Finite Group Databasebeta

← C3⋊D3×#1009 #13181637

Subgroups — C3⋊D3×#1009 #13181637

Order 1728.

6052 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724684C211yesmaximal, characteristic, complemented
2C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#1009C211yesmaximal, characteristic, complemented
4#11724597C212yesmaximal, complemented
5C3⋊D3×#239C212yesmaximal, complemented
6#11724588C216yesmaximal, complemented
7D3×D4×C3⋊D3C216yesmaximal, complemented
8#11724581C213yesmaximal, complemented
9#11724579C213yesmaximal, complemented
10C3⋊D3×#235C213yesmaximal, complemented
11C2×C3⋊D3×D12C213yesmaximal, complemented
12C3⋊D3×H(5,𝔽2)—31nomaximal
13D3×#1009—34nomaximal
14C22×D3×C3⋊D3C2216yescomplemented
15C33×#41C2211yescharacteristic, complemented
16#89080C2212yescomplemented
17D4×C3⋊(C3⋊D3)C2216yescomplemented
18#89076C2213yescomplemented
19C2×C4⋊(C3⋊(C3⋊D3))C2213yescomplemented
20C3×#3832C2211yescharacteristic, complemented
21C3×Q8×C3⋊D3C2211yescharacteristic, complemented
22C3×#3830C2213yescomplemented
23C3×D4×C3⋊D3C2213yescomplemented
24C3×#3828C2213yescomplemented
25C2×C3×C4×C3⋊D3C2213yescomplemented
26C32×#239C2212yescomplemented
27C32×D3×D4C2216yescomplemented
28C32×#235C2213yescomplemented
29C2×C32×D12C2213yescomplemented
30#89039C22112yescomplemented
31C3⋊D3×#67C2216yescomplemented
32D3×#638C22112yescomplemented
33C2×#6291C2216yescomplemented
34#89028C2216yescomplemented
35#89026C2216yescomplemented
36C3⋊D3×D12C2213yescomplemented
37C3⋊D3×D12C2216yescomplemented
38C3⋊D3×D12C2216yescomplemented
39C3⋊D3×D12C2216yescomplemented
40D3×C4⋊(C3⋊D3)C2216yescomplemented
41C4×D3×C3⋊D3C2216yescomplemented
42#89022C2216yescomplemented
43#89020C2216yescomplemented
44#89018C2213yescomplemented
45C3⋊D3×Dic6C2211yescharacteristic, complemented
46#89015C2216yescomplemented
47#89014C2213yescomplemented
48C32×H(5,𝔽2)—31no—
49#64366—31no—
50#64366—32no—
51#64366—33no—
52#64366—34no—
53#64366—64no—
54#41×C3⋊D3—32no—
55#41×C3⋊D3—33no—
56#41×C3⋊D3D311yescharacteristic, complemented
57#64361—36no—
58#64361—33no—
59C2×D4×C3⋊D3—36no—
60C2×D4×C3⋊D3—33no—
61C3×#1009D314yescomplemented
62C3×D3×#41—34no—
63#64320—38no—
64D3×#239—38no—
65#64314—324no—
66D32×D4—324no—
67#64308—312no—
68#64307—312no—
69D3×#235—312no—
70C2×D3×D12—312no—
71C22×C3⋊(C3⋊D3)C2316yescomplemented
72C22×C3×C3⋊D3C2313yes—
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
81C4⋊(C3⋊(C3⋊D3))C2313yescomplemented
82C4⋊(C3⋊(C3⋊D3))C2316yescomplemented
83C4×C3⋊(C3⋊D3)C2316yescomplemented
84#6308C2311yescharacteristic, complemented
85C3×#638C2316yescomplemented
86C2×C3×C3⋊Dic3C2313yescomplemented
87C3×C4⋊(C3⋊D3)C2313yescomplemented
