Finite Group Databasebeta

← #72222767

Subgroups — #72222767

Order 2304.

1381 conjugacy classes of subgroups.

The subgroup lattice has 1229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#82035C211yesmaximal, characteristic
2D3×#5197C211yesmaximal, characteristic, complemented
3#11860210C211yesmaximal, characteristic, complemented
4#11797980C211yesmaximal, characteristic, complemented
5#11797979C211yesmaximal, characteristic, complemented
6C3×#71515C211yesmaximal, characteristic, complemented
7#11797956C211yesmaximal, characteristic, complemented
8#11797940C211yesmaximal, characteristic, complemented
9#11797939C211yesmaximal, characteristic, complemented
10#11797924C211yesmaximal, characteristic, complemented
11#11797923C211yesmaximal, characteristic, complemented
12#11797132C211yesmaximal, characteristic, complemented
13#11796949C211yesmaximal, characteristic, complemented
14#11796858C211yesmaximal, characteristic, complemented
15D3×#4512C211yesmaximal, characteristic, complemented
16#10948638—31nomaximal
17#10948634—31nomaximal
18C3×D3×#135C2211yescharacteristic
19C2×C3×#912C2211yescharacteristic
20D3×#948—21no—
21Dic3×#237—21no—
22C32×#509C2211yescharacteristic
23#10592896C2211yescharacteristic
24#10592851C2211yescharacteristic, complemented
25C3×#5197C2211yescharacteristic
26C3×#5195C2211yescharacteristic
27C3×#5152C2211yescharacteristic, complemented
28C3×#5147C2211yescharacteristic
29C3×#4916C412yescomplemented
30C3×#4915C412yescomplemented
31C3×#4912C412yescomplemented
32C3×#4911C412yescomplemented
33C3×#4909C2211yescharacteristic
34C3×D3×M32C2211yescharacteristic
35#10591676—21no—
36#10591674—21no—
37D3×#837—21no—
38#10591446—21no—
39#10591440—21no—
40#10591420—21no—
41#10590920C2211yescharacteristic
42#10590916C2211yescharacteristic
43D3×#819C2211yescharacteristic
44#10590819C2211yescharacteristic, complemented
45#10590812C2211yescharacteristic, complemented
46#10590706C2211yescharacteristic
47D3×#815C2211yescharacteristic
48D3×#812C2211yescharacteristic
49#10589432C2211yescharacteristic
50#10589429C2211yescharacteristic, complemented
51#10589379C2211yescharacteristic, complemented
52#10589378C2211yescharacteristic, complemented
53C3×#4566C2211yescharacteristic
54C3×#4563C2211yescharacteristic, complemented
55C3×#4513C2211yescharacteristic, complemented
56C3×#4512C2211yescharacteristic, complemented
57#10589137C2211yescharacteristic, complemented
58#10589136C2211yescharacteristic, complemented
59#10589130C2211yescharacteristic, complemented
60#10589129C2211yescharacteristic, complemented
61#10589124C2211yescharacteristic
62#10589123C2211yescharacteristic
63#10589106C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C3×#3414—31no—
66C2×#5197—31no—
67#83897—31no—
68#82035D311yescharacteristic
69D3×#444—31no—
70#79864—31no—
71C3×AGL(1,ℤ/16)—31no—
72#72081—31no—
73#72076—31no—
74#71521—31no—
75#71521—31no—
76#71521—31no—
77#71521—31no—
78#71515—31no—
79#71515—31no—
80#71515—31no—
81#71515—31no—
82#71515—61no—
83#71515D311yescharacteristic, complemented
84#71427—31no—
85C2×#4512—31no—
86#70928—31no—
87#70918—31no—
88#69312—31no—
89#69309—31no—
90#69256—31no—
91#69254—31no—
92#69251—31no—
93#69248—31no—
94#69090—31no—
95D3×#347—31no—
96C3×D3×#41—21no—
97C2×C3×#237—21no—
98C32×#135C2311yescharacteristic
99C2×C32×D8C2311yescharacteristic
100#64157—21no—
101D4×C3⋊Dic3—21no—
102C3×#950—21no—
103C3×#948—21no—
104C3×D4×Dic3—21no—
105C2×C3×#214—21no—
106C3×#919C2×C411yescharacteristic, complemented
