Finite Group Databasebeta

← #11905969

Subgroups — #11905969

Order 1152.

3945 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C3×#5832C211yesmaximal, characteristic, complemented
4C3×#5830C211yesmaximal, characteristic, complemented
5#10595433C212yesmaximal, complemented
6#10595363C212yesmaximal, complemented
7#10595300C212yesmaximal, complemented
8#10595292C218yesmaximal, complemented
9#10595168C212yesmaximal, complemented
10#10595074C214yesmaximal, complemented
11#10595045C211yesmaximal, characteristic, complemented
12C2×#63911C211yesmaximal, characteristic, complemented
13#10594954C211yesmaximal, characteristic, complemented
14#10594919C214yesmaximal, complemented
15#86316—31nomaximal
16#86242—31nomaximal
17C2×C32×#41C2211yescharacteristic, complemented
18#64366—28no—
19C2×#3832C2212yescomplemented
20C2×D4×C3⋊D3C2212yescomplemented
21C2×D4×C3⋊D3C2214yescomplemented
22C2×#3828C2211yescharacteristic
23C2×#3828C2212yescomplemented
24C22×C4⋊(C3⋊D3)C2212yescomplemented
25C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×#235C2211yescharacteristic, complemented
27C22×C3×D12C2211yescharacteristic, complemented
28C2×#3811C2218yescomplemented
29C2×D3×#67C2214yescomplemented
30C22×#626C2214yescomplemented
31#64307—28no—
32C2×#3802C2212yescomplemented
33C2×D3×D12C2212yescomplemented
34C2×#3796C2212yescomplemented
35C2×#3795C2212yescomplemented
36C3×#947C2212yescomplemented
37C3×#947C2211yescharacteristic, complemented
38C3×#944C2211yescharacteristic, complemented
39C3×#940C2212yescomplemented
40C3×#940C2211yescharacteristic, complemented
41C3×#939C2214yescomplemented
42C3×#937C2214yescomplemented
43C3×#936C2211yescharacteristic, complemented
44C3×#930C2214yescomplemented
45C3×C4×#67C2214yescomplemented
46C3×#926C2211yescharacteristic, complemented
47C2×C3×C4×Dic3C2211yescharacteristic, complemented
48#63981C2218yescomplemented
49#63981C2214yescomplemented
50#63979C2218yescomplemented
51#63971C2218yescomplemented
52#63952C2214yescomplemented
53#63923C2218yescomplemented
54#63912C2218yescomplemented
55#63911C2214yescomplemented
56#63911C2212yescomplemented
57#63911C2212yescomplemented
58#63911C2212yescomplemented
59#63910C2218yescomplemented
60#63909C2214yescomplemented
61#63894C2212yescomplemented
62C4×#624C2212yescomplemented
63#63881C2218yescomplemented
64#63874C2212yescomplemented
65#63864C2212yescomplemented
66#63844C2212yescomplemented
67C2×#1009—31no—
68C2×#1009—31no—
69C2×#1009—31no—
70C2×#1009—61no—
71C2×#1004—31no—
72C3×#535—31no—
73C3×#532—31no—
74#5832D311yescharacteristic, complemented
75#5830—31no—
76#5830D311yescharacteristic, complemented
77C2×#940—31no—
78#5725—32no—
79#5715—32no—
80D3×#127—32no—
81D3×#127—32no—
82#5674—32no—
83#5674—32no—
84#5674—32no—
85#5668—32no—
86#5609—38no—
87#5609—34no—
88#5599—34no—
89#5590—38no—
90#5553—34no—
91D4×D12—34no—
92#5525—31no—
93#5522—31no—
94C2×#874—31no—
95C4×#235—31no—
96C23×C3⋊D3C2312yes—
97C23×C3⋊D3C2314yes—
98C23×C3×D3C2312yes—
99C22×D32C2314yes—
