Finite Group Databasebeta

← #72222766

Subgroups — #72222766

Order 2304.

1413 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#509C211yesmaximal, characteristic
2#11861215C211yesmaximal, characteristic, complemented
3#11860685C211yesmaximal, characteristic, complemented
4#11797986C211yesmaximal, characteristic, complemented
5#11797985C211yesmaximal, characteristic, complemented
6#11797980C211yesmaximal, characteristic, complemented
7#11797979C211yesmaximal, characteristic, complemented
8#11797970C211yesmaximal, characteristic, complemented
9#11797969C211yesmaximal, characteristic, complemented
10C3×#71515C211yesmaximal, characteristic, complemented
11#11797956C211yesmaximal, characteristic, complemented
12#11797132C211yesmaximal, characteristic, complemented
13D3×#4563C211yesmaximal, characteristic, complemented
14#11796858C211yesmaximal, characteristic, complemented
15#11795942C211yesmaximal, characteristic, complemented
16#10948663—31nomaximal
17#10948658—31nomaximal
18C3×D3×#135C2211yescharacteristic
19C2×C3×D3×D8C2211yescharacteristic
20#10595441—21no—
21#10595215—21no—
22C32×#509C2211yescharacteristic
23#10592896C2211yescharacteristic, complemented
24#10592851C2211yescharacteristic, complemented
25C3×#5197C2211yescharacteristic, complemented
26C3×#5193C2211yescharacteristic
27C3×#5152C2211yescharacteristic, complemented
28C3×#5147C2211yescharacteristic
29C3×#4914C412yescomplemented
30C3×D3×SD32C412yescomplemented
31C3×#4911C412yescomplemented
32C3×D3×D16C412yescomplemented
33C3×#4908C2211yescharacteristic
34C3×D3×M32C2211yescharacteristic
35#10591675—21no—
36#10591673—21no—
37#10591670—21no—
38#10591435—21no—
39Dic3×#213—21no—
40#10591421—21no—
41#10590920C2211yescharacteristic, complemented
42#10590916C2211yescharacteristic, complemented
43D3×#819C2211yescharacteristic
44#10590781C2211yescharacteristic, complemented
45#10590771C2211yescharacteristic, complemented
46#10590706C2211yescharacteristic
47#10590693C2211yescharacteristic
48D3×#812C2211yescharacteristic
49#10589432C2211yescharacteristic, complemented
50#10589429C2211yescharacteristic, complemented
51#10589379C2211yescharacteristic, complemented
52#10589378C2211yescharacteristic, complemented
53C3×#4566C2211yescharacteristic, complemented
54C3×#4563C2211yescharacteristic, complemented
55C3×#4513C2211yescharacteristic, complemented
56C3×#4512C2211yescharacteristic, complemented
57#10589137C2211yescharacteristic, complemented
58#10589136C2211yescharacteristic, complemented
59#10589127C2211yescharacteristic, complemented
60#10589126C2211yescharacteristic, complemented
61#10589124C2211yescharacteristic, complemented
62#10589123C2211yescharacteristic, complemented
63#10589106C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C2×C3×#509—31no—
66#83910—31no—
67#83823—31no—
68D3×#509D311yescharacteristic
69#79899—31no—
70#79867—31no—
71C3×AGL(1,ℤ/16)—31no—
72#72076—31no—
73C2×#4563—31no—
74#71515—31no—
75#71515—31no—
76#71515—31no—
77#71515—31no—
78#71515—31no—
79#71515—31no—
80#71515—31no—
81#71515—31no—
82#71515—61no—
83#71515D311yescharacteristic, complemented
84#71427—31no—
85#71425—31no—
86#70929—31no—
87#70918—31no—
88#69312—31no—
89#69310—31no—
90D3×#361—31no—
91#69254—31no—
92#69251—31no—
93#69249—31no—
94#69091—31no—
95#69087—31no—
96C3×D3×#41—21no—
97C2×C3×D3×D4—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×#213—21no—
106C3×#919C2×C411yescharacteristic, complemented
107C3×D3×Q16C2×C411yescharacteristic, complemented
