Finite Group Databasebeta

← #11865164

Subgroups — #11865164

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3#10595040C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592935C211yesmaximal, characteristic, complemented
6#10591684C214yesmaximal, complemented
7#10591665C214yesmaximal, complemented
8#10591110C211yesmaximal, characteristic, complemented
9#10591076C211yesmaximal, characteristic, complemented
10#84122—31nomaximal
11#83957—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—21no—
14C3×#1010C2212yescomplemented
15C3×#1009—21no—
16C3×#1009C2212yescomplemented
17C3×D3×#41—22no—
18C3×D3×#41—22no—
19C3×#1007—21no—
20C3×#1004—21no—
21C3×#1004—22no—
22C2×C3×#235—22no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26#64135C2211yescharacteristic, complemented
27C2×#3748C2211yescharacteristic, complemented
28C3×#949—22no—
29C3×#949C2214yescomplemented
30C2×C3×#215—21no—
31C2×C3×#213—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33#63976—22no—
34#63914C2212yescomplemented
35#63908—22no—
36#63863C2212yescomplemented
37C2×#3715—21no—
38#63823—22no—
39#63823C2214yescomplemented
40C2×#3713—21no—
41#63664C2214yescomplemented
42#63568C2214yescomplemented
43#63560C2212yescomplemented
44#63558C2212yescomplemented
45C3×#585—31no—
46#5964D311yescharacteristic, complemented
47C2×C3×AGL(1,ℤ/8)—31no—
48#5830—31no—
49C2×#949—31no—
50C2×#949D311yescharacteristic, complemented
51#5805—31no—
52C2×#932—31no—
53#5245—34no—
54#5241—34no—
55#5237—31no—
56#5236—31no—
57#5236—31no—
58#5236—31no—
59#5236—61no—
60#5201—34no—
61#5198—34no—
62#5139—31no—
63#5132—31no—
64C23×C3×D3—21no—
65C32×#41—21no—
66C32×#41—21no—
67C32×#41D412yescomplemented
68C32×#41C2312yes—
69C2×C32×Q8D411yescharacteristic, complemented
70C2×C32×D4—21no—
71C2×C32×D4D411yescharacteristic, complemented
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—24no—
75C2×C3×#67—21no—
76C2×C3×#67D412yes—
77C3×#239—22no—
78C3×#239—22no—
79C3×D3×Q8—22no—
80C3×D3×Q8—22no—
81C3×#237—24no—
82C3×#237—22no—
83C3×#237—22no—
84C3×#237—24no—
85C3×D3×D4—24no—
86C3×D3×D4—22no—
87C3×D3×D4—24no—
88C3×D3×D4—22no—
89C3×#235—24no—
90C3×#235—24no—
91C3×#235—21no—
92C3×#235—21no—
93C3×#235—21no—
94C3×#235—21no—
95C3×#235—21no—
96C3×#235—21no—
97C3×#235—22no—
98C3×#235—22no—
99C3×#235D412yescomplemented
100C3×#235C2312yes—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic, complemented
108C2×C3×D12C2312yes—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—24no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3D412yes—
113C2×C3×Dic6—22no—
114C2×C3×Dic6D411yescharacteristic, complemented
115C2×C3×Dic6C2311yescharacteristic
116C2×#625—24no—
117#3757—21no—
118C4⋊(C3⋊Dic3)—21no—
119C4×C3⋊Dic3C2312yes—
120#3748—21no—
121#3748C2312yes—
122C2×C3⋊(C3⋊C8)—21no—
123C3×#215—24no—
124C3×#213—24no—
125C3×#208—21no—
126C3×#208C2312yes—
127C2×C3×C3⋊C8—21no—
128(C2×D3)⋊Dic3—24no—
129#3715—24no—
130#3713—24no—
131#3021—91noSylow
132C3×2−1+4—32no—
133C3×2−1+4—61no—
134C3×2−1+4—61no—
135C3×H(5,𝔽2)—32no—
136C3×H(5,𝔽2)—62no—
137C3×H(5,𝔽2)—61no—
138C3×H(5,𝔽2)—61no—
139C2×C3×#41—21no—
140C2×C3×#41—31no—
141C2×C3×#41—31no—
142C2×C3×#41—62no—
143C2×C3×#41—62no—
144C2×C3×#41—62no—
145C2×C3×#41C2×D311yescharacteristic
146C2×C3×#41C2×D311yescharacteristic
147C22×C3×D4—31no—
148#1010—21no—
149#1010C2×D312yescomplemented
150#1009—21no—
151#1009C2×D312yescomplemented
152D3×#41—22no—