107C3×D3×Q16C2×C411yescharacteristic, complemented
108C3×#916—21no—
109C3×D3×SD16—21no—
110C3×#912—21no—
111C3×#912—21no—
112C3×#912C2×C412yes—
113C3×#912C2×C412yes—
114C3×#912C2×C411yescharacteristic, complemented
115C3×D3×D8C2×C411yescharacteristic, complemented
116C2×C3×Dic12C2311yescharacteristic
117C3×#904C2311yescharacteristic
118C2×C3×D3×C8C2311yescharacteristic
119#67⋊Dic3—41no—
120Dic3×#67—41no—
121#63955—41no—
122C2×Dic32—41no—
123C4×D3×Dic3D411yescharacteristic
124#63843—21no—
125Dic3×Dic6—21no—
126#63841—21no—
127#63815—21no—
128#63815—41no—
129#63814—21no—
130#63814—41no—
131D3×#208—21no—
132D3×#208—41no—
133C2×D3×C3⋊C8—41no—
134C2×D3×C3⋊C8D411yescharacteristic
135C32×SD32C2×C412yescomplemented
136C32×D16C2×C412yescomplemented
137C32×M32C2311yescharacteristic
138#63664—21no—
139#63659—21no—
140#63646C2311yescharacteristic
141#63644C2311yescharacteristic
142#63642C2311yescharacteristic
143#63639C2311yescharacteristic
144C3×#837—21no—
145C3×#832—21no—
146C3×#829C2×C412yescomplemented
147C3×#827C2×C412yescomplemented
148C3×#827C2×C412yescomplemented
149C3×#826C2×C412yescomplemented
150C3×#819C2311yescharacteristic
151C3×#817C2311yescharacteristic
152C3×#815C2311yescharacteristic
153C3×#812C2311yescharacteristic
154C3×#812C2311yescharacteristic
155C3×Dic24C2×C412yescomplemented
156C3×#800C2×C412yescomplemented
157C3×#798C2×C412yescomplemented
158C3×D3×C16C2×C412yescomplemented
159#63577—21no—
160#63575—21no—
161#63569—21no—
162#63568—21no—
163#63566—21no—
164#63565—21no—
165#63555D411yescharacteristic
166#63554D411yescharacteristic
167#63543—21no—
168D3×C3⋊C16—21no—
169#33468—91noSylow
170C2×C3×#135—31no—
171C2×C3×#135—31no—
172Dic3×#41—61no—
173C2×#948—61no—
174D3×#135C2×D311yescharacteristic
175C2×#912C2×D311yescharacteristic
176D3×#131—61no—
177C4×#237—61no—
178C3×#510—31no—
179C3×#510—32no—
180C3×#510—31no—
181C3×#509—21no—
182C3×#509—31no—
183C3×#509—32no—
184C3×#509C2×D311yescharacteristic
185C3×#509C2×D311yescharacteristic
186C3×#508—32no—
187C3×#508—32no—
188C2×C3×M32—31no—
189C3×#444—31no—
190C3×#442—31no—
191C2×#837—61no—
192#5233—61no—
193#5197—31no—
194#5197—31no—
195#5197—31no—
196#5197—31no—
197#5197—61no—
198#5197—61no—
199#5197—61no—
200#5197C2×D311yescharacteristic
201#5195C2×D311yescharacteristic
202#5184—31no—
203#5184—31no—
204#5164—61no—
205#5164—61no—
206#5152—31no—
207#5152—31no—
208#5152—61no—
209#5152C2×D311yescharacteristic, complemented
210#5147C2×D311yescharacteristic
211#5145—61no—
212C2×#819—31no—
213#5106—31no—
214C2×#815—31no—
215C2×#812—31no—
216#5018—61no—
217#4916Dic312yescomplemented
218#4915Dic312yescomplemented
219#4912Dic312yescomplemented
220#4911Dic312yescomplemented
221#4909C2×D311yescharacteristic
222D3×M32—31no—
223D3×M32C2×D311yescharacteristic
224#4894—31no—
225D3×#108—31no—
226#4860—31no—
227#4853—31no—
228#4823—61no—
229D3×#104—61no—
230#4772—61no—
231#4757—61no—
232#4717—31no—
233#4716—31no—
234D3×#97—31no—
235C3×#365—31no—
236C3×#361—31no—
237C3×#360—31no—
238C3×#347—31no—
239#4566—31no—
240#4566—31no—
241#4566—31no—
242#4566—31no—
243#4566—61no—
244#4566C2×D311yescharacteristic
245#4565—31no—
246#4565—31no—
247#4563—31no—
248#4563—31no—
249#4563—61no—
250#4563C2×D311yescharacteristic, complemented
251#4518—31no—
252#4517—31no—
253#4513—31no—
254#4513—31no—
255#4513—31no—
256#4513—31no—
257#4513—61no—
258#4513C2×D311yescharacteristic, complemented
259#4512—31no—
260#4512—31no—
261#4512—31no—
262#4512—31no—
263#4512—31no—
264#4512—61no—
265#4512C2×D311yescharacteristic, complemented
