Finite Group Databasebeta

← #11864991

Subgroups — #11864991

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3#10595032C211yesmaximal, characteristic, complemented
4#10594786C211yesmaximal, characteristic, complemented
5C2×#63664C211yesmaximal, characteristic, complemented
6#10591687C212yesmaximal, complemented
7#10591684C212yesmaximal, complemented
8#10591665C212yesmaximal, complemented
9#10591664C212yesmaximal, complemented
10C2×#63568C211yesmaximal, characteristic, complemented
11#10591076C211yesmaximal, characteristic, complemented
12#84121—31nomaximal
13#84004—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C3×#1010—21no—
16C3×#1010C2212yes—
17C3×#1009—21no—
18C3×#1009C2212yes—
19C3×D3×#41—22no—
20C3×D3×#41—22no—
21C3×#1007—21no—
22C3×#1004—21no—
23C3×#1004—22no—
24C2×C3×#235—22no—
25C2×C3×#235C2211yescharacteristic
26C2×C3×#235C2211yescharacteristic
27C2×C3×#235C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
29C2×#3748C2211yescharacteristic, complemented
30C3×#951C2212yescomplemented
31C3×#950—22no—
32C3×#949C2212yescomplemented
33C3×#942—21no—
34C3×#932—21no—
35C2×C3×#208C2211yescharacteristic, complemented
36#63980—22no—
37#63914C2211yescharacteristic, complemented
38C4×#625—22no—
39#63873C2211yescharacteristic, complemented
40#63863C2211yescharacteristic, complemented
41#63863C2211yescharacteristic, complemented
42#63827—21no—
43#63827C2212yescomplemented
44#63823—21no—
45#63823C2212yescomplemented
46#63822—22no—
47#63664C2212yescomplemented
48#63664C2212yescomplemented
49#63568C2212yescomplemented
50#63568C2212yescomplemented
51#63560C2212yescomplemented
52#63558C2212yescomplemented
53C3×#585—31no—
54#5964D311yescharacteristic, complemented
55C3×#575—31no—
56#5832—31no—
57#5832—31no—
58#5822—31no—
59#5822—31no—
60#5822D311yescharacteristic, complemented
61#5246—32no—
62#5245—32no—
63#5242—32no—
64#5241—32no—
65#5237—31no—
66C2×#837—31no—
67C2×#837—31no—
68C2×#837—31no—
69C2×#837—61no—
70#5205—32no—
71#5202—32no—
72#5201—32no—
73#5198—32no—
74C2×#825—31no—
75#5132—31no—
76C32×#41—21no—
77C32×#41—21no—
78C32×#41D412yescomplemented
79C32×#41C2312yes—
80C2×C32×Q8D411yescharacteristic, complemented
81C2×C32×D4—21no—
82C2×C32×D4D411yescharacteristic, complemented
83C22×C32×C4—21no—
84C22×C32×C4C2311yescharacteristic
85C22×C3⋊Dic3—21no—
86C2×C3×#67—24no—
87C2×C3×#67—21no—
88C2×C3×#67—21no—
89C2×C3×#67D412yes—
90C3×#239—22no—
91C3×#239—22no—
92C3×D3×Q8—22no—
93C3×D3×Q8—22no—
94C3×#237—24no—
95C3×#237—22no—
96C3×#237—22no—
97C3×#237—24no—
98C3×D3×D4—24no—
99C3×D3×D4—22no—
100C3×D3×D4—24no—
101C3×D3×D4—22no—
102C3×#235—24no—
103C3×#235—24no—
104C3×#235—21no—
105C3×#235—21no—
106C3×#235—21no—
107C3×#235—21no—
108C3×#235—21no—
109C3×#235—21no—
110C3×#235—22no—
111C3×#235—21no—
112C3×#235—21no—
113C3×#235—21no—
114C3×#235—21no—
115C3×#235—22no—
116C3×#235D412yescomplemented
117C3×#235C2312yes—
118C2×C3×D12—22no—
119C2×C3×D12D411yescharacteristic, complemented
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3D412yes—
126C2×C3×Dic6—22no—
127C2×C3×Dic6D411yescharacteristic, complemented
