Finite Group Databasebeta

← #11886911

Subgroups — #11886911

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596306C211yesmaximal, characteristic, complemented
2C3×#5835C211yesmaximal, characteristic, complemented
3#10595461C211yesmaximal, characteristic, complemented
4#10595454C211yesmaximal, characteristic, complemented
5C3×#5241C211yesmaximal, characteristic, complemented
6#10591678C211yesmaximal, characteristic, complemented
7#10591677C211yesmaximal, characteristic, complemented
8#10591675C211yesmaximal, characteristic, complemented
9#10591667C211yesmaximal, characteristic, complemented
10#10591666C211yesmaximal, characteristic, complemented
11#10591662C211yesmaximal, characteristic, complemented
12#10591523C211yesmaximal, characteristic, complemented
13#10591508C211yesmaximal, characteristic, complemented
14#10591482C211yesmaximal, characteristic, complemented
15#10591406C211yesmaximal, characteristic, complemented
16#84010—31nomaximal
17#80282—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19#64366C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic, complemented
21#64307C2211yescharacteristic, complemented
22#64159—21no—
23#64159C2211yescharacteristic
24#64158—21no—
25#64158C2211yescharacteristic, complemented
26#64157C2211yescharacteristic, complemented
27#64141—21no—
28#64141C2211yescharacteristic, complemented
29C2×#3753—21no—
30C2×#3753C2211yescharacteristic, complemented
31C3×#950—21no—
32C3×#950C2211yescharacteristic
33C3×#949—21no—
34C3×#949C2211yescharacteristic, complemented
35C3×#949C2211yescharacteristic, complemented
36C3×#949C2211yescharacteristic, complemented
37C3×#948C2211yescharacteristic, complemented
38C3×#940C2211yescharacteristic, complemented
39C3×#932—21no—
40C3×#932C2211yescharacteristic, complemented
41C2×C3×#213—21no—
42C2×C3×#213C2211yescharacteristic, 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, complemented
53#63825C2211yescharacteristic, complemented
54C2×#3714C2211yescharacteristic, 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#63559C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69C3×#576—31no—
70#5835—31no—
71#5835—31no—
72#5835—31no—
73#5835—61no—
74#5835D311yescharacteristic, complemented
75#5774—31no—
76#5774—31no—
77#5769—31no—
78C3×#453—31no—
79#5241—31no—
80#5241D311yescharacteristic, complemented
81#5199—31no—
82#5199—31no—
83#5199—31no—
84#5199—31no—
85#5198—31no—
86#5198—31no—
87#5196—31no—
88#5160—31no—
89#5151—31no—
90#5144—31no—
91#5142—31no—
92#5077—31no—
93#5073—31no—
94#4824—31no—
95#4824—31no—
96#4822—31no—
97#4822—31no—
98#4749—31no—
99#4749—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
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
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—
125C2×#626—41no—
126#3802—21no—
127D3×D12—21no—
128#3796—21no—
129#3795—21no—
130#3756D411yescharacteristic, complemented
131#3755—21no—
132#3755D411yescharacteristic, complemented
133#3754—21no—
134#3754D411yescharacteristic, complemented
135#3753—21no—
136#3753—21no—
137#3753—21no—
138#3753—21no—
139#3753D411yescharacteristic, complemented
140#3748—21no—
141#3748C2311yescharacteristic
