Finite Group Databasebeta

← #11886599

Subgroups — #11886599

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#10596307C211yesmaximal, characteristic, complemented
2C3×#5835C211yesmaximal, characteristic, complemented
3#10595462C211yesmaximal, characteristic, complemented
4#10595454C211yesmaximal, characteristic, complemented
5C3×#5241C211yesmaximal, characteristic, complemented
6#10591688C211yesmaximal, characteristic, complemented
7#10591686C211yesmaximal, characteristic, complemented
8#10591679C211yesmaximal, characteristic, complemented
9#10591678C211yesmaximal, characteristic, complemented
10#10591676C211yesmaximal, characteristic, complemented
11#10591663C211yesmaximal, characteristic, complemented
12#10591523C211yesmaximal, characteristic, complemented
13#10591507C211yesmaximal, characteristic, complemented
14#10591469C211yesmaximal, characteristic, complemented
15#10591406C211yesmaximal, characteristic, complemented
16#84009—31nomaximal
17#80280—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19#64367C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic
21#64307C2211yescharacteristic, complemented
22#64160—21no—
23#64160C2211yescharacteristic, complemented
24#64159—21no—
25#64159C2211yescharacteristic
26#64157C2211yescharacteristic, complemented
27C2×#3754—21no—
28C2×#3754C2211yescharacteristic, complemented
29#64141—21no—
30#64141C2211yescharacteristic, complemented
31C3×#950—21no—
32C3×#950C2211yescharacteristic
33C3×#949—21no—
34C3×#949C2211yescharacteristic
35C3×#949C2211yescharacteristic, complemented
36C3×#949C2211yescharacteristic, complemented
37C3×#948C2211yescharacteristic, complemented
38C3×#940C2211yescharacteristic, complemented
39C3×#932—21no—
40C3×#932C2211yescharacteristic
41C2×C3×#213—21no—
42C2×C3×#213C2211yescharacteristic, complemented
43#63951—21no—
44#63947—21no—
45#63940—21no—
46#63939—21no—
47#63936—21no—
48#63932—21no—
49#63927—21no—
50D3×#213—21no—
51#63860C2211yescharacteristic, complemented
52#63831C2211yescharacteristic, complemented
53#63830C2211yescharacteristic, complemented
54C2×#3716C2211yescharacteristic, complemented
55C2×#3713C2211yescharacteristic, complemented
56#63817C2211yescharacteristic, complemented
57#63815C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61#63578C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63554C2211yescharacteristic, complemented
69C3×#576—31no—
70#5836—31no—
71#5836—31no—
72#5836—61no—
73#5835—31no—
74#5835D311yescharacteristic, complemented
75#5775—31no—
76#5774—31no—
77#5770—31no—
78C3×#453—31no—
79#5242—31no—
80#5241D311yescharacteristic, complemented
81#5201—31no—
82#5200—31no—
83#5200—31no—
84#5199—31no—
85#5199—31no—
86#5198—31no—
87#5197—31no—
88#5160—31no—
89#5154—31no—
90#5145—31no—
91#5141—31no—
92#5077—31no—
93#5074—31no—
94#4827—31no—
95#4825—31no—
96#4823—31no—
97#4823—31no—
98#4749—31no—
99#4748—31no—
100C32×#41—21no—
101C32×#41—21no—
102C32×#41C2311yescharacteristic
103C32×#41C2311yescharacteristic
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—41no—
107C2×C32×D4C2311yescharacteristic
108Q8×C3⋊D3—21no—
109#3830—21no—
110#3830—41no—
111#3828—21no—
112#3828C2311yescharacteristic
113C2×#634—21no—
114C2×#634C2311yescharacteristic
115C2×C3×#67—41no—
116C3×#239—21no—
117C3×D3×D4—21no—
118C3×D3×D4—41no—
119C3×#235—21no—
120C3×#235C2311yescharacteristic
121C2×C3×D12—21no—
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124D3×#67—41no—
125#3802—21no—
126D3×D12—21no—
127#3796—21no—
128#3795—21no—
129#3756—21no—
130#3756D411yescharacteristic, complemented
131#3755D411yescharacteristic, complemented
132#3754—21no—
133#3754—21no—
134#3754—21no—
135#3754—21no—
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×#216D411yescharacteristic, complemented
