Finite Group Databasebeta

← #11901218

Subgroups — #11901218

Order 1152.

3557 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C3×#5830C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595364C212yesmaximal, complemented
6#10595363C212yesmaximal, complemented
7#10595242C214yesmaximal, complemented
8#10595168C212yesmaximal, complemented
9#10595167C212yesmaximal, complemented
10#10595160C214yesmaximal, complemented
11#10595042C211yesmaximal, characteristic, complemented
12#10594969C211yesmaximal, characteristic, complemented
13#10594923C214yesmaximal, complemented
14#10594922C214yesmaximal, complemented
15#10594866C211yesmaximal, characteristic, complemented
16#86338—31nomaximal
17#86313—31nomaximal
18C2×C32×#41C2211yescharacteristic
19#41×C3⋊D3—28no—
20C2×#3832C2211yescharacteristic, complemented
21C2×Q8×C3⋊D3C2211yescharacteristic, complemented
22C2×#3830C2212yes—
23C2×#3830C2211yescharacteristic, complemented
24C2×D4×C3⋊D3C2212yes—
25C2×D4×C3⋊D3C2211yescharacteristic, complemented
26C2×#3828C2211yescharacteristic
27C2×#3828C2212yescomplemented
28C22×C4×C3⋊D3C2211yescharacteristic
29C22×C4×C3⋊D3C2212yescomplemented
30C22×C3×D12C2211yescharacteristic, complemented
31C22×C3×Dic6C2211yescharacteristic, complemented
32C22×#626C2212yes—
33C22×D3×Dic3C2212yescomplemented
34C2×#3796—28no—
35C2×#3796C2212yes—
36C2×#3796C2212yes—
37C2×#3796C2212yescomplemented
38C2×#3796C2212yescomplemented
39C3×#947C2212yescomplemented
40C3×#944C2212yescomplemented
41C3×#940C2212yescomplemented
42C3×#937C2214yescomplemented
43C3×#936C2212yescomplemented
44C3×#935C2214yescomplemented
45C3×#930C2214yescomplemented
46C3×#926C2211yescharacteristic, complemented
47C3×#926C2211yescharacteristic, complemented
48C3×#924C2214yescomplemented
49#63981C2218yescomplemented
50#63977C2214yescomplemented
51#63974C2212yes—
52#67⋊Dic3C2218yescomplemented
53#63971C2218yescomplemented
54#63966C2214yescomplemented
55#63958C2218yescomplemented
56#63957C2212yescomplemented
57#63916C2214yescomplemented
58#63911C2212yescomplemented
59#63910C2218yescomplemented
60#63900C2212yescomplemented
61#63896C2218yescomplemented
62C4×#624C2212yescomplemented
63#63881C2218yescomplemented
64#63874C2212yescomplemented
65#63871C2214yescomplemented
66#63866C2212yescomplemented
67#63864C2212yescomplemented
68#63860C2212yescomplemented
69#63853C2218yescomplemented
70#63849C2212yescomplemented
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C2×D3×#41—61no—
74C22×#239—31no—
75C22×#237—31no—
76C3×#536—31no—
77C3×#535—31no—
78#5830D311yescharacteristic, complemented
79#5825D311yescharacteristic, complemented
80#5816—31no—
81#5805—31no—
82#5725—32no—
83#5724—32no—