142C2×C3⋊(C3⋊C8)—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144C3×#216D411yescharacteristic, complemented
145C3×#215—21no—
146C3×#215—21no—
147C3×#215—21no—
148C3×#215D411yescharacteristic, complemented
149C3×#214—21no—
150C3×#214D411yescharacteristic, complemented
151C3×#213—21no—
152C3×#213—21no—
153C3×#213—21no—
154C3×#213—21no—
155C3×#213—21no—
156C3×#213—21no—
157C3×#213D411yescharacteristic, complemented
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#3292—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#1009—31no—
183#1009—31no—
184#1009—31no—
185#1009—61no—
186#1009C2×D311yescharacteristic, complemented
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#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#940—31no—
227#940C2×D311yescharacteristic, complemented
228#932—21no—
229#932—31no—
230#932—31no—
231#932—31no—
232#932—61no—
233#932—61no—
234#932—61no—
235#932—61no—
236#932—62no—
237#932C2×D311yescharacteristic, complemented
238C2×#213—21no—
239C2×#213—31no—
240C2×#213—31no—
241C2×#213—31no—
242C2×#213—31no—
243C2×#213—31no—
244C2×#213—61no—
245C2×#213—61no—
246C2×#213—61no—
247C2×#213—61no—
248C2×#213—62no—
249C2×#213C2×D311yescharacteristic, complemented
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×#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#823—31no—
280#823—31no—
281#823—31no—
282#823—31no—
283#822—31no—
284#822—31no—
285#822—31no—
286#819—31no—
287C8×Dic3—31no—
288#805—31no—
289#805—31no—
290C4×C3⋊C8—31no—
291C23×C32—21no—
292C23×C32—41no—
293C22×C3⋊D3—21no—
294C22×C3⋊D3—41no—
295C22×C3×D3—21no—
296C22×C3×D3—21no—
297C22×C3×D3—41no—
298C2×D32—41no—
299C32×Q8C2×D411yescharacteristic
300C32×Q8C2×D411yescharacteristic
301C32×D4—21no—
302C32×D4—21no—
303C32×D4—21no—
304C32×D4—21no—
305C32×D4—41no—
306C32×D4—41no—
307C32×D4C2×D411yescharacteristic
308C32×D4C2×D411yescharacteristic
309C2×C32×C4—21no—
310C2×C32×C4—21no—
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—
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#626—82no—
337#625—41no—
338D3×Dic3—41no—
339C3⋊(C3⋊C8)—21no—
340C3⋊(C3⋊C8)C2×D411yescharacteristic
341C3⋊(C3⋊C8)C2×D411yescharacteristic
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8—21no—
345C3×C3⋊C8C2×D411yescharacteristic
346C3×C3⋊C8C2×D411yescharacteristic
347#576—31no—
348#576—91no—
349#576—91no—
350#576—91no—
351#493—91no—
352#472—91no—
353#472—91no—
354#472—91no—
355#472—91no—
356#453—31no—
357#453—91no—
358#453—91no—
359#453—91no—
360#443—91no—
361#443—91no—
362C3×#41—22no—
363C3×#41—21no—
364C3×#41—21no—
365C3×#41—21no—
366C3×#41—21no—
367C3×#41—21no—
368C3×#41—21no—
369C3×#41—31no—
370C3×#41—41no—
371C3×#41—61no—
372C3×#41—61no—
373C3×#41C22×D311yescharacteristic
374C3×#41C22×D311yescharacteristic
375C3×#41C22×D311yescharacteristic
376C3×#41C22×D311yescharacteristic
377C2×C3×D4—22no—
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—41no—
386C2×C3×D4—41no—
387C2×C3×D4—41no—
388C2×C3×D4—42no—
389C2×C3×D4—61no—
390C2×C3×D4—61no—
391C2×C3×D4—121no—
392C2×C3×D4—121no—
393C2×C3×D4C22×D311yescharacteristic
394C2×C3×D4C22×D311yescharacteristic
395C2×#67—41no—