100C32×#41—24no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C2×C32×D4C2312yes—
104C22×C32×C4C2312yes—
105C22×C32×C4C2311yescharacteristic
106C2×#638C2314yes—
107C2×#638C2312yes—
108#3832—28no—
109D4×C3⋊D3—216no—
110D4×C3⋊D3—28no—
111#3828—28no—
112#3828D418yescomplemented
113C2×C4⋊(C3⋊D3)—24no—
114C2×C4⋊(C3⋊D3)—28no—
115C2×C4⋊(C3⋊D3)C2312yes—
116C2×C4⋊(C3⋊D3)C2312yes—
117C2×C4⋊(C3⋊D3)C2314yes—
118C2×C4⋊(C3⋊D3)C2311yescharacteristic
119C2×C4×C3⋊D3C2314yes—
120C2×C4×C3⋊D3C2312yes—
121C2×#634C2311yescharacteristic
122C2×C3×#67C2314yes—
123C2×C3×#67C2312yes—
124C2×C3×#67C2318yes—
125C22×C3×Dic3C2312yes—
126C3×#235—24no—
127C2×C3×D12—24no—
128C2×C3×D12C2312yes—
129C2×C3×D12C2312yes—
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133#3811—416no—
134D3×#67—216no—
135C2×#626—48no—
136C2×#626C2314yes—
137C2×#626C2318yes—
138C2×#626C2318yes—
139C2×#626C2318yes—
140C2×#625C2314yes—
141C2×#624C2314yes—
142C2×D3×Dic3C2314yes—
143#3802—28no—
144D3×D12—28no—
145#3796—28no—
146#3795—28no—
147C3×#217C2312yes—
148C3×#217C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2318yes—
151C3×C4⋊Dic3C2312yes—
152C3×Dic3⋊C4C2314yes—
153C3×C4×Dic3C2312yes—
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2311yescharacteristic
156C3×C4×Dic3C2312yes—
157#3724C2314yes—
158#3722C2318yes—
159#3722C2314yes—
160Dic32C2314yes—
161#3498—91noSylow
162C2×C3×#41—21no—
163C2×C3×#41—31no—
164C2×C3×#41C2×D311yescharacteristic, complemented
165C2×C3×#41C2×D311yescharacteristic, complemented
166C22×C3×D4—31no—
167C22×#67—34no—
168C22×#67—34no—
169#1009—68no—
170#1009—68no—
171#1009—68no—
172#1009—616no—
173C2×#239—32no—
174C2×#239—32no—
175C2×#239—32no—
176C2×#239—62no—
177#1004—68no—
178C2×#237—32no—
179C2×#237—32no—
180C2×D3×D4—34no—
181C2×D3×D4—32no—
182C2×D3×D4—32no—
183C2×D3×D4—34no—
184C2×D3×D4—34no—
185C2×D3×D4—38no—
186C2×D3×D4—38no—
187C2×D3×D4—32no—
188C2×D3×D4—32no—
189C2×D3×D4—32no—
190C2×D3×D4—62no—
191C2×D3×D4—64no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—32no—
195C2×#235—32no—
196C2×#235—32no—
197C2×#235—61no—
198C2×#235—62no—
199C2×#235C2×D311yescharacteristic, complemented
200C22×D12—31no—
201C22×D12—31no—
202C22×D12—32no—
203C22×D12—32no—
204C22×D12—34no—
205C22×D12—32no—
206C22×D12—61no—
207C22×D12—62no—
208C22×D12C2×D311yescharacteristic, complemented
209C3×C4⋊Q8—31no—
210C3×#127—31no—
211C3×#127—32no—
212C3×#124—32no—
213C3×#124—31no—
214C3×#124—31no—
215C3×#121—34no—
216C3×#121—34no—
217C3×#120—34no—
218C3×C4×D4—34no—
219C3×#117—31no—
220C2×C3×C42—31no—
221#947—32no—
222#947C2×D311yescharacteristic, complemented
223#947C2×D312yescomplemented
224#944C2×D311yescharacteristic, complemented
225#940—38no—
226#940—38no—
227#940—32no—
228#940—32no—
229#940—32no—
230#940—34no—
231#940C2×D312yescomplemented
232#940C2×D311yescharacteristic, complemented
233#939—38no—
234#939C2×D314yescomplemented
235#937—38no—
236#937—34no—
237#937C2×D314yescomplemented
238#936C2×D311yescharacteristic, complemented
239#930—34no—