108C3×#916—21no—
109C3×D3×SD16—21no—
110C3×#912C2×C411yescharacteristic, complemented
111C3×D3×D8—21no—
112C3×D3×D8—21no—
113C3×D3×D8C2×C412yes—
114C3×D3×D8C2×C412yes—
115C3×D3×D8C2×C411yescharacteristic, complemented
116C3×#904C2311yescharacteristic
117C2×C3×D24C2311yescharacteristic
118C2×C3×D3×C8C2311yescharacteristic
119#67⋊Dic3—41no—
120Dic3×#67—41no—
121D3×#217—41no—
122C2×(C2×D3)⋊Dic3—41no—
123#63898—21no—
124Dic3×D12—21no—
125#63855D411yescharacteristic
126#63841—21no—
127C2×#3711—41no—
128C2×#3711D411yescharacteristic
129#63815—21no—
130#63815—41no—
131#63814—21no—
132#63814—41no—
133D3×#208—21no—
134D3×#208—41no—
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×#828C2×C412yescomplemented
147C3×#827C2×C412yescomplemented
148C3×#826C2×C412yescomplemented
149C3×#826C2×C412yescomplemented
150C3×#819C2311yescharacteristic
151C3×#817C2311yescharacteristic
152C3×#815C2311yescharacteristic
153C3×#812C2311yescharacteristic
154C3×#812C2311yescharacteristic
155C3×#800C2×C412yescomplemented
156C3×D48C2×C412yescomplemented
157C3×#798C2×C412yescomplemented
158C3×D3×C16C2×C412yescomplemented
159#63577—21no—
160#63575—21no—
161#63569—21no—
162#63568—21no—
163#63563—21no—
164#63562—21no—
165#63553D411yescharacteristic
166Dic3×C3⋊C8D411yescharacteristic
167#63543—21no—
168D3×C3⋊C16—21no—
169#33471—91noSylow
170C2×C3×#135—31no—
171C22×C3×D8—31no—
172#5819—61no—
173#5798—61no—
174D3×#135C2×D311yescharacteristic
175C2×D3×D8C2×D311yescharacteristic
176#5750—61no—
177#5545—61no—
178C3×#509—21no—
179C3×#509—31no—
180C3×#509—31no—
181C3×#509—32no—
182C3×#509—32no—
183C3×#509—31no—
184C3×#509C2×D311yescharacteristic
185C3×#509C2×D311yescharacteristic
186C2×C3×SD32—32no—
187C2×C3×D16—32no—
188C2×C3×M32—31no—
189C3×#444—31no—
190C3×#442—31no—
191#5236—61no—
192#5215—61no—
193#5197—31no—
194#5197—31no—
195#5197—31no—
196#5197—31no—
197#5197—61no—
198#5197C2×D311yescharacteristic, complemented
199#5196—61no—
200#5196—61no—
201#5193C2×D311yescharacteristic
202#5152—31no—
203#5152—31no—
204#5152—31no—
205#5152—31no—
206#5152—61no—
207#5152C2×D311yescharacteristic, complemented
208Dic3×D8—61no—
209Dic3×D8—61no—
210#5147C2×D311yescharacteristic
211#5144—61no—
212C2×#819—31no—
213#5106—31no—
214#5101—31no—
215C2×#812—31no—
216C4×#213—61no—
217#4914Dic312yescomplemented
218D3×SD32Dic312yescomplemented
219#4911Dic312yescomplemented
220D3×D16Dic312yescomplemented
221#4908C2×D311yescharacteristic
222D3×M32—31no—
223D3×M32C2×D311yescharacteristic
224#4894—31no—
225D3×#108—31no—
226#4869—31no—
227#4860—31no—
228#4824—61no—
229#4821—61no—
230#4770—61no—
231#4756—61no—
232#4717—31no—
233#4711—31no—
234#4708—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, complemented
245#4563—31no—
246#4563—31no—
247#4563—31no—
248#4563—31no—
249#4563—61no—
250#4563C2×D311yescharacteristic, complemented
251#4518—31no—
252#4516—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#4495—31no—
267#4494—31no—
268#4488—31no—
269#4487—31no—
270#4466—31no—
271C23×C3×D3—41no—
272C32×#41—21no—
273C2×C32×D4—21no—
274C22×C3⋊Dic3—41no—
275C2×C3×#67—41no—
276C22×C3×Dic3—41no—
277C3×#239—21no—
278C3×D3×Q8—21no—
279C3×#237—21no—
280C3×#237—41no—
281C3×D3×D4—22no—
282C3×D3×D4—22no—
283C3×D3×D4—21no—
284C3×D3×D4—41no—
285C3×D3×D4—41no—
286C3×D3×D4—41no—
287C3×#235—21no—
288C3×#235—41no—
289C2×C3×D12—21no—
290C2×C3×C4×D3—41no—
291C2×C3×C4×D3C2×D411yescharacteristic
292C2×D3×Dic3—41no—
293C2×D3×Dic3—41no—