266#4496—31no—
267#4494—31no—
268#4488—31no—
269#4487—31no—
270#4466—31no—
271C32×#41—21no—
272C2×C32×D4—21no—
273C22×C3⋊Dic3—41no—
274C2×C3×#67—41no—
275C22×C3×Dic3—41no—
276C22×C3×Dic3—41no—
277C3×#239—21no—
278C3×D3×Q8—21no—
279C3×#237—22no—
280C3×#237—22no—
281C3×#237—21no—
282C3×#237—41no—
283C3×#237—41no—
284C3×#237—41no—
285C3×D3×D4—21no—
286C3×D3×D4—41no—
287C3×#235—21no—
288C3×#235—41no—
289C2×C3×C4×D3—41no—
290C2×C3×C4×D3C2×D411yescharacteristic
291C2×C3×Dic6—21no—
292C2×D3×Dic3—21no—
293C32×Q16C22×C411yescharacteristic
294C32×SD16—21no—
295C32×D8—21no—
296C32×D8C22×C411yescharacteristic
297C32×D8C22×C412yes—
298C2×C32×C8C2411yescharacteristic
299#3757—41no—
300C4⋊(C3⋊Dic3)—21no—
301C4×C3⋊Dic3C2×D411yescharacteristic
302#3748—21no—
303#3748—41no—
304C2×C3⋊(C3⋊C8)—41no—
305C2×C3⋊(C3⋊C8)C2×D411yescharacteristic
306C3×#217—41no—
307C3×#216—21no—
308C3×#215—21no—
309C3×#214—22no—
310C3×#214—22no—
311C3×#214—21no—
312C3×#213—21no—
313C3×C4⋊Dic3—21no—
314C3×C4×Dic3C2×D411yescharacteristic
315C3×#208—21no—
316C3×#208—41no—
317C2×C3×C3⋊C8—41no—
318C2×C3×C3⋊C8C2×D411yescharacteristic
319C2×C3×C3⋊C8C2×D411yescharacteristic
320C3×Dic12—21no—
321C3×Dic12C22×C411yescharacteristic
322C3×Dic12C22×C412yes—
323C3×D24C22×C411yescharacteristic
324C3×#204—21no—
325C3×D3×C8C22×C411yescharacteristic
326C3×D3×C8C22×C411yescharacteristic
327C3×D3×C8#4111yescharacteristic
328C3×D3×C8#4111yescharacteristic
329Dic3⋊Dic3—41no—
330Dic3⋊Dic3—41no—
331(C2×D3)⋊Dic3—41no—
332Dic32—21no—
333Dic32—41no—
334Dic32—41no—
335Dic32—41no—
336#3711—41no—
337#3711—41no—
338#3711—41no—
339D3×C3⋊C8—21no—
340D3×C3⋊C8—21no—
341D3×C3⋊C8—41no—
342D3×C3⋊C8—41no—
343D3×C3⋊C8—41no—
344C32×C16C22×C412yes—
345C3⋊(C3⋊C16)—21no—
346C3×C3⋊C16—21no—
347C3×C3⋊C16C22×C412yes—
348#3414—31no—
349C2×#444—91no—
350#2943—91no—
351AGL(1,ℤ/16)—31no—
352AGL(1,ℤ/16)—91no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355#2180—91no—
356#2180—91no—
357#2180—91no—
358#2180—91no—
359#2155—91no—
360#2148—91no—
361#2145—91no—
362C2×#347—91no—
363C2×C3×#41—61no—
364C2×C3×#41—61no—
365D3×#41—21no—
366C2×#237—21no—
367C3×#135—21no—
368C3×#135—31no—
369C3×#135—32no—
370C3×#135—31no—
371C3×#135—32no—
372C3×#135—31no—
373C3×#135—61no—
374C3×#135—61no—
375C3×#135—61no—
376C3×#135—61no—
377C3×#135C22×D311yescharacteristic
378C3×#135C22×D311yescharacteristic
379C2×C3×Q16—31no—
380C2×C3×Q16—31no—
381C2×C3×SD16—61no—
382C2×C3×SD16—61no—
383C2×C3×D8—21no—
384C2×C3×D8—31no—
385C2×C3×D8C22×D311yescharacteristic
386C2×C3×D8C22×D311yescharacteristic
387C3×#131—61no—
388C22×C3×C8—31no—
389C3×C4×D4—61no—
390#950—21no—
391#948—21no—
392#948—61no—
393#948—61no—
394#948—61no—
395#948—61no—
396#948—121no—
397#948—121no—
398#948—121no—
399Q8×Dic3—61no—
400Q8×Dic3—61no—
401D4×Dic3—21no—
402D4×Dic3—61no—
403D4×Dic3—61no—
404D4×Dic3—121no—
405D4×Dic3—121no—
406D4×Dic3—121no—
407C2×#214—21no—
408C4×#67—121no—
409#926—61no—
410#926—121no—
411C2×C4×Dic3—31no—
412C2×C4×Dic3—121no—
413C2×C4×Dic3—121no—
414C2×#208—61no—
415C2×#208—121no—
416C22×C3⋊C8—31no—
417C22×C3⋊C8—121no—
418#919C2×Dic311yescharacteristic, complemented
419D3×Q16C2×Dic311yescharacteristic, complemented
420#916—21no—
421D3×SD16—21no—
422#912—21no—
423#912—21no—
424#912C2×Dic312yes—
425#912C2×Dic312yes—
426#912C2×Dic311yescharacteristic, complemented
427D3×D8C2×Dic311yescharacteristic, complemented
428#907—61no—
429#907—121no—
430D3×M16—61no—
431D3×M16—121no—
432C2×Dic12C22×D311yescharacteristic
433#904C22×D311yescharacteristic