84#5716—32no—
85#5715—32no—
86#5675—32no—
87#5674—32no—
88#5668—32no—
89#5668—32no—
90#5656—34no—
91#5653—34no—
92#5629—34no—
93#5627—34no—
94#5608—34no—
95#5606—34no—
96#5589—34no—
97#5586—34no—
98#5526—31no—
99#5525—31no—
100D3×#117—31no—
101D3×#117—31no—
102C23×C3⋊D3C2312yes—
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2312yes—
105C32×#41—24no—
106C2×C32×Q8C2311yescharacteristic
107C2×C32×D4C2312yes—
108C2×C32×D4C2311yescharacteristic
109C22×C32×C4C2312yes—
110C22×C32×C4C2311yescharacteristic
111C2×#638C2312yes—
112C2×#638C2312yes—
113C2×#638C2312yes—
114C22×C3⋊Dic3C2312yes—
115C22×C3⋊Dic3C2311yescharacteristic
116#3832—24no—
117Q8×C3⋊D3—24no—
118#3830—28no—
119#3830—24no—
120D4×C3⋊D3—28no—
121D4×C3⋊D3—24no—
122#3828—24no—
123#3828—28no—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4⋊(C3⋊D3)C2312yes—
126C2×C4×C3⋊D3—28no—
127C2×C4×C3⋊D3D418yescomplemented
128C2×C4×C3⋊D3C2312yes—
129C2×C4×C3⋊D3C2312yes—
130C2×C4×C3⋊D3C2312yes—
131C2×C4×C3⋊D3C2311yescharacteristic
132C2×C4×C3⋊D3C2311yescharacteristic
133C2×C4×C3⋊D3C2311yescharacteristic
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×#634C2311yescharacteristic
136C2×#634C2312yes—
137C2×C3×#67C2318yes—
138C22×C3×Dic3C2312yes—
139C2×C3×D12—24no—
140C2×C3×D12C2312yes—
141C2×C3×D12C2312yes—
142C2×C3×Dic6—24no—
143C2×C3×Dic6C2312yes—
144C2×C3×Dic6C2312yes—
145C2×#626—28no—
146C2×#626C2314yes—
147C2×#626C2314yes—
148C2×#626C2318yes—
149C2×#624C2314yes—
150C2×D3×Dic3—28no—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yes—
153#3796—28no—
154#3796—28no—
155#3796—28no—
156#3796—28no—
157C3×#217C2318yes—
158C3×#217C2312yes—
159C3×#217C2312yes—
160C3×(C2×D3)⋊C4C2318yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×Dic3⋊C4C2318yes—
164C3×C4×Dic3C2312yes—
165C3×C4×Dic3C2312yes—
166#3724C2314yes—
167Dic3⋊Dic3C2318yes—
168#3722C2314yes—
169#3722C2318yes—
170(C2×D3)⋊Dic3C2318yes—
171Dic32C2314yes—
172#3449—91noSylow
173C2×C3×#41—21no—
174C2×C3×#41C2×D311yescharacteristic
175C2×C3×#41C2×D311yescharacteristic
176C22×C3×Q8—31no—
177C22×C3×D4—31no—
178C22×#67—32no—
179C23×Dic3—32no—
180D3×#41—68no—
181D3×#41—68no—
182D3×#41—616no—
183C2×#239—31no—
184C2×#239—31no—
185C2×#239—32no—
186C2×#239—32no—
187C2×#239—32no—
188C2×#239—32no—
189C2×#239—61no—
190C2×#239—68no—
191C2×D3×Q8—31no—
192C2×D3×Q8—31no—
193C2×D3×Q8—61no—
194C2×#237—32no—
195C2×#237—31no—
196C2×#237—31no—
197C2×#237—32no—
198C2×#237—32no—
199C2×#237—32no—
200C2×#237—32no—
201C2×#237—32no—
202C2×#237—62no—
203C2×#237—61no—
204C2×#237—68no—
205C2×D3×D4—32no—
206C2×D3×D4—31no—
207C2×D3×D4—31no—
208C2×D3×D4—32no—
209C2×D3×D4—62no—
210C2×D3×D4—61no—
211C2×#235—31no—
212C2×#235—31no—
213C2×#235—32no—
