Finite Group Databasebeta

← #11886589

Subgroups — #11886589

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596308C211yesmaximal, characteristic, complemented
2C3×#5837C211yesmaximal, characteristic, complemented
3#10595461C211yesmaximal, characteristic, complemented
4#10595454C211yesmaximal, characteristic, complemented
5C3×#5245C211yesmaximal, characteristic, complemented
6#10591678C211yesmaximal, characteristic, complemented
7#10591677C211yesmaximal, characteristic, complemented
8#10591676C211yesmaximal, characteristic, complemented
9#10591667C211yesmaximal, characteristic, complemented
10#10591666C211yesmaximal, characteristic, complemented
11#10591663C211yesmaximal, characteristic, complemented
12#10591659C211yesmaximal, characteristic, complemented
13#10591643C211yesmaximal, characteristic, complemented
14#10591619C211yesmaximal, characteristic, complemented
15#10591542C211yesmaximal, characteristic, complemented
16#84015—31nomaximal
17#80287—31nomaximal
18C32×2−1+4C2211yescharacteristic, complemented
19#64366C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic, complemented
21#64307C2211yescharacteristic
22#64159—21no—
23#64159C2211yescharacteristic
24#64158—21no—
25#64158C2211yescharacteristic, complemented
26#64157C2211yescharacteristic, complemented
27#64151—21no—
28#64151C2211yescharacteristic, complemented
29C2×#3755—21no—
30C2×#3755C2211yescharacteristic, complemented
31C3×#950—21no—
32C3×#950C2211yescharacteristic
33C3×#949—21no—
34C3×#949C2211yescharacteristic, complemented
35C3×#949C2211yescharacteristic, complemented
36C3×#949C2211yescharacteristic, complemented
37C3×#948C2211yescharacteristic, complemented
38C3×#947C2211yescharacteristic, complemented
39C3×#942—21no—
40C3×#942C2211yescharacteristic, complemented
41C2×C3×#215—21no—
42C2×C3×#215C2211yescharacteristic, complemented
43#63950—21no—
44#63947—21no—
45#63941—21no—
46#63939—21no—
47#63937—21no—
48#63932—21no—
49#63926—21no—
50D3×#213—21no—
51#63911C2211yescharacteristic, complemented
52#63830C2211yescharacteristic
53#63825C2211yescharacteristic
54C2×#3714C2211yescharacteristic, complemented
55C2×#3713C2211yescharacteristic, complemented
56#63817C2211yescharacteristic, complemented
57#63815C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61#63578C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63559C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63554C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5837—31no—
72#5837—61no—
73#5837D311yescharacteristic, complemented
74#5835—31no—
75#5774—31no—
76#5774—31no—
77#5769—31no—
78C3×#454—31no—
79#5245D311yescharacteristic, complemented
80#5241—31no—
81#5203—31no—
82#5202—31no—
83#5199—31no—
84#5199—31no—
85#5199—31no—
86#5198—31no—
87#5197—31no—
88#5177—31no—
89#5176—31no—
90#5145—31no—
91#5142—31no—
92#5061—31no—
93#5058—31no—
94#4823—31no—
95#4823—31no—
96#4822—31no—
97#4822—31no—
98#4754—31no—
99#4754—31no—
100C32×#41—21no—
101C32×#41—21no—
102C32×#41—41no—
103C32×#41C2311yescharacteristic
104C32×#41C2311yescharacteristic