144C3×#215—21no—
145C3×#215—21no—
146C3×#215—21no—
147C3×#215D411yescharacteristic, complemented
148C3×#214—21no—
149C3×#214D411yescharacteristic, complemented
150C3×#213—21no—
151C3×#213—21no—
152C3×#213—21no—
153C3×#213—21no—
154C3×#213—21no—
155C3×#213—21no—
156C3×#213D411yescharacteristic, complemented
157C3×C4×Dic3C2311yescharacteristic
158C3×#208—21no—
159C3×#208C2311yescharacteristic
160C3×#208C2311yescharacteristic
161C3×#208C2311yescharacteristic
162C2×C3×C3⋊C8—21no—
163C2×C3×C3⋊C8C2311yescharacteristic
164(C2×D3)⋊Dic3—41no—
165#3719—21no—
166#3716—21no—
167#3716—21no—
168#3716—21no—
169#3716—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×H(5,𝔽2)—21no—
179C3×H(5,𝔽2)—31no—
180C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
181C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
182#1010—31no—
183#1010—31no—
184#1010—61no—
185#1009—31no—
186#1009C2×D311yescharacteristic
187#1004—31no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—61no—
193C3×AGL(1,ℤ/8)—61no—
194C3×#135—31no—
195C3×#135—61no—
196C2×C3×D8—31no—
197C2×C3×D8—61no—
198C3×#131—31no—
199C3×#127—31no—
200#951—31no—
201#951—31no—
202#951—31no—
203#951—61no—
204#951—61no—
205#951—61no—
206#951—62no—
207#950—21no—
208#950—31no—
209#950—31no—
210#950—61no—
211#950—61no—
212#950—61no—
213#950—61no—
214#950—62no—
215#950C2×D311yescharacteristic
216#949—21no—
217#949—61no—
218#949C2×D311yescharacteristic
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#940C2×D311yescharacteristic, complemented
227#936—31no—
228C2×#214—31no—
229C2×#214—31no—
230C2×#214—31no—
231C2×#214—61no—
232C2×#214—61no—
233C2×#214—61no—
234C2×#214—62no—
235#932—21no—
236#932—31no—
237#932—31no—
238#932—31no—
239#932—61no—
240#932—61no—
241#932—61no—
242#932—61no—
243#932—62no—
244#932C2×D311yescharacteristic
245C2×#213—21no—
246C2×#213—31no—
247C2×#213—31no—
248C2×#213—61no—
249C2×#213C2×D311yescharacteristic, complemented
250#918—61no—
251#916—61no—
252#916—61no—
253#915—61no—
254#914—61no—
255D3×SD16—61no—
256D3×SD16—61no—
257#912—61no—
258#911—61no—
259#911—61no—
260#911—61no—
261D3×D8—61no—
262#909—31no—
263#908—31no—
264#907—31no—
265#907—31no—
266C2×#204—31no—
267#901—31no—
268#875—31no—
269C3×#104—31no—
270C3×#104—31no—
271C3×#100—31no—
272#837—31no—
273#837C2×D311yescharacteristic, complemented
274#837C2×D311yescharacteristic, complemented
275#833—31no—
276#833—31no—
277#833C2×D311yescharacteristic, complemented
278#825—31no—
279#824—31no—
280#824—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—
291C23×C32—21no—
292C23×C32—41no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—41no—
296C2×D32—41no—
297C32×Q8C2×D411yescharacteristic
298C32×Q8C2×D411yescharacteristic
299C32×D4—21no—
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—21no—
303C32×D4—41no—
304C32×D4—41no—
305C32×D4C2×D411yescharacteristic
306C32×D4C2×D411yescharacteristic
307C2×C32×C4—21no—
308C2×C32×C4—21no—
309C2×C32×C4—41no—
310C2×C32×C4C2411yescharacteristic
311#638—21no—
312#638—41no—
313C2×C3⋊Dic3—21no—
314C2×C3⋊Dic3—41no—
315C4⋊(C3⋊D3)C2×D411yescharacteristic
316C4×C3⋊D3—21no—
317C4×C3⋊D3—41no—
318#634—21no—
319#634—21no—
320#634—41no—
321#634C2×D411yescharacteristic
322C3×#67—21no—
323C3×#67—41no—
324C3×#67—82no—
325C2×C3×Dic3—21no—
326C3×D12—21no—
327C3×D12—21no—
328C3×D12—21no—
329C3×D12—21no—
330C3×D12—41no—
331C3×D12C2×D411yescharacteristic
332C3×C4×D3—21no—
333C3×C4×D3—41no—
334C3×Dic6C2×D411yescharacteristic
335#626—41no—
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—91no—
347#577—91no—
348#576—31no—
349#576—91no—
350#496—91no—
351#472—91no—
352#472—91no—
353#471—91no—
354#471—91no—
355#455—91no—
356#454—91no—
357#453—31no—