214C2×#235—32no—
215C2×#235—61no—
216C2×#235—62no—
217C22×D12—32no—
218C22×D12C2×D311yescharacteristic, complemented
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—32no—
222C22×C4×D3—32no—
223C22×C4×D3—32no—
224C22×C4×D3—61no—
225C22×C4×D3—62no—
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×C4⋊Q8—32no—
228C3×#127—32no—
229C3×#124—32no—
230C3×#124—32no—
231C3×#123—34no—
232C3×C22⋊Q8—34no—
233C3×#121—34no—
234C3×#120—34no—
235C3×#117—31no—
236C3×#117—31no—
237#953—34no—
238#947—32no—
239#947C2×D312yescomplemented
240#946—34no—
241#944—32no—
242#944C2×D312yescomplemented
243#940—32no—
244#940C2×D312yescomplemented
245#939—38no—
246#938—38no—
247#938—34no—
248#937—38no—
249#937C2×D314yescomplemented
250#936—32no—
251#936C2×D312yescomplemented
252#935C2×D314yescomplemented
253D4×Dic3—38no—
254#930C2×D314yescomplemented
255#929—34no—
256#926C2×D311yescharacteristic, complemented
257#926C2×D311yescharacteristic, complemented
258#924C2×D314yescomplemented
259#897—34no—
260#896—38no—
261#895—34no—
262#895—38no—
263#894—38no—
264#893—38no—
265#892—32no—
266#892—32no—
267D3×C4⋊C4—32no—
268D3×C4⋊C4—32no—
269#886—34no—
270#884—38no—
271#884—38no—
272#884—38no—
273#883—38no—
274#882—34no—
275#882—38no—
276#67⋊C4—38no—
277#67⋊C4—38no—
278D3×C22⋊C4—32no—
279D3×C22⋊C4—32no—
280#878—38no—
281#877—32no—
282#877—32no—
283#875—32no—
284#875—32no—
285#874—32no—
286#872—32no—
287#872—32no—
288C42×D3—32no—
289C42×D3—32no—
290#869—32no—
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—24no—
294C22×C3⋊D3—42no—
295C22×C3⋊D3—44no—
296C22×C3⋊D3C2×D414yes—
297C22×C3⋊D3C2412yes—
298C22×C3⋊D3C2411yescharacteristic
299C22×C3⋊D3C2411yescharacteristic
300C22×C3×D3—24no—
301C22×C3×D3—44no—
302C22×C3×D3C2414yes—
303C32×Q8—22no—
304C32×D4—24no—
305C32×D4—22no—
306C2×C32×C4—24no—
307C2×C32×C4C2×D414yes—
308C2×C32×C4C2412yes—
309C2×C32×C4C2411yescharacteristic
310C2×C32×C4C2411yescharacteristic
311#638—24no—
312#638—24no—
313#638—24no—
314C2×C3⋊Dic3—24no—
315C2×C3⋊Dic3C2×D414yes—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2411yescharacteristic
318C2×C3⋊Dic3C2411yescharacteristic
319C4⋊(C3⋊D3)—24no—
320C4⋊(C3⋊D3)—22no—
321C4×C3⋊D3—24no—
322C4×C3⋊D3—24no—
323C4×C3⋊D3—24no—
324C4×C3⋊D3C2×D414yes—
325C4×C3⋊D3C2×D414yes—
326C4×C3⋊D3C2×D414yes—
327C4×C3⋊D3C2×D414yes—
328#634—22no—
329#634—24no—
330C3×#67—48no—
331C2×C3×Dic3—24no—
332C2×C3×Dic3C2414yes—
333C2×C3×Dic3C2414yes—
334C2×C3×Dic3C2414yes—
335C3×D12—24no—
336C3×D12—24no—
337C3×Dic6—24no—
338C3×Dic6—24no—
339#626—28no—
340#626—28no—
341#626—48no—
342#624—44no—
343D3×Dic3—28no—
344D3×Dic3—28no—
345C22×#41—91no—
346C22×#41—91no—
347#537—94no—
348#536—31no—
349#536—91no—
