Finite Group Databasebeta

← #13181639

Subgroups — #13181639

Order 1728.

6044 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#64366C211yesmaximal, characteristic, complemented
3C32×#1009C211yesmaximal, characteristic, complemented
4#11724597C212yesmaximal, complemented
5#11724596C212yesmaximal, complemented
6#11724587C216yesmaximal, complemented
7D3×D4×C3⋊D3C216yesmaximal, complemented
8#11724580C213yesmaximal, complemented
9#11724579C213yesmaximal, complemented
10#11724578C213yesmaximal, complemented
11C2×#89026C213yesmaximal, complemented
12C3⋊D3×H(5,𝔽2)—31nomaximal
13#10596692—34nomaximal
14C22×D3×C3⋊D3C2216yescomplemented
15C33×#41C2211yescharacteristic, complemented
16#89080C2211yescharacteristic, complemented
17Q8×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
18#89078C2213yescomplemented
19D4×C3⋊(C3⋊D3)C2213yescomplemented
20#89076C2213yescomplemented
21C2×C4×C3⋊(C3⋊D3)C2213yescomplemented
22C3×#3832C2212yescomplemented
23C3×D4×C3⋊D3C2216yescomplemented
24C3×#3828C2213yescomplemented
25C2×C3×C4⋊(C3⋊D3)C2213yescomplemented
26C32×#239C2212yescomplemented
27C32×D3×D4C2216yescomplemented
28C32×#235C2213yescomplemented
29C2×C32×D12C2213yescomplemented
30#89039C2216yescomplemented
31C3⋊D3×#67C22112yescomplemented
32D3×#638C22112yescomplemented
33C2×#6290C2216yescomplemented
34#89029C2216yescomplemented
35#89026C2213yescomplemented
36#89026C2216yescomplemented
37#89026C2216yescomplemented
38#89026C2216yescomplemented
39C3⋊D3×D12C2216yescomplemented
40D3×C4⋊(C3⋊D3)C2216yescomplemented
41C4×D3×C3⋊D3C2216yescomplemented
42#89021C2216yescomplemented
43#89020C2216yescomplemented
44#89019C2211yescharacteristic, complemented
45#89017C2213yescomplemented
46#89015C2213yescomplemented
47#89014C2216yescomplemented
48C32×H(5,𝔽2)—31no—
49#64366—32no—
50#64366—33no—
51#64366D311yescharacteristic, complemented
52#41×C3⋊D3—31no—
53#41×C3⋊D3—32no—
54#41×C3⋊D3—33no—
55#41×C3⋊D3—34no—
56#41×C3⋊D3—64no—
57#64361—36no—
58#64361—33no—
59C2×D4×C3⋊D3—36no—
60C2×D4×C3⋊D3—33no—
61C3×#1009—34no—
62C3×#1009D314yescomplemented
63#64320—38no—
64#64319—38no—
65#64313—324no—
66D32×D4—324no—
67#64307—312no—
68#64307—312no—
69#64306—312no—
70C2×#3802—312no—
71C22×C3⋊(C3⋊D3)C2313yes—
72C22×C3×C3⋊D3C2316yescomplemented
73C22×C32×D3C2316yescomplemented
74C2×D3×C3⋊D3—412no—
75C2×D3×C3⋊D3C2316yes—
76C2×D3×C3⋊D3C23112yescomplemented
77C33×Q8C2311yescharacteristic, complemented
78C33×D4C2313yescomplemented
79C2×C33×C4C2313yescomplemented
80#6312C2316yescomplemented
81C2×C3⋊(C3⋊Dic3)C2313yescomplemented
82C4⋊(C3⋊(C3⋊D3))C2313yescomplemented
83C4×C3⋊(C3⋊D3)C2311yescharacteristic
84C4×C3⋊(C3⋊D3)C2313yes—