128C2×C3×Dic6C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic
130C2×#625—22no—
131C4×C3⋊Dic3—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134#3748—21no—
135#3748C2312yes—
136C2×C3⋊(C3⋊C8)—21no—
137C3×#216—22no—
138C3×#215—22no—
139C3×#214—22no—
140C3×#213—22no—
141C3×#208—21no—
142C3×#208C2312yes—
143C2×C3×C3⋊C8—21no—
144#3724—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147#3718—22no—
148#3715—22no—
149#3715—22no—
150#3713—22no—
151#3018—91noSylow
152C3×2−1+4—32no—
153C3×2−1+4—61no—
154C3×2−1+4—61no—
155C3×H(5,𝔽2)—32no—
156C3×H(5,𝔽2)—62no—
157C3×H(5,𝔽2)—61no—
158C3×H(5,𝔽2)—61no—
159C2×C3×#41—21no—
160C2×C3×#41—31no—
161C2×C3×#41—31no—
162C2×C3×#41—31no—
163C2×C3×#41—62no—
164C2×C3×#41—62no—
165C2×C3×#41—62no—
166C2×C3×#41C2×D311yescharacteristic
167C2×C3×#41C2×D311yescharacteristic
168#1010—21no—
169#1010C2×D312yes—
170#1009—21no—
171#1009C2×D312yes—
172D3×#41—22no—
173D3×#41—22no—
174#1007—21no—
175#1004—21no—
176#1004—22no—
177C2×#235—22no—
178C2×#235C2×D311yescharacteristic
179C2×#235C2×D311yescharacteristic
180C2×#235C2×D311yescharacteristic, complemented
181C3×#137—32no—
182C3×#137—61no—
183C3×AGL(1,ℤ/8)—32no—
184C3×AGL(1,ℤ/8)—61no—
185C3×#135—62no—
186C2×C3×M16—31no—
187#951—32no—
188#951—61no—
189#951C2×D312yescomplemented
190#950—22no—
191#950—62no—
192#950—62no—
193#949—32no—
194#949—61no—
195#949C2×D312yescomplemented
196#947—31no—
197#947—31no—
198#944—31no—
199#944—31no—
200#942—21no—
201#942—32no—
202#942—61no—
203#940—31no—
204#940—31no—
205#939—62no—
206#939—62no—
207#936—31no—
208#936—31no—
209#932—21no—
210#932—32no—
211#932—61no—
212C4×#67—62no—
213C4×#67—62no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—61no—
217C2×#208—31no—
218C2×#208—31no—
219C2×#208—61no—
220C2×#208C2×D311yescharacteristic, complemented
221#837—32no—
222#837—32no—
223#837—32no—
224#837—32no—
225#837—32no—
226#837—32no—
227#837—62no—
228#837—62no—
229#836—32no—
230#833—32no—
231#825—32no—
232#825—32no—
233#824—32no—
234#823—32no—
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D412yes—
241C32×Q8—21no—
242C32×Q8C2×D412yes—
243C32×D4—22no—
244C32×D4—22no—
245C32×D4—21no—
246C32×D4C2×D412yes—
247C2×C32×C4—21no—
248C2×C32×C4—22no—
249C2×C32×C4—22no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259C3×#67—24no—
260C3×#67—24no—
261C3×#67—22no—
262C3×#67—22no—
263C3×#67—22no—
264C3×#67—22no—
265C3×#67—41no—
266C3×#67—41no—
267C2×C3×Dic3—24no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3C2×D412yes—
271C3×D12—24no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12C2×D412yes—
278C3×C4×D3—24no—
279C3×C4×D3—24no—
280C3×C4×D3—22no—
281C3×C4×D3—22no—
282C3×C4×D3—22no—
283C3×C4×D3—22no—
284C3×C4×D3—41no—
285C3×C4×D3—41no—
286C3×Dic6—24no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6C2×D412yes—
293#625—44no—
294C3⋊(C3⋊C8)—22no—
295C3×C3⋊C8—22no—
296#585—31no—
297#575—31no—
298#575—91no—
299#532—91no—
300#456—92no—
301#455—92no—
302#454—92no—
303#453—92no—
304C2×#104—91no—
305C2×#104—91no—
306#413—91no—
307C3×#41—21no—
308C3×#41—21no—
309C3×#41—21no—
310C3×#41—21no—
311C3×#41—22no—
312C3×#41—22no—
313C3×#41—32no—