105C2×C32×Q8—21no—
106C2×C32×Q8—21no—
107C2×C32×Q8C2311yescharacteristic
108#3832—21no—
109D4×C3⋊D3—21no—
110D4×C3⋊D3—41no—
111#3828—21no—
112#3828C2311yescharacteristic
113C2×C4⋊(C3⋊D3)—21no—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C3×#239—21no—
116C3×D3×D4—21no—
117C3×D3×D4—41no—
118C3×#235—21no—
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123D3×#67—41no—
124C2×#626—41no—
125#3802—21no—
126D3×D12—21no—
127#3796—21no—
128#3795—21no—
129#3756—21no—
130#3756D411yescharacteristic, complemented
131#3755—21no—
132#3755—21no—
133#3755—21no—
134#3755—21no—
135#3755D411yescharacteristic, complemented
136#3754D411yescharacteristic, complemented
137#3753—21no—
138#3753D411yescharacteristic, complemented
139#3748—21no—
140#3748C2311yescharacteristic
141C2×C3⋊(C3⋊C8)—21no—
142C2×C3⋊(C3⋊C8)C2311yescharacteristic
143C3×#216—21no—
144C3×#216D411yescharacteristic, complemented
145C3×#215—21no—
146C3×#215—21no—
147C3×#215—21no—
148C3×#215—21no—
149C3×#215—21no—
150C3×#215—21no—
151C3×#215D411yescharacteristic, complemented
152C3×#214D411yescharacteristic, complemented
153C3×#213—21no—
154C3×#213—21no—
155C3×#213—21no—
156C3×#213D411yescharacteristic, complemented
157C3×(C2×D3)⋊C4—41no—
158C3×C4×Dic3C2311yescharacteristic
159C3×#208—21no—
160C3×#208C2311yescharacteristic
161C3×#208C2311yescharacteristic
162C3×#208C2311yescharacteristic
163C2×C3×C3⋊C8—21no—
164C2×C3×C3⋊C8C2311yescharacteristic
165#3717—21no—
166#3716—21no—
167#3714—21no—
168#3714—21no—
169#3714—21no—
170#3714—21no—
171#3713—21no—
172#3713—21no—
173#3712—21no—
174#3711—21no—
175#3710—21no—
176D3×C3⋊C8—21no—
177#3288—91noSylow
178C3×2−1+4—21no—
179C3×2−1+4C2×D311yescharacteristic, complemented
180C3×2−1+4C2×D311yescharacteristic, complemented
181C3×H(5,𝔽2)—31no—
182#1009—31no—
183#1009—31no—
184#1009—31no—
185#1009—61no—
186#1009C2×D311yescharacteristic, complemented
187#1004—31no—
188C3×#137—31no—
189C3×#137—61no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—31no—
193C3×AGL(1,ℤ/8)—61no—
194C3×#135—31no—
195C3×#135—61no—
196C2×C3×SD16—31no—
197C2×C3×SD16—61no—
198C3×#131—31no—
199C3×#124—31no—
200#950—21no—
201#950—31no—
202#950—31no—
203#950—61no—
204#950—61no—
205#950—61no—
206#950—61no—
207#950—62no—
208#950C2×D311yescharacteristic
209#949—21no—
210#949—31no—
211#949—31no—
212#949—31no—
213#949—61no—
214#949—61no—
215#949—61no—
216#949—61no—
217#949—62no—
218#949C2×D311yescharacteristic, complemented
219#949C2×D311yescharacteristic, complemented
220#949C2×D311yescharacteristic, complemented
221#948—31no—
222#948—31no—
223#948—31no—
224#948—61no—
225#948C2×D311yescharacteristic, complemented
226#947C2×D311yescharacteristic, complemented
227#942—21no—
228#942—31no—
229#942—31no—
230#942—61no—
231#942—61no—
232#942—61no—
233#942—62no—
234#942C2×D311yescharacteristic, complemented
235C2×#215—21no—
236C2×#215—31no—
237C2×#215—31no—
238C2×#215—61no—
239C2×#215—61no—
240C2×#215—61no—
241C2×#215—62no—
242C2×#215C2×D311yescharacteristic, complemented
243#940—31no—
244#932—31no—
245#932—61no—