294C32×Q16C22×C411yescharacteristic
295C32×SD16—21no—
296C32×D8—21no—
297C32×D8C22×C412yes—
298C32×D8C22×C411yescharacteristic
299C2×C32×C8C2411yescharacteristic
300#3757—41no—
301C4⋊(C3⋊Dic3)—21no—
302C4×C3⋊Dic3C2×D411yescharacteristic
303#3748—21no—
304#3748—41no—
305C2×C3⋊(C3⋊C8)—41no—
306C2×C3⋊(C3⋊C8)C2×D411yescharacteristic
307C3×#217—41no—
308C3×#216—21no—
309C3×#215—21no—
310C3×#214—21no—
311C3×#213—22no—
312C3×#213—22no—
313C3×#213—21no—
314C3×C4⋊Dic3—21no—
315C3×C4×Dic3C2×D411yescharacteristic
316C3×#208—21no—
317C3×#208—41no—
318C2×C3×C3⋊C8—41no—
319C2×C3×C3⋊C8C2×D411yescharacteristic
320C2×C3×C3⋊C8C2×D411yescharacteristic
321C3×Dic12C22×C411yescharacteristic
322C3×D24—21no—
323C3×D24C22×C412yes—
324C3×D24C22×C411yescharacteristic
325C3×#204—21no—
326C3×D3×C8C22×C411yescharacteristic
327C3×D3×C8C22×C411yescharacteristic
328C3×D3×C8#4111yescharacteristic
329C3×D3×C8#4111yescharacteristic
330Dic3⋊Dic3—21no—
331(C2×D3)⋊Dic3—21no—
332(C2×D3)⋊Dic3—41no—
333(C2×D3)⋊Dic3—41no—
334(C2×D3)⋊Dic3—41no—
335Dic32—41no—
336#3711—21no—
337#3711—21no—
338#3711—41no—
339#3711—41no—
340#3711—41no—
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—
348C2×#509—31no—
349#2957—91no—
350#2948—91no—
351AGL(1,ℤ/16)—31no—
352AGL(1,ℤ/16)—91no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355AGL(1,ℤ/16)—91no—
356AGL(1,ℤ/16)—91no—
357AGL(1,ℤ/16)—91no—
358AGL(1,ℤ/16)—91no—
359#2155—91no—
360C2×#361—91no—
361#2145—91no—
362#2110—91no—
363C2×C3×#41—61no—
364C22×C3×D4—61no—
365D3×#41—21no—
366C2×D3×D4—21no—
367C3×#135—21no—
368C3×#135—31no—
369C3×#135—31no—
370C3×#135—31no—
371C3×#135—61no—
372C3×#135—61no—
373C3×#135C22×D311yescharacteristic
374C3×#135C22×D311yescharacteristic
375C2×C3×Q16—31no—
376C2×C3×SD16—61no—
377C2×C3×D8—21no—
378C2×C3×D8—31no—
379C2×C3×D8—32no—
380C2×C3×D8—32no—
381C2×C3×D8—31no—
382C2×C3×D8—61no—
383C2×C3×D8—61no—
384C2×C3×D8—61no—
385C2×C3×D8C22×D311yescharacteristic
386C2×C3×D8C22×D311yescharacteristic
387C3×#131—61no—
388C22×C3×C8—31no—
389C3×C4×D4—61no—
390C2×#217—121no—
391C2×#217—121no—
392#950—21no—
393#948—21no—
394#948—61no—
395#948—61no—
396#948—61no—
397#948—61no—
398#948—121no—
399#948—121no—
400#948—121no—
401D4×Dic3—21no—
402D4×Dic3—61no—
403D4×Dic3—61no—
404D4×Dic3—61no—
405D4×Dic3—61no—
406D4×Dic3—121no—
407D4×Dic3—121no—
408D4×Dic3—121no—
409C2×#213—21no—
410C4×#67—121no—
411C2×(C2×D3)⋊C4—121no—
412#926—31no—
413#926—61no—
414C2×#208—31no—
415C2×#208—61no—
416C2×#208—121no—
417C2×#208—121no—
418#919C2×Dic311yescharacteristic, complemented
419D3×Q16C2×Dic311yescharacteristic, complemented
420#916—21no—
421D3×SD16—21no—
422#912C2×Dic311yescharacteristic, complemented
423D3×D8—21no—
424D3×D8—21no—
425D3×D8C2×Dic312yes—
426D3×D8C2×Dic312yes—
427D3×D8C2×Dic311yescharacteristic, complemented
428#907—61no—
429#907—121no—
430D3×M16—61no—
431D3×M16—121no—
432#904C22×D311yescharacteristic
433C2×D24C22×D311yescharacteristic
434#901—61no—
435#901—121no—
436C2×ΓL(1,𝔽25)—31no—
437C2×ΓL(1,𝔽25)—121no—
438C2×D3×C8C22×D311yescharacteristic
439#893—61no—
440#892—61no—
441#67⋊C4—121no—
442D3×C22⋊C4—121no—
443C4×D12—61no—
444#872—31no—
445C3×SD32—22no—
446C3×SD32—32no—
447C3×SD32—32no—
448C3×SD32—32no—
449C3×SD32C4×D312yescomplemented
450C3×SD32C2×Dic312yescomplemented
451C3×D16—22no—
452C3×D16—32no—
453C3×D16—32no—
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#832—21no—
476#832—61no—
477#832—61no—
478#832—61no—
479#832—61no—
480#832—121no—
481#828C2×Dic312yescomplemented