350#536—92no—
351#535—31no—
352#535—91no—
353#535—92no—
354#534—94no—
355#532—92no—
356#532—92no—
357#525—94no—
358#525—94no—
359C2×#117—91no—
360C24×C3—32no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—32no—
364C23×D3—32no—
365C23×D3—61no—
366C23×D3—62no—
367C23×D3C22×D312yes—
368C3×#41—28no—
369C3×#41—24no—
370C3×#41—24no—
371C2×C3×Q8—21no—
372C2×C3×Q8—32no—
373C2×C3×Q8—32no—
374C2×C3×Q8—64no—
375C2×C3×Q8C22×D311yescharacteristic
376C2×C3×Q8C22×D311yescharacteristic
377C2×C3×D4—22no—
378C2×C3×D4—21no—
379C2×C3×D4—38no—
380C2×C3×D4—32no—
381C2×C3×D4—32no—
382C2×C3×D4—64no—
383C2×C3×D4C22×D312yes—
384C2×C3×D4C22×D311yescharacteristic
385C2×C3×D4C22×D312yes—
386C2×C3×D4C22×D311yescharacteristic
387C22×C3×C4—22no—
388C22×C3×C4—21no—
389C22×C3×C4—32no—
390C22×C3×C4C22×D312yes—
391C22×C3×C4C22×D312yes—
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67—32no—
395C2×#67—32no—
396C2×#67—32no—
397C2×#67—32no—
398C2×#67—32no—
399C2×#67—32no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—38no—
403C2×#67—62no—
404C2×#67—62no—
405C2×#67—62no—
406C2×#67—68no—
407C2×#67C22×D318yes—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—32no—
411C22×Dic3—32no—
412C22×Dic3—34no—
413C22×Dic3—34no—
414C22×Dic3—61no—
415C22×Dic3—62no—
416C22×Dic3—68no—
417C22×Dic3C22×D312yes—
418#239—68no—
419#239—68no—
420#239—68no—
421#239—68no—
422#239—64no—
423#239—64no—
424#239—68no—
425D3×Q8—64no—
426D3×Q8—64no—
427D3×Q8—68no—
428#237—68no—
429#237—68no—
430#237—68no—
431#237—68no—
432#237—64no—
433#237—64no—
434#237—68no—
435#237—68no—
436#237—68no—
437#237—616no—
438D3×D4—64no—
439D3×D4—64no—
440D3×D4—68no—
441D3×D4—68no—
442D3×D4—68no—
443D3×D4—616no—
444#235—68no—
445#235—68no—
446#235—616no—
447#235—68no—
448#235—64no—
449#235—64no—
450C2×D12—24no—
451C2×D12—34no—
452C2×D12—34no—
453C2×D12—31no—
454C2×D12—31no—
455C2×D12—32no—
456C2×D12—32no—
457C2×D12—38no—
458C2×D12—62no—
459C2×D12—61no—
460C2×D12—68no—
461C2×D12C22×D312yes—
462C2×D12C22×D312yes—
463C2×C4×D3—38no—
464C2×C4×D3—38no—
465C2×C4×D3—31no—
466C2×C4×D3—31no—
467C2×C4×D3—31no—
468C2×C4×D3—31no—
469C2×C4×D3—31no—
470C2×C4×D3—31no—
471C2×C4×D3—31no—
472C2×C4×D3—31no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—32no—
476C2×C4×D3—32no—
477C2×C4×D3—32no—
478C2×C4×D3—32no—
479C2×C4×D3—32no—
480C2×C4×D3—32no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—61no—
484C2×C4×D3—61no—
485C2×C4×D3—62no—
486C2×C4×D3—61no—
487C2×C4×D3—62no—
488C2×C4×D3—61no—
489C2×C4×D3—62no—
490C2×C4×D3—68no—
491C2×C4×D3—68no—
492C2×C4×D3—68no—
493C2×C4×D3—68no—
494C2×C4×D3—616no—
495C2×Dic6—24no—
496C2×Dic6—31no—
497C2×Dic6—31no—
498C2×Dic6—32no—
499C2×Dic6—32no—
500C2×Dic6—62no—