314C3×#41—32no—
315C3×#41—41no—
316C3×#41—41no—
317C3×#41—62no—
318C3×#41—62no—
319C3×#41—64no—
320C3×#41—64no—
321C3×#41—64no—
322C3×#41—64no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—62no—
327C3×#41—61no—
328C3×#41—61no—
329C3×#41—61no—
330C3×#41—61no—
331C3×#41—61no—
332C3×#41—61no—
333C3×#41—61no—
334C3×#41—61no—
335C3×#41—61no—
336C3×#41—61no—
337C3×#41#6712yescomplemented
338C3×#41#6712yescomplemented
339C3×#41C22×D312yes—
340C3×#41C22×D312yes—
341C2×C3×Q8—21no—
342C2×C3×Q8—31no—
343C2×C3×Q8—31no—
344C2×C3×Q8—31no—
345C2×C3×Q8—62no—
346C2×C3×Q8—62no—
347C2×C3×Q8—62no—
348C2×C3×Q8#6711yescharacteristic, complemented
349C2×C3×Q8#6711yescharacteristic, complemented
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—21no—
353C2×C3×D4—32no—
354C2×C3×D4—31no—
355C2×C3×D4—31no—
356C2×C3×D4—31no—
357C2×C3×D4—41no—
358C2×C3×D4—62no—
359C2×C3×D4—64no—
360C2×C3×D4—64no—
361C2×C3×D4—62no—
362C2×C3×D4—64no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—61no—
366C2×C3×D4#6711yescharacteristic, complemented
367C2×C3×D4#6711yescharacteristic, complemented
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—32no—
372C22×C3×C4—41no—
373C22×C3×C4—64no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C2×#67—24no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67#6712yes—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—121no—
387#239—22no—
388#239—22no—
389D3×Q8—22no—
390D3×Q8—22no—
391#237—24no—
392#237—22no—
393#237—22no—
394#237—24no—
395D3×D4—24no—
396D3×D4—22no—
397D3×D4—24no—
398D3×D4—22no—
399#235—24no—
400#235—24no—
401#235—21no—
402#235—21no—
403#235—21no—
404#235—21no—
405#235—21no—
406#235—21no—
407#235—22no—
408#235—21no—
409#235—21no—
410#235—21no—
411#235—21no—
412#235—22no—
413#235#6712yescomplemented
414#235C22×D312yes—
415C2×D12—22no—
416C2×D12#6711yescharacteristic, complemented
417C2×D12C22×D311yescharacteristic
418C2×D12C22×D311yescharacteristic
419C2×C4×D3—24no—
420C2×C4×D3—21no—
421C2×C4×D3—21no—
422C2×C4×D3#6712yes—
423C2×Dic6—22no—
424C2×Dic6#6711yescharacteristic, complemented
425C2×Dic6C22×D311yescharacteristic
426C2×Dic6C22×D311yescharacteristic
427C3×Q16—62no—
428C3×SD16—62no—
429C3×SD16—62no—
430C3×D8—62no—
431C3×M16—32no—
432C3×M16—61no—
433C2×C3×C8—61no—
434#217—62no—
435#217—62no—
436#216—22no—
437#216—62no—
438#216—62no—
439#215—22no—
440#215—62no—
441#215—62no—
442#214—22no—
443#214—62no—
444#214—62no—
445#213—22no—
446#213—62no—
447#213—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—31no—
455C4×Dic3—31no—
456C4×Dic3—61no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—121no—
461#208—21no—
462#208—32no—
463#208—32no—
464#208—62no—
465#208—61no—
466#208—61no—
467#208—121no—
468#208C22×D312yes—
469C2×C3⋊C8—21no—
470C2×C3⋊C8—61no—
471C2×C3⋊C8—61no—
472C2×C3⋊C8—121no—
473C22×C32—22no—
474C22×C32—41no—
475C22×C32—81no—
476C22×C32#12011yescharacteristic
477C22×C32#12011yescharacteristic
478C22×C32C22×D411yescharacteristic
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—42no—
482C2×C3×D3—42no—
483C2×C3×D3—41no—
484C2×C3×D3—81no—
485C2×C3×D3—84no—
