Finite Group Databasebeta

← #11865221

Subgroups — #11865221

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592935C211yesmaximal, characteristic, complemented
6#10591687C214yesmaximal, complemented
7#10591664C214yesmaximal, complemented
8#10591110C211yesmaximal, characteristic, complemented
9#10591076C211yesmaximal, characteristic, complemented
10#84123—31nomaximal
11#83993—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—21no—
14C3×#1010C2212yes—
15C3×#1009—21no—
16C3×#1009C2212yes—
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×Dic6C2211yescharacteristic, complemented
26#64135C2211yescharacteristic, complemented
27C2×#3748C2211yescharacteristic, complemented
28C3×#951—22no—
29C3×#951C2214yescomplemented
30C2×C3×#216—21no—
31C2×C3×#214—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33#63961—22no—
34#63873C2212yescomplemented
35#63863C2212yescomplemented
36#63856—22no—
37C2×#3718—21no—
38#63827—22no—
39#63827C2214yescomplemented
40C2×#3715—21no—
41#63664C2214yescomplemented
42#63568C2214yescomplemented
43#63560C2212yescomplemented
44#63558C2212yescomplemented
45C3×#585—31no—
46#5964D311yescharacteristic
47C2×C3×#137—31no—
48#5825—31no—
49C2×#951—31no—
50C2×#951D311yescharacteristic, complemented
51#5816—31no—
52C2×#942—31no—
53#5246—34no—
54#5242—34no—
55#5237—31no—
56#5236—31no—
57#5236—31no—
58#5236—31no—
59#5236—61no—
60#5205—34no—
61#5202—34no—
62#5139—31no—
63#5132—31no—
64C32×#41—21no—
65C32×#41—21no—
66C32×#41D412yes—
67C32×#41C2312yes—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—21no—
75C2×C3×#67D412yes—
76C22×C3×Dic3—21no—
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×#235D412yes—
100C3×#235C2312yes—
101C2×C3×D12—22no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D412yes—
107C2×C3×Dic6—22no—
108C2×C3×Dic6—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6D411yescharacteristic
114C2×C3×Dic6C2312yes—
115C2×C3×Dic6C2311yescharacteristic
116#3757—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4×C3⋊Dic3C2312yes—
119#3748—21no—
120#3748C2312yes—
121C2×C3⋊(C3⋊C8)—21no—
122C3×#216—24no—
123C3×#214—24no—
124C3×#208—21no—
125C3×#208C2312yes—
126C2×C3×C3⋊C8—21no—
127#3724—24no—
128(C2×D3)⋊Dic3—24no—
129#3718—24no—
130#3715—24no—
131#3022—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×Q8—31no—
148#1010—21no—
149#1010C2×D312yes—
150#1009—21no—
151#1009C2×D312yes—
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×Dic6C2×D311yescharacteristic, complemented
161C3×#137—34no—
162C3×#137—62no—
163C2×C3×Q16—61no—
164C2×C3×SD16—61no—
165C2×C3×M16—31no—
166#951—22no—
167#951—34no—
168#951—62no—
169#951C2×D314yescomplemented
170#947—32no—
171#946—62no—
172#944—32no—
173#944—32no—
174C2×#216—21no—
175C2×#216—61no—
176C2×#216—61no—
177#942—34no—
178#942—62no—
179C2×#215—61no—
180#936—32no—
181#935—62no—
182C2×#214—21no—
183C2×#214—61no—
184#929—62no—
185#926—31no—
186#926—31no—
187#926—61no—
188#924—62no—
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×D3C2×D412yes—
207C32×Q8—21no—
208C32×Q8C2×D412yes—
209C32×D4—22no—
210C32×D4—22no—
211C32×D4—21no—
212C32×D4C2×D412yes—
213C2×C32×C4—21no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2×D411yescharacteristic
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2411yescharacteristic
222C2×C3⋊Dic3—22no—
223C3×#67—24no—
224C3×#67—24no—
225C3×#67—22no—
226C3×#67—22no—
227C3×#67—22no—
228C3×#67—22no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3C2×D412yes—
235C3×D12—24no—
236C3×D12—21no—
237C3×D12—21no—
238C3×D12—21no—
239C3×D12C2×D412yes—