240#930C2×D314yescomplemented
241C4×#67—34no—
242C4×#67C2×D314yescomplemented
243#926C2×D311yescharacteristic, complemented
244C2×C4×Dic3C2×D311yescharacteristic, complemented
245#895—34no—
246#895—38no—
247#893—38no—
248#893—32no—
249#887—32no—
250#884—38no—
251#884—38no—
252#884—38no—
253#884—38no—
254#882—38no—
255#882—34no—
256#882—38no—
257#882—38no—
258#67⋊C4—34no—
259#67⋊C4—38no—
260#875—32no—
261#874—32no—
262#874—32no—
263#874—32no—
264#874—34no—
265C4×D12—32no—
266#872—32no—
267#872—32no—
268C42×D3—32no—
269C42×D3—32no—
270C4×Dic6—32no—
271C23×C32C2412yes—
272C23×C32C2411yescharacteristic
273C22×C3⋊D3—24no—
274C22×C3⋊D3—28no—
275C22×C3⋊D3—44no—
276C22×C3⋊D3—48no—
277C22×C3⋊D3C2414yes—
278C22×C3⋊D3C2412yes—
279C22×C3×D3—24no—
280C22×C3×D3—44no—
281C22×C3×D3C2412yes—
282C22×C3×D3C2414yes—
283C2×D32—28no—
284C2×D32—48no—
285C32×Q8—22no—
286C32×D4—24no—
287C32×D4—22no—
288C2×C32×C4—24no—
289C2×C32×C4C2×D414yescomplemented
290C2×C32×C4C2412yes—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2411yescharacteristic
293#638—28no—
294#638C2×D418yescomplemented
295C2×C3⋊Dic3C2412yes—
296C4⋊(C3⋊D3)—28no—
297C4⋊(C3⋊D3)—24no—
298C4⋊(C3⋊D3)—24no—
299C4⋊(C3⋊D3)C2×D414yescomplemented
300C4×C3⋊D3—28no—
301C4×C3⋊D3C2×D418yescomplemented
302#634C2×D414yescomplemented
303C3×#67—24no—
304C3×#67—28no—
305C3×#67—48no—
306C2×C3×Dic3—24no—
307C2×C3×Dic3C2414yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×D12—24no—
312C3×D12—24no—
313C3×D12—22no—
314C3×C4×D3—24no—
315C3×Dic6—22no—
316#626—28no—
317#626—216no—
318#626—48no—
319#626—48no—
320#625—28no—
321#624—28no—
322D3×Dic3—28no—
323C2×H(5,𝔽2)—91no—
324C2×H(5,𝔽2)—91no—
325#550—94no—
326D42—94no—
327D42—98no—
328#535—31no—
329#535—91no—
330#535—92no—
331#535—92no—
332#532—31no—
333#532—92no—
334C2×#127—91no—
335C2×#127—92no—
336C4×#41—91no—
337C24×C3—32no—
338C23×D3—34no—
339C23×D3—32no—
340C23×D3—32no—
341C23×D3—34no—
342C23×D3—34no—
343C23×D3—34no—
344C23×D3—62no—
345C23×D3—64no—
346C23×D3C22×D312yes—
347C3×#41—28no—
348C3×#41—24no—
349C3×#41—24no—
350C3×#41—64no—
351C2×C3×Q8—21no—
352C2×C3×Q8—31no—
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×D4—22no—
356C2×C3×D4—21no—
357C2×C3×D4—32no—
358C2×C3×D4—34no—
359C2×C3×D4—38no—
360C2×C3×D4—32no—
361C2×C3×D4—31no—
362C2×C3×D4—32no—
363C2×C3×D4—64no—
364C2×C3×D4C22×D311yescharacteristic
365C2×C3×D4C22×D312yes—
366C2×C3×D4C22×D312yes—
367C2×C3×D4C22×D311yescharacteristic
368C22×C3×C4—22no—
369C22×C3×C4—21no—
370C22×C3×C4—32no—
371C22×C3×C4—32no—
372C22×C3×C4C22×D312yes—
373C22×C3×C4C22×D312yes—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C2×#67—32no—
377C2×#67—32no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—38no—
383C2×#67—34no—
384C2×#67—38no—
385C2×#67—38no—
386C2×#67—62no—
387C2×#67—64no—
388C2×#67—616no—
389C2×#67—128no—
390C2×#67C22×D312yes—
391C2×#67C22×D314yes—
392C2×#67C22×D318yes—
393C22×Dic3—34no—
394C22×Dic3C22×D312yes—
395#239—68no—
396#239—68no—
397#239—68no—
398#239—616no—
