C22×D3214yes—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—32no—
751C2×C4—32no—
752C2×C4—32no—
753C2×C4—32no—
754C2×C4—68no—
755C2×C4—62no—
756C2×C4—91no—
757C2×C4—92no—
758C2×C4—92no—
759C2×C4—188no—
760C2×C4—188no—
761C2×C4C22×D3211yescharacteristic
762C8—32no—
763C8—32no—
764C8—92no—
765C8C22×D3212yes—
766C2×C3—21no—
767C2×C3—22no—
768C2×C3—44no—
769C2×C3—44no—
770C2×C3—62no—
771C2×C3—62no—
772C2×C3—84no—
773C2×C3—124no—
774C2×C3#575712yescomplemented
775C2×C3#576912yescomplemented
776C2×C3C22×D3×D411yescharacteristic
777C2×C3C22×D3×D411yescharacteristic
778D3—22no—
779D3—22no—
780D3—44no—
781D3—64no—
782D3—62no—
783D3—62no—
784D3—124no—
785D3—124no—
786D3—244no—
787C22—24no—
788C22—32no—
789C22—32no—
790C22—44no—
791C22—62no—
792C22—62no—
793C22—64no—
794C22—92no—
795C22—124no—
796C22—182no—
797C22—184no—
798C22—248no—
799C22—364no—
800C22—728no—
801C22—728no—
802C22D32×D411yescharacteristic
803C4—32no—
804C4—32no—
805C4—64no—
806C4—92no—
807C4D32×D411yescharacteristic
808C4C23×D3211yescharacteristic
809C3—21no—
810C3C2×#575711yescharacteristic, complemented
811C3C2×#576911yescharacteristic, complemented
812C2—44no—
813C2—62no—
814C2—62no—
815C2—124no—
816C2—182no—
817C2—364no—
818C2#1059473412yesdirect product factor
819C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. C2×C3×#912C2semidirect
4. C2×C3×D3×D8C2semidirect
5. C2×#63937C2semidirect
6. C2×#63934C2semidirect
7. C2×#63925C2semidirect
8. #10594734C2direct (N × H)
9. C2×#63810C2semidirect
10. C2×#63808C2semidirect
11. C2×#63803C2semidirect
12. C2×D3×D24C2semidirect
15. C2×D4×C3⋊D3C22semidirect
16. C2×C3×#237C22semidirect
17. C2×C3×D3×D4C22semidirect
23. #64314C22semidirect
24. C2×D3×D12C22semidirect
25. C2×#3799C22semidirect
27. C2×#3796C22semidirect
28. C2×C32×D8C22semidirect
29. C2×#3753C22semidirect
30. D8×C3⋊D3C22semidirect
31. C2×#3745C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. C2×C3×#214C22semidirect
34. C2×C3×#213C22semidirect
35. C3×#912C22semidirect
36. C3×D3×D8C22semidirect
37. C2×C3×Dic12C22semidirect
38. C2×C3×D24C22semidirect
39. C2×C3×D3×C8C22semidirect
40. C2×C3×D3×C8C22semidirect
41. #63937C22semidirect
42. #63934C22semidirect
43. #63925C22semidirect
44. C2×#3717C22semidirect
45. C2×#3715C22semidirect
46. C2×#3714C22semidirect
47. C2×#3712C22semidirect
48. C2×#3711C22semidirect
49. C2×#3711C22semidirect
50. #63810C22semidirect
51. #63808C22semidirect
52. #63803C22semidirect
53. D3×D24C22semidirect
67. C2×#912D3semidirect
74. C2×D3×D8D3semidirect
85. D4×C3⋊D3C23semidirect
92. C3×#237C23semidirect
94. C3×D3×D4C23semidirect
113. D3×D12C23semidirect
115. #3799C23semidirect
119. #3796C23semidirect
120. C32×D8C23semidirect
122. #3753C23semidirect
124. #3745C23semidirect
125. C8×C3⋊D3C23semidirect
126. C3×#214C23semidirect
127. C3×#213C23semidirect
130. C3×Dic12C23semidirect
131. C3×D24C23semidirect
132. C3×D3×C8C23semidirect
133. C3×D3×C8C23semidirect
134. #3717C23semidirect
135. #3715C23semidirect
136. #3714C23semidirect
137. #3712C23semidirect
138. #3711C23semidirect
139. #3711C23semidirect
153. C2×#237C2×D3semidirect
161. C2×D3×D4C2×D3semidirect
175. C2×C3×D8C2×D3semidirect
176. C2×C3×D8C2×D3semidirect
183. C2×#214C2×D3semidirect
189. C2×#213C2×D3semidirect
197. #912C2×D3semidirect
204. D3×D8C2×D3semidirect
205. C2×Dic12C2×D3semidirect
212. C2×D24C2×D3semidirect
223. C2×D3×C8C2×D3semidirect
224. C2×D3×C8C2×D3semidirect
330. #237C22×D3semidirect
343. D3×D4C22×D3semidirect
379. C3×D8C22×D3semidirect
380. C3×D8C22×D3semidirect
391. #214C22×D3semidirect
396. #213C22×D3semidirect
404. Dic12C22×D3semidirect
409. D24C22×D3semidirect
418. D3×C8C22×D3semidirect
419. D3×C8C22×D3semidirect
473. C2×D8D32semidirect
594. C2×C32#576semidirect
651. D8C2×D32semidirect
717. C32C2×#576semidirect
774. C2×C3#5757semidirect
775. C2×C3#5769semidirect
810. C3C2×#5757semidirect
811. C3C2×#5769semidirect
818. C2#10594734direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643142
C2×D8×C3⋊D32
C2×C3×#9122
C2×C3×D3×D82
C2×#639372
C2×#639342
C2×#639252
#105947342
C2×#638102
C2×#638082
C2×#638032
C2×D3×D242
C2×#57693
C2×#57573