85C4×C3⋊(C3⋊D3)C2313yescomplemented
86C4×C3⋊(C3⋊D3)C2313yescomplemented
87#6308C2313yescomplemented
88C3×#638C2316yescomplemented
89C3×C4⋊(C3⋊D3)C2313yescomplemented
90C3×C4⋊(C3⋊D3)C2316yescomplemented
91C3×C4×C3⋊D3C2316yescomplemented
92C3×#634C2311yescharacteristic, complemented
93C32×#67C2316yescomplemented
94C32×D12C2316yescomplemented
95C32×D12C2313yescomplemented
96C32×C4×D3C2316yescomplemented
97C32×Dic6C2311yescharacteristic, complemented
98#6293C2312yescomplemented
99#6292C2316yescomplemented
100#6291C2316yescomplemented
101#6290C23112yescomplemented
102#6290C2316yescomplemented
103#6289C2312yes—
104Dic3×C3⋊D3C2316yescomplemented
105D3×C3⋊Dic3C2316yescomplemented
106D3×H(5,𝔽2)—94no—
107D3×H(5,𝔽2)—91no—
108C23×C3⋊D3—36no—
109C22×D32—324no—
110C32×#41—24no—
111C32×#41—32no—
112C32×#41—33no—
113C32×#41C2×D314yescomplemented
114C32×#41C2×D311yescharacteristic, complemented
115C2×C32×D4—36no—
116C2×C32×D4—33no—
117C2×#638—36no—
118C2×#638—312no—
119#3832—31no—
120#3832—34no—
121#3832—33no—
122#3832—64no—
123#3832C2×D312yescomplemented
124Q8×C3⋊D3—31no—
125Q8×C3⋊D3—34no—
126Q8×C3⋊D3—31no—
127Q8×C3⋊D3—64no—
128#3830—33no—
129#3830—312no—
130#3830—36no—
131#3830—36no—
132#3830—33no—
133#3830—612no—
134D4×C3⋊D3—312no—
135D4×C3⋊D3—33no—
136D4×C3⋊D3—312no—
137D4×C3⋊D3—36no—
138D4×C3⋊D3—36no—
139D4×C3⋊D3—33no—
140D4×C3⋊D3—36no—
141D4×C3⋊D3—36no—
142D4×C3⋊D3—36no—
143D4×C3⋊D3—612no—
144D4×C3⋊D3C2×D316yescomplemented
145#3828—33no—
146#3828—312no—
147#3828—36no—
148#3828—36no—
149#3828—612no—
150#3828C2×D313yescomplemented
151C2×C4⋊(C3⋊D3)—36no—
152C2×C4⋊(C3⋊D3)C2×D313yescomplemented
153C2×C4×C3⋊D3—33no—
154C2×C4×C3⋊D3—312no—
155C2×C4×C3⋊D3—36no—
156C2×C4×C3⋊D3—612no—
157C3×#239—38no—
158C3×#239C2×D318yescomplemented
159C3×D3×D4—324no—
160C3×D3×D4C2×D3124yescomplemented
161C3×#235—312no—
162C3×#235C2×D3112yescomplemented
163C2×C3×D12—312no—
164C2×C3×D12C2×D3112yescomplemented
165#3811—324no—
166D3×#67—348no—
167D3×#67—348no—
168C2×#625—324no—
169#3805—324no—
170#3802—312no—
171#3802—324no—
172#3802—324no—
173#3802—324no—
174D3×D12—324no—
175D3×D12—324no—
176C4×D32—324no—
177#3798—324no—
178#3797—34no—
179#3796—312no—
180#3796—312no—
181#3795—324no—
182#3795—324no—
183C22×C33C2413yes—
184C2×C3⋊(C3⋊D3)—26no—
185C2×C3⋊(C3⋊D3)C2413yes—
186C2×C3⋊(C3⋊D3)C2411yescharacteristic
187C2×C3×C3⋊D3—46no—
188C2×C3×C3⋊D3C2416yes—
189C2×C32×D3—46no—
190C2×C32×D3C2416yes—
191D3×C3⋊D3—212no—
192D3×C3⋊D3—412no—
193C33×C4C2411yescharacteristic
194C33×C4C2413yes—
195C3⋊(C3⋊Dic3)C2413yes—
196C3⋊(C3⋊Dic3)C2411yescharacteristic
197C3×C3⋊Dic3C2412yes—
198C32×Dic3C2412yes—
199C3×H(5,𝔽2)—34no—
200C3×H(5,𝔽2)—91no—