399#237—68no—
400#237—68no—
401D3×D4—68no—
402D3×D4—68no—
403D3×D4—68no—
404D3×D4—68no—
405D3×D4—68no—
406D3×D4—616no—
407D3×D4—616no—
408D3×D4—616no—
409D3×D4—616no—
410D3×D4—632no—
411D3×D4—1216no—
412D3×D4—1216no—
413#235—24no—
414#235—38no—
415#235—38no—
416#235—68no—
417#235—68no—
418#235—68no—
419#235—68no—
420#235—616no—
421C2×D12—24no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—38no—
425C2×D12—34no—
426C2×D12—32no—
427C2×D12—32no—
428C2×D12—32no—
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—32no—
432C2×D12—38no—
433C2×D12—38no—
434C2×D12—61no—
435C2×D12—62no—
436C2×D12—64no—
437C2×D12—62no—
438C2×D12—68no—
439C2×D12—68no—
440C2×D12—68no—
441C2×D12—616no—
442C2×D12—68no—
443C2×D12—64no—
444C2×D12—64no—
445C2×D12—128no—
446C2×D12C22×D312yes—
447C2×D12C22×D312yes—
448C2×D12C22×D311yescharacteristic
449C2×C4×D3—32no—
450C2×C4×D3—32no—
451C2×C4×D3—34no—
452C2×C4×D3—34no—
453C2×C4×D3—34no—
454C2×C4×D3—34no—
455C2×C4×D3—34no—
456C2×C4×D3—62no—
457C2×C4×D3—64no—
458C2×C4×D3C22×D312yes—
459C2×Dic6—31no—
460C2×Dic6—31no—
461C2×Dic6—61no—
462C2×Dic6C22×D311yescharacteristic
463C3×C4⋊C4—32no—
464C3×C4⋊C4—34no—
465C3×C22⋊C4—32no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—38no—
468C3×C22⋊C4—34no—
469C3×C42—32no—
470C3×C42—31no—
471C3×C42—32no—
472C3×C42—31no—
473#217C22×D312yes—
474#217C22×D314yes—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—38no—
478(C2×D3)⋊C4—38no—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D318yes—
481C4⋊Dic3C22×D312yes—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4C22×D314yes—
485C4×Dic3—34no—
486C4×Dic3—34no—
487C4×Dic3C22×D311yescharacteristic
488C4×Dic3C22×D312yes—
489C4×Dic3C22×D311yescharacteristic
490C4×Dic3C22×D312yes—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—24no—
494C22×C32C22×D412yes—
495C22×C32C2511yescharacteristic
496C2×C3⋊D3—24no—
497C2×C3⋊D3—24no—
498C2×C3⋊D3—28no—
499C2×C3⋊D3—88no—
500C2×C3⋊D3—84no—
501C2×C3⋊D3C22×D414yes—
502C2×C3×D3—24no—
503C2×C3×D3—22no—
504C2×C3×D3—28no—
505C2×C3×D3—24no—
506C2×C3×D3—84no—
507D32—88no—
508C32×C4—22no—
509C32×C4C22×D412yes—
510C32×C4C22×D412yes—
511C3⋊Dic3C22×D414yes—
512C3×Dic3—22no—
513C3×Dic3—24no—
514C3×Dic3—22no—
515C3×Dic3H(5,𝔽2)14yescomplemented
516H(5,𝔽2)—188no—
517H(5,𝔽2)—188no—
518C2×#41—31no—
519C2×#41—92no—
520C2×#41—92no—
521C2×#41—92no—
522C2×#41—91no—
523C2×#41—92no—
524C2×#41D3211yescharacteristic, complemented
525C22×D4—31no—
526C22×D4—92no—
527C22×D4—94no—
528C22×D4—92no—
529C22×D4—98no—
530C22×D4—94no—
531C22×D4—92no—
532C22×D4—94no—
533C22×D4—91no—
534C22×D4—92no—
535C4⋊Q8—31no—
536#127—31no—
537#127—32no—
538#127—92no—
539#127—92no—
540#127—92no—
541#127—94no—
542#127—98no—
543#124—31no—
544#124—32no—
545#124—31no—
546#124—92no—
547#121—34no—
548#121—34no—
549#121—98no—
550#121—98no—
551#121—98no—
552#121—94no—
553#120—34no—
554#120—98no—
555#120—94no—
556#120—98no—
557C4×Q8—92no—
558C4×D4—34no—
559C4×D4—92no—
560C4×D4—98no—
561C4×D4—94no—
562#117—31no—