240C3×C4×D3—24no—
241C3×C4×D3—24no—
242C3×C4×D3—22no—
243C3×C4×D3—22no—
244C3×C4×D3—22no—
245C3×C4×D3—22no—
246C3×Dic6—24no—
247C3×Dic6—21no—
248C3×Dic6—21no—
249C3×Dic6—21no—
250C3×Dic6—22no—
251C3×Dic6—22no—
252C3×Dic6—41no—
253C3×Dic6—41no—
254C3×Dic6C2×D412yes—
255C3⋊(C3⋊C8)—22no—
256C3×C3⋊C8—22no—
257#585—31no—
258C2×#137—31no—
259C2×#137—91no—
260#536—91no—
261#456—94no—
262#455—94no—
263#421—91no—
264#421—91no—
265#413—91no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—22no—
271C3×#41—22no—
272C3×#41—32no—
273C3×#41—32no—
274C3×#41—41no—
275C3×#41—41no—
276C3×#41—62no—
277C3×#41—62no—
278C3×#41—64no—
279C3×#41—64no—
280C3×#41—64no—
281C3×#41—64no—
282C3×#41—62no—
283C3×#41—62no—
284C3×#41—62no—
285C3×#41—62no—
286C3×#41—61no—
287C3×#41—61no—
288C3×#41—61no—
289C3×#41—61no—
290C3×#41—61no—
291C3×#41—61no—
292C3×#41#6712yes—
293C3×#41#6712yes—
294C3×#41C22×D312yes—
295C3×#41C22×D312yes—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—32no—
300C2×C3×Q8—62no—
301C2×C3×Q8—62no—
302C2×C3×Q8—62no—
303C2×C3×Q8—61no—
304C2×C3×Q8—61no—
305C2×C3×Q8—61no—
306C2×C3×Q8—61no—
307C2×C3×Q8—61no—
308C2×C3×Q8#6711yescharacteristic
309C2×C3×Q8#6711yescharacteristic
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—32no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—41no—
317C2×C3×D4—62no—
318C2×C3×D4—64no—
319C2×C3×D4—64no—
320C2×C3×D4—62no—
321C2×C3×D4—64no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4#6711yescharacteristic
325C2×C3×D4#6711yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—32no—
330C22×C3×C4—41no—
331C22×C3×C4—64no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—24no—
337C2×#67—21no—
338C2×#67#6712yes—
339C22×Dic3—21no—
340#239—22no—
341#239—22no—
342D3×Q8—22no—
343D3×Q8—22no—
344#237—24no—
345#237—22no—
346#237—22no—
347#237—24no—
348D3×D4—24no—
349D3×D4—22no—
350D3×D4—24no—
351D3×D4—22no—
352#235—24no—
353#235—24no—
354#235—21no—
355#235—21no—
356#235—21no—
357#235—21no—
358#235—21no—
359#235—21no—
360#235—22no—
361#235—22no—
362#235#6712yes—
363#235C22×D312yes—
364C2×D12—22no—
365C2×D12#6711yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—24no—
368C2×C4×D3—21no—
369C2×C4×D3#6712yes—
370C2×Dic6—22no—
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6#6711yescharacteristic
377C2×Dic6C22×D312yes—
378C2×Dic6C22×D311yescharacteristic
379C3×Q16—64no—
380C3×SD16—64no—
381C3×M16—32no—
382C3×M16—61no—
383C2×C3×C8—61no—
384#217—64no—
385#217—61no—
386#217—61no—
387#217—121no—
388#216—24no—
389#216—64no—
390#216—64no—
391#215—64no—
392#214—24no—
393#214—64no—
394(C2×D3)⋊C4—64no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—121no—
398Dic3⋊C4—64no—
399Dic3⋊C4—64no—
400C4×Dic3—32no—
401C4×Dic3—32no—
402C4×Dic3—62no—
403#208—21no—
404#208—32no—
405#208—32no—
406#208—62no—
407#208—61no—
408#208—61no—
409#208—121no—
410#208C22×D312yes—
411C2×C3⋊C8—21no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—121no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—81no—
418C22×C32#12011yescharacteristic
419C22×C32#12011yescharacteristic
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—42no—
424C2×C3×D3—81no—
425C2×C3×D3—84no—
426C32×C4—22no—
427C32×C4#12011yescharacteristic
428C32×C4#12011yescharacteristic
429C32×C4C22×D411yescharacteristic
430C32×C4C22×D411yescharacteristic
431C3⋊Dic3—42no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—42no—
4352−1+4—32no—
4362−1+4—61no—
4372−1+4—61no—
438H(5,𝔽2)—32no—
439H(5,𝔽2)—62no—
440H(5,𝔽2)—61no—
441H(5,𝔽2)—61no—
442C2×#41—31no—
443C2×#41—31no—