396C2×#67—121no—
397C2×#67—121no—
398#239—21no—
399#239—61no—
400#239—61no—
401#239—61no—
402#239—121no—
403#237—61no—
404#237—61no—
405D3×D4—21no—
406D3×D4—41no—
407D3×D4—61no—
408D3×D4—61no—
409D3×D4—61no—
410D3×D4—61no—
411D3×D4—61no—
412D3×D4—121no—
413D3×D4—121no—
414D3×D4—121no—
415D3×D4—121no—
416D3×D4—122no—
417#235—21no—
418#235—31no—
419#235—31no—
420#235—61no—
421#235—61no—
422#235—61no—
423#235—61no—
424#235—62no—
425#235C22×D311yescharacteristic
426C2×D12—21no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—61no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—62no—
434C2×D12—121no—
435C2×D12C22×D311yescharacteristic
436C2×D12C22×D311yescharacteristic
437C3×Q16—31no—
438C3×SD16—31no—
439C3×SD16—31no—
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×D8—61no—
449C3×D8—61no—
450C3×D8—61no—
451C3×M16—31no—
452C3×M16—31no—
453C3×M16—31no—
454C3×M16—61no—
455C2×C3×C8—31no—
456C2×C3×C8—61no—
457C3×C42—31no—
458#216—31no—
459#216—31no—
460#216—61no—
461#216#6711yescharacteristic, complemented
462#215—21no—
463#215—21no—
464#215—21no—
465#215—31no—
466#215—31no—
467#215—61no—
468#215—61no—
469#215—62no—
470#215—61no—
471#215—61no—
472#215#6711yescharacteristic, complemented
473#214—21no—
474#214—31no—
475#214—31no—
476#214—61no—
477#214—61no—
478#214—61no—
479#214—61no—
480#214—62no—
481#214#6711yescharacteristic, complemented
482#213—21no—
483#213—21no—
484#213—21no—
485#213—21no—
486#213—21no—
487#213—21no—
488#213—31no—
489#213—31no—
490#213—61no—
491#213—61no—
492#213—61no—
493#213—61no—
494#213—61no—
495#213—61no—
496#213—61no—
497#213—61no—
498#213—61no—
499#213—61no—
500#213—61no—
501#213—61no—
502#213—61no—
503#213—62no—
504#213—62no—
505#213—62no—
506#213—62no—
507#213—61no—
508#213—61no—
509#213—61no—
510#213—61no—
511#213#6711yescharacteristic, complemented
512C4×Dic3C22×D311yescharacteristic
513#208—21no—
514#208—31no—
515#208—31no—
516#208—61no—
517#208—61no—
518#208—61no—
519#208—61no—
520#208—62no—
521#208C22×D311yescharacteristic
522#208C22×D311yescharacteristic
523#208C22×D311yescharacteristic
524C2×C3⋊C8—21no—
525C2×C3⋊C8—31no—
526C2×C3⋊C8—31no—
527C2×C3⋊C8—61no—
528C2×C3⋊C8—61no—
529C2×C3⋊C8—61no—
530C2×C3⋊C8—61no—
531C2×C3⋊C8—62no—
532C2×C3⋊C8C22×D311yescharacteristic
533D24—61no—
534D24—61no—
535D24—61no—
536D24—61no—
537#204—61no—
538#204—61no—
539ΓL(1,𝔽25)—61no—
540ΓL(1,𝔽25)—61no—
541ΓL(1,𝔽25)—61no—
542D3×C8—61no—
543D3×C8—61no—
544D3×C8—61no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32—81no—
549C22×C32—161no—
550C22×C32H(5,𝔽2)11yescharacteristic
551C2×C3⋊D3—21no—
552C2×C3⋊D3—41no—
553C2×C3⋊D3—81no—
554C2×C3⋊D3—161no—
555C2×C3×D3—21no—
556C2×C3×D3—41no—
557C2×C3×D3—41no—
558C2×C3×D3—81no—
559C2×C3×D3—81no—
560C2×C3×D3—161no—
561D32—161no—
562C32×C4—21no—
563C32×C4—21no—
564C32×C4C22×D411yescharacteristic
565C32×C4C22×D411yescharacteristic
566C3⋊Dic3—21no—
567C3×Dic3—22no—
568C3×Dic3—21no—
569H(5,𝔽2)—31no—
570H(5,𝔽2)—91no—
571H(5,𝔽2)—91no—
572H(5,𝔽2)D3211yescharacteristic, complemented
573AGL(1,ℤ/8)—31no—
574AGL(1,ℤ/8)—31no—
575AGL(1,ℤ/8)—31no—
576AGL(1,ℤ/8)—31no—
577AGL(1,ℤ/8)—61no—
578AGL(1,ℤ/8)—61no—
579AGL(1,ℤ/8)—91no—