482#827C2×Dic312yescomplemented
483#826C2×Dic312yescomplemented
484#826C2×Dic312yescomplemented
485#825—61no—
486#822—61no—
487#821—61no—
488#819—31no—
489#819—31no—
490#819—61no—
491#819—61no—
492#819C22×D311yescharacteristic
493#818—61no—
494#817—31no—
495#817—31no—
496#817—61no—
497#817C22×D311yescharacteristic
498#815—31no—
499#815—31no—
500#815—61no—
501#815C22×D311yescharacteristic
502C8×Dic3—31no—
503C8×Dic3—31no—
504C8×Dic3—31no—
505#812—31no—
506#812—31no—
507#812—61no—
508#812—61no—
509#812C22×D311yescharacteristic
510#812C22×D311yescharacteristic
511C2×C3⋊C16—61no—
512#809—61no—
513#807—61no—
514#805—61no—
515C4×C3⋊C8—31no—
516#800C2×Dic312yescomplemented
517D48C2×Dic312yescomplemented
518#798—61no—
519#798C2×Dic312yescomplemented
520D3×C16—61no—
521D3×C16C2×Dic312yescomplemented
522C23×C32—41no—
523C22×C3×D3—41no—
524C22×C3×D3—42no—
525C22×C3×D3—42no—
526C22×C3×D3—41no—
527C22×C3×D3—161no—
528C22×C3×D3—161no—
529C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
530C32×Q8—21no—
531C32×D4—22no—
532C32×D4—21no—
533C32×D4—41no—
534C32×D4—41no—
535C2×C32×C4—41no—
536C2×C32×C4C22×D411yescharacteristic
537C2×C3⋊Dic3—21no—
538C2×C3⋊Dic3—41no—
539C2×C3⋊Dic3—161no—
540C3×#67—41no—
541C3×#67—41no—
542C3×#67—41no—
543C3×#67—42no—
544C3×#67—42no—
545C2×C3×Dic3—21no—
546C2×C3×Dic3—41no—
547C2×C3×Dic3—41no—
548C2×C3×Dic3—161no—
549C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
550C3×D12—21no—
551C3×D12—22no—
552C3×D12—41no—
553C3×D12—41no—
554C3×C4×D3—41no—
555C3×C4×D3—41no—
556C3×C4×D3—41no—
557C3×C4×D3C4×D411yescharacteristic
558C3×C4×D3C4×D411yescharacteristic
559C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
560C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
561C3×Dic6—21no—
562C3×Dic6—41no—
563D3×Dic3—161no—
564D3×Dic3—161no—
565C32×C8C23×C411yescharacteristic
566C32×C8C2×#4111yescharacteristic
567C3⋊(C3⋊C8)—21no—
568C3⋊(C3⋊C8)—41no—
569C3×C3⋊C8—21no—
570C3×C3⋊C8—41no—
571C3×C3⋊C8C4×D411yescharacteristic
572C3×C3⋊C8C4×D411yescharacteristic
573C2×#135—31no—
574C22×D8—31no—
575#568—181no—
576#518—181no—
577#509—31no—
578#509—31no—
579#509—32no—
580#509—32no—
581#509—31no—
582#509D3211yescharacteristic
583C2×SD32—32no—
584C2×D16—32no—
585C2×M32—31no—
586C2×M32—91no—
587#444—31no—
588#444—91no—
589#444—91no—
590#444—91no—
591#443—181no—
592#443—181no—
593#442—31no—
594#442—91no—
595#442—91no—
596#442—91no—
597C4×D8—181no—
598C4×D8—181no—
599C2×#108—91no—
600#427—91no—
601#421—181no—
602#418—181no—
603#405—91no—
604#365—31no—
605#365—91no—
606#365—91no—
607#365—91no—
608#361—31no—
609#361—91no—
610#361—91no—
611#361—91no—
612#360—31no—
613#360—91no—
614#360—91no—
615#360—91no—
616#347—31no—
617#347—91no—
618#347—91no—
619#347—91no—
620C24×C3—121no—
621C23×D3—41no—
622C3×#41—21no—
623C3×#41—21no—
624C3×#41—41no—
625C3×#41—61no—
626C3×#41—61no—
627C3×#41—61no—
628C3×#41—121no—
629C3×#41—121no—
630C2×C3×Q8—61no—
631C2×C3×D4—21no—
632C2×C3×D4—21no—
633C2×C3×D4—41no—
634C2×C3×D4—62no—
635C2×C3×D4—62no—
636C2×C3×D4—61no—
637C2×C3×D4—61no—
638C2×C3×D4—121no—
639C2×C3×D4—121no—
640C2×C3×D4—121no—
641C2×C3×D4—121no—
642C22×C3×C4—31no—
643C22×C3×C4—121no—
644C22×C3×C4—121no—
645C2×#67—41no—
646C22×Dic3—41no—
647C22×Dic3—121no—
648C22×Dic3—121no—
649C22×Dic3—121no—
650C22×Dic3—121no—
651C22×Dic3—241no—
652#239—21no—
653D3×Q8—21no—
654#237—21no—
655#237—41no—
656D3×D4—22no—
657D3×D4—22no—
658D3×D4—21no—
659D3×D4—41no—
660D3×D4—41no—
661D3×D4—41no—
662#235—21no—
