Finite Group Databasebeta

← #72222845

Subgroups — #72222845

Order 2304.

2372 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#87187C211yesmaximal, characteristic
2#11899423C211yesmaximal, characteristic, complemented
3#11858549C211yesmaximal, characteristic, complemented
4#11796862C211yesmaximal, characteristic, complemented
5#11796858C214yesmaximal, complemented
6C3×#72076C211yesmaximal, characteristic, complemented
7C2×#10589124C211yesmaximal, characteristic, complemented
8D3×#4566C214yesmaximal, complemented
9C2×#10589432C211yesmaximal, characteristic, complemented
10#10948134—31nomaximal
11#10948132—31nomaximal
12C3×#5964—21no—
13C2×C32×#135C2211yescharacteristic
14C3×#5822—21no—
15C3×#5771C412yescomplemented
16C3×#5770—22no—
17C3×#5769C412yescomplemented
18C3×#5768—22no—
19C3×D3×#135C2214yes—
20C3×#5766C412yescomplemented
21C3×#5762—22no—
22C3×#5757C412yescomplemented
23C2×C3×#904C2211yescharacteristic
24C2×C3×#901C2211yescharacteristic
25#10594992—21no—
26C2×#63644C2211yescharacteristic, complemented
27C2×#63639C2211yescharacteristic, complemented
28C3×#5106C2211yescharacteristic, complemented
29C2×C3×#812C2211yescharacteristic, complemented
30#10591131—21no—
31#10590706C2212yescomplemented
32#10590683—22no—
33D3×#817C2212yescomplemented
34#10590622—22no—
35#10590621—22no—
36D3×#812C2214yescomplemented
37#10589432C2214yescomplemented
38C3×#4566C2212yescomplemented
39C3×#4566C2212yescomplemented
40#10589124C2214yescomplemented
41#10589123C2212yescomplemented
42#10589123C2212yescomplemented
43C3×#3584—31no—
44#87187D311yescharacteristic
45#83784—31no—
46#83780—31no—
47#82007—31no—
48#79178—31no—
49C3×#2145—31no—
50#72076—31no—
51#72076—34no—
52#72076D311yescharacteristic, complemented
53C2×#4566—31no—
54C2×#4566—34no—
55C2×#4566—31no—
56C2×#4566—31no—
57C2×#4566—61no—
58C2×#4518—31no—
59#70656—31no—
60#69251—34no—
61D3×#360—34no—
62C2×C32×#41—21no—
63C3×#1010—22no—
64C3×#1010—41no—
65C3×#1009—22no—
66C3×#1009—41no—
67C3×D3×#41—24no—
68C3×D3×#41—42no—
69C3×#1007—22no—
70C3×#1004—22no—
71C3×#1004—42no—
72C2×C3×#235—21no—
73C2×C3×#235—42no—
74C2×C3×#235D411yescharacteristic
75C32×#135—21no—
76C32×#135—21no—
77C32×#135C2×C412yescomplemented
78C32×#135C2312yes—
79C2×C32×Q16C2×C411yescharacteristic, complemented
80C2×C32×SD16—21no—
81C2×C32×D8C2×C411yescharacteristic, complemented
82C22×C32×C8C2311yescharacteristic
83C2×C4⋊(C3⋊Dic3)—21no—
84C3×#951—22no—
85C3×#950—24no—
86C3×#949—22no—
87C3×#942—22no—
88C3×#932—22no—
89C3×#926—21no—
90C2×C3×#208D411yescharacteristic
91C3×#919C2×C414yescomplemented
92C3×#918—24no—
93C3×D3×Q16C2×C414yescomplemented
94C3×#916—24no—
95C3×#915—24no—
96C3×#914—24no—
97C3×D3×SD16—24no—
98C3×#912C2×C414yescomplemented
99C3×#911—24no—
100C3×D3×D8C2×C414yescomplemented
101C2×C3×Dic12C2×C411yescharacteristic, complemented
102C3×#904—21no—
103C3×#904—21no—
104C3×#904C2×C412yescomplemented
105C3×#904C2312yes—
106C2×C3×D24C2×C411yescharacteristic, complemented
107C2×C3×#204—21no—
108C3×#901C2×C412yes—
109C3×#901C2×C412yes—
110C3×#901D412yes—
111C3×#901D412yes—
112C2×C3×ΓL(1,𝔽25)D412yes—
113C2×C3×D3×C8C2312yes—
114#67⋊Dic3—42no—
115Dic3×D12—41no—
116D3×C4⋊Dic3—22no—
117Dic3×Dic6—41no—
118#63841—22no—
119#63644—21no—
120#63644C2312yes—
121#63639—21no—
122#63639C2312yes—
123C2×C3⋊(C3⋊C16)—21no—
124C3×#818—21no—
125C3×#817C2311yescharacteristic
126C3×#817C2311yescharacteristic