201#1009—34no—
202#1009—912no—
203#1009—98no—
204#1009—92no—
205#1009—93no—
206#1009C3⋊D311yescharacteristic, complemented
207D3×#41—912no—
208D3×#41—98no—
209D3×#41—94no—
210D3×#41—91no—
211D3×#41—92no—
212D3×#41—93no—
213D3×#41—184no—
214#1004—912no—
215#1004—924no—
216#1004—96no—
217#1004—93no—
218C2×D3×D4—912no—
219C2×D3×D4—924no—
220C2×D3×D4—96no—
221C2×D3×D4—93no—
222C23×C32—36no—
223C22×C3⋊D3—33no—
224C22×C3⋊D3—36no—
225C22×C3⋊D3—312no—
226C22×C3⋊D3—312no—
227C22×C3⋊D3—612no—
228C22×C3⋊D3—1212no—
229C22×C3⋊D3C22×D316yescomplemented
230C22×C3×D3—324no—
231C22×C3×D3C22×D3124yescomplemented
232C2×D32—324no—
233C2×D32—348no—
234C2×D32—1248no—
235C32×Q8—24no—
236C32×Q8—31no—
237C32×Q8C22×D314yescomplemented
238C32×Q8C22×D311yescharacteristic, complemented
239C32×D4—212no—
240C32×D4—36no—
241C32×D4—36no—
242C32×D4—33no—
243C32×D4C22×D3112yescomplemented
244C32×D4C22×D313yescomplemented
245C2×C32×C4—212no—
246C2×C32×C4—36no—
247C2×C32×C4C22×D3112yescomplemented
248C2×C32×C4C22×D313yescomplemented
249#638—36no—
250#638—312no—
251#638—36no—
252#638—36no—
253#638—324no—
254#638—624no—
255#638C22×D316yescomplemented
256C2×C3⋊Dic3—33no—
257C2×C3⋊Dic3—36no—
258C2×C3⋊Dic3—312no—
259C2×C3⋊Dic3—612no—
260C4⋊(C3⋊D3)—36no—
261C4⋊(C3⋊D3)—33no—
262C4⋊(C3⋊D3)—312no—
263C4⋊(C3⋊D3)—612no—
264C4⋊(C3⋊D3)C22×D316yescomplemented
265C4⋊(C3⋊D3)C22×D313yescomplemented
266C4×C3⋊D3—36no—
267C4×C3⋊D3—33no—
268C4×C3⋊D3—31no—
269C4×C3⋊D3—33no—
270C4×C3⋊D3—33no—
271C4×C3⋊D3—32no—
272C4×C3⋊D3—34no—
273C4×C3⋊D3—312no—
274C4×C3⋊D3—312no—
275C4×C3⋊D3—312no—
276C4×C3⋊D3—64no—
277C4×C3⋊D3—612no—
278C4×C3⋊D3—612no—
279C4×C3⋊D3—612no—
280C4×C3⋊D3C22×D316yescomplemented
281#634—33no—
282#634—32no—
283#634—312no—
284#634—612no—
285#634C22×D311yescharacteristic, complemented
286C3×#67—324no—
287C3×#67C22×D3124yescomplemented
288C3×D12—324no—
289C3×D12—312no—
290C3×D12C22×D3124yescomplemented
291C3×D12C22×D3112yescomplemented
292C3×C4×D3—324no—
293C3×C4×D3C22×D3124yescomplemented
294C3×Dic6—34no—
295C3×Dic6C22×D314yescomplemented
296#627—38no—
297#626—324no—
298#626—324no—
299#625—348no—
300#625—324no—
301#624—38no—
302D3×Dic3—324no—
303D3×Dic3—324no—
304C2×H(5,𝔽2)—271noSylow
305C2×C33—23no—
306C2×C33C2511yescharacteristic
307C3⋊(C3⋊D3)—23no—
308C3⋊(C3⋊D3)H(5,𝔽2)12yescomplemented
309C3×C3⋊D3—26no—
310C32×D3—26no—
311C23×D3—924no—
312C23×D3—96no—
313C3×#41—24no—
314C3×#41—38no—
315C3×#41—312no—
316C3×#41—92no—
317C3×#41—93no—
318C3×#41D3214yescomplemented
319C3×#41C2×C3⋊D311yescharacteristic, complemented
320C2×C3×D4—324no—
321C2×C3×D4—312no—
322C2×C3×D4—96no—
323C2×C3×D4—93no—
324C2×#67—948no—
325C2×#67—924no—