563#117—92no—
564C2×C42—31no—
565C2×C42—92no—
566C23×C3—22no—
567C23×C3—21no—
568C23×C3—34no—
569C23×C3—32no—
570C23×C3—64no—
571C23×C3—124no—
572C23×C3C23×D312yes—
573C23×C3C23×D312yes—
574C23×C3C23×D311yescharacteristic
575C23×C3C23×D311yescharacteristic
576C22×D3—24no—
577C22×D3—32no—
578C22×D3—32no—
579C22×D3—34no—
580C22×D3—34no—
581C22×D3—44no—
582C22×D3—62no—
583C22×D3—64no—
584C22×D3—68no—
585C22×D3—68no—
586C22×D3—68no—
587C22×D3—68no—
588C22×D3—616no—
589C22×D3—68no—
590C22×D3—64no—
591C22×D3—64no—
592C22×D3—128no—
593C22×D3—128no—
594C22×D3—124no—
595C22×D3—128no—
596C22×D3—128no—
597C22×D3—124no—
598C22×D3—244no—
599C22×D3—248no—
600C22×D3C23×D314yes—
601C22×D3C23×D312yes—
602C3×Q8—24no—
603C3×Q8—22no—
604C3×Q8—22no—
605C3×Q8—62no—
606C3×D4—28no—
607C3×D4—24no—
608C3×D4—24no—
609C3×D4—24no—
610C3×D4—22no—
611C3×D4—22no—
612C3×D4—68no—
613C3×D4—64no—
614C3×D4—62no—
615C3×D4—64no—
616C3×D4—64no—
617C3×D4—128no—
618C2×C3×C4—28no—
619C2×C3×C4—24no—
620C2×C3×C4—24no—
621C2×C3×C4—21no—
622C2×C3×C4—22no—
623C2×C3×C4—21no—
624C2×C3×C4—24no—
625C2×C3×C4—32no—
626C2×C3×C4—34no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—64no—
630C2×C3×C4—64no—
631C2×C3×C4D3×D414yescomplemented
632C2×C3×C4D3×D414yescomplemented
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D311yescharacteristic
639#67—24no—
640#67—28no—
641#67—38no—
642#67—38no—
643#67—48no—
644#67—68no—
645#67—68no—
646#67—68no—
647#67—68no—
648#67—68no—
649#67—68no—
650#67—616no—
651#67—616no—
652#67—128no—
653#67—128no—
654C2×Dic3—24no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—62no—
658C2×Dic3—68no—
659C2×Dic3C23×D314yes—
660C2×Dic3C23×D312yes—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663D12—24no—
664D12—24no—
665D12—22no—
666D12—34no—
667D12—34no—
668D12—64no—
669D12—68no—
670D12—68no—
671D12—68no—
672D12—616no—
673D12—68no—
674D12—616no—
675D12—68no—
676D12—64no—
677D12—64no—
678D12—64no—
679D12—64no—
680D12—128no—
681D12—128no—
682C4×D3—24no—
683C4×D3—38no—
684C4×D3—38no—
685C4×D3—68no—
686C4×D3—68no—
687C4×D3—68no—
688C4×D3—68no—
689C4×D3—68no—
690C4×D3—616no—
691C4×D3—68no—
692Dic6—22no—
693Dic6—34no—
694Dic6—34no—
695Dic6—64no—
696C2×C32—22no—
697C2×C32—42no—
698C2×C32C23×D411yescharacteristic
699C2×C32C2×H(5,𝔽2)12yes—
700C3⋊D3—24no—
701C3⋊D3—44no—
702C3×D3—42no—
703C3×D3—44no—
704C24—32no—
705C24—94no—
706C24—94no—
707C24—92no—
708#41—24no—
709#41—64no—
710#41—98no—
711#41—188no—
712#41—188no—
713#41—188no—
714#41—188no—
715C2×Q8—31no—
716C2×Q8—91no—
717C2×Q8C2×D3211yescharacteristic
718C2×D4—34no—
719C2×D4—32no—
720C2×D4—38no—
721C2×D4—32no—
722C2×D4—32no—
723C2×D4—31no—
724C2×D4—64no—
725C2×D4—98no—
726C2×D4—94no—
727C2×D4—98no—
728C2×D4—98no—
729C2×D4—92no—
730C2×D4—94no—
731C2×D4—94no—
732C2×D4—91no—
733C2×D4—94no—
734C2×D4—92no—
735C2×D4—92no—
736C2×D4—188no—
737C2×D4—188no—
738C2×D4—188no—
739C2×D4—188no—
740C2×D4—1816no—
741C2×D4—1816no—
742C2×D4—184no—
743C2×D4—368no—
744C2×D4—3616no—
745C2×D4C2×D3212yes—