127C3×#812—21no—
128C3×#812C2312yes—
129C2×C3×C3⋊C16—21no—
130#63575—22no—
131#63573—22no—
132#63543—24no—
133D3×C3⋊C16—24no—
134#33388—91noSylow
135C3×#585—61no—
136#5964—21no—
137C3×#578—32no—
138C3×#578—32no—
139C3×#577—62no—
140C3×#577—62no—
141C3×#576—32no—
142C3×#576—32no—
143C3×#575—62no—
144C3×#575—61no—
145C2×C3×#135—21no—
146C2×C3×#135—34no—
147C2×C3×#135—31no—
148C2×C3×#135C2×D311yescharacteristic
149C2×C3×#135C2×D311yescharacteristic
150C2×C3×#131—31no—
151#5827—61no—
152#5822—21no—
153#5771Dic312yescomplemented
154#5770—22no—
155#5769Dic312yescomplemented
156#5768—22no—
157D3×#135C2×D314yes—
158#5766Dic312yescomplemented
159#5762—22no—
160#5757Dic312yescomplemented
161C2×#904C2×D311yescharacteristic
162C2×#901C2×D311yescharacteristic
163#5523—61no—
164C2×C3×M32—31no—
165C3×#427—31no—
166#5140—62no—
167#5140—62no—
168#5121—62no—
169#5121—61no—
170#5106—32no—
171#5106C2×D311yescharacteristic, complemented
172C2×#817—31no—
173C2×#817—31no—
174C2×#817—32no—
175C2×#817—61no—
176C2×#812—31no—
177C2×#812—31no—
178C2×#812—34no—
179C2×#812—61no—
180C2×#812C2×D311yescharacteristic, complemented
181#4995—61no—
182#4907—62no—
183D3×M32—34no—
184#4901—62no—
185#4881—62no—
186#4860—32no—
187D3×#106—32no—
188C3×#360—32no—
189C3×#360—32no—
190#4566—34no—
191#4566—34no—
192#4566—32no—
193#4566—32no—
194#4566—34no—
195#4566—64no—
196#4566C2×D312yescomplemented
197#4566C2×D312yescomplemented
198#4518—34no—
199#4488—32no—
200#4488—32no—
201C32×#41—22no—
202C32×#41—22no—
203C32×#41—41no—
204C32×#41—41no—
205C2×C32×Q8—21no—
206C2×C32×D4—21no—
207C2×C32×D4—41no—
208C22×C32×C4—41no—
209C22×C32×C4C2×D411yescharacteristic
210C22×C3⋊Dic3—41no—
211C2×C3×#67—41no—
212C2×C3×#67—44no—
213C2×C3×#67D812yes—
214C3×#239—24no—
215C3×#239—42no—
216C3×D3×Q8—24no—
217C3×D3×Q8—42no—
218C3×#237—24no—
219C3×#237—44no—
220C3×#237—44no—
221C3×#237—42no—
222C3×D3×D4—24no—
223C3×D3×D4—44no—
224C3×D3×D4—44no—
225C3×D3×D4—42no—
226C3×#235—22no—
227C3×#235—22no—
228C3×#235—41no—
229C3×#235—41no—
230C3×#235—44no—
231C3×#235—42no—
232C3×#235—44no—
233C3×#235—42no—
234C3×#235C22⋊C412yes—
235C3×#235C22⋊C412yes—
236C3×#235SD1612yes—
237C3×#235SD1612yes—
238C2×C3×D12—21no—
239C2×C3×D12—42no—
240C2×C3×D12D811yescharacteristic
241C2×C3×C4×D3—41no—
242C2×C3×C4×D3—44no—
243C2×C3×C4×D3C2×D412yes—
244C2×C3×Dic6—21no—
245C2×C3×Dic6—42no—
246C2×C3×Dic6D811yescharacteristic
247C2×D3×Dic3—42no—
248C32×Q16—21no—
249C32×Q16C22×C412yes—
250C32×SD16—22no—
251C32×SD16—22no—
252C32×D8—21no—
253C32×D8C22×C412yes—
254C2×C32×C8C22×C411yescharacteristic
255C2×C32×C8C22×C411yescharacteristic
256C2×C32×C8C2×D411yescharacteristic
257C2×C32×C8C2×D411yescharacteristic
258C2×C32×C8C2×D411yescharacteristic
259C2×C32×C8C2411yescharacteristic
260C4⋊(C3⋊Dic3)—22no—
261C4⋊(C3⋊Dic3)—41no—
262C3×#217—41no—
263C3×#216—24no—
264C3×#215—24no—
265C3×#214—24no—
266C3×#213—24no—
267C3×C4⋊Dic3—21no—
268C3×C4⋊Dic3—21no—
269C3×C4×Dic3—41no—
270C3×#208C22⋊C412yes—
271C3×#208C22⋊C412yes—
272C2×C3×C3⋊C8C2×D412yes—
273C3×Dic12—21no—
274C3×Dic12C22×C412yes—
275C3×D24—21no—
276C3×D24C22×C412yes—
277C3×#204—22no—
278C3×#204—22no—
279C3×ΓL(1,𝔽25)C22⋊C414yes—
280C3×ΓL(1,𝔽25)C22⋊C414yes—
281C3×D3×C8C22×C414yes—
282C3×D3×C8C2×D414yes—
283Dic3⋊Dic3—42no—
284(C2×D3)⋊Dic3—42no—
285Dic32—42no—
286C3⋊(C3⋊C16)—22no—
287C3×C3⋊C16—22no—
288#3584—31no—
289#3407—91no—
290#2912—91no—
291#2145—31no—