444C2×#41—62no—
445C2×#41—62no—
446C2×#41—62no—
447C2×#41D3211yescharacteristic
448C22×Q8—31no—
449#137—34no—
450#137—62no—
451#137—94no—
452#137—182no—
453C2×Q16—61no—
454C2×Q16—181no—
455C2×SD16—61no—
456C2×SD16—181no—
457C2×M16—31no—
458C2×M16—91no—
459C4⋊Q8—92no—
460#124—92no—
461#123—182no—
462C22⋊Q8—182no—
463#117—91no—
464#104—94no—
465#104—94no—
466#101—92no—
467#100—92no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—32no—
472C23×C3—41no—
473C23×C3—64no—
474C23×C3—61no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3—24no—
478C22×D3—21no—
479C22×D3C2×#6712yes—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—22no—
483C3×Q8—32no—
484C3×Q8—41no—
485C3×Q8—64no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—62no—
490C3×Q8—62no—
491C3×Q8—121no—
492C3×Q8—121no—
493C3×Q8C2×#6712yes—
494C3×Q8C2×#6712yes—
495C3×D4—22no—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—22no—
502C3×D4—32no—
503C3×D4—41no—
504C3×D4—42no—
505C3×D4—42no—
506C3×D4—64no—
507C3×D4—64no—
508C3×D4—64no—
509C3×D4—62no—
510C3×D4—62no—
511C3×D4—62no—
512C3×D4—62no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4C2×#6712yes—
517C3×D4C2×#6712yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—32no—
531C2×C3×C4—42no—
532C2×C3×C4—42no—
533C2×C3×C4—41no—
534C2×C3×C4—64no—
535C2×C3×C4—64no—
536C2×C3×C4—64no—
537C2×C3×C4—61no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—62no—
543C2×C3×C4—121no—
544C2×C3×C4—121no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4C2×#6711yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557#67—24no—
558#67—24no—
559#67—22no—
560#67—22no—
561#67—22no—
562#67—22no—
563C2×Dic3—24no—
564C2×Dic3—21no—
565C2×Dic3—22no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—122no—
571C2×Dic3C2×#6712yes—
572D12—24no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12C2×#6712yes—
577C4×D3—24no—
578C4×D3—24no—
579C4×D3—22no—
580C4×D3—22no—
581C4×D3—22no—
582C4×D3—22no—
583Dic6—24no—
584Dic6—21no—
585Dic6—21no—
586Dic6—21no—
587Dic6—22no—
588Dic6—22no—
589Dic6—41no—
590Dic6—41no—
591Dic6C2×#6712yes—
592C3×C8—62no—
593C3⋊C8—22no—
594C3⋊C8—62no—
595C3⋊C8—62no—
596C3⋊C8—122no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—42no—
601C2×C32C2×#12011yescharacteristic
602C3×D3—42no—
603C3×D3—42no—
604#41—21no—
605#41—21no—
606#41—32no—
607#41—32no—
608#41—62no—
609#41—62no—
610#41—64no—
611#41—64no—
612#41—64no—
613#41—64no—
614#41—62no—
615#41—62no—
616#41—62no—
617#41—62no—
618#41—61no—
619#41—61no—
620#41—61no—
621#41—61no—
622#41—61no—
623#41—61no—
624#41#62512yes—
625#41C2×D3212yes—
626C2×Q8—31no—
627C2×Q8—32no—
628C2×Q8—31no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—62no—
632C2×Q8—61no—
633C2×Q8—61no—
634C2×Q8—61no—
635C2×Q8—61no—
636C2×Q8—61no—
637C2×Q8#62511yescharacteristic
638C2×D4—21no—
639C2×D4—32no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—62no—
643C2×D4—64no—
644C2×D4—64no—
645C2×D4—62no—
646C2×D4—64no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4#62511yescharacteristic
650C22×C4—21no—
651C22×C4—32no—
652C22×C4—64no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4C2×D3211yescharacteristic
656Q16—64no—
657Q16—184no—
658SD16—64no—
659SD16—184no—
660M16—32no—
661M16—61no—
662M16—92no—
663M16—181no—
664C2×C8—61no—
665C2×C8—181no—
666C4⋊C4—184no—
667C4⋊C4—181no—
668C22⋊C4—184no—
669C22⋊C4—181no—
670C42—92no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—42no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—82no—
685C22×C3—122no—
686C22×C3—241no—
687C22×C3—244no—