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—61no—
371C3×#41—61no—
372C3×#41C22×D311yescharacteristic
373C3×#41C22×D311yescharacteristic
374C3×#41C22×D311yescharacteristic
375C3×#41C22×D311yescharacteristic
376C2×C3×D4—22no—
377C2×C3×D4—21no—
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—41no—
385C2×C3×D4—41no—
386C2×C3×D4—41no—
387C2×C3×D4—42no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C2×C3×D4—121no—
391C2×C3×D4—121no—
392C2×C3×D4C22×D311yescharacteristic
393C2×C3×D4C22×D311yescharacteristic
394C2×#67—41no—
395C2×#67—121no—
396#239—21no—
397#239—61no—
398D3×Q8—61no—
399D3×Q8—61no—
400D3×Q8—121no—
401#237—61no—
402#237—61no—
403#237—61no—
404#237—61no—
405#237—121no—
406#237—121no—
407#237—121no—
408#237—122no—
409D3×D4—21no—
410D3×D4—41no—
411D3×D4—61no—
412D3×D4—61no—
413D3×D4—61no—
414D3×D4—121no—
415#235—21no—
416#235—31no—
417#235—31no—
418#235—61no—
419#235—61no—
420#235—61no—
421#235—61no—
422#235—62no—
423#235C22×D311yescharacteristic
424C2×D12—21no—
425C2×D12—61no—
426C2×D12C22×D311yescharacteristic
427C2×D12C22×D311yescharacteristic
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—61no—
431C2×Dic6—61no—
432C2×Dic6—61no—
433C2×Dic6—62no—
434C3×Q16—31no—
435C3×SD16—31no—
436C3×SD16—31no—
437C3×SD16—61no—
438C3×SD16—61no—
439C3×SD16—61no—
440C3×SD16—61no—
441C3×D8—31no—
442C3×D8—61no—
443C3×D8—61no—
444C3×D8—61no—
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×C42—31no—
455#217—121no—
456#216—31no—
457#216—31no—
458#216—61no—
459#216—61no—
460#216—62no—
461#216—61no—
462#216—61no—
463#216#6711yescharacteristic, complemented
464#215—21no—
465#215—21no—
466#215—21no—
467#215—31no—
468#215—31no—
469#215—61no—
470#215#6711yescharacteristic, complemented
471#214—21no—
472#214—31no—
473#214—31no—
474#214—61no—
475#214—61no—
476#214—61no—
477#214—61no—
478#214—61no—
479#214—61no—
480#214—61no—
481#214—61no—
482#214—61no—
483#214—62no—
484#214—62no—
485#214—62no—
486#214—62no—
487#214—61no—
488#214—61no—
489#214—61no—
490#214—61no—
491#214#6711yescharacteristic, complemented
492#213—21no—
493#213—21no—
494#213—21no—
495#213—21no—
496#213—21no—
497#213—21no—
498#213—31no—
499#213—31no—
500#213—61no—
501#213—61no—
502#213—61no—
503#213—61no—
504#213—61no—
505#213—61no—
506#213—61no—
507#213—61no—
508#213—62no—
509#213#6711yescharacteristic, complemented
510(C2×D3)⋊C4—121no—
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
532Dic12—61no—
533D24—61no—
534#204—61no—
535#204—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×C32—41no—
547C22×C32—81no—
548C22×C32—161no—
549C22×C32H(5,𝔽2)11yescharacteristic
550C2×C3⋊D3—21no—
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×C4C22×D411yescharacteristic
561C32×C4C22×D411yescharacteristic
562C3⋊Dic3—21no—
563C3⋊Dic3—41no—
564C3×Dic3—21no—
565C3×Dic3—41no—
5662−1+4—91no—
567H(5,𝔽2)—31no—
568H(5,𝔽2)—91no—
569H(5,𝔽2)D3211yescharacteristic, complemented
570#137—91no—
571#137—91no—
572#137—181no—
573#137—181no—
574AGL(1,ℤ/8)—31no—
575AGL(1,ℤ/8)—31no—
576AGL(1,ℤ/8)—31no—
577AGL(1,ℤ/8)—31no—
578AGL(1,ℤ/8)—61no—
579AGL(1,ℤ/8)—61no—
580AGL(1,ℤ/8)—91no—
581AGL(1,ℤ/8)—91no—
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—91no—
593C2×SD16—91no—
594C2×SD16—181no—
595C2×SD16—181no—
596C2×D8—31no—
597C2×D8—61no—
598C2×D8—91no—
599C2×D8—181no—
600#131—31no—
601#131—91no—
602#131—91no—
603#131—91no—
604#127—31no—
605#124—91no—
606#108—91no—
607#108—91no—
608#104—31no—
609#104—31no—
610#104—91no—
611#104—91no—
612#101—91no—
613#100—31no—
614#100—91no—
615#100—91no—
616#97—91no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—41no—
622C23×C3—42no—
623C23×C3—61no—
624C23×C3—61no—
625C23×C3—121no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—41no—
629C22×D3—121no—