246C2×#213—31no—
247C2×#213—31no—
248C2×#213—31no—
249C2×#213—61no—
250#919—61no—
251#916—61no—
252#916—61no—
253#914—61no—
254#914—61no—
255#914—61no—
256#914—61no—
257#911—61no—
258#911—61no—
259D3×D8—61no—
260D3×D8—61no—
261D3×D8—61no—
262#908—31no—
263#908—31no—
264#907—31no—
265#907—31no—
266C2×D24—31no—
267#901—31no—
268#874—31no—
269C3×#104—31no—
270C3×#104—31no—
271C3×#101—31no—
272#837—31no—
273#837C2×D311yescharacteristic, complemented
274#837C2×D311yescharacteristic, complemented
275#836C2×D311yescharacteristic, complemented
276#833—31no—
277#833—31no—
278#825—31no—
279#823—31no—
280#823—31no—
281#823—31no—
282#823—31no—
283#822—31no—
284#822—31no—
285#822—31no—
286#819—31no—
287#815—31no—
288#805—31no—
289#805—31no—
290#803—31no—
291C22×C3⋊D3—21no—
292C22×C3⋊D3—41no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—41no—
296C2×D32—41no—
297C32×Q8—21no—
298C32×Q8—21no—
299C32×Q8—41no—
300C32×Q8C2×D411yescharacteristic
301C32×Q8C2×D411yescharacteristic
302C32×D4—21no—
303C32×D4—21no—
304C32×D4—41no—
305C32×D4C2×D411yescharacteristic
306C32×D4C2×D411yescharacteristic
307C2×C32×C4—21no—
308C2×C32×C4—21no—
309C2×C32×C4—21no—
310C2×C32×C4—41no—
311C2×C32×C4—41no—
312C2×C32×C4C2411yescharacteristic
313#638—21no—
314#638—41no—
315C4⋊(C3⋊D3)—21no—
316C4⋊(C3⋊D3)—21no—
317C4⋊(C3⋊D3)—41no—
318C4⋊(C3⋊D3)C2×D411yescharacteristic
319C4×C3⋊D3—21no—
320C4×C3⋊D3—41no—
321#634C2×D411yescharacteristic
322C3×#67—21no—
323C3×#67—41no—
324C2×C3×Dic3—21no—
325C3×D12—21no—
326C3×D12—21no—
327C3×D12—21no—
328C3×D12—21no—
329C3×D12—41no—
330C3×D12C2×D411yescharacteristic
331C3×C4×D3—21no—
332C3×C4×D3—41no—
333C3×Dic6C2×D411yescharacteristic
334#626—41no—
335#626—82no—
336#625—41no—
337D3×Dic3—41no—
338C3⋊(C3⋊C8)—21no—
339C3⋊(C3⋊C8)C2×D411yescharacteristic
340C3⋊(C3⋊C8)C2×D411yescharacteristic
341C3×C3⋊C8—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8C2×D411yescharacteristic
345C3×C3⋊C8C2×D411yescharacteristic
346#577—31no—
347#577—91no—
348#576—91no—
349#576—91no—
350#496—91no—
351#472—91no—
352#472—91no—
353#471—91no—
354#471—91no—
355#455—91no—
356#454—31no—
357#453—91no—
358#453—91no—
359#444—91no—
360#444—91no—
361C3×#41—22no—
362C3×#41—21no—
363C3×#41—21no—
364C3×#41—21no—
365C3×#41—21no—
366C3×#41—21no—
367C3×#41—21no—
368C3×#41—31no—
369C3×#41—41no—
370C3×#41—41no—
371C3×#41—41no—
372C3×#41—42no—
373C3×#41—61no—
374C3×#41—61no—
375C3×#41C22×D311yescharacteristic
376C3×#41C22×D311yescharacteristic
377C3×#41C22×D311yescharacteristic
378C3×#41C22×D311yescharacteristic
379C2×C3×Q8—22no—
380C2×C3×Q8—21no—
381C2×C3×Q8—21no—
382C2×C3×Q8—21no—
383C2×C3×Q8—21no—
384C2×C3×Q8—21no—
385C2×C3×Q8—41no—
386C2×C3×Q8C22×D311yescharacteristic
387C2×C3×Q8C22×D311yescharacteristic
388C2×C3×D4—31no—
389C2×C3×D4—31no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—121no—
393C2×#67—121no—
394C2×#67—121no—
395#239—21no—
396#239—61no—
397#239—61no—
398#239—61no—
399#239—121no—
400#237—61no—
401#237—61no—
402D3×D4—21no—
403D3×D4—41no—
404D3×D4—61no—
405D3×D4—61no—
406D3×D4—61no—
407D3×D4—61no—