486C32×C4—22no—
487C32×C4#12011yescharacteristic
488C32×C4#12011yescharacteristic
489C32×C4C22×D411yescharacteristic
490C32×C4C22×D411yescharacteristic
491C3⋊Dic3—22no—
492C3⋊Dic3—41no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—41no—
4962−1+4—32no—
4972−1+4—61no—
4982−1+4—61no—
499H(5,𝔽2)—32no—
500H(5,𝔽2)—62no—
501H(5,𝔽2)—61no—
502H(5,𝔽2)—61no—
503C2×#41—31no—
504C2×#41—31no—
505C2×#41—31no—
506C2×#41—62no—
507C2×#41—62no—
508C2×#41—62no—
509C2×#41D3211yescharacteristic
510#137—32no—
511#137—61no—
512#137—92no—
513#137—181no—
514AGL(1,ℤ/8)—32no—
515AGL(1,ℤ/8)—61no—
516AGL(1,ℤ/8)—92no—
517AGL(1,ℤ/8)—181no—
518#135—62no—
519#135—182no—
520C2×M16—31no—
521C2×M16—91no—
522C4⋊Q8—91no—
523#127—91no—
524#124—91no—
525#124—91no—
526#121—182no—
527C4×D4—182no—
528C2×C42—91no—
529#104—92no—
530#104—92no—
531#104—92no—
532#104—92no—
533#101—92no—
534#100—92no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—32no—
539C23×C3—41no—
540C23×C3—64no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3D3×D411yescharacteristic
544C23×C3C2×#6711yescharacteristic
545C22×D3—24no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3C2×#6712yes—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—22no—
552C3×Q8—32no—
553C3×Q8—41no—
554C3×Q8—64no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—61no—
560C3×Q8C2×#6712yes—
561C3×Q8C2×#6712yes—
562C3×D4—22no—
563C3×D4—22no—
564C3×D4—22no—
565C3×D4—22no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—22no—
569C3×D4—32no—
570C3×D4—41no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—64no—
574C3×D4—64no—
575C3×D4—64no—
576C3×D4—62no—
577C3×D4—62no—
578C3×D4—62no—
579C3×D4—62no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—121no—
586C3×D4—121no—
587C3×D4C2×#6712yes—
588C3×D4C2×#6712yes—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—32no—
602C2×C3×C4—42no—
603C2×C3×C4—42no—
604C2×C3×C4—41no—
605C2×C3×C4—64no—
606C2×C3×C4—64no—
607C2×C3×C4—64no—
608C2×C3×C4—61no—
609C2×C3×C4—62no—
610C2×C3×C4—62no—
611C2×C3×C4—62no—
612C2×C3×C4—62no—
613C2×C3×C4—61no—
614C2×C3×C4—121no—
615C2×C3×C4—121no—
616C2×C3×C4D3×D411yescharacteristic
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4D3×D411yescharacteristic
619C2×C3×C4C2×#6711yescharacteristic
620C2×C3×C4C2×#6711yescharacteristic
621C2×C3×C4C2×#6711yescharacteristic
622C2×C3×C4C2×#6711yescharacteristic
623C2×C3×C4C2×#6711yescharacteristic
624C2×C3×C4C2×#6711yescharacteristic
625C2×C3×C4C2×#6711yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627C2×C3×C4C23×D311yescharacteristic
628#67—24no—
629#67—24no—
630#67—22no—
631#67—22no—
632#67—22no—
633#67—22no—
634#67—41no—
635#67—41no—
636#67—124no—
637#67—124no—
638C2×Dic3—24no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—122no—
648C2×Dic3—122no—
649C2×Dic3—124no—
650C2×Dic3C2×#6712yes—
651D12—24no—
652D12—21no—
653D12—21no—
654D12—21no—
655D12—21no—
656D12—21no—
657D12C2×#6712yes—
658C4×D3—24no—
659C4×D3—24no—
660C4×D3—22no—
661C4×D3—22no—
662C4×D3—22no—
663C4×D3—22no—
664C4×D3—41no—
665C4×D3—41no—
666Dic6—24no—
667Dic6—21no—
668Dic6—21no—
669Dic6—21no—
670Dic6—21no—