663#235—41no—
664C2×D12—21no—
665C2×C4×D3—41no—
666C2×C4×D3—121no—
667C2×C4×D3—121no—
668C2×C4×D3D3×D411yescharacteristic
669C3×Q16—21no—
670C3×Q16—31no—
671C3×Q16—61no—
672C3×Q16C2×C4×D311yescharacteristic
673C3×Q16C22×Dic311yescharacteristic
674C3×SD16—21no—
675C3×SD16—21no—
676C3×SD16—41no—
677C3×SD16—61no—
678C3×SD16—61no—
679C3×SD16—61no—
680C3×D8—21no—
681C3×D8—21no—
682C3×D8—21no—
683C3×D8—22no—
684C3×D8—31no—
685C3×D8—32no—
686C3×D8—41no—
687C3×D8—62no—
688C3×D8—62no—
689C3×D8—61no—
690C3×D8—61no—
691C3×D8C2×C4×D311yescharacteristic
692C3×D8C2×C4×D312yes—
693C3×D8C22×Dic311yescharacteristic
694C3×D8C22×Dic312yes—
695C3×M16—61no—
696C3×M16—121no—
697C2×C3×C8—21no—
698C2×C3×C8—31no—
699C2×C3×C8—31no—
700C2×C3×C8—31no—
701C2×C3×C8—31no—
702C2×C3×C8—31no—
703C2×C3×C8—31no—
704C2×C3×C8—121no—
705C2×C3×C8C23×D311yescharacteristic
706C2×C3×C8C23×D311yescharacteristic
707C3×C4⋊C4—61no—
708C3×C22⋊C4—121no—
709C3×C42—31no—
710#217—41no—
711#217—61no—
712#217—121no—
713#217—121no—
714#217—121no—
715#217—121no—
716#217—121no—
717#217—241no—
718#216—21no—
719#215—21no—
720#214—21no—
721#213—22no—
722#213—22no—
723#213—21no—
724(C2×D3)⋊C4—61no—
725(C2×D3)⋊C4—121no—
726(C2×D3)⋊C4—121no—
727(C2×D3)⋊C4—121no—
728C4⋊Dic3—21no—
729C4⋊Dic3—61no—
730C4⋊Dic3—61no—
731C4⋊Dic3—61no—
732C4⋊Dic3—121no—
733Dic3⋊C4—61no—
734C4×Dic3—31no—
735C4×Dic3—31no—
736C4×Dic3—61no—
737C4×Dic3—121no—
738C4×Dic3—121no—
739C4×Dic3D3×D411yescharacteristic
740#208—21no—
741#208—41no—
742#208—61no—
743#208—61no—
744#208—61no—
745#208—61no—
746#208—121no—
747#208—121no—
748#208—121no—
749#208—121no—
750#208—121no—
751#208—121no—
752#208—241no—
753C2×C3⋊C8—31no—
754C2×C3⋊C8—31no—
755C2×C3⋊C8—41no—
756C2×C3⋊C8—61no—
757C2×C3⋊C8—121no—
758C2×C3⋊C8—121no—
759C2×C3⋊C8—121no—
760C2×C3⋊C8—121no—
761C2×C3⋊C8—121no—
762C2×C3⋊C8—241no—
763C2×C3⋊C8D3×D411yescharacteristic
764C2×C3⋊C8D3×D411yescharacteristic
765Dic12C22×Dic311yescharacteristic
766D24—21no—
767D24C22×Dic311yescharacteristic
768D24C22×Dic312yes—
769#204—21no—
770ΓL(1,𝔽25)—61no—
771ΓL(1,𝔽25)—61no—
772ΓL(1,𝔽25)—121no—
773ΓL(1,𝔽25)—121no—
774ΓL(1,𝔽25)—121no—
775D3×C8—121no—
776D3×C8—121no—
777D3×C8—121no—
778D3×C8#23711yescharacteristic
779D3×C8#23711yescharacteristic
780D3×C8C22×Dic311yescharacteristic
781D3×C8C22×Dic311yescharacteristic
782C3×C16—22no—
783C3×C16—32no—
784C3×C16—61no—
785C3×C16C2×C4×D312yes—
786C3×C16C22×Dic312yes—
787C3⋊C16—21no—
788C3⋊C16—61no—
789C3⋊C16—61no—
790C3⋊C16—121no—
791C3⋊C16C22×Dic312yes—
792C22×C32—41no—
793C22×C32—42no—
794C22×C32—81no—
795C22×C32—81no—
796C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
797C2×C3×D3—41no—
798C2×C3×D3—41no—
799C2×C3×D3—42no—
800C2×C3×D3—81no—
801C2×C3×D3—81no—
802C2×C3×D3—161no—
803C2×C3×D3—162no—
804C2×C3×D3—162no—
805C2×C3×D3#44211yescharacteristic
806C2×C3×D3#44211yescharacteristic
807C32×C4—41no—
808C32×C4C2×C4×D411yescharacteristic
809C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
810C3⋊Dic3—41no—
811C3⋊Dic3—81no—
812C3×Dic3—41no—
813C3×Dic3—41no—
814C3×Dic3—81no—
815C3×Dic3#44211yescharacteristic
816C3×Dic3#44211yescharacteristic
817C2×#41—61no—
818C22×D4—61no—
819#135—31no—
820#135—31no—
821#135—31no—
822#135—61no—
823#135—61no—
824#135C2×D3211yescharacteristic
825C2×Q16—31no—
826C2×SD16—61no—
827C2×D8—32no—
828C2×D8—32no—
829C2×D8—31no—
830C2×D8—31no—
831C2×D8—61no—
832C2×D8—61no—
833C2×D8—61no—
834C2×D8C2×D3211yescharacteristic
835#131—61no—
836#131—181no—
837#131—181no—