580AGL(1,ℤ/8)—91no—
581AGL(1,ℤ/8)—91no—
582AGL(1,ℤ/8)—91no—
583AGL(1,ℤ/8)—181no—
584AGL(1,ℤ/8)—181no—
585AGL(1,ℤ/8)—181no—
586AGL(1,ℤ/8)—181no—
587AGL(1,ℤ/8)—181no—
588AGL(1,ℤ/8)—181no—
589#135—31no—
590#135—61no—
591#135—91no—
592#135—181no—
593#135—181no—
594#135—181no—
595C2×D8—31no—
596C2×D8—61no—
597C2×D8—91no—
598C2×D8—91no—
599C2×D8—91no—
600C2×D8—181no—
601C2×D8—181no—
602C2×D8—181no—
603#131—31no—
604#131—91no—
605#131—91no—
606#131—91no—
607#127—31no—
608#127—91no—
609#108—91no—
610#108—91no—
611#104—31no—
612#104—31no—
613#104—91no—
614#104—91no—
615#100—31no—
616#100—91no—
617#100—91no—
618#100—91no—
619C4×C8—91no—
620C23×C3—21no—
621C23×C3—21no—
622C23×C3—41no—
623C23×C3—41no—
624C23×C3—41no—
625C23×C3—42no—
626C23×C3—61no—
627C23×C3—61no—
628C23×C3—121no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—41no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—121no—
635C22×D3—121no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3—121no—
639C22×D3—122no—
640C3×Q8—21no—
641C3×Q8—21no—
642C3×Q8—31no—
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—22no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—21no—
658C3×D4—21no—
659C3×D4—31no—
660C3×D4—41no—
661C3×D4—41no—
662C3×D4—41no—
663C3×D4—41no—
664C3×D4—41no—
665C3×D4—41no—
666C3×D4—42no—
667C3×D4—42no—
668C3×D4—61no—
669C3×D4—61no—
670C3×D4—61no—
671C3×D4—61no—
672C3×D4—61no—
673C3×D4—121no—
674C3×D4—121no—
675C3×D4—242no—
676C3×D4D3×D411yescharacteristic
677C3×D4D3×D411yescharacteristic
678C3×D4D3×D411yescharacteristic
679C3×D4C2×#6711yescharacteristic
680C2×C3×C4—22no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—42no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—121no—
693C2×C3×C4C23×D311yescharacteristic
694C2×C3×C4C23×D311yescharacteristic
695#67—21no—
696#67—41no—
697#67—61no—
698#67—61no—
699#67—82no—
700#67—121no—
701#67—121no—
702#67—121no—
703#67—121no—
704#67—121no—
705#67—121no—
706#67—122no—
707#67—242no—
708C2×Dic3—21no—
709C2×Dic3—121no—
710D12—21no—
711D12—21no—
712D12—21no—
713D12—21no—
714D12—31no—
715D12—31no—
716D12—41no—
717D12—61no—
718D12—62no—
719D12—61no—
720D12—61no—
721D12—61no—
722D12—61no—
723D12—121no—
724D12—121no—
725D12—121no—
726D12—122no—
727D12—121no—
728D12—242no—
729D12C2×#6711yescharacteristic
730C4×D3—21no—
731C4×D3—41no—
732C4×D3—61no—
733C4×D3—61no—
734C4×D3—121no—
735C4×D3—121no—
736C4×D3—121no—
737C4×D3—121no—
738C4×D3—122no—
739Dic6—31no—
740Dic6—31no—
741Dic6—61no—
742Dic6C2×#6711yescharacteristic
743C3×C8—31no—
744C3×C8—31no—
745C3×C8—61no—
746C3×C8—61no—
747C3×C8—61no—
748C3⋊C8—21no—
749C3⋊C8—21no—
750C3⋊C8—21no—
751C3⋊C8—31no—
752C3⋊C8—31no—
753C3⋊C8—31no—
754C3⋊C8—31no—
755C3⋊C8—61no—
756C3⋊C8—61no—
757C3⋊C8—62no—
758C3⋊C8—61no—
759C3⋊C8—61no—
760C3⋊C8C2×#6711yescharacteristic
761C3⋊C8C2×#6711yescharacteristic
762C2×C32—21no—
763C2×C32—41no—
764C2×C32—41no—
765C2×C32—81no—
766C2×C32D4211yescharacteristic
767C3⋊D3—41no—
768C3⋊D3—81no—
769C3×D3—41no—
770C3×D3—81no—
771C3×D3—81no—
772#41—21no—
773#41—21no—
774#41—31no—
775#41—61no—
776#41—61no—
777#41—91no—
778#41—181no—
779#41—181no—
780#41—181no—
781#41—181no—
782#41C2×D3211yescharacteristic