408D3×D4—61no—
409D3×D4—121no—
410D3×D4—121no—
411D3×D4—121no—
412D3×D4—121no—
413D3×D4—122no—
414#235—21no—
415#235—31no—
416#235—31no—
417#235—61no—
418#235—61no—
419#235—61no—
420#235—61no—
421#235—62no—
422#235C22×D311yescharacteristic
423C2×D12—21no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12—61no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—121no—
432C2×D12C22×D311yescharacteristic
433C2×D12C22×D311yescharacteristic
434C3×Q16—31no—
435C3×Q16—61no—
436C3×SD16—31no—
437C3×SD16—31no—
438C3×SD16—61no—
439C3×SD16—61no—
440C3×SD16—61no—
441C3×SD16—61no—
442C3×SD16—61no—
443C3×SD16—61no—
444C3×D8—31no—
445C3×D8—61no—
446C3×D8—61no—
447C3×D8—61no—
448C3×M16—31no—
449C3×M16—31no—
450C3×M16—31no—
451C3×M16—61no—
452C2×C3×C8—31no—
453C2×C3×C8—61no—
454C3×C22⋊C4—121no—
455C3×C42—31no—
456#216—21no—
457#216—31no—
458#216—31no—
459#216—61no—
460#216—61no—
461#216—61no—
462#216—62no—
463#216#6711yescharacteristic, complemented
464#215—21no—
465#215—21no—
466#215—21no—
467#215—21no—
468#215—21no—
469#215—21no—
470#215—31no—
471#215—31no—
472#215—61no—
473#215—61no—
474#215—61no—
475#215—61no—
476#215—61no—
477#215—61no—
478#215—61no—
479#215—61no—
480#215—62no—
481#215—62no—
482#215—62no—
483#215—62no—
484#215—61no—
485#215—61no—
486#215#6711yescharacteristic, complemented
487#214—31no—
488#214—31no—
489#214—61no—
490#214—61no—
491#214#6711yescharacteristic, complemented
492#213—21no—
493#213—21no—
494#213—21no—
495#213—31no—
496#213—31no—
497#213—61no—
498#213—61no—
499#213—61no—
500#213—61no—
501#213—61no—
502#213—61no—
503#213—61no—
504#213—62no—
505#213—61no—
506#213—61no—
507#213—61no—
508#213—61no—
509#213#6711yescharacteristic, complemented
510(C2×D3)⋊C4—41no—
511C4×Dic3C22×D311yescharacteristic
512#208—21no—
513#208—31no—
514#208—31no—
515#208—61no—
516#208—61no—
517#208—61no—
518#208—61no—
519#208—62no—
520#208C22×D311yescharacteristic
521#208C22×D311yescharacteristic
522#208C22×D311yescharacteristic
523C2×C3⋊C8—21no—
524C2×C3⋊C8—31no—
525C2×C3⋊C8—31no—
526C2×C3⋊C8—61no—
527C2×C3⋊C8—61no—
528C2×C3⋊C8—61no—
529C2×C3⋊C8—61no—
530C2×C3⋊C8—62no—
531C2×C3⋊C8C22×D311yescharacteristic
532D24—61no—
533D24—61no—
534D24—61no—
535D24—61no—
536#204—61no—
537#204—61no—
538ΓL(1,𝔽25)—61no—
539ΓL(1,𝔽25)—61no—
540ΓL(1,𝔽25)—61no—
541D3×C8—61no—
542D3×C8—61no—
543D3×C8—61no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32H(5,𝔽2)11yescharacteristic
547C2×C3⋊D3—21no—
548C2×C3⋊D3—41no—
549C2×C3⋊D3—81no—
550C2×C3⋊D3—161no—
551C2×C3×D3—21no—
552C2×C3×D3—41no—
553C2×C3×D3—41no—
554C2×C3×D3—81no—
555C2×C3×D3—81no—
556C2×C3×D3—161no—
557D32—161no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4—41no—
561C32×C4C22×D411yescharacteristic
562C32×C4C22×D411yescharacteristic
563C3⋊Dic3—21no—
564C3×Dic3—21no—
565C3×Dic3—41no—
5662−1+4D3211yescharacteristic, complemented
567H(5,𝔽2)—31no—
568H(5,𝔽2)—91no—
569H(5,𝔽2)—91no—
570#137—31no—
571#137—61no—
572#137—91no—
573#137—181no—
574AGL(1,ℤ/8)—31no—
575AGL(1,ℤ/8)—31no—
576AGL(1,ℤ/8)—31no—
577AGL(1,ℤ/8)—61no—
578AGL(1,ℤ/8)—91no—