434#901—61no—
435#901—121no—
436C2×D3×C8—31no—
437C2×D3×C8—121no—
438C2×D3×C8C22×D311yescharacteristic
439#892—61no—
440#887—61no—
441#67⋊C4—121no—
442#877—121no—
443C42×D3—31no—
444C4×Dic6—61no—
445C3×Q32—32no—
446C3×Q32—32no—
447C3×SD32—22no—
448C3×SD32—32no—
449C3×SD32—32no—
450C3×SD32—32no—
451C3×SD32C4×D312yescomplemented
452C3×SD32C2×Dic312yescomplemented
453C3×D16—22no—
454C3×D16—32no—
455C3×D16C4×D312yescomplemented
456C3×D16C2×Dic312yescomplemented
457C3×M32—21no—
458C3×M32—31no—
459C3×M32—32no—
460C3×M32—31no—
461C3×M32C22×D311yescharacteristic
462C3×M32C22×D311yescharacteristic
463C2×C3×C16—32no—
464C3×#108—31no—
465C3×#106—31no—
466C3×#104—61no—
467C3×#102—61no—
468C3×#97—31no—
469#837—21no—
470#837—61no—
471#837—61no—
472#837—61no—
473#837—61no—
474#837—121no—
475#835—61no—
476#835—61no—
477#832—21no—
478#832—61no—
479#832—61no—
480#832—121no—
481#829C2×Dic312yescomplemented
482#827C2×Dic312yescomplemented
483#827C2×Dic312yescomplemented
484#826C2×Dic312yescomplemented
485#825—61no—
486#822—61no—
487#819—31no—
488#819—31no—
489#819—61no—
490#819—61no—
491#819C22×D311yescharacteristic
492#818—61no—
493#817—31no—
494#817—31no—
495#817—61no—
496#817C22×D311yescharacteristic
497#816—61no—
498#815—31no—
499#815—31no—
500#815—31no—
501#815—31no—
502#815—31no—
503#815—61no—
504#815C22×D311yescharacteristic
505#812—31no—
506#812—31no—
507#812—61no—
508#812—61no—
509#812C22×D311yescharacteristic
510#812C22×D311yescharacteristic
511C2×C3⋊C16—61no—
512#810—61no—
513#807—61no—
514#805—61no—
515#803—31no—
516Dic24C2×Dic312yescomplemented
517#800C2×Dic312yescomplemented
518#798—61no—
519#798C2×Dic312yescomplemented
520D3×C16—61no—
521D3×C16C2×Dic312yescomplemented
522C23×C32—41no—
523C22×C3×D3—41no—
524C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
525C32×Q8—21no—
526C32×D4—21no—
527C32×D4—22no—
528C32×D4—41no—
529C32×D4—41no—
530C2×C32×C4—41no—
531C2×C32×C4C22×D411yescharacteristic
532C2×C3⋊Dic3—21no—
533C2×C3⋊Dic3—41no—
534C2×C3⋊Dic3—82no—
535C3×#67—41no—
536C3×#67—41no—
537C3×#67—42no—
538C3×#67—42no—
539C3×#67—41no—
540C2×C3×Dic3—21no—
541C2×C3×Dic3—41no—
542C2×C3×Dic3—41no—
543C2×C3×Dic3—42no—
544C2×C3×Dic3—42no—
545C2×C3×Dic3—41no—
546C2×C3×Dic3—82no—
547C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
548C3×D12—21no—
549C3×D12—41no—
550C3×C4×D3—41no—
551C3×C4×D3—41no—
552C3×C4×D3—41no—
553C3×C4×D3C4×D411yescharacteristic
554C3×C4×D3C4×D411yescharacteristic
555C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
556C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
557C3×Dic6—21no—
558C3×Dic6—22no—
559C3×Dic6—41no—
560C3×Dic6—41no—
561D3×Dic3—81no—
562C32×C8C23×C411yescharacteristic
563C32×C8C2×#4111yescharacteristic
564C3⋊(C3⋊C8)—21no—
565C3⋊(C3⋊C8)—41no—
566C3×C3⋊C8—21no—
567C3×C3⋊C8—41no—
568C3×C3⋊C8C4×D411yescharacteristic
569C3×C3⋊C8C4×D411yescharacteristic
570C2×#135—31no—
571C2×#135—31no—
572C2×#131—181no—
573C4×#41—181no—
574#510—31no—
575#510—32no—
576#510—31no—
577#509—31no—
578#509—32no—
579#509D3211yescharacteristic
580#508—32no—
581#508—32no—
582C2×M32—31no—
583C2×M32—91no—
584#444—31no—
585#444—91no—
586#444—91no—
587#444—91no—
588#444—181no—
589#444—181no—
590#442—31no—
591#442—91no—
592#441—91no—
593#441—91no—
594#440—181no—
595#440—181no—
596C2×#108—91no—
597#427—91no—
598C2×#104—181no—
599#416—181no—
600C2×#97—91no—
601#365—31no—
602#365—91no—
603#365—91no—
604#365—91no—
605#362—91no—
606#362—91no—
607#361—31no—
608#361—91no—
609#360—31no—
610#360—91no—