326C2×#67—96no—
327C2×#67—912no—
328#239—38no—
329#239—912no—
330#239—94no—
331#239—91no—
332#239—93no—
333#239—184no—
334#239C2×C3⋊D312yescomplemented
335D3×Q8—94no—
336D3×Q8—94no—
337D3×Q8—91no—
338D3×Q8—91no—
339D3×Q8—184no—
340#237—912no—
341#237—924no—
342#237—924no—
343#237—912no—
344#237—93no—
345#237—96no—
346#237—96no—
347#237—93no—
348#237—1812no—
349D3×D4—324no—
350D3×D4—924no—
351D3×D4—912no—
352D3×D4—924no—
353D3×D4—924no—
354D3×D4—924no—
355D3×D4—924no—
356D3×D4—948no—
357D3×D4—912no—
358D3×D4—912no—
359D3×D4—93no—
360D3×D4—96no—
361D3×D4—96no—
362D3×D4—93no—
363D3×D4—96no—
364D3×D4—96no—
365D3×D4—96no—
366D3×D4—1812no—
367D3×D4C2×C3⋊D316yescomplemented
368#235—312no—
369#235—924no—
370#235—924no—
371#235—912no—
372#235—93no—
373#235—96no—
374#235—96no—
375#235—1812no—
376#235C2×C3⋊D313yescomplemented
377C2×D12—312no—
378C2×D12—924no—
379C2×D12—96no—
380C2×D12C2×C3⋊D313yescomplemented
381C2×C4×D3—924no—
382C2×C4×D3—912no—
383C2×C4×D3—93no—
384C2×C4×D3—96no—
385C2×C4×D3—1812no—
386C22×C32—212no—
387C22×C32—36no—
388C22×C32—126no—
389C22×C32C23×D3112yes—
390C22×C32C23×D313yes—
391C2×C3⋊D3—31no—
392C2×C3⋊D3—33no—
393C2×C3⋊D3—34no—
394C2×C3⋊D3—312no—
395C2×C3⋊D3—46no—
396C2×C3⋊D3—64no—
397C2×C3⋊D3—612no—
398C2×C3⋊D3—612no—
399C2×C3⋊D3—66no—
400C2×C3⋊D3—624no—
401C2×C3⋊D3—1224no—
402C2×C3⋊D3—1212no—
403C2×C3⋊D3C23×D316yes—
404C2×C3×D3—324no—
405C2×C3×D3—424no—
406C2×C3×D3—1224no—
407C2×C3×D3C23×D3124yes—
408D32—648no—
409D32—1248no—
410C32×C4—212no—
411C32×C4—24no—
412C32×C4—32no—
413C32×C4C23×D314yes—
414C32×C4C23×D3112yes—
415C32×C4C23×D313yes—
416C32×C4C23×D311yescharacteristic
417C3⋊Dic3—33no—
418C3⋊Dic3—31no—
419C3⋊Dic3—312no—
420C3⋊Dic3—34no—
421C3⋊Dic3—612no—
422C3⋊Dic3—64no—
423C3⋊Dic3C23×D312yes—
424C3×Dic3—38no—
425C3×Dic3C23×D318yes—
426H(5,𝔽2)—31no—
427H(5,𝔽2)—91no—
428H(5,𝔽2)—276no—
429H(5,𝔽2)—273no—
430H(5,𝔽2)—273no—
431H(5,𝔽2)—272no—
432C2×#41—272no—
433C2×#41—273no—
434C2×#41—271no—
435C22×D4—276no—
436C22×D4—273no—
437C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
438C23×C3—324no—
439C23×C3—96no—
440C22×D3—324no—
441C22×D3—924no—
442C22×D3—948no—
443C22×D3—912no—
444C22×D3—93no—
445C22×D3—96no—
446C22×D3—912no—
447C22×D3—1812no—
448C22×D3—3612no—
449C22×D3—3648no—
450C22×D3C22×C3⋊D316yescomplemented
451C3×Q8—24no—
452C3×Q8—34no—
453C3×Q8—91no—
454C3×Q8C2×D3214yescomplemented
455C3×Q8C22×C3⋊D311yescharacteristic, complemented
456C3×D4—212no—
457C3×D4—324no—
458C3×D4—312no—
459C3×D4—324no—
460C3×D4—96no—
461C3×D4—96no—
462C3×D4—93no—
463C3×D4C2×D32112yescomplemented
464C3×D4C22×C3⋊D313yescomplemented
465C2×C3×C4—212no—
466C2×C3×C4—324no—