153D3×#41—22no—
154#1007—21no—
155#1004—21no—
156#1004—22no—
157C2×#235—22no—
158C2×#235C2×D311yescharacteristic
159C2×#235C2×D311yescharacteristic
160C22×D12C2×D311yescharacteristic, complemented
161C3×AGL(1,ℤ/8)—34no—
162C3×AGL(1,ℤ/8)—62no—
163C2×C3×SD16—61no—
164C2×C3×D8—61no—
165C2×C3×M16—31no—
166#953—62no—
167#949—22no—
168#949—34no—
169#949—62no—
170#949C2×D314yescomplemented
171#947—32no—
172C2×#215—21no—
173C2×#215—61no—
174#940—32no—
175#940—32no—
176#938—62no—
177#937—62no—
178#936—32no—
179C2×#214—61no—
180#932—34no—
181#932—62no—
182C2×#213—21no—
183C2×#213—61no—
184C2×#213—61no—
185#930—62no—
186#926—31no—
187#926—31no—
188#926—61no—
189C2×#208—31no—
190C2×#208—31no—
191C2×#208—61no—
192C2×#208C2×D311yescharacteristic, complemented
193#837—34no—
194#837—34no—
195#837—34no—
196#837—64no—
197#836—32no—
198#833—32no—
199#825—34no—
200#824—32no—
201#823—32no—
202C23×C32—21no—
203C23×C32C2×D411yescharacteristic
204C22×C3×D3—24no—
205C22×C3×D3—21no—
206C22×C3×D3—22no—
207C22×C3×D3—41no—
208C22×C3×D3—41no—
209C22×C3×D3—82no—
210C22×C3×D3C2×D412yes—
211C32×Q8—21no—
212C32×Q8C2×D412yes—
213C32×D4—22no—
214C32×D4—22no—
215C32×D4—21no—
216C32×D4C2×D412yes—
217C2×C32×C4—21no—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4C2×D411yescharacteristic
224C2×C32×C4C2×D411yescharacteristic
225C2×C32×C4C2411yescharacteristic
226C2×C3⋊Dic3—22no—
227C3×#67—24no—
228C3×#67—24no—
229C3×#67—22no—
230C3×#67—22no—
231C3×#67—22no—
232C3×#67—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3C2×D412yes—
236C3×D12—24no—
237C3×D12—21no—
238C3×D12—21no—
239C3×D12—21no—
240C3×D12—22no—
241C3×D12—22no—
242C3×D12—41no—
243C3×D12—41no—
244C3×D12C2×D412yes—
245C3×C4×D3—24no—
246C3×C4×D3—24no—
247C3×C4×D3—22no—
248C3×C4×D3—22no—
249C3×C4×D3—22no—
250C3×C4×D3—22no—
251C3×Dic6—24no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6C2×D412yes—
256#625—84no—
257C3⋊(C3⋊C8)—22no—
258C3×C3⋊C8—22no—
259#585—31no—
260C2×AGL(1,ℤ/8)—31no—
261C2×AGL(1,ℤ/8)—91no—
262#535—91no—
263#454—94no—
264#453—94no—
265#421—91no—
266#421—91no—
267#413—91no—
268C24×C3—61no—
269C23×D3—21no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—22no—
275C3×#41—22no—
276C3×#41—32no—
277C3×#41—32no—
278C3×#41—41no—
279C3×#41—41no—
280C3×#41—62no—
281C3×#41—62no—
282C3×#41—64no—
283C3×#41—64no—
284C3×#41—64no—
285C3×#41—64no—
286C3×#41—62no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—62no—
290C3×#41—61no—
291C3×#41—61no—
292C3×#41—61no—
293C3×#41—61no—
294C3×#41—61no—
295C3×#41—61no—
296C3×#41#6712yescomplemented
297C3×#41#6712yescomplemented
298C3×#41C22×D312yes—
299C3×#41C22×D312yes—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×Q8—62no—
304C2×C3×Q8—62no—
305C2×C3×Q8—62no—
306C2×C3×Q8#6711yescharacteristic, complemented
307C2×C3×Q8#6711yescharacteristic, complemented
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—32no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—32no—
315C2×C3×D4—41no—
316C2×C3×D4—62no—
317C2×C3×D4—64no—
318C2×C3×D4—64no—
319C2×C3×D4—62no—
320C2×C3×D4—64no—
321C2×C3×D4—61no—
322C2×C3×D4—62no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4#6711yescharacteristic, complemented
329C2×C3×D4#6711yescharacteristic, complemented
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—32no—
334C22×C3×C4—41no—
335C22×C3×C4—64no—
336C22×C3×C4—61no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—24no—