611#360—91no—
612#360—91no—
613#347—31no—
614#347—91no—
615#347—91no—
616#347—91no—
617C3×#41—21no—
618C3×#41—21no—
619C3×#41—41no—
620C3×#41—62no—
621C3×#41—62no—
622C3×#41—61no—
623C3×#41—61no—
624C3×#41—61no—
625C3×#41—121no—
626C3×#41—121no—
627C3×#41—121no—
628C3×#41—121no—
629C2×C3×Q8—61no—
630C2×C3×Q8—61no—
631C2×C3×D4—21no—
632C2×C3×D4—21no—
633C2×C3×D4—41no—
634C2×C3×D4—61no—
635C2×C3×D4—121no—
636C2×C3×D4—121no—
637C22×C3×C4—31no—
638C22×C3×C4—121no—
639C22×C3×C4—121no—
640C22×C3×C4—121no—
641C2×#67—41no—
642C22×Dic3—41no—
643C22×Dic3—41no—
644C22×Dic3—61no—
645C22×Dic3—121no—
646C22×Dic3—121no—
647C22×Dic3—241no—
648#239—21no—
649D3×Q8—21no—
650#237—22no—
651#237—22no—
652#237—21no—
653#237—41no—
654#237—41no—
655#237—41no—
656D3×D4—21no—
657D3×D4—41no—
658#235—21no—
659#235—41no—
660C2×C4×D3—41no—
661C2×C4×D3—61no—
662C2×C4×D3D3×D411yescharacteristic
663C2×Dic6—21no—
664C3×Q16—21no—
665C3×Q16—31no—
666C3×Q16—32no—
667C3×Q16—61no—
668C3×Q16—61no—
669C3×Q16C2×C4×D311yescharacteristic
670C3×Q16C22×Dic311yescharacteristic
671C3×SD16—21no—
672C3×SD16—21no—
673C3×SD16—41no—
674C3×SD16—62no—
675C3×SD16—62no—
676C3×SD16—61no—
677C3×SD16—61no—
678C3×SD16—61no—
679C3×D8—21no—
680C3×D8—21no—
681C3×D8—21no—
682C3×D8—22no—
683C3×D8—31no—
684C3×D8—41no—
685C3×D8—61no—
686C3×D8C2×C4×D312yes—
687C3×D8C2×C4×D311yescharacteristic
688C3×D8C22×Dic312yes—
689C3×D8C22×Dic311yescharacteristic
690C3×M16—61no—
691C3×M16—121no—
692C2×C3×C8—21no—
693C2×C3×C8—31no—
694C2×C3×C8—31no—
695C2×C3×C8—31no—
696C2×C3×C8—31no—
697C2×C3×C8—31no—
698C2×C3×C8—31no—
699C2×C3×C8—121no—
700C2×C3×C8C23×D311yescharacteristic
701C2×C3×C8C23×D311yescharacteristic
702C3×C4⋊C4—61no—
703C3×C22⋊C4—121no—
704C3×C42—31no—
705#217—41no—
706#217—121no—
707#217—121no—
708#217—121no—
709#217—241no—
710#216—21no—
711#215—21no—
712#214—22no—
713#214—22no—
714#214—21no—
715#213—21no—
716(C2×D3)⋊C4—121no—
717C4⋊Dic3—21no—
718C4⋊Dic3—61no—
719C4⋊Dic3—61no—
720C4⋊Dic3—121no—
721C4⋊Dic3—121no—
722C4⋊Dic3—121no—
723Dic3⋊C4—121no—
724Dic3⋊C4—121no—
725C4×Dic3—31no—
726C4×Dic3—31no—
727C4×Dic3—61no—
728C4×Dic3—61no—
729C4×Dic3—61no—
730C4×Dic3—121no—
731C4×Dic3—121no—
732C4×Dic3—121no—
733C4×Dic3—121no—
734C4×Dic3—121no—
735C4×Dic3—121no—
736C4×Dic3D3×D411yescharacteristic
737#208—21no—
738#208—41no—
739#208—61no—
740#208—61no—
741#208—121no—
742#208—121no—
743#208—121no—
744#208—121no—
745#208—121no—
746#208—121no—
747#208—241no—
748C2×C3⋊C8—31no—
749C2×C3⋊C8—31no—
750C2×C3⋊C8—41no—
751C2×C3⋊C8—61no—
752C2×C3⋊C8—61no—
753C2×C3⋊C8—61no—
754C2×C3⋊C8—121no—
755C2×C3⋊C8—121no—
756C2×C3⋊C8—121no—
757C2×C3⋊C8—121no—
758C2×C3⋊C8—121no—
759C2×C3⋊C8—241no—
760C2×C3⋊C8D3×D411yescharacteristic
761C2×C3⋊C8D3×D411yescharacteristic
762Dic12—21no—
763Dic12C22×Dic312yes—
764Dic12C22×Dic311yescharacteristic
765D24C22×Dic311yescharacteristic
766#204—21no—
767ΓL(1,𝔽25)—121no—
768ΓL(1,𝔽25)—121no—
769ΓL(1,𝔽25)—121no—
770D3×C8—61no—
771D3×C8—61no—
772D3×C8—121no—
773D3×C8—121no—
774D3×C8—121no—
775D3×C8#23711yescharacteristic
776D3×C8#23711yescharacteristic
777D3×C8C22×Dic311yescharacteristic
778D3×C8C22×Dic311yescharacteristic
779C3×C16—22no—
780C3×C16—32no—
781C3×C16—61no—
782C3×C16C2×C4×D312yes—
783C3×C16C22×Dic312yes—
784C3⋊C16—21no—
785C3⋊C16—61no—
786C3⋊C16—61no—
787C3⋊C16—121no—
788C3⋊C16C22×Dic312yes—
789C22×C32—42no—
790C22×C32—41no—
791C22×C32—81no—
792C22×C32—81no—
793C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
794C2×C3×D3—41no—
795C2×C3×D3—41no—
796C2×C3×D3—82no—