630C22×D3—121no—
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—31no—
634C3×Q8D3×D411yescharacteristic
635C3×Q8D3×D411yescharacteristic
636C3×Q8D3×D411yescharacteristic
637C3×Q8C2×#6711yescharacteristic
638C3×D4—22no—
639C3×D4—21no—
640C3×D4—21no—
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—22no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—31no—
651C3×D4—41no—
652C3×D4—41no—
653C3×D4—41no—
654C3×D4—41no—
655C3×D4—41no—
656C3×D4—41no—
657C3×D4—42no—
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×D4—242no—
667C3×D4D3×D411yescharacteristic
668C3×D4D3×D411yescharacteristic
669C3×D4D3×D411yescharacteristic
670C3×D4C2×#6711yescharacteristic
671C2×C3×C4—22no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—42no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—121no—
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686#67—21no—
687#67—41no—
688#67—61no—
689#67—61no—
690#67—82no—
691#67—121no—
692#67—121no—
693#67—121no—
694#67—121no—
695#67—121no—
696#67—121no—
697#67—122no—
698C2×Dic3—21no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—121no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—122no—
706D12—21no—
707D12—21no—
708D12—21no—
709D12—21no—
710D12—31no—
711D12—31no—
712D12—41no—
713D12—61no—
714D12—121no—
715D12C2×#6711yescharacteristic
716C4×D3—21no—
717C4×D3—41no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—121no—
721C4×D3—121no—
722C4×D3—121no—
723C4×D3—121no—
724C4×D3—122no—
725Dic6—31no—
726Dic6—31no—
727Dic6—61no—
728Dic6—62no—
729Dic6—61no—
730Dic6—61no—
731Dic6—61no—
732Dic6—61no—
733Dic6—121no—
734Dic6—121no—
735Dic6—121no—
736Dic6—122no—
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×C32—81no—
761C2×C32D4211yescharacteristic
762C3⋊D3—41no—
763C3×D3—41no—
764C3×D3—81no—
765C3×D3—81no—
766#41—21no—
767#41—21no—
768#41—31no—
769#41—61no—
770#41—61no—
771#41—91no—
772#41—181no—
773#41—181no—
774#41—181no—
775#41—181no—
776#41—361no—
777#41C2×D3211yescharacteristic
778#41C2×D3211yescharacteristic
779C2×Q8—91no—
780C2×Q8—181no—
781C2×Q8—181no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—31no—
785C2×D4—31no—
786C2×D4—41no—
787C2×D4—61no—
788C2×D4—61no—
789C2×D4—121no—
790C2×D4—121no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—361no—
794C2×D4C2×D3211yescharacteristic
795Q16—31no—
796Q16—91no—
797Q16—181no—
798Q16—181no—
799SD16—31no—
800SD16—31no—
801SD16—61no—
802SD16—61no—
803SD16—61no—
804SD16—61no—
805SD16—91no—
806SD16—91no—
807SD16—181no—
808SD16—181no—
809SD16—181no—
810SD16—181no—
811SD16—181no—
812SD16—181no—
813SD16—181no—
814SD16—181no—
815D8—31no—
816D8—61no—
817D8—61no—
818D8—61no—
819D8—61no—
820D8—61no—
821D8—61no—
822D8—91no—
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—361no—
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—42no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—61no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—161no—
859C22×C3—161no—
860C22×C3—161no—
861C22×C3—162no—
862C22×C3—241no—
863C22×C3—241no—
864C22×C3—481no—
865C22×C3#100411yescharacteristic
866C22×C3#100411yescharacteristic
867C2×D3—21no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—81no—
873C2×D3—81no—
874C2×D3—121no—
875C2×D3—161no—
876C2×D3—481no—
877C2×D3—481no—
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—61no—
887C3×C4—121no—
888C3×C4C2×D3×D411yescharacteristic
889C3×C4C2×D3×D411yescharacteristic
890C3×C4C2×D3×D411yescharacteristic
891C3×C4C22×#6711yescharacteristic
892Dic3—21no—
893Dic3—41no—
894Dic3—61no—
895Dic3—61no—
896Dic3—121no—
897Dic3—122no—
898Dic3—121no—
899Dic3—121no—
900C32#328811yescharacteristic, complemented, Sylow
901C23—21no—
902C23—41no—
903C23—61no—
904C23—61no—
905C23—121no—