88C3×C4×C3⋊D3C2311yescharacteristic
89C3×C4×C3⋊D3C2313yes—
90C3×C4×C3⋊D3C2313yescomplemented
91C3×C4×C3⋊D3C2313yescomplemented
92C3×#634C2313yescomplemented
93C32×#67C2316yescomplemented
94C32×D12C2313yescomplemented
95C32×D12C2316yescomplemented
96C32×C4×D3C2316yescomplemented
97C32×Dic6C2311yescharacteristic, complemented
98#6293C2312yescomplemented
99#6292C2316yescomplemented
100#6291C23112yescomplemented
101#6291C2316yescomplemented
102#6290C2316yescomplemented
103#6289C2316yescomplemented
104Dic3×C3⋊D3C2312yes—
105D3×C3⋊Dic3C2316yescomplemented
106D3×H(5,𝔽2)—94no—
107C2×#1009—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—312no—
118C2×#638—36no—
119#3832—32no—
120#3832—38no—
121#3832—33no—
122#3832—68no—
123#3832C2×D311yescharacteristic, complemented
124Q8×C3⋊D3—31no—
125Q8×C3⋊D3C2×D311yescharacteristic, complemented
126#3830—36no—
127#3830—33no—
128#3830—36no—
129#3830C2×D313yescomplemented
130D4×C3⋊D3—36no—
131D4×C3⋊D3—36no—
132D4×C3⋊D3—324no—
133D4×C3⋊D3—312no—
134D4×C3⋊D3—36no—
135D4×C3⋊D3—36no—
136D4×C3⋊D3—33no—
137D4×C3⋊D3—36no—
138D4×C3⋊D3—36no—
139D4×C3⋊D3—624no—
140D4×C3⋊D3C2×D313yescomplemented
141#3828—33no—
142#3828—312no—
143#3828—36no—
144#3828—36no—
145#3828—612no—
146#3828C2×D313yescomplemented
147C2×C4⋊(C3⋊D3)—33no—
148C2×C4⋊(C3⋊D3)—312no—
149C2×C4⋊(C3⋊D3)—36no—
150C2×C4⋊(C3⋊D3)—612no—
151C2×C4×C3⋊D3—36no—
152C2×C4×C3⋊D3C2×D313yescomplemented
153C3×#239—34no—
154C3×#239C2×D318yescomplemented
155C3×D3×Q8—34no—
156C3×#237—312no—
157C3×D3×D4—312no—
158C3×D3×D4C2×D3124yescomplemented
159C3×#235—312no—
160C3×#235C2×D3112yescomplemented
161C2×C3×D12C2×D3112yescomplemented
162C2×C3×C4×D3—312no—
163#3811—348no—
164D3×#67—348no—
165D3×#67—324no—
166C2×#626—324no—
167#3804—324no—
168#3802—324no—
169D3×D12—312no—
170D3×D12—324no—
171D3×D12—324no—
172D3×D12—324no—
173D3×D12—324no—
174C4×D32—324no—
175#3799—324no—
176#3799—312no—
177#3798—324no—
178#3796—324no—
179#3795—312no—
180D3×Dic6—34no—
181C22×C33C2413yes—
182C2×C3⋊(C3⋊D3)—46no—
183C2×C3⋊(C3⋊D3)C2416yes—
184C2×C3×C3⋊D3—26no—
185C2×C3×C3⋊D3C2413yes—
186C2×C3×C3⋊D3C2411yescharacteristic
187C2×C32×D3—46no—
188C2×C32×D3C2416yes—
189D3×C3⋊D3—212no—
190D3×C3⋊D3—412no—
191C33×C4C2411yescharacteristic
192C33×C4C2413yes—
193C3⋊(C3⋊Dic3)C2412yes—
194C3×C3⋊Dic3C2413yes—
195C3×C3⋊Dic3C2411yescharacteristic
196C32×Dic3C2412yes—
197C3×H(5,𝔽2)—34no—
198C2×C3×#41—91no—
199#1009—912no—
200#1009—98no—
201#1009—94no—
202#1009—91no—
203#1009—92no—
204#1009—96no—
205#1009—93no—
206#1009—93no—
207#1009—184no—
208#1009C3⋊D311yescharacteristic, direct product factor
209D3×#41—34no—
210D3×#41—912no—
211D3×#41—98no—
212C2×#239—92no—