838#131—181no—
839#131—361no—
840#131—361no—
841C2×M16—91no—
842C2×M16—181no—
843C2×M16—361no—
844C2×M16—361no—
845C22×C8—31no—
846C4×D4—61no—
847C4×D4—181no—
848C4×D4—181no—
849C4×D4—181no—
850C4×D4—361no—
851C4×D4—361no—
852#117—91no—
853#117—181no—
854C2×C22⋊C4—361no—
855C2×C22⋊C4—361no—
856SD32—32no—
857SD32—32no—
858SD32—32no—
859SD32D3×Dic312yescomplemented
860D16—32no—
861D16—32no—
862D16—32no—
863D16D3×Dic312yescomplemented
864M32—31no—
865M32—32no—
866M32—31no—
867M32—91no—
868M32—181no—
869M32C2×D3211yescharacteristic
870C2×C16—32no—
871C2×C16—181no—
872#108—31no—
873#108—91no—
874#108—181no—
875#107—181no—
876#106—31no—
877#106—91no—
878#104—61no—
879#104—181no—
880#104—181no—
881#104—181no—
882#102—61no—
883#102—181no—
884#102—181no—
885#102—181no—
886#97—31no—
887#97—91no—
888C4×C8—91no—
889C4×C8—91no—
890C23×C3—31no—
891C23×C3—41no—
892C23×C3—41no—
893C23×C3—81no—
894C23×C3—121no—
895C23×C3—122no—
896C23×C3—122no—
897C23×C3—121no—
898C23×C3—481no—
899C23×C3—481no—
900C22×D3—41no—
901C22×D3—41no—
902C22×D3—42no—
903C22×D3—42no—
904C22×D3—161no—
905C22×D3—161no—
906C22×D3#91111yescharacteristic
907C3×Q8—21no—
908C3×Q8—21no—
909C3×Q8—41no—
910C3×Q8—61no—
911C3×Q8—121no—
912C3×D4—22no—
913C3×D4—21no—
914C3×D4—22no—
915C3×D4—21no—
916C3×D4—42no—
917C3×D4—41no—
918C3×D4—41no—
919C3×D4—41no—
920C3×D4—41no—
921C3×D4—41no—
922C3×D4—62no—
923C3×D4—61no—
924C3×D4—81no—
925C3×D4—81no—
926C3×D4—122no—
927C3×D4—122no—
928C3×D4—121no—
929C3×D4—121no—
930C3×D4—121no—
931C3×D4—121no—
932C3×D4—121no—
933C2×C3×C4—21no—
934C2×C3×C4—31no—
935C2×C3×C4—31no—
936C2×C3×C4—31no—
937C2×C3×C4—31no—
938C2×C3×C4—31no—
939C2×C3×C4—41no—
940C2×C3×C4—41no—
941C2×C3×C4—61no—
942C2×C3×C4—81no—
943C2×C3×C4—121no—
944C2×C3×C4—121no—
945C2×C3×C4—121no—
946C2×C3×C4—121no—
947C2×C3×C4—121no—
948C2×C3×C4—481no—
949C2×C3×C4C2×D3×D411yescharacteristic
950C2×C3×C4C2×D3×D411yescharacteristic
951#67—41no—
952#67—41no—
953#67—41no—
954#67—42no—
955#67—42no—
956C2×Dic3—21no—
957C2×Dic3—41no—
958C2×Dic3—41no—
959C2×Dic3—61no—
960C2×Dic3—61no—
961C2×Dic3—121no—
962C2×Dic3—121no—
963C2×Dic3—121no—
964C2×Dic3—161no—
965C2×Dic3—241no—
966C2×Dic3—481no—
967C2×Dic3—481no—
968C2×Dic3—481no—
969C2×Dic3—481no—
970C2×Dic3—482no—
971C2×Dic3#91111yescharacteristic
972D12—21no—
973D12—22no—
974D12—41no—
975D12—41no—
976C4×D3—41no—
977C4×D3—41no—
978C4×D3—41no—
979C4×D3—481no—
980C4×D3—481no—
981C4×D3#91111yescharacteristic
982C4×D3#91111yescharacteristic
983C4×D3D4×Dic311yescharacteristic
984C4×D3D4×Dic311yescharacteristic
985Dic6—21no—
986Dic6—41no—
987C3×C8—21no—
988C3×C8—21no—
989C3×C8—31no—
990C3×C8—31no—
991C3×C8—61no—
992C3×C8—121no—
993C3×C8C22×C4×D311yescharacteristic
994C3×C8C2×#23711yescharacteristic
995C3×C8D3×#4111yescharacteristic
996C3×C8C23×Dic311yescharacteristic
997C3⋊C8—21no—
998C3⋊C8—41no—
999C3⋊C8—61no—
1000C3⋊C8—61no—
1001C3⋊C8—121no—
1002C3⋊C8—121no—
1003C3⋊C8—121no—
1004C3⋊C8—241no—
1005C3⋊C8D4×Dic311yescharacteristic
1006C3⋊C8D4×Dic311yescharacteristic
1007C2×C32—21no—
1008C2×C32—82no—
1009C2×C32—81no—
1010C2×C32C2×#44211yescharacteristic
1011C3×D3—21no—
1012C3×D3—21no—
1013C3×D3—82no—
1014C3×D3—81no—
1015C24—121no—
1016#41—21no—
1017#41—61no—
1018#41—61no—
1019#41—61no—
1020#41—121no—
1021#41—121no—
1022C2×Q8—61no—
1023C2×D4—21no—
1024C2×D4—62no—
1025C2×D4—62no—
1026C2×D4—61no—
1027C2×D4—61no—
1028C2×D4—121no—
1029C2×D4—121no—
1030C2×D4—121no—
1031C2×D4—121no—
1032C22×C4—31no—
1033C22×C4—121no—