783#41C2×D3211yescharacteristic
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—31no—
787C2×D4—31no—
788C2×D4—41no—
789C2×D4—61no—
790C2×D4—61no—
791C2×D4—91no—
792C2×D4—121no—
793C2×D4—121no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—181no—
797C2×D4—181no—
798C2×D4—361no—
799C2×D4—361no—
800C2×D4—361no—
801C2×D4C2×D3211yescharacteristic
802Q16—31no—
803Q16—91no—
804SD16—31no—
805SD16—31no—
806SD16—61no—
807SD16—61no—
808SD16—61no—
809SD16—61no—
810SD16—91no—
811SD16—91no—
812SD16—181no—
813SD16—181no—
814SD16—181no—
815SD16—181no—
816D8—31no—
817D8—61no—
818D8—61no—
819D8—61no—
820D8—61no—
821D8—61no—
822D8—61no—
823D8—91no—
824D8—181no—
825D8—181no—
826D8—181no—
827D8—181no—
828D8—181no—
829D8—181no—
830D8—181no—
831D8—181no—
832D8—181no—
833D8—181no—
834M16—31no—
835M16—31no—
836M16—31no—
837M16—61no—
838M16—91no—
839M16—181no—
840M16—181no—
841M16—181no—
842C2×C8—31no—
843C2×C8—61no—
844C2×C8—91no—
845C2×C8—181no—
846C2×C8—181no—
847C2×C8—181no—
848C42—31no—
849C22×C3—22no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—41no—
856C22×C3—42no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—61no—
860C22×C3—81no—
861C22×C3—81no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—161no—
865C22×C3—161no—
866C22×C3—161no—
867C22×C3—162no—
868C22×C3—241no—
869C22×C3—241no—
870C22×C3—481no—
871C22×C3#100411yescharacteristic
872C22×C3#100411yescharacteristic
873C2×D3—21no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—81no—
879C2×D3—81no—
880C2×D3—121no—
881C2×D3—122no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—161no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—481no—
888C2×D3—481no—
889C2×D3—481no—
890C2×D3—481no—
891C2×D3—481no—
892C2×D3—482no—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—21no—
900C3×C4—41no—
901C3×C4—62no—
902C3×C4—61no—
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C2×D3×D411yescharacteristic
906C3×C4C22×#6711yescharacteristic
907Dic3—22no—
908Dic3—21no—
909Dic3—61no—
910Dic3—61no—
911Dic3—121no—
912C32#329211yescharacteristic, complemented, Sylow
913C23—21no—
914C23—41no—
915C23—61no—
916C23—61no—
917C23—121no—
918C23—181no—
919C23—361no—
920C23—361no—
921Q8—31no—
922Q8—91no—
923Q8D3×#6711yescharacteristic
924Q8#381111yescharacteristic
925D4—21no—
926D4—21no—
927D4—21no—
928D4—21no—
929D4—31no—
930D4—41no—
931D4—41no—
932D4—61no—
933D4—61no—
934D4—61no—
935D4—61no—
936D4—61no—
937D4—91no—
938D4—121no—
939D4—121no—
940D4—181no—
941D4—181no—
942D4—181no—
943D4—242no—
944D4—361no—
945D4—361no—
946D4—361no—
947D4—361no—
948D4—722no—
949D4D3×#6711yescharacteristic
950D4#381111yescharacteristic
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—41no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—121no—
957C2×C4—181no—
958C2×C4—361no—
959C2×C4—361no—
960C2×C4C22×D3211yescharacteristic
961C8—31no—
962C8—31no—
963C8—61no—
964C8—61no—
965C8—61no—
966C8—91no—
967C8—91no—
968C8—181no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—41no—
973C2×C3—42no—
974C2×C3—41no—
975C2×C3—41no—
976C2×C3—41no—
977C2×C3—41no—
978C2×C3—81no—
979C2×C3—82no—
980C2×C3—81no—
981C2×C3—81no—