340C2×#67—21no—
341C2×#67—64no—
342C2×#67—64no—
343C2×#67#6712yes—
344#239—22no—
345#239—22no—
346D3×Q8—22no—
347D3×Q8—22no—
348#237—24no—
349#237—22no—
350#237—22no—
351#237—24no—
352D3×D4—24no—
353D3×D4—22no—
354D3×D4—24no—
355D3×D4—22no—
356#235—24no—
357#235—24no—
358#235—21no—
359#235—21no—
360#235—21no—
361#235—21no—
362#235—21no—
363#235—21no—
364#235—22no—
365#235—22no—
366#235#6712yescomplemented
367#235C22×D312yes—
368C2×D12—22no—
369C2×D12—21no—
370C2×D12—21no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12#6711yescharacteristic, complemented
375C2×D12C22×D312yes—
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—24no—
378C2×C4×D3—21no—
379C2×C4×D3#6712yes—
380C2×Dic6—22no—
381C2×Dic6#6711yescharacteristic, complemented
382C2×Dic6C22×D311yescharacteristic
383C3×SD16—64no—
384C3×D8—64no—
385C3×M16—32no—
386C3×M16—61no—
387C2×C3×C8—61no—
388#217—61no—
389#217—61no—
390#217—64no—
391#217—121no—
392#215—24no—
393#215—64no—
394#214—64no—
395#213—24no—
396#213—64no—
397#213—64no—
398(C2×D3)⋊C4—64no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—121no—
402C4×Dic3—32no—
403C4×Dic3—32no—
404C4×Dic3—62no—
405#208—21no—
406#208—32no—
407#208—32no—
408#208—62no—
409#208—61no—
410#208—61no—
411#208—121no—
412#208C22×D312yes—
413C2×C3⋊C8—21no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—121no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—81no—
420C22×C32#12011yescharacteristic
421C22×C32#12011yescharacteristic
422C22×C32C22×D411yescharacteristic
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—42no—
426C2×C3×D3—44no—
427C2×C3×D3—42no—
428C2×C3×D3—81no—
429C2×C3×D3—84no—
430C2×C3×D3—82no—
431C2×C3×D3—82no—
432C32×C4—22no—
433C32×C4#12011yescharacteristic
434C32×C4#12011yescharacteristic
435C32×C4C22×D411yescharacteristic
436C32×C4C22×D411yescharacteristic
437C3⋊Dic3—42no—
438C3×Dic3—22no—
439C3×Dic3—22no—
4402−1+4—32no—
4412−1+4—61no—
4422−1+4—61no—
443H(5,𝔽2)—32no—
444H(5,𝔽2)—62no—
445H(5,𝔽2)—61no—
446H(5,𝔽2)—61no—
447C2×#41—31no—
448C2×#41—31no—
449C2×#41—62no—
450C2×#41—62no—
451C2×#41—62no—
452C2×#41D3211yescharacteristic
453C22×D4—31no—
454AGL(1,ℤ/8)—34no—
455AGL(1,ℤ/8)—62no—
456AGL(1,ℤ/8)—94no—
457AGL(1,ℤ/8)—182no—
458C2×SD16—61no—
459C2×SD16—181no—
460C2×D8—61no—
461C2×D8—181no—
462C2×M16—31no—
463C2×M16—91no—
464#127—92no—
465#124—92no—
466#121—182no—
467#120—182no—
468#117—91no—
469#104—94no—
470#104—94no—
471#101—92no—
472#100—92no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—32no—
477C23×C3—41no—
478C23×C3—64no—
479C23×C3—61no—
480C23×C3—62no—
481C23×C3—121no—
482C23×C3—121no—
483C23×C3—242no—
484C23×C3D3×D411yescharacteristic
485C23×C3C2×#6711yescharacteristic
486C22×D3—24no—
487C22×D3—21no—
488C22×D3—22no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—82no—
492C22×D3C2×#6712yes—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—22no—
496C3×Q8—32no—
497C3×Q8—41no—
498C3×Q8—64no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8C2×#6712yes—
503C3×Q8C2×#6712yes—
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—42no—
514C3×D4—42no—
515C3×D4—64no—
516C3×D4—64no—
517C3×D4—64no—
518C3×D4—62no—
519C3×D4—62no—
520C3×D4—62no—
521C3×D4—62no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—62no—
526C3×D4—62no—
527C3×D4—121no—
528C3×D4—121no—
529C3×D4C2×#6712yes—
530C3×D4C2×#6712yes—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—32no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—41no—