1034C22×C4—121no—
1035C22×C4—361no—
1036C22×C4—361no—
1037C22×C4—361no—
1038Q16—31no—
1039Q16—61no—
1040Q16C2×D3×Dic311yescharacteristic
1041SD16—21no—
1042SD16—61no—
1043SD16—61no—
1044SD16—61no—
1045D8—21no—
1046D8—31no—
1047D8—32no—
1048D8—62no—
1049D8—62no—
1050D8—61no—
1051D8—61no—
1052D8C2×D3×Dic311yescharacteristic
1053D8C2×D3×Dic312yes—
1054M16—61no—
1055M16—121no—
1056M16—181no—
1057M16—181no—
1058M16—181no—
1059M16—361no—
1060M16—361no—
1061M16—361no—
1062M16—361no—
1063C2×C8—31no—
1064C2×C8—31no—
1065C2×C8—31no—
1066C2×C8—31no—
1067C2×C8—31no—
1068C2×C8—31no—
1069C2×C8—91no—
1070C2×C8—121no—
1071C2×C8—361no—
1072C2×C8—361no—
1073C2×C8—361no—
1074C2×C8—361no—
1075C2×C8C22×D3211yescharacteristic
1076C4⋊C4—61no—
1077C4⋊C4—181no—
1078C4⋊C4—181no—
1079C22⋊C4—121no—
1080C22⋊C4—181no—
1081C22⋊C4—361no—
1082C22⋊C4—361no—
1083C22⋊C4—361no—
1084C22⋊C4—361no—
1085C42—31no—
1086C42—91no—
1087C42—361no—
1088C16—32no—
1089C16—61no—
1090C16—181no—
1091C16C2×D3×Dic312yes—
1092C22×C3—21no—
1093C22×C3—31no—
1094C22×C3—31no—
1095C22×C3—41no—
1096C22×C3—42no—
1097C22×C3—41no—
1098C22×C3—42no—
1099C22×C3—81no—
1100C22×C3—82no—
1101C22×C3—81no—
1102C22×C3—81no—
1103C22×C3—81no—
1104C22×C3—81no—
1105C22×C3—121no—
1106C22×C3—121no—
1107C22×C3—122no—
1108C22×C3—161no—
1109C22×C3—161no—
1110C22×C3—241no—
1111C22×C3—241no—
1112C22×C3—482no—
1113C22×C3—482no—
1114C22×C3—481no—
1115C22×C3C2×#91111yescharacteristic
1116C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1117C2×D3—41no—
1118C2×D3—41no—
1119C2×D3—42no—
1120C2×D3—81no—
1121C2×D3—81no—
1122C2×D3—162no—
1123C2×D3—162no—
1124C2×D3—161no—
1125C2×D3#515211yescharacteristic
1126C2×D3#515211yescharacteristic
1127C3×C4—21no—
1128C3×C4—21no—
1129C3×C4—31no—
1130C3×C4—31no—
1131C3×C4—41no—
1132C3×C4—41no—
1133C3×C4—81no—
1134C3×C4—121no—
1135C3×C4—121no—
1136C3×C4—241no—
1137C3×C4C4×D3×D411yescharacteristic
1138C3×C4C2×#91111yescharacteristic
1139C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1140C3×C4C2×D4×Dic311yescharacteristic
1141Dic3—41no—
1142Dic3—41no—
1143Dic3—81no—
1144Dic3—121no—
1145Dic3—121no—
1146Dic3—241no—
1147Dic3—241no—
1148Dic3—241no—
1149Dic3—481no—
1150Dic3#515211yescharacteristic
1151Dic3#515211yescharacteristic
1152C32#3347111yescharacteristic, complemented, Sylow
1153C23—31no—
1154C23—41no—
1155C23—121no—
1156C23—122no—
1157C23—122no—
1158C23—121no—
1159C23—481no—
1160C23—481no—
1161Q8—21no—
1162Q8—61no—
1163Q8—121no—
1164D4—22no—
1165D4—21no—
1166D4—41no—
1167D4—41no—
1168D4—62no—
1169D4—61no—
1170D4—122no—
1171D4—122no—
1172D4—121no—
1173D4—121no—
1174D4—121no—
1175D4—121no—
1176D4—121no—
1177C2×C4—31no—
1178C2×C4—31no—
1179C2×C4—31no—
1180C2×C4—31no—
1181C2×C4—31no—
1182C2×C4—41no—
1183C2×C4—61no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—181no—
1190C2×C4—361no—
1191C2×C4—481no—
1192C2×C4—1441no—
1193C2×C4—1441no—
1194C2×C4—1441no—
1195C2×C4D32×D411yescharacteristic
1196C8—31no—
1197C8—31no—
1198C8—61no—
1199C8—121no—
1200C8—181no—
1201C8—361no—
1202C8D3×#23711yescharacteristic
1203C8C22×D3×Dic311yescharacteristic
1204C2×C3—21no—
1205C2×C3—21no—
1206C2×C3—21no—
1207C2×C3—41no—
1208C2×C3—61no—
1209C2×C3—61no—
1210C2×C3—82no—
1211C2×C3—81no—
1212C2×C3—82no—
1213C2×C3—81no—
1214C2×C3—162no—
1215C2×C3—161no—
1216C2×C3—242no—
1217C2×C3—241no—
1218C2×C3D3×#44211yescharacteristic
1219C2×C3C2×#515211yescharacteristic
1220D3—21no—
1221D3—21no—
1222D3—82no—
1223D3—81no—
1224C22—31no—
1225C22—31no—
1226C22—41no—