982C2×C3—121no—
983C2×C3—241no—
984C2×C3—241no—
985C2×C3#559011yescharacteristic
986C2×C3D4×#6711yescharacteristic
987D3—41no—
988D3—81no—
989D3—81no—
990D3—121no—
991D3—121no—
992D3—241no—
993D3—242no—
994D3—241no—
995D3—241no—
996C22—21no—
997C22—21no—
998C22—41no—
999C22—61no—
1000C22—81no—
1001C22—121no—
1002C22—121no—
1003C22—161no—
1004C22—181no—
1005C22—241no—
1006C22—241no—
1007C22—361no—
1008C22—481no—
1009C22—721no—
1010C22—1441no—
1011C22—1441no—
1012C22#6433011yescharacteristic
1013C4—21no—
1014C4—21no—
1015C4—62no—
1016C4—61no—
1017C4—181no—
1018C4C2×D3×#6711yescharacteristic
1019C4C2×#381111yescharacteristic
1020C3—21no—
1021C3#8028211yescharacteristic, complemented
1022C3#8401011yescharacteristic, complemented
1023C2—21no—
1024C2—41no—
1025C2—41no—
1026C2—81no—
1027C2—121no—
1028C2—241no—
1029C2—241no—
1030C2—361no—
1031C2—721no—
1032C2#1059552611yescharacteristic
subgroupG/H
centerC2#10595526
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×H(5,𝔽2)C22
socleC2×C32D42
hypercenterH(5,𝔽2)D32
hypocenterC32#3292
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. #10596306C2semidirect
2. C3×#5835C2semidirect
3. #10595461C2semidirect
4. #10595454C2semidirect
5. C3×#5241C2semidirect
6. #10591678C2semidirect
7. #10591677C2semidirect
8. #10591675C2semidirect
9. #10591667C2semidirect
10. #10591666C2semidirect
11. #10591662C2semidirect
12. #10591523C2semidirect
13. #10591508C2semidirect
14. #10591482C2semidirect
15. #10591406C2semidirect
18. C32×H(5,𝔽2)C22semidirect
19. #64366C22semidirect
20. C3×#1009C22semidirect
21. #64307C22semidirect
25. #64158C22semidirect
26. #64157C22semidirect
28. #64141C22semidirect
30. C2×#3753C22semidirect
34. C3×#949C22semidirect
35. C3×#949C22semidirect
36. C3×#949C22semidirect
37. C3×#948C22semidirect
38. C3×#940C22semidirect
40. C3×#932C22semidirect
42. C2×C3×#213C22semidirect
51. #63911C22semidirect
52. #63830C22semidirect
53. #63825C22semidirect
54. C2×#3714C22semidirect
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. #63559C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. Dic3×C3⋊C8C22semidirect
74. #5835D3semidirect
80. #5241D3semidirect
130. #3756D4semidirect
132. #3755D4semidirect
134. #3754D4semidirect
139. #3753D4semidirect
144. C3×#216D4semidirect
148. C3×#215D4semidirect
150. C3×#214D4semidirect
157. C3×#213D4semidirect
180. C3×H(5,𝔽2)C2×D3semidirect
181. C3×H(5,𝔽2)C2×D3semidirect
186. #1009C2×D3semidirect
218. #949C2×D3semidirect
219. #949C2×D3semidirect
220. #949C2×D3semidirect
225. #948C2×D3semidirect
227. #940C2×D3semidirect
237. #932C2×D3semidirect
249. C2×#213C2×D3semidirect
273. #837C2×D3semidirect
274. #837C2×D3semidirect
277. #833C2×D3semidirect
461. #216#67semidirect
472. #215#67semidirect
481. #214#67semidirect
511. #213#67semidirect
572. H(5,𝔽2)D32semidirect
912. C32#3292semidirect
1021. C3#80282semidirect
1022. C3#84010semidirect

Maximal subgroups

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

subgroupindex
#105963062
C3×#58352
#105954612
#105954542
C3×#52412
#105916782
#105916772
#105916752
#105916672
#105916662
#105916622
#105915232
#105915082
#105914822
#105914062
#840103
#802823