547C2×C3×C4—64no—
548C2×C3×C4—64no—
549C2×C3×C4—64no—
550C2×C3×C4—61no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—62no—
554C2×C3×C4—62no—
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4C2×#6711yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C2×#6711yescharacteristic
561C2×C3×C4C2×#6711yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C2×#6711yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567#67—24no—
568#67—24no—
569#67—22no—
570#67—22no—
571#67—22no—
572#67—22no—
573#67—244no—
574#67—244no—
575C2×Dic3—24no—
576C2×Dic3—21no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—122no—
580C2×Dic3C2×#6712yes—
581D12—24no—
582D12—21no—
583D12—22no—
584D12—21no—
585D12—21no—
586D12—22no—
587D12—41no—
588D12—41no—
589D12C2×#6712yes—
590C4×D3—24no—
591C4×D3—24no—
592C4×D3—22no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—22no—
596Dic6—24no—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6C2×#6712yes—
601C3×C8—62no—
602C3⋊C8—22no—
603C3⋊C8—62no—
604C3⋊C8—62no—
605C3⋊C8—122no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—42no—
610C2×C32C2×#12011yescharacteristic
611C3×D3—42no—
612C3×D3—42no—
613C3×D3—82no—
614C24—61no—
615#41—21no—
616#41—21no—
617#41—32no—
618#41—32no—
619#41—62no—
620#41—62no—
621#41—64no—
622#41—64no—
623#41—64no—
624#41—64no—
625#41—62no—
626#41—62no—
627#41—62no—
628#41—62no—
629#41—61no—
630#41—61no—
631#41—61no—
632#41—61no—
633#41—61no—
634#41—61no—
635#41#62512yescomplemented
636#41C2×D3212yes—
637C2×Q8—31no—
638C2×Q8—31no—
639C2×Q8—62no—
640C2×Q8—62no—
641C2×Q8—62no—
642C2×Q8#62511yescharacteristic, complemented
643C2×D4—21no—
644C2×D4—32no—
645C2×D4—31no—
646C2×D4—32no—
647C2×D4—31no—
648C2×D4—62no—
649C2×D4—64no—
650C2×D4—64no—
651C2×D4—62no—
652C2×D4—64no—
653C2×D4—61no—
654C2×D4—62no—
655C2×D4—61no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—184no—
661C2×D4#62511yescharacteristic, complemented
662C22×C4—21no—
663C22×C4—32no—
664C22×C4—64no—
665C22×C4—61no—
666C22×C4C2×D3211yescharacteristic
667SD16—64no—
668SD16—184no—
669D8—64no—
670D8—184no—
671M16—32no—
672M16—61no—
673M16—92no—
674M16—181no—
675C2×C8—61no—
676C2×C8—181no—
677C4⋊C4—181no—
678C22⋊C4—184no—
679C22⋊C4—181no—
680C42—92no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—42no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—82no—
695C22×C3—122no—
696C22×C3—124no—
697C22×C3—122no—
698C22×C3—241no—
699C22×C3—242no—
700C22×C3—242no—
701C22×C3—244no—
702C22×C3#93711yescharacteristic
703C22×C3#93711yescharacteristic
704C22×C3#95311yescharacteristic
705C22×C3#95311yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C22×#6711yescharacteristic
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—42no—
711C2×D3—44no—
712C2×D3—42no—
713C2×D3—81no—
714C2×D3—84no—
715C2×D3—82no—
716C2×D3—82no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—42no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4#93711yescharacteristic
727C3×C4#93711yescharacteristic
728C3×C4#95311yescharacteristic
729C3×C4#95311yescharacteristic
730C3×C4C2×D3×D411yescharacteristic
731C3×C4C22×#6711yescharacteristic
732C3×C4C22×#6711yescharacteristic
733C3×C4C22×#6711yescharacteristic
734Dic3—22no—
735Dic3—22no—
736Dic3—122no—
737Dic3—122no—
738Dic3—242no—
739C32#302111yescharacteristic, complemented, Sylow
740C23—21no—
741C23—32no—