1227C22—42no—
1228C22—81no—
1229C22—81no—
1230C22—121no—
1231C22—121no—
1232C22—122no—
1233C22—241no—
1234C22—241no—
1235C22—482no—
1236C22—482no—
1237C22—481no—
1238C22D3×#91111yescharacteristic
1239C4—31no—
1240C4—31no—
1241C4—41no—
1242C4—121no—
1243C4—121no—
1244C4—241no—
1245C4—361no—
1246C4—721no—
1247C4D3×#91111yescharacteristic
1248C4D3×D4×Dic311yescharacteristic
1249C3—21no—
1250C3#1094865811yescharacteristic, complemented
1251C3#1094866311yescharacteristic, complemented
1252C2—21no—
1253C2—61no—
1254C2—61no—
1255C2—82no—
1256C2—81no—
1257C2—242no—
1258C2—241no—
1259C2D3×#515211yescharacteristic
subgroupG/H
centerC2D3×#5152
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#509C22
socleC2×C32C2×#442
prime radicalC3×D3×#509C2
cosocleC2×C32×C8C24
hypercenter#509D32
hypocenterC32#33471
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. #11861215C2semidirect
3. #11860685C2semidirect
4. #11797986C2semidirect
5. #11797985C2semidirect
6. #11797980C2semidirect
7. #11797979C2semidirect
8. #11797970C2semidirect
9. #11797969C2semidirect
10. C3×#71515C2semidirect
11. #11797956C2semidirect
12. #11797132C2semidirect
13. D3×#4563C2semidirect
14. #11796858C2semidirect
15. #11795942C2semidirect
23. #10592896C22semidirect
24. #10592851C22semidirect
25. C3×#5197C22semidirect
27. C3×#5152C22semidirect
29. C3×#4914C4semidirect
30. C3×D3×SD32C4semidirect
31. C3×#4911C4semidirect
32. C3×D3×D16C4semidirect
41. #10590920C22semidirect
42. #10590916C22semidirect
44. #10590781C22semidirect
45. #10590771C22semidirect
49. #10589432C22semidirect
50. #10589429C22semidirect
51. #10589379C22semidirect
52. #10589378C22semidirect
53. C3×#4566C22semidirect
54. C3×#4563C22semidirect
55. C3×#4513C22semidirect
56. C3×#4512C22semidirect
57. #10589137C22semidirect
58. #10589136C22semidirect
59. #10589127C22semidirect
60. #10589126C22semidirect
61. #10589124C22semidirect
62. #10589123C22semidirect
63. #10589106C22semidirect
64. #10589105C22semidirect
83. #71515D3semidirect
106. C3×#919C2×C4semidirect
107. C3×D3×Q16C2×C4semidirect
110. C3×#912C2×C4semidirect
115. C3×D3×D8C2×C4semidirect
135. C32×SD32C2×C4semidirect
136. C32×D16C2×C4semidirect
146. C3×#828C2×C4semidirect
147. C3×#827C2×C4semidirect
148. C3×#826C2×C4semidirect
149. C3×#826C2×C4semidirect
155. C3×#800C2×C4semidirect
156. C3×D48C2×C4semidirect
157. C3×#798C2×C4semidirect
158. C3×D3×C16C2×C4semidirect
198. #5197C2×D3semidirect
207. #5152C2×D3semidirect
217. #4914Dic3semidirect
218. D3×SD32Dic3semidirect
219. #4911Dic3semidirect
220. D3×D16Dic3semidirect
244. #4566C2×D3semidirect
250. #4563C2×D3semidirect
258. #4513C2×D3semidirect
265. #4512C2×D3semidirect
418. #919C2×Dic3semidirect
419. D3×Q16C2×Dic3semidirect
422. #912C2×Dic3semidirect
427. D3×D8C2×Dic3semidirect
449. C3×SD32C4×D3semidirect
450. C3×SD32C2×Dic3semidirect
455. C3×D16C4×D3semidirect
456. C3×D16C2×Dic3semidirect
481. #828C2×Dic3semidirect
482. #827C2×Dic3semidirect
483. #826C2×Dic3semidirect
484. #826C2×Dic3semidirect
516. #800C2×Dic3semidirect
517. D48C2×Dic3semidirect
519. #798C2×Dic3semidirect
521. D3×C16C2×Dic3semidirect
859. SD32D3×Dic3semidirect
863. D16D3×Dic3semidirect
1152. C32#33471semidirect
1250. C3#10948658semidirect
1251. C3#10948663semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#5092
#118612152
#118606852
#117979862
#117979852
#117979802
#117979792
#117979702
#117979692
C3×#715152
#117979562
#117971322
D3×#45632
#117968582
#117959422
#109486633
#109486583