579AGL(1,ℤ/8)—91no—
580AGL(1,ℤ/8)—91no—
581AGL(1,ℤ/8)—181no—
582AGL(1,ℤ/8)—181no—
583AGL(1,ℤ/8)—181no—
584AGL(1,ℤ/8)—181no—
585AGL(1,ℤ/8)—181no—
586#135—31no—
587#135—61no—
588#135—91no—
589#135—181no—
590#135—181no—
591#135—181no—
592C2×SD16—31no—
593C2×SD16—61no—
594C2×SD16—91no—
595C2×SD16—181no—
596C2×D8—91no—
597C2×D8—91no—
598C2×D8—181no—
599C2×D8—181no—
600#131—31no—
601#131—91no—
602#131—91no—
603#131—91no—
604#127—91no—
605#124—31no—
606#108—91no—
607#108—91no—
608#104—31no—
609#104—31no—
610#104—91no—
611#104—91no—
612#101—31no—
613#100—91no—
614#100—91no—
615#100—91no—
616#97—91no—
617C23×C3—61no—
618C23×C3—61no—
619C23×C3—121no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—41no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—122no—
631C3×Q8—22no—
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—21no—
635C3×Q8—21no—
636C3×Q8—21no—
637C3×Q8—21no—
638C3×Q8—31no—
639C3×Q8—41no—
640C3×Q8—41no—
641C3×Q8—41no—
642C3×Q8—42no—
643C3×Q8D3×D411yescharacteristic
644C3×Q8D3×D411yescharacteristic
645C3×Q8D3×D411yescharacteristic
646C3×Q8C2×#6711yescharacteristic
647C3×D4—22no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—31no—
655C3×D4—41no—
656C3×D4—41no—
657C3×D4—41no—
658C3×D4—42no—
659C3×D4—61no—
660C3×D4—61no—
661C3×D4—61no—
662C3×D4—61no—
663C3×D4—61no—
664C3×D4—121no—
665C3×D4—121no—
666C3×D4D3×D411yescharacteristic
667C3×D4D3×D411yescharacteristic
668C3×D4D3×D411yescharacteristic
669C3×D4C2×#6711yescharacteristic
670C2×C3×C4—22no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—42no—
685C2×C3×C4—42no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—121no—
689C2×C3×C4C23×D311yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691#67—21no—
692#67—41no—
693#67—61no—
694#67—61no—
695#67—121no—
696#67—121no—
697#67—121no—
698#67—121no—
699#67—121no—
700#67—121no—
701#67—122no—
702#67—242no—
703C2×Dic3—21no—
704C2×Dic3—121no—
705D12—21no—
706D12—21no—
707D12—21no—
708D12—21no—
709D12—31no—
710D12—31no—
711D12—41no—
712D12—61no—
713D12—62no—
714D12—61no—
715D12—61no—
716D12—61no—
717D12—61no—
718D12—121no—
719D12—121no—
720D12—121no—
721D12—122no—
722D12—121no—
723D12—242no—
724D12C2×#6711yescharacteristic
725C4×D3—21no—
726C4×D3—41no—
727C4×D3—61no—
728C4×D3—61no—
729C4×D3—121no—
730C4×D3—121no—
731C4×D3—121no—
732C4×D3—121no—
733C4×D3—122no—
734Dic6—31no—
735Dic6—31no—
736Dic6—61no—
737Dic6C2×#6711yescharacteristic
738C3×C8—31no—
739C3×C8—31no—
740C3×C8—61no—
741C3×C8—61no—
742C3×C8—61no—
743C3⋊C8—21no—
744C3⋊C8—21no—
745C3⋊C8—21no—
746C3⋊C8—31no—
747C3⋊C8—31no—
748C3⋊C8—31no—
749C3⋊C8—31no—
750C3⋊C8—61no—
751C3⋊C8—61no—
752C3⋊C8—62no—
753C3⋊C8—61no—
754C3⋊C8—61no—
755C3⋊C8C2×#6711yescharacteristic
756C3⋊C8C2×#6711yescharacteristic
757C2×C32—21no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32D4211yescharacteristic
761C3⋊D3—41no—
762C3⋊D3—81no—
763C3×D3—41no—
764C3×D3—81no—
765C3×D3—81no—
766#41—21no—
767#41—21no—
768#41—31no—
769#41—41no—
770#41—61no—
771#41—61no—
772#41—91no—
773#41—181no—
774#41—181no—
775#41—181no—