467C2×C3×C4—96no—
468C2×C3×C4C2×D32112yescomplemented
469C2×C3×C4C22×C3⋊D313yescomplemented
470#67—324no—
471#67—924no—
472#67—948no—
473#67—924no—
474#67—924no—
475#67—96no—
476#67—912no—
477#67—96no—
478#67—96no—
479#67—1824no—
480#67C22×C3⋊D316yescomplemented
481C2×Dic3—924no—
482C2×Dic3—912no—
483C2×Dic3—93no—
484C2×Dic3—96no—
485C2×Dic3—1812no—
486D12—312no—
487D12—324no—
488D12—924no—
489D12—96no—
490D12—912no—
491D12—93no—
492D12—1812no—
493D12C22×C3⋊D316yescomplemented
494D12C22×C3⋊D313yescomplemented
495C4×D3—324no—
496C4×D3—98no—
497C4×D3—924no—
498C4×D3—96no—
499C4×D3—94no—
500C4×D3—912no—
501C4×D3—912no—
502C4×D3—912no—
503C4×D3—93no—
504C4×D3—91no—
505C4×D3—93no—
506C4×D3—93no—
507C4×D3—92no—
508C4×D3—184no—
509C4×D3—1812no—
510C4×D3—1812no—
511C4×D3—1812no—
512C4×D3C22×C3⋊D316yescomplemented
513Dic6—34no—
514Dic6—98no—
515Dic6—912no—
516Dic6—93no—
517Dic6—92no—
518Dic6—1812no—
519Dic6C22×C3⋊D311yescharacteristic, complemented
520C2×C32—23no—
521C2×C32—24no—
522C2×C32—212no—
523C2×C32—412no—
524C2×C32—66no—
525C2×C32C24×D314yes—
526C2×C32C24×D311yescharacteristic
527C3⋊D3—26no—
528C3⋊D3—32no—
529C3⋊D3—38no—
530C3⋊D3—68no—
531C3⋊D3—63no—
532C3⋊D3—612no—
533C3⋊D3—1212no—
534C3×D3—224no—
535C3×D3—624no—
536C24—276no—
537#41—32no—
538#41—33no—
539#41—92no—
540#41—93no—
541#41—276no—
542#41—276no—
543#41—276no—
544#41—276no—
545#41—273no—
546#41—273no—
547#41—271no—
548#41—273no—
549#41—273no—
550#41D3×C3⋊D311yescharacteristic, complemented
551C2×Q8—271no—
552C2×Q8—271no—
553C2×D4—36no—
554C2×D4—33no—
555C2×D4—96no—
556C2×D4—93no—
557C2×D4—276no—
558C2×D4—276no—
559C2×D4—276no—
560C2×D4—276no—
561C2×D4—273no—
562C2×D4—276no—
563C2×D4—276no—
564C2×D4—2712no—
565C2×D4—2712no—
566C2×D4—276no—
567C2×D4—273no—
568C22×C4—276no—
569C22×C4—273no—
570C22×C3—212no—
571C22×C3—324no—
572C22×C3—96no—
573C22×C3—1224no—
574C22×C3—366no—
575C22×C3C22×D32112yes—
576C22×C3C23×C3⋊D313yes—
577C2×D3—324no—
578C2×D3—46no—
579C2×D3—94no—
580C2×D3—91no—
581C2×D3—912no—
582C2×D3—93no—
583C2×D3—1224no—
584C2×D3—184no—
585C2×D3—1812no—
586C2×D3—1812no—
587C2×D3—1848no—
588C2×D3—186no—
589C2×D3—1824no—
590C2×D3—3624no—
591C2×D3—3612no—
592C2×D3—3648no—
593C2×D3C23×C3⋊D316yes—
594C3×C4—212no—
595C3×C4—24no—
596C3×C4—38no—
597C3×C4—92no—
598C3×C4C22×D3214yes—
599C3×C4C22×D32112yes—
600C3×C4C23×C3⋊D313yes—
601C3×C4C23×C3⋊D311yescharacteristic
602Dic3—38no—
603Dic3—94no—
604Dic3—912no—
605Dic3—93no—
606Dic3—91no—
607Dic3—1812no—
608Dic3—184no—
609Dic3C23×C3⋊D312yes—
610C32—24no—
611C32D3×H(5,𝔽2)14yescomplemented
612C32D3×H(5,𝔽2)11yescharacteristic, complemented
613C23—36no—
614C23—96no—
615C23—276no—