671Dic6—21no—
672Dic6C2×#6712yes—
673C3×C8—62no—
674C3⋊C8—22no—
675C3⋊C8—62no—
676C3⋊C8—62no—
677C3⋊C8—122no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—42no—
682C2×C32C2×#12011yescharacteristic
683C3×D3—42no—
684C3×D3—42no—
685C3×D3—81no—
686#41—21no—
687#41—21no—
688#41—32no—
689#41—32no—
690#41—62no—
691#41—62no—
692#41—64no—
693#41—64no—
694#41—64no—
695#41—64no—
696#41—62no—
697#41—62no—
698#41—62no—
699#41—62no—
700#41—61no—
701#41—61no—
702#41—61no—
703#41—61no—
704#41—61no—
705#41—61no—
706#41—61no—
707#41—61no—
708#41—61no—
709#41—61no—
710#41#62512yescomplemented
711#41C2×D3212yes—
712C2×Q8—31no—
713C2×Q8—31no—
714C2×Q8—31no—
715C2×Q8—62no—
716C2×Q8—62no—
717C2×Q8—62no—
718C2×Q8#62511yescharacteristic, complemented
719C2×D4—21no—
720C2×D4—32no—
721C2×D4—31no—
722C2×D4—31no—
723C2×D4—31no—
724C2×D4—62no—
725C2×D4—64no—
726C2×D4—64no—
727C2×D4—62no—
728C2×D4—64no—
729C2×D4—61no—
730C2×D4—62no—
731C2×D4—61no—
732C2×D4—182no—
733C2×D4#62511yescharacteristic, complemented
734C22×C4—21no—
735C22×C4—32no—
736C22×C4—64no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—181no—
740C22×C4C2×D3211yescharacteristic
741Q16—62no—
742Q16—182no—
743SD16—62no—
744SD16—62no—
745SD16—182no—
746SD16—182no—
747D8—62no—
748D8—182no—
749M16—32no—
750M16—61no—
751M16—92no—
752M16—181no—
753C2×C8—61no—
754C2×C8—181no—
755C4⋊C4—182no—
756C22⋊C4—182no—
757C22⋊C4—182no—
758C42—91no—
759C42—91no—
760C42—181no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—42no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—42no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—82no—
775C22×C3—122no—
776C22×C3—122no—
777C22×C3—121no—
778C22×C3—241no—
779C22×C3—244no—
780C22×C3#93711yescharacteristic
781C22×C3#93711yescharacteristic
782C22×C3#95311yescharacteristic
783C22×C3#95311yescharacteristic
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C22×#6711yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—42no—
789C2×D3—42no—
790C2×D3—41no—
791C2×D3—81no—
792C2×D3—84no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—42no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—121no—
803C3×C4#93711yescharacteristic
804C3×C4#93711yescharacteristic
805C3×C4#95311yescharacteristic
806C3×C4#95311yescharacteristic
807C3×C4C2×D3×D411yescharacteristic
808C3×C4C22×#6711yescharacteristic
809C3×C4C22×#6711yescharacteristic
810C3×C4C22×#6711yescharacteristic
811Dic3—22no—
812Dic3—22no—
813Dic3—41no—
814Dic3—62no—
815Dic3—62no—
816Dic3—122no—
817Dic3—121no—
818Dic3—121no—
819Dic3—122no—
820C32#301811yescharacteristic, complemented, Sylow
821C23—21no—
822C23—32no—
823C23—64no—
824C23—61no—
825C23—61no—
826C23D3×#6711yescharacteristic
827Q8—21no—
828Q8—32no—
829Q8—64no—
830Q8—61no—
831Q8—61no—
832Q8—61no—
833Q8—61no—
834Q8—61no—
835Q8C2×#62512yes—
836D4—22no—
837D4—22no—
838D4—21no—
839D4—32no—
840D4—64no—
841D4—64no—
842D4—64no—
843D4—62no—
844D4—62no—
845D4—62no—
846D4—62no—
847D4—61no—
848D4—61no—
849D4—61no—
850D4—61no—
851D4—61no—
852D4—121no—
853D4—121no—
854D4—364no—
855D4C2×#62512yes—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—32no—