688C22×C3#93711yescharacteristic
689C22×C3#93711yescharacteristic
690C22×C3#95311yescharacteristic
691C22×C3#95311yescharacteristic
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C22×#6711yescharacteristic
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—42no—
697C2×D3—81no—
698C2×D3—84no—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—42no—
706C3×C4—62no—
707C3×C4—62no—
708C3×C4—122no—
709C3×C4#93711yescharacteristic
710C3×C4#93711yescharacteristic
711C3×C4#95311yescharacteristic
712C3×C4#95311yescharacteristic
713C3×C4C2×D3×D411yescharacteristic
714C3×C4C22×#6711yescharacteristic
715C3×C4C22×#6711yescharacteristic
716C3×C4C22×#6711yescharacteristic
717Dic3—22no—
718Dic3—22no—
719Dic3—42no—
720Dic3—122no—
721Dic3—122no—
722Dic3—242no—
723C32#302211yescharacteristic, complemented, Sylow
724C23—21no—
725C23—32no—
726C23—64no—
727C23—61no—
728C23D3×#6711yescharacteristic
729Q8—21no—
730Q8—32no—
731Q8—64no—
732Q8—61no—
733Q8—61no—
734Q8—61no—
735Q8—62no—
736Q8—62no—
737Q8—121no—
738Q8—121no—
739Q8C2×#62512yes—
740D4—22no—
741D4—22no—
742D4—21no—
743D4—32no—
744D4—64no—
745D4—64no—
746D4—64no—
747D4—62no—
748D4—62no—
749D4—62no—
750D4—62no—
751D4—61no—
752D4—61no—
753D4—61no—
754D4C2×#62512yes—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—32no—
759C2×C4—64no—
760C2×C4—64no—
761C2×C4—64no—
762C2×C4—61no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—182no—
771C2×C4C2×#62511yescharacteristic
772C2×C4C2×#62511yescharacteristic
773C2×C4D3×#6711yescharacteristic
774C2×C4D3×#6711yescharacteristic
775C2×C4D3×#6711yescharacteristic
776C2×C4C22×D3211yescharacteristic
777C8—62no—
778C8—182no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—41no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3—82no—
792C2×C3—122no—
793C2×C3—122no—
794C2×C3C2×#93711yescharacteristic
795C2×C3C2×#95311yescharacteristic
796D3—42no—
797D3—42no—
798C22—22no—
799C22—41no—
800C22—62no—
801C22—62no—
802C22—81no—
803C22—122no—
804C22—241no—
805C22—244no—
806C22#6397611yescharacteristic
807C22#6397611yescharacteristic
808C22C2×D3×#6711yescharacteristic
809C4—22no—
810C4—62no—
811C4—62no—
812C4—122no—
813C4—362no—
814C4#6397611yescharacteristic
815C4#6397611yescharacteristic
816C4C22×#62511yescharacteristic
817C4C2×D3×#6711yescharacteristic
818C3—21no—
819C3#8399311yescharacteristic, complemented
820C3#8412311yescharacteristic, complemented
821C2—21no—
822C2—21no—
823C2—21no—
824C2—42no—
825C2—122no—
826C2—122no—
827C2C2×#6397611yescharacteristic
subgroupG/H
centerC2C2×#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
prime radicalC3×#5964C2
hypercenterC2×#41D32
hypocenterC32#3022
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
2. C2×C3×#951C2semidirect
3. #10594855C2semidirect
4. C2×#63827C2semidirect
5. #10592935C2semidirect
6. #10591687C2semidirect
7. #10591664C2semidirect
8. #10591110C2semidirect
9. #10591076C2semidirect
25. C22×C3×Dic6C22semidirect
26. #64135C22semidirect
27. C2×#3748C22semidirect
29. C3×#951C22semidirect
32. C2×C3×#208C22semidirect
34. #63873C22semidirect
35. #63863C22semidirect
39. #63827C22semidirect
41. #63664C22semidirect
42. #63568C22semidirect
43. #63560C22semidirect
44. #63558C22semidirect
50. C2×#951D3semidirect
160. C22×Dic6C2×D3semidirect
169. #951C2×D3semidirect
192. C2×#208C2×D3semidirect
723. C32#3022semidirect
819. C3#83993semidirect
820. C3#84123semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C2×C3×#9512
#105948552
C2×#638272
#105929352
#105916872
#105916642
#105911102
#105910762
#841233
#839933