906C23—361no—
907Q8—31no—
908Q8—91no—
909Q8—181no—
910Q8—181no—
911Q8—361no—
912Q8D3×#6711yescharacteristic
913Q8#381111yescharacteristic
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—31no—
919D4—41no—
920D4—41no—
921D4—61no—
922D4—61no—
923D4—61no—
924D4—61no—
925D4—61no—
926D4—91no—
927D4—121no—
928D4—121no—
929D4—181no—
930D4—242no—
931D4—361no—
932D4—361no—
933D4—361no—
934D4D3×#6711yescharacteristic
935D4#381111yescharacteristic
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—41no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—121no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4—361no—
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—82no—
967C2×C3—81no—
968C2×C3—81no—
969C2×C3—121no—
970C2×C3—241no—
971C2×C3—241no—
972C2×C3#559011yescharacteristic
973C2×C3D4×#6711yescharacteristic
974D3—41no—
975D3—81no—
976D3—81no—
977D3—121no—
978D3—121no—
979D3—241no—
980C22—21no—
981C22—21no—
982C22—41no—
983C22—61no—
984C22—81no—
985C22—121no—
986C22—121no—
987C22—161no—
988C22—181no—
989C22—241no—
990C22—241no—
991C22—481no—
992C22—1441no—
993C22#6433011yescharacteristic
994C4—21no—
995C4—21no—
996C4—61no—
997C4—121no—
998C4—181no—
999C4—361no—
1000C4C2×D3×#6711yescharacteristic
1001C4C2×#381111yescharacteristic
1002C3—21no—
1003C3#8028011yescharacteristic, complemented
1004C3#8400911yescharacteristic, complemented
1005C2—21no—
1006C2—41no—
1007C2—41no—
1008C2—81no—
1009C2—121no—
1010C2—241no—
1011C2—241no—
1012C2—361no—
1013C2#1059552611yescharacteristic
subgroupG/H
centerC2#10595526
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×H(5,𝔽2)C22
socleC2×C32D42
hypercenterH(5,𝔽2)D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #10596307C2semidirect
2. C3×#5835C2semidirect
3. #10595462C2semidirect
4. #10595454C2semidirect
5. C3×#5241C2semidirect
6. #10591688C2semidirect
7. #10591686C2semidirect
8. #10591679C2semidirect
9. #10591678C2semidirect
10. #10591676C2semidirect
11. #10591663C2semidirect
12. #10591523C2semidirect
13. #10591507C2semidirect
14. #10591469C2semidirect
15. #10591406C2semidirect
18. C32×H(5,𝔽2)C22semidirect
19. #64367C22semidirect
21. #64307C22semidirect
23. #64160C22semidirect
26. #64157C22semidirect
28. C2×#3754C22semidirect
30. #64141C22semidirect
35. C3×#949C22semidirect
36. C3×#949C22semidirect
37. C3×#948C22semidirect
38. C3×#940C22semidirect
42. C2×C3×#213C22semidirect
51. #63860C22semidirect
52. #63831C22semidirect
53. #63830C22semidirect
54. C2×#3716C22semidirect
55. C2×#3713C22semidirect
56. #63817C22semidirect
57. #63815C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#833C22semidirect
61. #63578C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63561C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63554C22semidirect
74. #5835D3semidirect
80. #5241D3semidirect
130. #3756D4semidirect
131. #3755D4semidirect
136. #3754D4semidirect
138. #3753D4semidirect
143. C3×#216D4semidirect
147. C3×#215D4semidirect
149. C3×#214D4semidirect
156. C3×#213D4semidirect
180. C3×H(5,𝔽2)C2×D3semidirect
181. C3×H(5,𝔽2)C2×D3semidirect
219. #949C2×D3semidirect
220. #949C2×D3semidirect
225. #948C2×D3semidirect
226. #940C2×D3semidirect
249. C2×#213C2×D3semidirect
273. #837C2×D3semidirect
274. #837C2×D3semidirect
277. #833C2×D3semidirect
463. #216#67semidirect
470. #215#67semidirect
491. #214#67semidirect
509. #213#67semidirect
569. H(5,𝔽2)D32semidirect
900. C32#3288semidirect
1003. C3#80280semidirect
1004. C3#84009semidirect

Maximal subgroups

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

subgroupindex
#105963072
C3×#58352
#105954622
#105954542
C3×#52412
#105916882
#105916862
#105916792
#105916782
#105916762
#105916632
#105915232
#105915072
#105914692
#105914062
#840093
#802803