797C2×C3×D3#44211yescharacteristic
798C2×C3×D3#44211yescharacteristic
799C32×C4—41no—
800C32×C4C2×C4×D411yescharacteristic
801C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
802C3⋊Dic3—41no—
803C3⋊Dic3—81no—
804C3×Dic3—41no—
805C3×Dic3—41no—
806C3×Dic3—42no—
807C3×Dic3—81no—
808C3×Dic3#44211yescharacteristic
809C3×Dic3#44211yescharacteristic
810C2×#41—61no—
811C2×#41—61no—
812#135—31no—
813#135—32no—
814#135—32no—
815#135—31no—
816#135—31no—
817#135—61no—
818#135—61no—
819#135—61no—
820#135—61no—
821#135C2×D3211yescharacteristic
822C2×Q16—31no—
823C2×Q16—31no—
824C2×SD16—61no—
825C2×SD16—61no—
826C2×D8—31no—
827C2×D8C2×D3211yescharacteristic
828#131—61no—
829#131—181no—
830#131—181no—
831#131—181no—
832#131—361no—
833#131—361no—
834C2×M16—181no—
835C2×M16—361no—
836C22×C8—31no—
837C22×C8—91no—
838C22×C8—361no—
839C4×Q8—181no—
840C4×Q8—181no—
841C4×D4—61no—
842C4×D4—181no—
843C4×D4—361no—
844C4×D4—361no—
845#117—181no—
846#117—361no—
847C2×C42—91no—
848C2×C42—361no—
849Q32—32no—
850Q32—32no—
851SD32—32no—
852SD32—32no—
853SD32—32no—
854SD32D3×Dic312yescomplemented
855D16—32no—
856D16D3×Dic312yescomplemented
857M32—31no—
858M32—32no—
859M32—31no—
860M32—91no—
861M32—181no—
862M32C2×D3211yescharacteristic
863C2×C16—32no—
864C2×C16—181no—
865#108—31no—
866#108—91no—
867#108—181no—
868#107—181no—
869#106—31no—
870#106—91no—
871#104—61no—
872#104—181no—
873#104—181no—
874#104—181no—
875#103—181no—
876#103—181no—
877#102—61no—
878#102—181no—
879#97—31no—
880#97—91no—
881#97—91no—
882#97—91no—
883C23×C3—31no—
884C23×C3—41no—
885C23×C3—41no—
886C23×C3—81no—
887C23×C3—121no—
888C22×D3—41no—
889C22×D3#91111yescharacteristic
890C3×Q8—21no—
891C3×Q8—21no—
892C3×Q8—41no—
893C3×Q8—61no—
894C3×Q8—62no—
895C3×Q8—121no—
896C3×Q8—121no—
897C3×D4—21no—
898C3×D4—22no—
899C3×D4—22no—
900C3×D4—21no—
901C3×D4—42no—
902C3×D4—41no—
903C3×D4—41no—
904C3×D4—41no—
905C3×D4—41no—
906C3×D4—41no—
907C3×D4—61no—
908C3×D4—81no—
909C3×D4—81no—
910C3×D4—121no—
911C3×D4—121no—
912C3×D4—122no—
913C3×D4—121no—
914C3×D4—122no—
915C3×D4—121no—
916C2×C3×C4—21no—
917C2×C3×C4—31no—
918C2×C3×C4—31no—
919C2×C3×C4—31no—
920C2×C3×C4—31no—
921C2×C3×C4—31no—
922C2×C3×C4—41no—
923C2×C3×C4—41no—
924C2×C3×C4—61no—
925C2×C3×C4—81no—
926C2×C3×C4—121no—
927C2×C3×C4—121no—
928C2×C3×C4—122no—
929C2×C3×C4—122no—
930C2×C3×C4—121no—
931C2×C3×C4—121no—
932C2×C3×C4—121no—
933C2×C3×C4—121no—
934C2×C3×C4—242no—
935C2×C3×C4C2×D3×D411yescharacteristic
936C2×C3×C4C2×D3×D411yescharacteristic
937#67—41no—
938#67—41no—
939#67—42no—
940#67—42no—
941#67—41no—
942C2×Dic3—21no—
943C2×Dic3—41no—
944C2×Dic3—41no—
945C2×Dic3—42no—
946C2×Dic3—42no—
947C2×Dic3—41no—
948C2×Dic3—61no—
949C2×Dic3—61no—
950C2×Dic3—82no—
951C2×Dic3—121no—
952C2×Dic3—121no—
953C2×Dic3—121no—
954C2×Dic3—241no—
955C2×Dic3—241no—
956C2×Dic3—242no—
957C2×Dic3—242no—
958C2×Dic3—482no—
959C2×Dic3#91111yescharacteristic
960D12—21no—
961D12—41no—
962C4×D3—41no—
963C4×D3—41no—
964C4×D3—41no—
965C4×D3—241no—
966C4×D3#91111yescharacteristic
967C4×D3#91111yescharacteristic
968C4×D3D4×Dic311yescharacteristic
969C4×D3D4×Dic311yescharacteristic
970Dic6—21no—
971Dic6—22no—
972Dic6—41no—
973Dic6—41no—
974C3×C8—21no—
975C3×C8—21no—
976C3×C8—31no—
977C3×C8—31no—
978C3×C8—61no—
979C3×C8—121no—
980C3×C8C22×C4×D311yescharacteristic
981C3×C8C2×#23711yescharacteristic
982C3×C8D3×#4111yescharacteristic
983C3×C8C23×Dic311yescharacteristic
984C3⋊C8—21no—
985C3⋊C8—41no—
986C3⋊C8—61no—
987C3⋊C8—61no—
988C3⋊C8—121no—
989C3⋊C8—121no—