292#2145—94no—
293#2145—91no—
294C2×#360—94no—
295C2×#360—91no—
296C2×#360—91no—
297C3×2−1+4—62no—
298C3×2−1+4—62no—
299C3×2−1+4—121no—
300C3×H(5,𝔽2)—62no—
301C3×H(5,𝔽2)—62no—
302C3×H(5,𝔽2)—122no—
303C3×H(5,𝔽2)—121no—
304C2×C3×#41—21no—
305C2×C3×#41—21no—
306C2×C3×#41—31no—
307C2×C3×#41—41no—
308C2×C3×#41—64no—
309C2×C3×#41—61no—
310C2×C3×#41—122no—
311C2×C3×#41—122no—
312#1010—22no—
313#1010—41no—
314#1009—22no—
315#1009—41no—
316D3×#41—24no—
317D3×#41—42no—
318#1007—22no—
319#1004—22no—
320#1004—42no—
321C2×#235—21no—
322C2×#235—42no—
323C2×#235#6711yescharacteristic
324C3×#137—64no—
325C3×#137—64no—
326C3×#137—62no—
327C3×#137—62no—
328C3×AGL(1,ℤ/8)—64no—
329C3×AGL(1,ℤ/8)—64no—
330C3×AGL(1,ℤ/8)—62no—
331C3×AGL(1,ℤ/8)—62no—
332C3×#135—21no—
333C3×#135—21no—
334C3×#135—21no—
335C3×#135—21no—
336C3×#135—22no—
337C3×#135—22no—
338C3×#135—34no—
339C3×#135—34no—
340C3×#135—32no—
341C3×#135—32no—
342C3×#135—41no—
343C3×#135—41no—
344C3×#135—64no—
345C3×#135—64no—
346C3×#135—61no—
347C3×#135—61no—
348C3×#135C4×D312yescomplemented
349C3×#135C2×Dic312yescomplemented
350C3×#135C22×D312yes—
351C3×#135C22×D312yes—
352C2×C3×Q16—21no—
353C2×C3×Q16—34no—
354C2×C3×Q16—31no—
355C2×C3×Q16C4×D311yescharacteristic, complemented
356C2×C3×Q16C2×Dic311yescharacteristic, complemented
357C2×C3×SD16—21no—
358C2×C3×SD16—21no—
359C2×C3×SD16—41no—
360C2×C3×SD16—64no—
361C2×C3×SD16—61no—
362C2×C3×D8—21no—
363C2×C3×D8—34no—
364C2×C3×D8—31no—
365C2×C3×D8C4×D311yescharacteristic, complemented
366C2×C3×D8C2×Dic311yescharacteristic, complemented
367C3×#131—32no—
368C3×#131—32no—
369C3×#131—32no—
370C3×#131—32no—
371C2×C3×M16—31no—
372C2×C3×M16—32no—
373C22×C3×C8—21no—
374C22×C3×C8—32no—
375C22×C3×C8C22×D311yescharacteristic
376C22×C3×C8C22×D311yescharacteristic
377C3×#117—61no—
378#951—22no—
379#950—24no—
380#949—22no—
381Q8×Dic3—121no—
382#942—22no—
383D4×Dic3—121no—
384D4×Dic3—122no—
385#932—22no—
386#926—21no—
387#926—62no—
388C2×C4⋊Dic3—62no—
389C2×C4⋊Dic3—61no—
390C2×C4⋊Dic3—61no—
391C2×C4⋊Dic3—121no—
392C2×#208#6711yescharacteristic
393#919C2×Dic314yescomplemented
394#918—24no—
395D3×Q16C2×Dic314yescomplemented
396#916—24no—
397#915—24no—
398#914—24no—
399D3×SD16—24no—
400#912C2×Dic314yescomplemented
401#911—24no—
402D3×D8C2×Dic314yescomplemented
403C2×Dic12C2×Dic311yescharacteristic, complemented
404#904—21no—
405#904—21no—
406#904C2×Dic312yescomplemented
407#904C22×D312yes—
408C2×D24C2×Dic311yescharacteristic, complemented
409C2×#204—21no—
410#901C2×Dic312yes—
411#901C2×Dic312yes—
412#901#6712yes—
413#901#6712yes—
414C2×ΓL(1,𝔽25)#6712yes—
415C2×D3×C8C22×D312yes—
416#892—62no—
417D3×C4⋊C4—62no—
418#67⋊C4—122no—
419C4×D12—121no—
420C4×Dic6—121no—
421C3×M32—32no—
422C3×M32—61no—
423C2×C3×C16—61no—
424C3×#107—61no—
425C3×#106—31no—
426C3×#106—31no—
427#818—21no—
428#818—62no—
429#817—32no—
430#817—32no—
431#817—62no—
432#817—62no—
433#817—61no—
434#817—61no—
435#817—121no—
436#817C22×D311yescharacteristic
437#817C22×D311yescharacteristic
438#812—21no—
439#812—32no—
440#812—32no—
441#812—62no—
442#812—64no—
443#812—61no—
444#812—61no—
445#812—121no—
446#812C22×D312yes—
447C2×C3⋊C16—21no—
448C2×C3⋊C16—64no—
449C2×C3⋊C16—61no—
450C2×C3⋊C16—61no—
451C2×C3⋊C16—121no—
452#808—62no—
453#807—62no—
454#798—64no—
455D3×C16—64no—
456C23×C32—41no—
457C23×C32C2×D811yescharacteristic
458C22×C3×D3—41no—
459C22×C3×D3—44no—
460C22×C3×D3C2×D812yes—