776#41—181no—
777#41C2×D3211yescharacteristic
778#41C2×D3211yescharacteristic
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8C2×D3211yescharacteristic
782C2×D4—31no—
783C2×D4—31no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—91no—
787C2×D4—121no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—361no—
793C2×D4—361no—
794C2×D4—361no—
795Q16—31no—
796Q16—61no—
797Q16—91no—
798Q16—181no—
799SD16—31no—
800SD16—31no—
801SD16—61no—
802SD16—61no—
803SD16—61no—
804SD16—61no—
805SD16—61no—
806SD16—61no—
807SD16—91no—
808SD16—91no—
809SD16—181no—
810SD16—181no—
811SD16—181no—
812SD16—181no—
813SD16—181no—
814SD16—181no—
815D8—31no—
816D8—61no—
817D8—61no—
818D8—61no—
819D8—91no—
820D8—181no—
821D8—181no—
822D8—181no—
823D8—181no—
824D8—181no—
825D8—181no—
826D8—181no—
827M16—31no—
828M16—31no—
829M16—31no—
830M16—61no—
831M16—91no—
832M16—181no—
833M16—181no—
834M16—181no—
835C2×C8—31no—
836C2×C8—61no—
837C2×C8—91no—
838C2×C8—181no—
839C2×C8—181no—
840C2×C8—181no—
841C22⋊C4—121no—
842C42—31no—
843C22×C3—22no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—41no—
850C22×C3—61no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—241no—
854C22×C3—241no—
855C22×C3—481no—
856C22×C3#100411yescharacteristic
857C22×C3#100411yescharacteristic
858C2×D3—21no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—81no—
864C2×D3—81no—
865C2×D3—121no—
866C2×D3—122no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—161no—
870C2×D3—241no—
871C2×D3—241no—
872C2×D3—481no—
873C2×D3—481no—
874C2×D3—481no—
875C2×D3—481no—
876C2×D3—481no—
877C2×D3—482no—
878C3×C4—22no—
879C3×C4—21no—
880C3×C4—21no—
881C3×C4—21no—
882C3×C4—21no—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—41no—
886C3×C4—42no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—61no—
890C3×C4—121no—
891C3×C4C2×D3×D411yescharacteristic
892C3×C4C2×D3×D411yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C22×#6711yescharacteristic
895Dic3—21no—
896Dic3—41no—
897Dic3—61no—
898Dic3—61no—
899Dic3—121no—
900C32#328811yescharacteristic, complemented, Sylow
901C23—61no—
902C23—61no—
903C23—121no—
904C23—181no—
905C23—361no—
906C23—361no—
907Q8—21no—
908Q8—21no—
909Q8—31no—
910Q8—41no—
911Q8—91no—
912Q8D3×#6711yescharacteristic
913Q8#381111yescharacteristic
914D4—21no—
915D4—21no—
916D4—31no—
917D4—41no—
918D4—61no—
919D4—61no—
920D4—61no—
921D4—61no—
922D4—61no—
923D4—91no—
924D4—121no—
925D4—121no—
926D4—181no—
927D4—181no—
928D4—181no—
929D4—361no—
930D4—361no—
931D4—361no—
932D4—361no—
933D4—722no—
934D4D3×#6711yescharacteristic
935D4#381111yescharacteristic
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—121no—
944C2×C4—181no—
945C2×C4—361no—
946C2×C4—361no—
947C2×C4C22×D3211yescharacteristic
948C8—31no—
949C8—31no—
950C8—61no—
951C8—61no—
952C8—61no—
953C8—91no—
954C8—91no—
955C8—181no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—41no—
960C2×C3—42no—
961C2×C3—41no—
962C2×C3—41no—
963C2×C3—41no—
964C2×C3—41no—
965C2×C3—81no—
966C2×C3—121no—
967C2×C3—241no—
968C2×C3—241no—
969C2×C3#559011yescharacteristic