501C2×Dic6—61no—
502C2×Dic6C22×D312yes—
503C2×Dic6C22×D312yes—
504C3×C4⋊C4—32no—
505C3×C4⋊C4—32no—
506C3×C4⋊C4—38no—
507C3×C22⋊C4—32no—
508C3×C22⋊C4—32no—
509C3×C22⋊C4—38no—
510C3×C22⋊C4—38no—
511C3×C42—32no—
512C3×C42—32no—
513#217—38no—
514#217C22×D312yes—
515#217C22×D312yes—
516#217C22×D318yes—
517(C2×D3)⋊C4—38no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—38no—
521(C2×D3)⋊C4—38no—
522(C2×D3)⋊C4C22×D318yes—
523C4⋊Dic3—38no—
524C4⋊Dic3C22×D312yes—
525C4⋊Dic3C22×D312yes—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—38no—
529Dic3⋊C4C22×D318yes—
530C4×Dic3—34no—
531C4×Dic3—34no—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D312yes—
534C22×C32—22no—
535C22×C32—22no—
536C22×C32—24no—
537C22×C32C22×D412yes—
538C22×C32C2511yescharacteristic
539C2×C3⋊D3—22no—
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—24no—
543C2×C3⋊D3—44no—
544C2×C3⋊D3—48no—
545C2×C3⋊D3C22×D412yes—
546C2×C3⋊D3C22×D412yes—
547C2×C3×D3—24no—
548C2×C3×D3—28no—
549C2×C3×D3—48no—
550C32×C4—22no—
551C32×C4C22×D412yes—
552C32×C4C22×D412yes—
553C3⋊Dic3—22no—
554C3⋊Dic3C22×D412yes—
555C3⋊Dic3C22×D412yes—
556C3×Dic3—24no—
557C3×Dic3—24no—
558C3×Dic3—24no—
559C2×#41—92no—
560C2×#41—92no—
561C2×#41—92no—
562C2×#41—92no—
563C2×#41—91no—
564C2×#41—92no—
565C2×#41—91no—
566C2×#41—91no—
567C2×#41—92no—
568C2×#41—188no—
569C2×#41—188no—
570C2×#41D3211yescharacteristic
571C22×Q8—31no—
572C22×Q8—91no—
573C22×D4—31no—
574C22×D4—92no—
575C22×D4—92no—
576C22×D4—91no—
577C23×C4—92no—
578C23×C4—91no—
579C23×C4—92no—
580C4⋊Q8—32no—
581C4⋊Q8—92no—
582#127—32no—
583#127—92no—
584#124—32no—
585#124—32no—
586#124—92no—
587#124—92no—
588#123—34no—
589#123—98no—
590#123—94no—
591C22⋊Q8—34no—
592C22⋊Q8—98no—
593C22⋊Q8—94no—
594#121—34no—
595#121—98no—
596#121—98no—
597#121—98no—
598#121—94no—
599#120—34no—
600#120—98no—
601#120—94no—
602C4×D4—98no—
603C4×D4—98no—
604#117—31no—
605#117—31no—
606#117—92no—
607#117—92no—
608#117—92no—
609C2×C4⋊C4—92no—
610C2×C22⋊C4—92no—
611C2×C42—92no—
612C23×C3—22no—
613C23×C3—21no—
614C23×C3—34no—
615C23×C3—64no—
616C23×C3—124no—
617C23×C3C23×D312yes—
618C23×C3C23×D312yes—
619C23×C3C23×D311yescharacteristic
620C23×C3C23×D311yescharacteristic
621C22×D3—24no—
622C22×D3—31no—
623C22×D3—31no—
624C22×D3—31no—
625C22×D3—31no—
626C22×D3—34no—
627C22×D3—34no—
628C22×D3—32no—
629C22×D3—32no—
630C22×D3—44no—
631C22×D3—61no—
632C22×D3—64no—
633C22×D3—61no—
634C22×D3—62no—
635C22×D3—64no—
636C22×D3—64no—
637C22×D3—68no—
638C22×D3—122no—
639C22×D3—124no—
640C22×D3—122no—
641C22×D3—124no—
642C22×D3—124no—
643C22×D3—128no—
644C22×D3C23×D314yes—
645C3×Q8—24no—
646C3×Q8—22no—
647C3×Q8—22no—
648C3×Q8—64no—
649C3×Q8—64no—