461C32×Q8—22no—
462C32×Q8—41no—
463C32×D4—22no—
464C32×D4—42no—
465C32×D4—42no—
466C32×D4—41no—
467C2×C32×C4—41no—
468C2×C32×C4—42no—
469C2×C32×C4—42no—
470C2×C32×C4C2×C22⋊C411yescharacteristic
471C2×C32×C4C2×C22⋊C411yescharacteristic
472C2×C32×C4C2×D811yescharacteristic
473C2×C32×C4C2×SD1611yescharacteristic
474C2×C32×C4C2×SD1611yescharacteristic
475C2×C32×C4C22×D411yescharacteristic
476C2×C3⋊Dic3—42no—
477C2×C3⋊Dic3—161no—
478C3×#67—42no—
479C3×#67—42no—
480C3×#67—44no—
481C3×#67—44no—
482C3×#67#10214yes—
483C3×#67#10214yes—
484C2×C3×Dic3—41no—
485C2×C3×Dic3—44no—
486C2×C3×Dic3—41no—
487C2×C3×Dic3—41no—
488C2×C3×Dic3C2×D812yes—
489C3×D12—22no—
490C3×D12—44no—
491C3×D12—41no—
492C3×D12#10212yes—
493C3×D12#10212yes—
494C3×C4×D3—44no—
495C3×C4×D3—42no—
496C3×C4×D3—42no—
497C3×C4×D3—44no—
498C3×C4×D3C2×C22⋊C414yes—
499C3×C4×D3C2×SD1614yes—
500C3×Dic6—22no—
501C3×Dic6—41no—
502C3×Dic6—44no—
503C3×Dic6#10212yes—
504C3×Dic6#10212yes—
505D3×Dic3—162no—
506C32×C8C2×C22⋊C411yescharacteristic
507C32×C8C2×C22⋊C411yescharacteristic
508C32×C8C23×C411yescharacteristic
509C32×C8C22×D411yescharacteristic
510C3×C3⋊C8C2×C22⋊C414yes—
511#585—61no—
512#578—32no—
513#578—32no—
514#577—62no—
515#577—62no—
516#576—32no—
517#576—32no—
518#575—62no—
519#575—61no—
520C2×#135—34no—
521C2×#135—31no—
522C2×#135D3211yescharacteristic
523C2×#131—31no—
524#520—181no—
525#504—182no—
526#504—182no—
527C2×M32—31no—
528C2×M32—94no—
529C2×M32—91no—
530#428—182no—
531#428—181no—
532#427—31no—
533#427—92no—
534C2×#106—92no—
535C2×#106—91no—
536#360—32no—
537#360—32no—
538#360—92no—
539#360—92no—
540#360—94no—
541#360—94no—
542C3×#41—22no—
543C3×#41—22no—
544C3×#41—22no—
545C3×#41—22no—
546C3×#41—32no—
547C3×#41—32no—
548C3×#41—32no—
549C3×#41—32no—
550C3×#41—42no—
551C3×#41—42no—
552C3×#41—41no—
553C3×#41—41no—
554C3×#41—41no—
555C3×#41—41no—
556C3×#41—64no—
557C3×#41—64no—
558C3×#41—62no—
559C3×#41—62no—
560C3×#41—81no—
561C3×#41—81no—
562C3×#41—124no—
563C3×#41—124no—
564C3×#41—124no—
565C3×#41—122no—
566C3×#41—122no—
567C3×#41—124no—
568C3×#41—122no—
569C3×#41—122no—
570C3×#41—121no—
571C3×#41—121no—
572C2×C3×Q8—21no—
573C2×C3×Q8—21no—
574C2×C3×Q8—31no—
575C2×C3×Q8—41no—
576C2×C3×Q8—64no—
577C2×C3×Q8—61no—
578C2×C3×Q8—122no—
579C2×C3×Q8—122no—
580C2×C3×D4—21no—
581C2×C3×D4—21no—
582C2×C3×D4—32no—
583C2×C3×D4—31no—
584C2×C3×D4—41no—
585C2×C3×D4—41no—
586C2×C3×D4—41no—
587C2×C3×D4—64no—
588C2×C3×D4—61no—
589C2×C3×D4—81no—
590C2×C3×D4—122no—
591C2×C3×D4—124no—
592C2×C3×D4—122no—
593C2×C3×D4—124no—
594C2×C3×D4—124no—
595C2×C3×D4—121no—
596C22×C3×C4—21no—
597C22×C3×C4—32no—
598C22×C3×C4—41no—
599C22×C3×C4—41no—
600C22×C3×C4—81no—
601C22×C3×C4—124no—
602C22×C3×C4—121no—
603C22×C3×C4D3×D411yescharacteristic
604C22×C3×C4C2×#6711yescharacteristic
605C2×#67—41no—
606C2×#67—44no—
607C2×#67#21312yes—
608C22×Dic3—122no—
609C22×Dic3—121no—
610C22×Dic3—121no—
611C22×Dic3—241no—
612#239—24no—
613#239—42no—
614D3×Q8—24no—
615D3×Q8—42no—
616#237—24no—
617#237—44no—
618#237—44no—
619#237—42no—
620D3×D4—24no—
621D3×D4—44no—
622D3×D4—44no—
623D3×D4—42no—
624#235—22no—
625#235—22no—
626#235—41no—
627#235—41no—
628#235—44no—
629#235—42no—
630#235—44no—
631#235—42no—
632#235#21412yes—
633#235#21412yes—
634#235#21712yes—
635#235#21712yes—
636C2×D12—21no—
637C2×D12—42no—
638C2×D12#21311yescharacteristic
639C2×C4×D3—41no—
640C2×C4×D3—44no—