860C2×C4—64no—
861C2×C4—64no—
862C2×C4—64no—
863C2×C4—61no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—61no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—362no—
874C2×C4C2×#62511yescharacteristic
875C2×C4C2×#62511yescharacteristic
876C2×C4D3×#6711yescharacteristic
877C2×C4D3×#6711yescharacteristic
878C2×C4D3×#6711yescharacteristic
879C2×C4C22×D3211yescharacteristic
880C8—62no—
881C8—182no—
882C2×C3—22no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—41no—
891C2×C3—41no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—82no—
895C2×C3—122no—
896C2×C3—122no—
897C2×C3—241no—
898C2×C3C2×#93711yescharacteristic
899C2×C3C2×#95311yescharacteristic
900D3—42no—
901D3—42no—
902D3—81no—
903C22—22no—
904C22—41no—
905C22—62no—
906C22—62no—
907C22—81no—
908C22—122no—
909C22—122no—
910C22—121no—
911C22—241no—
912C22—244no—
913C22#6397611yescharacteristic
914C22#6397611yescharacteristic
915C22C2×D3×#6711yescharacteristic
916C4—22no—
917C4—62no—
918C4—62no—
919C4—121no—
920C4—182no—
921C4—361no—
922C4#6397611yescharacteristic
923C4#6397611yescharacteristic
924C4C22×#62511yescharacteristic
925C4C2×D3×#6711yescharacteristic
926C3—21no—
927C3#8400411yescharacteristic, complemented
928C3#8412111yescharacteristic, complemented
929C2—21no—
930C2—21no—
931C2—21no—
932C2—42no—
933C2—122no—
934C2—122no—
935C2—241no—
936C2C2×#6397611yescharacteristic
subgroupG/H
centerC4#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3018
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C3×#5822C2semidirect
3. #10595032C2semidirect
4. #10594786C2semidirect
5. C2×#63664C2semidirect
6. #10591687C2semidirect
7. #10591684C2semidirect
8. #10591665C2semidirect
9. #10591664C2semidirect
10. C2×#63568C2semidirect
11. #10591076C2semidirect
27. C2×C3×#235C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
29. C2×#3748C22semidirect
30. C3×#951C22semidirect
32. C3×#949C22semidirect
35. C2×C3×#208C22semidirect
37. #63914C22semidirect
39. #63873C22semidirect
40. #63863C22semidirect
41. #63863C22semidirect
43. #63827C22semidirect
45. #63823C22semidirect
47. #63664C22semidirect
48. #63664C22semidirect
49. #63568C22semidirect
50. #63568C22semidirect
51. #63560C22semidirect
52. #63558C22semidirect
54. #5964D3semidirect
60. #5822D3semidirect
78. C32×#41D4semidirect
80. C2×C32×Q8D4semidirect
82. C2×C32×D4D4semidirect
116. C3×#235D4semidirect
119. C2×C3×D12D4semidirect
127. C2×C3×Dic6D4semidirect
180. C2×#235C2×D3semidirect
189. #951C2×D3semidirect
195. #949C2×D3semidirect
220. C2×#208C2×D3semidirect
337. C3×#41#67semidirect
338. C3×#41#67semidirect
348. C2×C3×Q8#67semidirect
349. C2×C3×Q8#67semidirect
366. C2×C3×D4#67semidirect
367. C2×C3×D4#67semidirect
413. #235#67semidirect
416. C2×D12#67semidirect
424. C2×Dic6#67semidirect
710. #41#625semidirect
718. C2×Q8#625semidirect
733. C2×D4#625semidirect
820. C32#3018semidirect
927. C3#84004semidirect
928. C3#84121semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C3×#58222
#105950322
#105947862
C2×#636642
#105916872
#105916842
#105916652
#105916642
C2×#635682
#105910762
#841213
#840043