616C23—2712no—
617C23—273no—
618C23—10812no—
619Q8—31no—
620Q8—91no—
621Q8—272no—
622Q8—273no—
623Q8C2×D3×C3⋊D311yescharacteristic, complemented
624D4—36no—
625D4—36no—
626D4—33no—
627D4—96no—
628D4—96no—
629D4—93no—
630D4—276no—
631D4—276no—
632D4—276no—
633D4—2712no—
634D4—276no—
635D4—273no—
636D4C2×D3×C3⋊D313yescomplemented
637C2×C4—36no—
638C2×C4—96no—
639C2×C4—272no—
640C2×C4—276no—
641C2×C4—276no—
642C2×C4—273no—
643C2×C4—273no—
644C2×C4—271no—
645C2×C4—273no—
646C2×C4—273no—
647C2×C4C2×D3×C3⋊D313yescomplemented
648C2×C3—212no—
649C2×C3—23no—
650C2×C3—24no—
651C2×C3—412no—
652C2×C3—624no—
653C2×C3—186no—
654C2×C3C23×D3214yes—
655C2×C3C24×C3⋊D311yescharacteristic
656D3—26no—
657D3—624no—
658D3—98no—
659D3—92no—
660D3—188no—
661D3—1812no—
662D3—183no—
663D3—3612no—
664C22—36no—
665C22—96no—
666C22—126no—
667C22—271no—
668C22—273no—
669C22—366no—
670C22—546no—
671C22—5412no—
672C22—10812no—
673C22C22×D3×C3⋊D313yes—
674C4—32no—
675C4—92no—
676C4—273no—
677C4—271no—
678C4C22×D3×C3⋊D313yes—
679C4C22×D3×C3⋊D311yescharacteristic
680C3—24no—
681C3#1059669214yescomplemented
682C3C3⋊D3×H(5,𝔽2)11yescharacteristic, complemented
683C2—23no—
684C2—66no—
685C2—186no—
686C2—272no—
687C2—543no—
688C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C23×D3×C3⋊D3
commutator, socle, cosocleC2×C33C25
FittingC33×#41C22
hypercenter#41D3×C3⋊D3
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊(C3⋊D3)C2semidirect
2. C3×#64366C2semidirect
3. C32×#1009C2semidirect
4. #11724597C2semidirect
5. #11724596C2semidirect
6. #11724587C2semidirect
7. D3×D4×C3⋊D3C2semidirect
8. #11724580C2semidirect
9. #11724579C2semidirect
10. #11724578C2semidirect
11. C2×#89026C2semidirect
14. C22×D3×C3⋊D3C22semidirect
15. C33×#41C22semidirect
16. #89080C22semidirect
17. Q8×C3⋊(C3⋊D3)C22semidirect
18. #89078C22semidirect
19. D4×C3⋊(C3⋊D3)C22semidirect
20. #89076C22semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C3×#3832C22semidirect
23. C3×D4×C3⋊D3C22semidirect
24. C3×#3828C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C32×#239C22semidirect
27. C32×D3×D4C22semidirect
28. C32×#235C22semidirect
29. C2×C32×D12C22semidirect
30. #89039C22semidirect
31. C3⋊D3×#67C22semidirect
32. D3×#638C22semidirect
33. C2×#6290C22semidirect
34. #89029C22semidirect
35. #89026C22semidirect
36. #89026C22semidirect
37. #89026C22semidirect
38. #89026C22semidirect
39. C3⋊D3×D12C22semidirect
40. D3×C4⋊(C3⋊D3)C22semidirect
41. C4×D3×C3⋊D3C22semidirect
42. #89021C22semidirect
43. #89020C22semidirect
44. #89019C22semidirect
45. #89017C22semidirect
46. #89015C22semidirect
47. #89014C22semidirect
51. #64366D3semidirect
62. C3×#1009D3semidirect