641C2×C4×D3—122no—
642C2×C4×D3C2×#6712yes—
643C2×Dic6—21no—
644C2×Dic6—42no—
645C2×Dic6#21311yescharacteristic
646C3×Q16—21no—
647C3×Q16—21no—
648C3×Q16—22no—
649C3×Q16—32no—
650C3×Q16—41no—
651C3×Q16—64no—
652C3×Q16—61no—
653C3×Q16C2×C4×D312yes—
654C3×Q16C22×Dic312yes—
655C3×SD16—22no—
656C3×SD16—22no—
657C3×SD16—22no—
658C3×SD16—22no—
659C3×SD16—42no—
660C3×SD16—42no—
661C3×SD16—64no—
662C3×SD16—64no—
663C3×SD16—62no—
664C3×SD16—62no—
665C3×D8—21no—
666C3×D8—21no—
667C3×D8—22no—
668C3×D8—32no—
669C3×D8—41no—
670C3×D8—64no—
671C3×D8—61no—
672C3×D8C2×C4×D312yes—
673C3×D8C22×Dic312yes—
674C3×M16—32no—
675C3×M16—32no—
676C3×M16—34no—
677C3×M16—34no—
678C2×C3×C8—21no—
679C2×C3×C8—21no—
680C2×C3×C8—21no—
681C2×C3×C8—21no—
682C2×C3×C8—21no—
683C2×C3×C8—21no—
684C2×C3×C8—32no—
685C2×C3×C8—34no—
686C2×C3×C8—34no—
687C2×C3×C8C2×C4×D311yescharacteristic
688C2×C3×C8C2×C4×D311yescharacteristic
689C2×C3×C8D3×D411yescharacteristic
690C2×C3×C8D3×D411yescharacteristic
691C2×C3×C8D3×D411yescharacteristic
692C2×C3×C8C22×Dic311yescharacteristic
693C2×C3×C8C22×Dic311yescharacteristic
694C2×C3×C8C2×#6711yescharacteristic
695C2×C3×C8C2×#6711yescharacteristic
696C2×C3×C8C2×#6711yescharacteristic
697C2×C3×C8C23×D311yescharacteristic
698C2×C3×C8C23×D311yescharacteristic
699C3×C4⋊C4—61no—
700C3×C4⋊C4—61no—
701C3×C22⋊C4—121no—
702C3×C42—121no—
703#217—41no—
704#217—122no—
705#216—24no—
706#215—24no—
707#214—24no—
708#213—24no—
709(C2×D3)⋊C4—122no—
710C4⋊Dic3—21no—
711C4⋊Dic3—21no—
712C4⋊Dic3—62no—
713C4⋊Dic3—62no—
714C4⋊Dic3—122no—
715C4⋊Dic3—122no—
716C4⋊Dic3—121no—
717C4⋊Dic3—121no—
718C4⋊Dic3—241no—
719Dic3⋊C4—122no—
720C4×Dic3—41no—
721C4×Dic3—122no—
722C4×Dic3—122no—
723#208#21712yes—
724#208#21712yes—
725C2×C3⋊C8C2×#6712yes—
726Dic12—21no—
727Dic12C22×Dic312yes—
728D24—21no—
729D24C22×Dic312yes—
730#204—22no—
731#204—22no—
732ΓL(1,𝔽25)#21714yes—
733ΓL(1,𝔽25)#21714yes—
734D3×C8C22×Dic314yes—
735D3×C8C2×#6714yes—
736C3×C16—62no—
737C3⋊C16—22no—
738C3⋊C16—62no—
739C3⋊C16—62no—
740C3⋊C16—122no—
741C22×C32—41no—
742C22×C32—42no—
743C22×C32—161no—
744C22×C32C2×#10211yescharacteristic
745C22×C32C2×#10211yescharacteristic
746C22×C32C22×D811yescharacteristic
747C2×C3×D3—42no—
748C2×C3×D3—42no—
749C2×C3×D3—164no—
750C2×C3×D3—161no—
751C2×C3×D3C2×#10214yes—
752C32×C4—42no—
753C32×C4C2×#10211yescharacteristic
754C32×C4C2×#10211yescharacteristic
755C32×C4C22×C22⋊C411yescharacteristic
756C32×C4C22×SD1611yescharacteristic
757C3⋊Dic3—82no—
758C3×Dic3—42no—
759C3×Dic3—81no—
760C3×Dic3—81no—
761C3×Dic3C2×#10214yes—
7622−1+4—62no—
7632−1+4—62no—
7642−1+4—121no—
765H(5,𝔽2)—62no—
766H(5,𝔽2)—62no—
767H(5,𝔽2)—122no—
768H(5,𝔽2)—121no—
769C2×#41—21no—
770C2×#41—31no—
771C2×#41—64no—
772C2×#41—61no—
773C2×#41—122no—
774C2×#41—122no—
775#137—64no—
776#137—64no—
777#137—62no—
778#137—62no—
779AGL(1,ℤ/8)—64no—
780AGL(1,ℤ/8)—64no—
781AGL(1,ℤ/8)—62no—
782AGL(1,ℤ/8)—62no—
783#135—21no—
784#135—21no—
785#135—34no—
786#135—34no—
787#135—32no—
788#135—32no—
789#135—64no—
790#135—64no—
791#135—61no—
792#135—61no—
793#135D3×Dic312yescomplemented
794#135C2×D3212yes—
795C2×Q16—34no—
796C2×Q16—31no—
797C2×Q16D3×Dic311yescharacteristic, complemented
798C2×SD16—21no—
799C2×SD16—64no—
800C2×SD16—61no—
801C2×D8—34no—
802C2×D8—31no—
803C2×D8D3×Dic311yescharacteristic, complemented
804#131—32no—
805#131—32no—
806#131—32no—
807#131—32no—
808C2×M16—31no—
809C2×M16—32no—