970C2×C3D4×#6711yescharacteristic
971D3—41no—
972D3—81no—
973D3—81no—
974D3—121no—
975D3—121no—
976D3—241no—
977D3—242no—
978D3—241no—
979D3—241no—
980C22—21no—
981C22—21no—
982C22—61no—
983C22—121no—
984C22—121no—
985C22—181no—
986C22—241no—
987C22—241no—
988C22—361no—
989C22—481no—
990C22—721no—
991C22—1441no—
992C22—1441no—
993C22#6433011yescharacteristic
994C4—21no—
995C4—21no—
996C4—41no—
997C4—61no—
998C4—121no—
999C4—181no—
1000C4C2×D3×#6711yescharacteristic
1001C4C2×#381111yescharacteristic
1002C3—21no—
1003C3#8028711yescharacteristic, complemented
1004C3#8401511yescharacteristic, complemented
1005C2—21no—
1006C2—41no—
1007C2—41no—
1008C2—121no—
1009C2—241no—
1010C2—241no—
1011C2—361no—
1012C2—721no—
1013C2#1059552611yescharacteristic
subgroupG/H
centerC2#10595526
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×2−1+4C22
socleC2×C32D42
hypercenter2−1+4D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #10596308C2semidirect
2. C3×#5837C2semidirect
3. #10595461C2semidirect
4. #10595454C2semidirect
5. C3×#5245C2semidirect
6. #10591678C2semidirect
7. #10591677C2semidirect
8. #10591676C2semidirect
9. #10591667C2semidirect
10. #10591666C2semidirect
11. #10591663C2semidirect
12. #10591659C2semidirect
13. #10591643C2semidirect
14. #10591619C2semidirect
15. #10591542C2semidirect
18. C32×2−1+4C22semidirect
19. #64366C22semidirect
20. C3×#1009C22semidirect
25. #64158C22semidirect
26. #64157C22semidirect
28. #64151C22semidirect
30. C2×#3755C22semidirect
34. C3×#949C22semidirect
35. C3×#949C22semidirect
36. C3×#949C22semidirect
37. C3×#948C22semidirect
38. C3×#947C22semidirect
40. C3×#942C22semidirect
42. C2×C3×#215C22semidirect
51. #63911C22semidirect
54. C2×#3714C22semidirect
55. C2×#3713C22semidirect
56. #63817C22semidirect
57. #63815C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#836C22semidirect
61. #63578C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63559C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63554C22semidirect
73. #5837D3semidirect
79. #5245D3semidirect
130. #3756D4semidirect
135. #3755D4semidirect
136. #3754D4semidirect
138. #3753D4semidirect
144. C3×#216D4semidirect
151. C3×#215D4semidirect
152. C3×#214D4semidirect
156. C3×#213D4semidirect
179. C3×2−1+4C2×D3semidirect
180. C3×2−1+4C2×D3semidirect
186. #1009C2×D3semidirect
218. #949C2×D3semidirect
219. #949C2×D3semidirect
220. #949C2×D3semidirect
225. #948C2×D3semidirect
226. #947C2×D3semidirect
234. #942C2×D3semidirect
242. C2×#215C2×D3semidirect
273. #837C2×D3semidirect
274. #837C2×D3semidirect
275. #836C2×D3semidirect
463. #216#67semidirect
486. #215#67semidirect
491. #214#67semidirect
509. #213#67semidirect
566. 2−1+4D32semidirect
900. C32#3288semidirect
1003. C3#80287semidirect
1004. C3#84015semidirect

Maximal subgroups

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

subgroupindex
#105963082
C3×#58372
#105954612
#105954542
C3×#52452
#105916782
#105916772
#105916762
#105916672
#105916662
#105916632
#105916592
#105916432
#105916192
#105915422
#840153
#802873