650C3×D4—28no—
651C3×D4—24no—
652C3×D4—24no—
653C3×D4—24no—
654C3×D4—22no—
655C3×D4—22no—
656C3×D4—64no—
657C3×D4—64no—
658C3×D4—128no—
659C2×C3×C4—28no—
660C2×C3×C4—24no—
661C2×C3×C4—24no—
662C2×C3×C4—22no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—24no—
666C2×C3×C4—34no—
667C2×C3×C4—34no—
668C2×C3×C4—34no—
669C2×C3×C4—64no—
670C2×C3×C4D3×D414yes—
671C2×C3×C4D3×D414yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678#67—48no—
679#67—68no—
680#67—68no—
681#67—64no—
682#67—64no—
683#67—64no—
684#67—64no—
685#67—68no—
686#67—68no—
687#67—68no—
688#67—64no—
689#67—64no—
690#67—128no—
691C2×Dic3—24no—
692C2×Dic3—34no—
693C2×Dic3—34no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—64no—
701C2×Dic3—61no—
702C2×Dic3—62no—
703C2×Dic3—61no—
704C2×Dic3—68no—
705C2×Dic3—68no—
706C2×Dic3—64no—
707C2×Dic3—64no—
708C2×Dic3—68no—
709C2×Dic3C23×D314yes—
710C2×Dic3C23×D314yes—
711C2×Dic3C23×D314yes—
712D12—24no—
713D12—24no—
714D12—64no—
715D12—64no—
716D12—68no—
717D12—64no—
718D12—68no—
719D12—68no—
720D12—62no—
721D12—62no—
722D12—128no—
723C4×D3—34no—
724C4×D3—34no—
725C4×D3—34no—
726C4×D3—34no—
727C4×D3—34no—
728C4×D3—34no—
729C4×D3—34no—
730C4×D3—34no—
731C4×D3—64no—
732C4×D3—64no—
733C4×D3—64no—
734C4×D3—64no—
735C4×D3—64no—
736C4×D3—64no—
737C4×D3—68no—
738C4×D3—68no—
739C4×D3—64no—
740C4×D3—64no—
741C4×D3—68no—
742C4×D3—68no—
743C4×D3—68no—
744C4×D3—64no—
745C4×D3—64no—
746C4×D3—124no—
747C4×D3—124no—
748Dic6—24no—
749Dic6—24no—
750Dic6—64no—
751Dic6—64no—
752Dic6—68no—
753Dic6—64no—
754Dic6—62no—
755Dic6—62no—
756C2×C32—22no—
757C2×C32—42no—
758C2×C32C23×D411yescharacteristic
759C2×C32#58512yes—
760C3⋊D3—22no—
761C3⋊D3—22no—
762C3⋊D3—42no—
763C3×D3—44no—
764C24—32no—
765C24—91no—
766C24—92no—
767#41—24no—
768#41—188no—
769#41—188no—
770#41—184no—
771#41—188no—
772#41—188no—
773#41—188no—
774#41—188no—
775#41—184no—
776#41—184no—
777C2×Q8—32no—
778C2×Q8—32no—
779C2×Q8—64no—
780C2×Q8—92no—
781C2×Q8—91no—
782C2×Q8—184no—
783C2×Q8C2×D3211yescharacteristic
784C2×D4—38no—
785C2×D4—32no—
786C2×D4—32no—
787C2×D4—64no—
788C2×D4—94no—
789C2×D4—94no—
790C2×D4—98no—
791C2×D4—92no—
792C2×D4—92no—
793C2×D4—92no—
794C2×D4—92no—
795C2×D4—91no—
796C2×D4—188no—
797C2×D4—184no—
798C2×D4—188no—
799C2×D4C2×D3212yes—
800C2×D4C2×D3211yescharacteristic
801C22×C4—32no—
802C22×C4—94no—
803C22×C4—94no—
804C22×C4—94no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—91no—
809C22×C4—91no—
810C22×C4—98no—
811C22×C4—92no—
812C22×C4—92no—
813C22×C4—92no—
814C22×C4—92no—
815C22×C4—188no—
816C22×C4—188no—
817C22×C4C2×D3212yes—
818C22×C4C2×D3211yescharacteristic
819C4⋊C4—32no—
820C4⋊C4—32no—
821C4⋊C4—38no—
822C4⋊C4—94no—