810C22×C8—32no—
811C22×C8C2×D3211yescharacteristic
812C4×Q8—361no—
813C4×D4—361no—
814C4×D4—362no—
815#117—61no—
816#117—182no—
817C2×C4⋊C4—182no—
818C2×C4⋊C4—181no—
819M32—32no—
820M32—61no—
821M32—92no—
822M32—184no—
823M32—181no—
824C2×C16—61no—
825C2×C16—184no—
826C2×C16—181no—
827#107—61no—
828#107—182no—
829#106—31no—
830#106—31no—
831#106—92no—
832#106—182no—
833#106—181no—
834C23×C3—21no—
835C23×C3—32no—
836C23×C3—41no—
837C23×C3—41no—
838C23×C3—81no—
839C23×C3—124no—
840C23×C3—121no—
841C23×C3D3×D811yescharacteristic
842C23×C3C2×#21311yescharacteristic
843C22×D3—41no—
844C22×D3—44no—
845C22×D3C2×#21312yes—
846C3×Q8—22no—
847C3×Q8—22no—
848C3×Q8—32no—
849C3×Q8—32no—
850C3×Q8—42no—
851C3×Q8—41no—
852C3×Q8—41no—
853C3×Q8—62no—
854C3×Q8—81no—
855C3×Q8—124no—
856C3×Q8—121no—
857C3×D4—22no—
858C3×D4—22no—
859C3×D4—34no—
860C3×D4—34no—
861C3×D4—32no—
862C3×D4—32no—
863C3×D4—42no—
864C3×D4—42no—
865C3×D4—42no—
866C3×D4—42no—
867C3×D4—42no—
868C3×D4—41no—
869C3×D4—41no—
870C3×D4—62no—
871C3×D4—81no—
872C3×D4—82no—
873C3×D4—82no—
874C3×D4—124no—
875C3×D4—124no—
876C3×D4—124no—
877C3×D4—122no—
878C3×D4—122no—
879C3×D4—121no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—21no—
885C2×C3×C4—21no—
886C2×C3×C4—32no—
887C2×C3×C4—34no—
888C2×C3×C4—34no—
889C2×C3×C4—41no—
890C2×C3×C4—41no—
891C2×C3×C4—42no—
892C2×C3×C4—42no—
893C2×C3×C4—42no—
894C2×C3×C4—42no—
895C2×C3×C4—82no—
896C2×C3×C4—82no—
897C2×C3×C4—81no—
898C2×C3×C4—124no—
899C2×C3×C4—124no—
900C2×C3×C4—124no—
901C2×C3×C4—121no—
902C2×C3×C4—122no—
903C2×C3×C4—122no—
904C2×C3×C4—121no—
905C2×C3×C4—121no—
906C2×C3×C4D3×C22⋊C411yescharacteristic
907C2×C3×C4D3×C22⋊C411yescharacteristic
908C2×C3×C4D3×D811yescharacteristic
909C2×C3×C4D3×SD1611yescharacteristic
910C2×C3×C4D3×SD1611yescharacteristic
911C2×C3×C4C2×#21311yescharacteristic
912C2×C3×C4C2×#21411yescharacteristic
913C2×C3×C4C2×#21411yescharacteristic
914C2×C3×C4C2×#21711yescharacteristic
915C2×C3×C4C2×#21711yescharacteristic
916C2×C3×C4C2×D3×D411yescharacteristic
917C2×C3×C4C22×#6711yescharacteristic
918#67—42no—
919#67—42no—
920#67—44no—
921#67—44no—
922#67#83214yes—
923#67#83214yes—
924C2×Dic3—41no—
925C2×Dic3—44no—
926C2×Dic3—41no—
927C2×Dic3—41no—
928C2×Dic3—122no—
929C2×Dic3—122no—
930C2×Dic3—242no—
931C2×Dic3—482no—
932C2×Dic3—481no—
933C2×Dic3—481no—
934C2×Dic3—482no—
935C2×Dic3C2×#21312yes—
936D12—22no—
937D12—44no—
938D12—41no—
939D12#83212yes—
940D12#83212yes—
941C4×D3—44no—
942C4×D3—42no—
943C4×D3—42no—
944C4×D3—44no—
945C4×D3—482no—
946C4×D3C2×#21414yes—
947C4×D3C2×#21714yes—
948Dic6—22no—
949Dic6—41no—
950Dic6—44no—
951Dic6#83212yes—
952Dic6#83212yes—
953C3×C8—21no—
954C3×C8—21no—
955C3×C8—21no—
956C3×C8—21no—
957C3×C8—34no—
958C3×C8D3×C22⋊C411yescharacteristic
959C3×C8D3×C22⋊C411yescharacteristic
960C3×C8C2×#21711yescharacteristic
961C3×C8C2×#21711yescharacteristic
962C3×C8C22×C4×D311yescharacteristic
963C3×C8C2×D3×D411yescharacteristic
964C3×C8C23×Dic311yescharacteristic
965C3×C8C22×#6711yescharacteristic
966C3⋊C8C2×#21714yes—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—82no—
971C2×C32C22×#10211yescharacteristic
972C3×D3—24no—
973C3×D3—82no—
974#41—22no—
975#41—22no—
976#41—32no—
977#41—32no—
978#41—32no—
979#41—32no—
980#41—41no—
981#41—41no—
982#41—64no—
983#41—64no—
984#41—62no—
985#41—62no—
986#41—124no—
987#41—124no—
988#41—124no—
989#41—122no—
990#41—122no—