990C3⋊C8—121no—
991C3⋊C8—241no—
992C3⋊C8D4×Dic311yescharacteristic
993C3⋊C8D4×Dic311yescharacteristic
994C2×C32—21no—
995C2×C32—81no—
996C2×C32—82no—
997C2×C32C2×#44211yescharacteristic
998C3×D3—21no—
999C3×D3—21no—
1000C3×D3—81no—
1001#41—21no—
1002#41—62no—
1003#41—62no—
1004#41—61no—
1005#41—61no—
1006#41—61no—
1007#41—121no—
1008#41—121no—
1009#41—121no—
1010#41—121no—
1011C2×Q8—61no—
1012C2×Q8—61no—
1013C2×D4—21no—
1014C2×D4—61no—
1015C2×D4—121no—
1016C2×D4—121no—
1017C22×C4—31no—
1018C22×C4—121no—
1019C22×C4—121no—
1020C22×C4—121no—
1021C22×C4—181no—
1022C22×C4—361no—
1023Q16—31no—
1024Q16—32no—
1025Q16—61no—
1026Q16—61no—
1027Q16C2×D3×Dic311yescharacteristic
1028SD16—21no—
1029SD16—62no—
1030SD16—62no—
1031SD16—61no—
1032SD16—61no—
1033SD16—61no—
1034D8—21no—
1035D8—31no—
1036D8—61no—
1037D8C2×D3×Dic312yes—
1038D8C2×D3×Dic311yescharacteristic
1039M16—61no—
1040M16—121no—
1041M16—181no—
1042M16—361no—
1043M16—361no—
1044M16—361no—
1045M16—361no—
1046C2×C8—31no—
1047C2×C8—31no—
1048C2×C8—31no—
1049C2×C8—31no—
1050C2×C8—31no—
1051C2×C8—31no—
1052C2×C8—91no—
1053C2×C8—121no—
1054C2×C8—181no—
1055C2×C8—181no—
1056C2×C8—361no—
1057C2×C8—361no—
1058C2×C8—361no—
1059C2×C8—361no—
1060C2×C8C22×D3211yescharacteristic
1061C4⋊C4—61no—
1062C4⋊C4—181no—
1063C4⋊C4—361no—
1064C4⋊C4—361no—
1065C22⋊C4—121no—
1066C22⋊C4—361no—
1067C22⋊C4—361no—
1068C42—31no—
1069C42—91no—
1070C42—181no—
1071C42—361no—
1072C42—361no—
1073C42—361no—
1074C16—32no—
1075C16—61no—
1076C16—181no—
1077C16C2×D3×Dic312yes—
1078C22×C3—21no—
1079C22×C3—31no—
1080C22×C3—31no—
1081C22×C3—42no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—42no—
1085C22×C3—81no—
1086C22×C3—82no—
1087C22×C3—81no—
1088C22×C3—81no—
1089C22×C3—81no—
1090C22×C3—81no—
1091C22×C3—121no—
1092C22×C3—121no—
1093C22×C3—161no—
1094C22×C3—161no—
1095C22×C3—242no—
1096C22×C3C2×#91111yescharacteristic
1097C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1098C2×D3—41no—
1099C2×D3—41no—
1100C2×D3—82no—
1101C2×D3#515211yescharacteristic
1102C2×D3#515211yescharacteristic
1103C3×C4—21no—
1104C3×C4—21no—
1105C3×C4—31no—
1106C3×C4—31no—
1107C3×C4—41no—
1108C3×C4—41no—
1109C3×C4—81no—
1110C3×C4—121no—
1111C3×C4—122no—
1112C3×C4—121no—
1113C3×C4—241no—
1114C3×C4C4×D3×D411yescharacteristic
1115C3×C4C2×#91111yescharacteristic
1116C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1117C3×C4C2×D4×Dic311yescharacteristic
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—42no—
1121Dic3—81no—
1122Dic3—121no—
1123Dic3—121no—
1124Dic3—241no—
1125Dic3—241no—
1126Dic3—241no—
1127Dic3—481no—
1128Dic3#515211yescharacteristic
1129Dic3#515211yescharacteristic
1130C32#3346811yescharacteristic, complemented, Sylow
1131C23—31no—
1132C23—41no—
1133C23—121no—
1134Q8—21no—
1135Q8—62no—
1136Q8—61no—
1137Q8—121no—
1138Q8—121no—
1139D4—22no—
1140D4—21no—
1141D4—41no—
1142D4—41no—
1143D4—61no—
1144D4—121no—
1145D4—121no—
1146D4—122no—
1147D4—121no—
1148D4—122no—
1149D4—121no—
1150C2×C4—31no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—31no—
1155C2×C4—41no—
1156C2×C4—61no—
1157C2×C4—121no—
1158C2×C4—121no—
1159C2×C4—122no—
1160C2×C4—122no—
1161C2×C4—121no—
1162C2×C4—121no—
1163C2×C4—121no—
1164C2×C4—121no—
1165C2×C4—181no—
1166C2×C4—242no—
1167C2×C4—361no—
1168C2×C4—721no—
1169C2×C4—722no—
1170C2×C4D32×D411yescharacteristic
1171C8—31no—
1172C8—31no—
1173C8—61no—
1174C8—121no—
1175C8—181no—
1176C8—361no—
1177C8D3×#23711yescharacteristic
1178C8C22×D3×Dic311yescharacteristic