823C4⋊C4—98no—
824C22⋊C4—32no—
825C22⋊C4—32no—
826C22⋊C4—38no—
827C22⋊C4—38no—
828C22⋊C4—94no—
829C22⋊C4—98no—
830C22⋊C4—98no—
831C42—32no—
832C42—32no—
833C42—94no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—24no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—24no—
840C22×C3—24no—
841C22×C3—22no—
842C22×C3—21no—
843C22×C3—42no—
844C22×C3—44no—
845C22×C3—64no—
846C22×C3—68no—
847C22×C3—128no—
848C22×C3C2×D3×D412yes—
849C22×C3C2×D3×D412yes—
850C22×C3C24×D311yescharacteristic
851C22×C3C24×D311yescharacteristic
852C2×D3—24no—
853C2×D3—28no—
854C2×D3—32no—
855C2×D3—32no—
856C2×D3—32no—
857C2×D3—32no—
858C2×D3—48no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—64no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—64no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—64no—
870C2×D3—64no—
871C2×D3—122no—
872C2×D3—124no—
873C2×D3—124no—
874C2×D3—124no—
875C2×D3—128no—
876C2×D3—1216no—
877C2×D3—128no—
878C2×D3—128no—
879C3×C4—24no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—22no—
883C3×C4—22no—
884C3×C4—64no—
885C3×C4—64no—
886C3×C4—64no—
887C3×C4C2×D3×D412yes—
888C3×C4C2×D3×D412yes—
889C3×C4C2×D3×D412yes—
890C3×C4C2×D3×D412yes—
891Dic3—24no—
892Dic3—24no—
893Dic3—24no—
894Dic3—32no—
895Dic3—32no—
896Dic3—32no—
897Dic3—32no—
898Dic3—62no—
899Dic3—62no—
900Dic3—64no—
901Dic3—62no—
902Dic3—62no—
903C32#344911yescharacteristic, complemented, Sylow
904C23—34no—
905C23—64no—
906C23—91no—
907C23—91no—
908C23—94no—
909C23—92no—
910C23—124no—
911C23—184no—
912C23—362no—
913C23—364no—
914C23C22×D3212yes—
915C23C22×D3211yescharacteristic
916Q8—22no—
917Q8—64no—
918Q8—64no—
919Q8—184no—
920Q8—182no—
921D4—24no—
922D4—22no—
923D4—64no—
924D4—64no—
925D4—128no—
926D4—184no—
927D4—188no—
928D4—188no—
929D4—184no—
930D4—184no—
931D4—184no—
932D4—182no—
933D4—368no—
934C2×C4—24no—
935C2×C4—34no—
936C2×C4—34no—
937C2×C4—34no—
938C2×C4—64no—
939C2×C4—94no—
940C2×C4—91no—
941C2×C4—91no—
942C2×C4—94no—
943C2×C4—94no—
944C2×C4—94no—
945C2×C4—94no—
946C2×C4—92no—
947C2×C4—184no—
948C2×C4—184no—
949C2×C4—188no—
950C2×C4—188no—
951C2×C4—184no—
952C2×C4—184no—
953C2×C4—364no—
954C2×C4#381114yes—
955C2×C4C22×D3212yes—
956C2×C4C22×D3211yescharacteristic
957C2×C4C22×D3211yescharacteristic
958C2×C3—22no—
959C2×C3—22no—
960C2×C3—22no—
961C2×C3—21no—
962C2×C3—42no—
963C2×C3—44no—
964C2×C3—42no—
965C2×C3—42no—
966C2×C3—124no—
967C2×C3C22×D3×D411yescharacteristic
968C2×C3C22×D3×D411yescharacteristic
969C2×C3#596612yes—
970C2×C3#596812yes—
971D3—44no—
972D3—64no—
973D3—62no—
974D3—62no—
975D3—62no—
976D3—62no—
977D3—122no—
978D3—124no—
979D3—122no—
980D3—122no—
981C22—22no—
982C22—24no—
983C22—22no—
984C22—68no—
985C22—64no—