991#41—124no—
992#41—122no—
993#41—122no—
994#41—121no—
995#41—121no—
996C2×Q8—21no—
997C2×Q8—31no—
998C2×Q8—64no—
999C2×Q8—61no—
1000C2×Q8—122no—
1001C2×Q8—122no—
1002C2×D4—21no—
1003C2×D4—32no—
1004C2×D4—31no—
1005C2×D4—41no—
1006C2×D4—64no—
1007C2×D4—61no—
1008C2×D4—122no—
1009C2×D4—124no—
1010C2×D4—122no—
1011C2×D4—124no—
1012C2×D4—124no—
1013C2×D4—121no—
1014C22×C4—32no—
1015C22×C4—41no—
1016C22×C4—124no—
1017C22×C4—121no—
1018C22×C4—362no—
1019C22×C4—361no—
1020C22×C4D3×#6711yescharacteristic
1021Q16—21no—
1022Q16—32no—
1023Q16—64no—
1024Q16—61no—
1025Q16C2×D3×Dic312yes—
1026SD16—22no—
1027SD16—22no—
1028SD16—64no—
1029SD16—64no—
1030SD16—62no—
1031SD16—62no—
1032D8—21no—
1033D8—32no—
1034D8—64no—
1035D8—61no—
1036D8C2×D3×Dic312yes—
1037M16—32no—
1038M16—32no—
1039M16—34no—
1040M16—34no—
1041C2×C8—32no—
1042C2×C8—34no—
1043C2×C8—34no—
1044C2×C8C2×D3×Dic311yescharacteristic
1045C2×C8C2×D3×Dic311yescharacteristic
1046C2×C8D3×#6711yescharacteristic
1047C2×C8D3×#6711yescharacteristic
1048C2×C8D3×#6711yescharacteristic
1049C2×C8C22×D3211yescharacteristic
1050C4⋊C4—61no—
1051C4⋊C4—61no—
1052C4⋊C4—182no—
1053C4⋊C4—362no—
1054C4⋊C4—361no—
1055C22⋊C4—121no—
1056C22⋊C4—362no—
1057C42—121no—
1058C42—362no—
1059C16—62no—
1060C16—182no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—34no—
1065C22×C3—41no—
1066C22×C3—41no—
1067C22×C3—42no—
1068C22×C3—42no—
1069C22×C3—42no—
1070C22×C3—82no—
1071C22×C3—122no—
1072C22×C3—122no—
1073C22×C3—161no—
1074C22×C3—161no—
1075C22×C3—162no—
1076C22×C3—481no—
1077C22×C3—484no—
1078C22×C3D3×#10211yescharacteristic
1079C22×C3D3×#10211yescharacteristic
1080C22×C3C2×#83211yescharacteristic
1081C22×C3C2×#83211yescharacteristic
1082C22×C3C2×D3×D811yescharacteristic
1083C22×C3C22×#21311yescharacteristic
1084C2×D3—42no—
1085C2×D3—42no—
1086C2×D3—164no—
1087C2×D3—161no—
1088C2×D3C2×#83214yes—
1089C3×C4—21no—
1090C3×C4—21no—
1091C3×C4—21no—
1092C3×C4—21no—
1093C3×C4—34no—
1094C3×C4—42no—
1095C3×C4—42no—
1096C3×C4—82no—
1097C3×C4—122no—
1098C3×C4—241no—
1099C3×C4—241no—
1100C3×C4D3×#10211yescharacteristic
1101C3×C4D3×#10211yescharacteristic
1102C3×C4C2×#83211yescharacteristic
1103C3×C4C2×#83211yescharacteristic
1104C3×C4C2×D3×C22⋊C411yescharacteristic
1105C3×C4C2×D3×SD1611yescharacteristic
1106C3×C4C22×#21411yescharacteristic
1107C3×C4C22×#21711yescharacteristic
1108Dic3—42no—
1109Dic3—81no—
1110Dic3—81no—
1111Dic3—242no—
1112Dic3—242no—
1113Dic3—482no—
1114Dic3C2×#83214yes—
1115C32#3338811yescharacteristic, complemented, Sylow
1116C23—32no—
1117C23—41no—
1118C23—124no—
1119C23—121no—
1120C23D3×#21311yescharacteristic
1121Q8—22no—
1122Q8—32no—
1123Q8—32no—
1124Q8—41no—
1125Q8—62no—
1126Q8—124no—
1127Q8—121no—
1128D4—22no—
1129D4—34no—
1130D4—34no—
1131D4—32no—
1132D4—32no—
1133D4—42no—
1134D4—42no—
1135D4—41no—
1136D4—62no—
1137D4—124no—
1138D4—124no—
1139D4—124no—
1140D4—122no—
1141D4—122no—
1142D4—121no—
1143C2×C4—32no—
1144C2×C4—34no—
1145C2×C4—34no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—124no—
1150C2×C4—124no—
1151C2×C4—124no—
1152C2×C4—121no—
1153C2×C4—122no—
1154C2×C4—122no—
1155C2×C4—121no—
1156C2×C4—121no—
1157C2×C4—362no—
1158C2×C4—1442no—
1159C2×C4—1441no—
1160C2×C4D3×#21311yescharacteristic
1161C2×C4D3×#21411yescharacteristic
1162C2×C4D3×#21411yescharacteristic
1163C2×C4D3×#21711yescharacteristic
1164C2×C4D3×#21711yescharacteristic