742C23—64no—
743C23—61no—
744C23—62no—
745C23—121no—
746C23—121no—
747C23—242no—
748C23D3×#6711yescharacteristic
749Q8—21no—
750Q8—32no—
751Q8—64no—
752Q8—61no—
753Q8—61no—
754Q8—61no—
755Q8C2×#62512yes—
756D4—22no—
757D4—22no—
758D4—21no—
759D4—32no—
760D4—64no—
761D4—64no—
762D4—64no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—62no—
767D4—61no—
768D4—62no—
769D4—61no—
770D4—62no—
771D4—61no—
772D4—121no—
773D4—121no—
774D4—724no—
775D4C2×#62512yes—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—32no—
780C2×C4—64no—
781C2×C4—64no—
782C2×C4—64no—
783C2×C4—61no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—182no—
789C2×C4C2×#62511yescharacteristic
790C2×C4C2×#62511yescharacteristic
791C2×C4D3×#6711yescharacteristic
792C2×C4D3×#6711yescharacteristic
793C2×C4D3×#6711yescharacteristic
794C2×C4C22×D3211yescharacteristic
795C8—62no—
796C8—182no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—41no—
805C2×C3—41no—
806C2×C3—41no—
807C2×C3—42no—
808C2×C3—42no—
809C2×C3—82no—
810C2×C3—122no—
811C2×C3—122no—
812C2×C3—242no—
813C2×C3C2×#93711yescharacteristic
814C2×C3C2×#95311yescharacteristic
815D3—42no—
816D3—42no—
817D3—82no—
818C22—22no—
819C22—41no—
820C22—62no—
821C22—62no—
822C22—81no—
823C22—122no—
824C22—124no—
825C22—122no—
826C22—241no—
827C22—242no—
828C22—242no—
829C22—244no—
830C22#6397611yescharacteristic
831C22#6397611yescharacteristic
832C22C2×D3×#6711yescharacteristic
833C4—22no—
834C4—62no—
835C4—62no—
836C4—362no—
837C4#6397611yescharacteristic
838C4#6397611yescharacteristic
839C4C22×#62511yescharacteristic
840C4C2×D3×#6711yescharacteristic
841C3—21no—
842C3#8395711yescharacteristic, complemented
843C3#8412211yescharacteristic, complemented
844C2—21no—
845C2—21no—
846C2—21no—
847C2—42no—
848C2—122no—
849C2—122no—
850C2—242no—
851C2C2×#6397611yescharacteristic
subgroupG/H
centerC2C2×#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3021
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C2×C3×#949C2semidirect
3. #10595040C2semidirect
4. C2×#63823C2semidirect
5. #10592935C2semidirect
6. #10591684C2semidirect
7. #10591665C2semidirect
8. #10591110C2semidirect
9. #10591076C2semidirect
14. C3×#1010C22semidirect
16. C3×#1009C22semidirect
25. C22×C3×D12C22semidirect
26. #64135C22semidirect
27. C2×#3748C22semidirect
29. C3×#949C22semidirect
32. C2×C3×#208C22semidirect
34. #63914C22semidirect
36. #63863C22semidirect
39. #63823C22semidirect
41. #63664C22semidirect
42. #63568C22semidirect
43. #63560C22semidirect
44. #63558C22semidirect
46. #5964D3semidirect
50. C2×#949D3semidirect
67. C32×#41D4semidirect
69. C2×C32×Q8D4semidirect
71. C2×C32×D4D4semidirect
99. C3×#235D4semidirect
107. C2×C3×D12D4semidirect
114. C2×C3×Dic6D4semidirect
149. #1010C2×D3semidirect
151. #1009C2×D3semidirect
160. C22×D12C2×D3semidirect
170. #949C2×D3semidirect
192. C2×#208C2×D3semidirect
296. C3×#41#67semidirect
297. C3×#41#67semidirect
306. C2×C3×Q8#67semidirect
307. C2×C3×Q8#67semidirect
328. C2×C3×D4#67semidirect
329. C2×C3×D4#67semidirect
366. #235#67semidirect
374. C2×D12#67semidirect
381. C2×Dic6#67semidirect
635. #41#625semidirect
642. C2×Q8#625semidirect
661. C2×D4#625semidirect
739. C32#3021semidirect
842. C3#83957semidirect
843. C3#84122semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C2×C3×#9492
#105950402
C2×#638232
#105929352
#105916842
#105916652
#105911102
#105910762
#841223
#839573