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—41no—
1183C2×C3—61no—
1184C2×C3—61no—
1185C2×C3—82no—
1186C2×C3—81no—
1187C2×C3—81no—
1188C2×C3—82no—
1189C2×C3—162no—
1190C2×C3—161no—
1191C2×C3—241no—
1192C2×C3D3×#44211yescharacteristic
1193C2×C3C2×#515211yescharacteristic
1194D3—21no—
1195D3—21no—
1196D3—81no—
1197C22—31no—
1198C22—31no—
1199C22—41no—
1200C22—42no—
1201C22—81no—
1202C22—81no—
1203C22—121no—
1204C22—121no—
1205C22—242no—
1206C22D3×#91111yescharacteristic
1207C4—31no—
1208C4—31no—
1209C4—41no—
1210C4—121no—
1211C4—122no—
1212C4—121no—
1213C4—241no—
1214C4—361no—
1215C4—721no—
1216C4D3×#91111yescharacteristic
1217C4D3×D4×Dic311yescharacteristic
1218C3—21no—
1219C3#1094863411yescharacteristic, complemented
1220C3#1094863811yescharacteristic, complemented
1221C2—21no—
1222C2—61no—
1223C2—61no—
1224C2—82no—
1225C2—81no—
1226C2—241no—
1227C2D3×#515211yescharacteristic
subgroupG/H
centerC2D3×#5152
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#509C22
socleC2×C32C2×#442
prime radicalC3×#82035C2
cosocleC2×C32×C8C24
hypercenter#509D32
hypocenterC32#33468
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
2. D3×#5197C2semidirect
3. #11860210C2semidirect
4. #11797980C2semidirect
5. #11797979C2semidirect
6. C3×#71515C2semidirect
7. #11797956C2semidirect
8. #11797940C2semidirect
9. #11797939C2semidirect
10. #11797924C2semidirect
11. #11797923C2semidirect
12. #11797132C2semidirect
13. #11796949C2semidirect
14. #11796858C2semidirect
15. D3×#4512C2semidirect
24. #10592851C22semidirect
27. C3×#5152C22semidirect
29. C3×#4916C4semidirect
30. C3×#4915C4semidirect
31. C3×#4912C4semidirect
32. C3×#4911C4semidirect
44. #10590819C22semidirect
45. #10590812C22semidirect
50. #10589429C22semidirect
51. #10589379C22semidirect
52. #10589378C22semidirect
54. C3×#4563C22semidirect
55. C3×#4513C22semidirect
56. C3×#4512C22semidirect
57. #10589137C22semidirect
58. #10589136C22semidirect
59. #10589130C22semidirect
60. #10589129C22semidirect
63. #10589106C22semidirect
64. #10589105C22semidirect
83. #71515D3semidirect
106. C3×#919C2×C4semidirect
107. C3×D3×Q16C2×C4semidirect
114. C3×#912C2×C4semidirect
115. C3×D3×D8C2×C4semidirect
135. C32×SD32C2×C4semidirect
136. C32×D16C2×C4semidirect
146. C3×#829C2×C4semidirect
147. C3×#827C2×C4semidirect
148. C3×#827C2×C4semidirect
149. C3×#826C2×C4semidirect
155. C3×Dic24C2×C4semidirect
156. C3×#800C2×C4semidirect
157. C3×#798C2×C4semidirect
158. C3×D3×C16C2×C4semidirect
209. #5152C2×D3semidirect
217. #4916Dic3semidirect
218. #4915Dic3semidirect
219. #4912Dic3semidirect
220. #4911Dic3semidirect
250. #4563C2×D3semidirect
258. #4513C2×D3semidirect
265. #4512C2×D3semidirect
418. #919C2×Dic3semidirect
419. D3×Q16C2×Dic3semidirect
426. #912C2×Dic3semidirect
427. D3×D8C2×Dic3semidirect
451. C3×SD32C4×D3semidirect
452. C3×SD32C2×Dic3semidirect
455. C3×D16C4×D3semidirect
456. C3×D16C2×Dic3semidirect
481. #829C2×Dic3semidirect
482. #827C2×Dic3semidirect
483. #827C2×Dic3semidirect
484. #826C2×Dic3semidirect
516. Dic24C2×Dic3semidirect
517. #800C2×Dic3semidirect
519. #798C2×Dic3semidirect
521. D3×C16C2×Dic3semidirect
854. SD32D3×Dic3semidirect
856. D16D3×Dic3semidirect
1130. C32#33468semidirect
1219. C3#10948634semidirect
1220. C3#10948638semidirect

Maximal subgroups

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

subgroupindex
C3×#820352
D3×#51972
#118602102
#117979802
#117979792
C3×#715152
#117979562
#117979402
#117979392
#117979242
#117979232
#117971322
#117969492
#117968582
D3×#45122
#109486383
#109486343