986C22—92no—
987C22—92no—
988C22—128no—
989C22—182no—
990C22—182no—
991C22—184no—
992C22—182no—
993C22—364no—
994C22—368no—
995C22C2×#381112yes—
996C22C23×D3211yescharacteristic
997C4—22no—
998C4—64no—
999C4—64no—
1000C4—64no—
1001C4—92no—
1002C4—92no—
1003C4—182no—
1004C4C2×#381112yes—
1005C4C2×#381112yes—
1006C3—21no—
1007C3#8631311yescharacteristic, complemented
1008C3#8633811yescharacteristic, complemented
1009C2—22no—
1010C2—42no—
1011C2—124no—
1012C2—182no—
1013C2—182no—
1014C2—362no—
1015C2#1059669812yes—
1016C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C22×#3796C2semidirect
3. C3×#5830C2semidirect
4. C3×#5825C2semidirect
5. #10595364C2semidirect
6. #10595363C2semidirect
7. #10595242C2semidirect
8. #10595168C2semidirect
9. #10595167C2semidirect
10. #10595160C2semidirect
11. #10595042C2semidirect
12. #10594969C2semidirect
13. #10594923C2semidirect
14. #10594922C2semidirect
15. #10594866C2semidirect
20. C2×#3832C22semidirect
21. C2×Q8×C3⋊D3C22semidirect
23. C2×#3830C22semidirect
25. C2×D4×C3⋊D3C22semidirect
27. C2×#3828C22semidirect
29. C22×C4×C3⋊D3C22semidirect
30. C22×C3×D12C22semidirect
31. C22×C3×Dic6C22semidirect
33. C22×D3×Dic3C22semidirect
37. C2×#3796C22semidirect
38. C2×#3796C22semidirect
39. C3×#947C22semidirect
40. C3×#944C22semidirect
41. C3×#940C22semidirect
42. C3×#937C22semidirect
43. C3×#936C22semidirect
44. C3×#935C22semidirect
45. C3×#930C22semidirect
46. C3×#926C22semidirect
47. C3×#926C22semidirect
48. C3×#924C22semidirect
49. #63981C22semidirect
50. #63977C22semidirect
52. #67⋊Dic3C22semidirect
53. #63971C22semidirect
54. #63966C22semidirect
55. #63958C22semidirect
56. #63957C22semidirect
57. #63916C22semidirect
58. #63911C22semidirect
59. #63910C22semidirect
60. #63900C22semidirect
61. #63896C22semidirect
62. C4×#624C22semidirect
63. #63881C22semidirect
64. #63874C22semidirect
65. #63871C22semidirect
66. #63866C22semidirect
67. #63864C22semidirect
68. #63860C22semidirect
69. #63853C22semidirect
70. #63849C22semidirect
78. #5830D3semidirect
79. #5825D3semidirect
127. C2×C4×C3⋊D3D4semidirect
218. C22×D12C2×D3semidirect
226. C22×Dic6C2×D3semidirect
239. #947C2×D3semidirect
242. #944C2×D3semidirect
244. #940C2×D3semidirect
249. #937C2×D3semidirect
251. #936C2×D3semidirect
252. #935C2×D3semidirect
254. #930C2×D3semidirect
256. #926C2×D3semidirect
257. #926C2×D3semidirect
258. #924C2×D3semidirect
903. C32#3449semidirect
1007. C3#86313semidirect
1008. C3#86338semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C22×#37962
C3×#58302
C3×#58252
#105953642
#105953632
#105952422
#105951682
#105951672
#105951602
#105950422
#105949692
#105949232
#105949222
#105948662
#863383
#863133