1165C2×C4C2×D3×#6711yescharacteristic
1166C8—34no—
1167C8D3×#21711yescharacteristic
1168C8D3×#21711yescharacteristic
1169C8C22×D3×Dic311yescharacteristic
1170C8C2×D3×#6711yescharacteristic
1171C2×C3—22no—
1172C2×C3—21no—
1173C2×C3—21no—
1174C2×C3—21no—
1175C2×C3—21no—
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—41no—
1180C2×C3—41no—
1181C2×C3—64no—
1182C2×C3—82no—
1183C2×C3—82no—
1184C2×C3—162no—
1185C2×C3—242no—
1186C2×C3C2×D3×#10211yescharacteristic
1187C2×C3C22×#83211yescharacteristic
1188D3—24no—
1189D3—82no—
1190C22—34no—
1191C22—41no—
1192C22—42no—
1193C22—122no—
1194C22—122no—
1195C22—161no—
1196C22—481no—
1197C22—484no—
1198C22D3×#83211yescharacteristic
1199C22D3×#83211yescharacteristic
1200C22C2×D3×#21311yescharacteristic
1201C4—34no—
1202C4—42no—
1203C4—122no—
1204C4—241no—
1205C4—241no—
1206C4—722no—
1207C4D3×#83211yescharacteristic
1208C4D3×#83211yescharacteristic
1209C4C2×D3×#21411yescharacteristic
1210C4C2×D3×#21711yescharacteristic
1211C3—21no—
1212C3#1094813211yescharacteristic, complemented
1213C3#1094813411yescharacteristic, complemented
1214C2—21no—
1215C2—21no—
1216C2—21no—
1217C2—64no—
1218C2—82no—
1219C2—242no—
1220C2C2×D3×#83211yescharacteristic
subgroupG/H
centerC2C2×D3×#832
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#135C22
socleC2×C32C22×#102
prime radicalC3×#87187C2
cosocleC2×C32×C8C24
hypercenterC2×#135D32
hypocenterC32#33388
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
2. #11899423C2semidirect
3. #11858549C2semidirect
4. #11796862C2semidirect
5. #11796858C2semidirect
6. C3×#72076C2semidirect
7. C2×#10589124C2semidirect
8. D3×#4566C2semidirect
9. C2×#10589432C2semidirect
15. C3×#5771C4semidirect
17. C3×#5769C4semidirect
20. C3×#5766C4semidirect
22. C3×#5757C4semidirect
26. C2×#63644C22semidirect
27. C2×#63639C22semidirect
28. C3×#5106C22semidirect
29. C2×C3×#812C22semidirect
31. #10590706C22semidirect
33. D3×#817C22semidirect
36. D3×#812C22semidirect
37. #10589432C22semidirect
38. C3×#4566C22semidirect
39. C3×#4566C22semidirect
40. #10589124C22semidirect
41. #10589123C22semidirect
42. #10589123C22semidirect
52. #72076D3semidirect
77. C32×#135C2×C4semidirect
79. C2×C32×Q16C2×C4semidirect
81. C2×C32×D8C2×C4semidirect
91. C3×#919C2×C4semidirect
93. C3×D3×Q16C2×C4semidirect
98. C3×#912C2×C4semidirect
100. C3×D3×D8C2×C4semidirect
101. C2×C3×Dic12C2×C4semidirect
104. C3×#904C2×C4semidirect
106. C2×C3×D24C2×C4semidirect
153. #5771Dic3semidirect
155. #5769Dic3semidirect
158. #5766Dic3semidirect
160. #5757Dic3semidirect
171. #5106C2×D3semidirect
180. C2×#812C2×D3semidirect
196. #4566C2×D3semidirect
197. #4566C2×D3semidirect
348. C3×#135C4×D3semidirect
349. C3×#135C2×Dic3semidirect
355. C2×C3×Q16C4×D3semidirect
356. C2×C3×Q16C2×Dic3semidirect
365. C2×C3×D8C4×D3semidirect
366. C2×C3×D8C2×Dic3semidirect
393. #919C2×Dic3semidirect
395. D3×Q16C2×Dic3semidirect
400. #912C2×Dic3semidirect
402. D3×D8C2×Dic3semidirect
403. C2×Dic12C2×Dic3semidirect
406. #904C2×Dic3semidirect
408. C2×D24C2×Dic3semidirect
793. #135D3×Dic3semidirect
797. C2×Q16D3×Dic3semidirect
803. C2×D8D3×Dic3semidirect
1115. C32#33388semidirect
1212. C3#10948132semidirect
1213. C3#10948134semidirect

Maximal subgroups

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

subgroupindex
C3×#871872
#118994232
#118585492
#117968622
#117968582
C3×#720762
C2×#105891242
D3×#45662
C2×#105894322
#109481343
#109481323