746C2×D4C2×D3211yescharacteristic
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—94no—
750C22×C4—94no—
751C22×C4—92no—
752C22×C4—94no—
753C22×C4C2×D3212yes—
754C22×C4C2×D3211yescharacteristic
755C4⋊C4—32no—
756C4⋊C4—34no—
757C4⋊C4—94no—
758C22⋊C4—32no—
759C22⋊C4—34no—
760C22⋊C4—34no—
761C22⋊C4—38no—
762C22⋊C4—94no—
763C22⋊C4—98no—
764C42—31no—
765C42—31no—
766C42—32no—
767C42—32no—
768C42—94no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—24no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—22no—
777C22×C3—21no—
778C22×C3—42no—
779C22×C3—44no—
780C22×C3—64no—
781C22×C3—62no—
782C22×C3—68no—
783C22×C3—64no—
784C22×C3—244no—
785C22×C3C2×D3×D412yes—
786C22×C3C2×D3×D412yes—
787C22×C3C24×D311yescharacteristic
788C22×C3C24×D311yescharacteristic
789C2×D3—22no—
790C2×D3—24no—
791C2×D3—24no—
792C2×D3—28no—
793C2×D3—34no—
794C2×D3—34no—
795C2×D3—64no—
796C2×D3—64no—
797C2×D3—64no—
798C2×D3—68no—
799C2×D3—64no—
800C2×D3—64no—
801C2×D3—68no—
802C2×D3—68no—
803C2×D3—84no—
804C2×D3—124no—
805C2×D3—128no—
806C2×D3—248no—
807C2×D3—248no—
808C2×D3—248no—
809C2×D3—248no—
810C2×D3—244no—
811C2×D3—244no—
812C2×D3—248no—
813C2×D3—2416no—
814C3×C4—24no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—34no—
820C3×C4—62no—
821C3×C4—64no—
822C3×C4—62no—
823C3×C4C2×D3×D412yes—
824C3×C4C2×D3×D412yes—
825C3×C4C2×D3×D412yes—
826C3×C4C2×D3×D412yes—
827Dic3—22no—
828Dic3—22no—
829Dic3—24no—
830Dic3—34no—
831Dic3—34no—
832Dic3—64no—
833Dic3#100914yescomplemented
834C32#349811yescharacteristic, complemented, Sylow
835C23—32no—
836C23—34no—
837C23—64no—
838C23—92no—
839C23—94no—
840C23—124no—
841C23—188no—
842C23—188no—
843C23—184no—
844C23—364no—
845C23—368no—
846C23—368no—
847C23C22×D3212yes—
848C23C22×D3211yescharacteristic
849Q8—22no—
850Q8—62no—
851Q8—94no—
852D4—24no—
853D4—22no—
854D4—68no—
855D4—64no—
856D4—64no—
857D4—64no—
858D4—62no—
859D4—98no—
860D4—94no—
861D4—128no—
862D4—188no—
863D4—1816no—
864D4—188no—
865D4—188no—
866D4—188no—
867D4—184no—
868D4—184no—
869D4—368no—
870D4—368no—
871C2×C4—24no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—34no—
875C2×C4—32no—
876C2×C4—64no—
877C2×C4—64no—
878C2×C4—92no—
879C2×C4—98no—
880C2×C4—188no—
881C2×C4—188no—
882C2×C4—188no—
883C2×C4#381114yescomplemented
884C2×C4C22×D3212yes—
885C2×C4C22×D3211yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C2×C3—22no—
888C2×C3—22no—
889C2×C3—22no—
890C2×C3—21no—
891C2×C3—42no—
892C2×C3—44no—
893C2×C3—42no—
894C2×C3—42no—
895C2×C3—122no—
896C2×C3—124no—
897C2×C3C22×D3×D411yescharacteristic
898C2×C3C22×D3×D411yescharacteristic
899C2×C3C2×#100912yes—
900C2×C3D3×H(5,𝔽2)12yes—
901D3—44no—
902D3—42no—
903D3—64no—
904D3—64no—
905D3—124no—
906D3—128no—
907D3—124no—
908D3—124no—
909C22—22no—
910C22—24no—
911C22—22no—
912C22—64no—
913C22—68no—
914C22—62no—
915C22—64no—
916C22—94no—
917C22—184no—
918C22—188no—
919C22—184no—
920C22—244no—
921C22—724no—
922C22—728no—
923C22—728no—
924C22C2×#381112yes—
925C22C23×D3211yescharacteristic