72. C22×C3×C3⋊D3C23semidirect
73. C22×C32×D3C23semidirect
76. C2×D3×C3⋊D3C23semidirect
77. C33×Q8C23semidirect
78. C33×D4C23semidirect
79. C2×C33×C4C23semidirect
80. #6312C23semidirect
81. C2×C3⋊(C3⋊Dic3)C23semidirect
82. C4⋊(C3⋊(C3⋊D3))C23semidirect
85. C4×C3⋊(C3⋊D3)C23semidirect
86. C4×C3⋊(C3⋊D3)C23semidirect
87. #6308C23semidirect
88. C3×#638C23semidirect
89. C3×C4⋊(C3⋊D3)C23semidirect
90. C3×C4⋊(C3⋊D3)C23semidirect
91. C3×C4×C3⋊D3C23semidirect
92. C3×#634C23semidirect
93. C32×#67C23semidirect
94. C32×D12C23semidirect
95. C32×D12C23semidirect
96. C32×C4×D3C23semidirect
97. C32×Dic6C23semidirect
98. #6293C23semidirect
99. #6292C23semidirect
100. #6291C23semidirect
101. #6290C23semidirect
102. #6290C23semidirect
104. Dic3×C3⋊D3C23semidirect
105. D3×C3⋊Dic3C23semidirect
113. C32×#41C2×D3semidirect
114. C32×#41C2×D3semidirect
123. #3832C2×D3semidirect
144. D4×C3⋊D3C2×D3semidirect
150. #3828C2×D3semidirect
152. C2×C4⋊(C3⋊D3)C2×D3semidirect
158. C3×#239C2×D3semidirect
160. C3×D3×D4C2×D3semidirect
162. C3×#235C2×D3semidirect
164. C2×C3×D12C2×D3semidirect
206. #1009C3⋊D3semidirect
229. C22×C3⋊D3C22×D3semidirect
231. C22×C3×D3C22×D3semidirect
237. C32×Q8C22×D3semidirect
238. C32×Q8C22×D3semidirect
243. C32×D4C22×D3semidirect
244. C32×D4C22×D3semidirect
247. C2×C32×C4C22×D3semidirect
248. C2×C32×C4C22×D3semidirect
255. #638C22×D3semidirect
264. C4⋊(C3⋊D3)C22×D3semidirect
265. C4⋊(C3⋊D3)C22×D3semidirect
280. C4×C3⋊D3C22×D3semidirect
285. #634C22×D3semidirect
287. C3×#67C22×D3semidirect
290. C3×D12C22×D3semidirect
291. C3×D12C22×D3semidirect
293. C3×C4×D3C22×D3semidirect
295. C3×Dic6C22×D3semidirect
308. C3⋊(C3⋊D3)H(5,𝔽2)semidirect
318. C3×#41D32semidirect
319. C3×#41C2×C3⋊D3semidirect
334. #239C2×C3⋊D3semidirect
367. D3×D4C2×C3⋊D3semidirect
376. #235C2×C3⋊D3semidirect
380. C2×D12C2×C3⋊D3semidirect
437. C33C2×H(5,𝔽2)semidirect
450. C22×D3C22×C3⋊D3semidirect
454. C3×Q8C2×D32semidirect
455. C3×Q8C22×C3⋊D3semidirect
463. C3×D4C2×D32semidirect
464. C3×D4C22×C3⋊D3semidirect
468. C2×C3×C4C2×D32semidirect
469. C2×C3×C4C22×C3⋊D3semidirect
480. #67C22×C3⋊D3semidirect
493. D12C22×C3⋊D3semidirect
494. D12C22×C3⋊D3semidirect
512. C4×D3C22×C3⋊D3semidirect
519. Dic6C22×C3⋊D3semidirect
550. #41D3×C3⋊D3semidirect
611. C32D3×H(5,𝔽2)semidirect
612. C32D3×H(5,𝔽2)semidirect
623. Q8C2×D3×C3⋊D3semidirect
636. D4C2×D3×C3⋊D3semidirect
647. C2×C4C2×D3×C3⋊D3semidirect
681. C3#10596692semidirect
682. C3C3⋊D3×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊(C3⋊D3)2
C3×#643662
C32×#10092
#117245972
#117245962
#117245872
D3×D4×C3⋊D32
#117245802
#117245792
#117245782
C2×#890262
C3⋊D3×H(5,𝔽2)3
#105966923