926C4—22no—
927C4—34no—
928C4—62no—
929C4—64no—
930C4—62no—
931C4—94no—
932C4C2×#381112yes—
933C4C2×#381112yes—
934C3—21no—
935C3#8624211yescharacteristic, complemented
936C3#8631611yescharacteristic, complemented
937C2—22no—
938C2—42no—
939C2—124no—
940C2—122no—
941C2—184no—
942C2—364no—
943C2D3×#100912yes—
944C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×#64307C2semidirect
3. C3×#5832C2semidirect
4. C3×#5830C2semidirect
5. #10595433C2semidirect
6. #10595363C2semidirect
7. #10595300C2semidirect
8. #10595292C2semidirect
9. #10595168C2semidirect
10. #10595074C2semidirect
11. #10595045C2semidirect
12. C2×#63911C2semidirect
13. #10594954C2semidirect
14. #10594919C2semidirect
17. C2×C32×#41C22semidirect
19. C2×#3832C22semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C2×D4×C3⋊D3C22semidirect
23. C2×#3828C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×#235C22semidirect
27. C22×C3×D12C22semidirect
28. C2×#3811C22semidirect
29. C2×D3×#67C22semidirect
30. C22×#626C22semidirect
32. C2×#3802C22semidirect
33. C2×D3×D12C22semidirect
34. C2×#3796C22semidirect
35. C2×#3795C22semidirect
36. C3×#947C22semidirect
37. C3×#947C22semidirect
38. C3×#944C22semidirect
39. C3×#940C22semidirect
40. C3×#940C22semidirect
41. C3×#939C22semidirect
42. C3×#937C22semidirect
43. C3×#936C22semidirect
44. C3×#930C22semidirect
45. C3×C4×#67C22semidirect
46. C3×#926C22semidirect
47. C2×C3×C4×Dic3C22semidirect
48. #63981C22semidirect
49. #63981C22semidirect
50. #63979C22semidirect
51. #63971C22semidirect
52. #63952C22semidirect
53. #63923C22semidirect
54. #63912C22semidirect
55. #63911C22semidirect
56. #63911C22semidirect
57. #63911C22semidirect
58. #63911C22semidirect
59. #63910C22semidirect
60. #63909C22semidirect
61. #63894C22semidirect
62. C4×#624C22semidirect
63. #63881C22semidirect
64. #63874C22semidirect
65. #63864C22semidirect
66. #63844C22semidirect
74. #5832D3semidirect
76. #5830D3semidirect
112. #3828D4semidirect
164. C2×C3×#41C2×D3semidirect
165. C2×C3×#41C2×D3semidirect
199. C2×#235C2×D3semidirect
208. C22×D12C2×D3semidirect
222. #947C2×D3semidirect
223. #947C2×D3semidirect
224. #944C2×D3semidirect
231. #940C2×D3semidirect
232. #940C2×D3semidirect
234. #939C2×D3semidirect
237. #937C2×D3semidirect
238. #936C2×D3semidirect
240. #930C2×D3semidirect
242. C4×#67C2×D3semidirect
243. #926C2×D3semidirect
244. C2×C4×Dic3C2×D3semidirect
289. C2×C32×C4C2×D4semidirect
294. #638C2×D4semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
301. C4×C3⋊D3C2×D4semidirect
302. #634C2×D4semidirect
515. C3×Dic3H(5,𝔽2)semidirect
524. C2×#41D32semidirect
631. C2×C3×C4D3×D4semidirect
632. C2×C3×C4D3×D4semidirect
833. Dic3#1009semidirect
834. C32#3498semidirect
883. C2×C4#3811semidirect
935. C3#86242semidirect
936. C3#86316semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×#643072
C3×#58322
C3×#58302
#105954332
#105953632
#105953002
#105952922
#105951682
#105950742
#105950452
C2×#639112
#105949542
#105949192
#863163
#862423