213#1004—912no—
214#1004—924no—
215C2×D3×D4—912no—
216C2×D3×D4—924no—
217C2×D3×D4—96no—
218C2×#235—93no—
219C22×D12—93no—
220C23×C32—36no—
221C22×C3⋊D3—36no—
222C22×C3⋊D3—36no—
223C22×C3⋊D3—312no—
224C22×C3⋊D3—324no—
225C22×C3⋊D3—624no—
226C22×C3⋊D3—1212no—
227C22×C3⋊D3C22×D313yes—
228C22×C3×D3—312no—
229C22×C3×D3C22×D3124yescomplemented
230C2×D32—324no—
231C2×D32—348no—
232C2×D32—1248no—
233C32×Q8—24no—
234C32×Q8—31no—
235C32×Q8C22×D314yescomplemented
236C32×Q8C22×D311yescharacteristic, complemented
237C32×D4—212no—
238C32×D4—36no—
239C32×D4—33no—
240C32×D4—36no—
241C32×D4C22×D3112yescomplemented
242C32×D4C22×D313yescomplemented
243C2×C32×C4—212no—
244C2×C32×C4—36no—
245C2×C32×C4C22×D3112yescomplemented
246C2×C32×C4C22×D313yescomplemented
247#638—36no—
248#638—36no—
249#638—36no—
250#638—312no—
251#638—324no—
252#638—624no—
253#638C22×D316yescomplemented
254C2×C3⋊Dic3—36no—
255C2×C3⋊Dic3C22×D313yescomplemented
256C4⋊(C3⋊D3)—36no—
257C4⋊(C3⋊D3)—33no—
258C4⋊(C3⋊D3)—36no—
259C4⋊(C3⋊D3)—312no—
260C4⋊(C3⋊D3)—324no—
261C4⋊(C3⋊D3)—612no—
262C4⋊(C3⋊D3)—624no—
263C4⋊(C3⋊D3)C22×D313yescomplemented
264C4×C3⋊D3—32no—
265C4×C3⋊D3—36no—
266C4×C3⋊D3—36no—
267C4×C3⋊D3—324no—
268C4×C3⋊D3—624no—
269C4×C3⋊D3C22×D313yes—
270C4×C3⋊D3C22×D311yescharacteristic
271C4×C3⋊D3C22×D313yescomplemented
272C4×C3⋊D3C22×D313yescomplemented
273#634—31no—
274#634—32no—
275#634—34no—
276#634—64no—
277#634C22×D313yescomplemented
278C3×#67—324no—
279C3×#67C22×D3124yescomplemented
280C2×C3×Dic3—312no—
281C3×D12—312no—
282C3×D12C22×D3112yescomplemented
283C3×D12C22×D3124yescomplemented
284C3×C4×D3—34no—
285C3×C4×D3—312no—
286C3×C4×D3—312no—
287C3×C4×D3—312no—
288C3×C4×D3C22×D3124yescomplemented
289C3×Dic6—312no—
290C3×Dic6C22×D314yescomplemented
291#627—38no—
292#626—348no—
293#626—324no—
294#626—324no—
295#625—324no—
296#624—324no—
297D3×Dic3—324no—
298D3×Dic3—38no—
299C2×H(5,𝔽2)—271noSylow
300C2×C33—23no—
301C2×C33C2511yescharacteristic
302C3⋊(C3⋊D3)—26no—
303C3×C3⋊D3—23no—
304C3×C3⋊D3H(5,𝔽2)12yescomplemented
305C32×D3—26no—
306C23×D3—924no—
307C23×D3—96no—
308C3×#41—24no—
309C3×#41—38no—
310C3×#41—312no—
311C3×#41—91no—
312C3×#41—93no—
313C3×#41—93no—
314C3×#41D3214yescomplemented
315C3×#41C2×C3⋊D311yescharacteristic, complemented
316C2×C3×Q8—91no—
317C2×C3×D4—324no—
318C2×C3×D4—312no—
319C2×C3×D4—93no—
320C22×C3×C4—93no—
321C2×#67—924no—
322C2×#67—948no—
323C2×#67—96no—
324#239—34no—
325#239—912no—
326#239—98no—
327#239—92no—
328#239—96no—
329#239—96no—
330#239—188no—
331#239C2×C3⋊D312yescomplemented
332D3×Q8—34no—
333D3×Q8—94no—
334#237—312no—
335#237—924no—
336#237—912no—
337#237—924no—
338D3×D4—312no—
339D3×D4—912no—
340D3×D4—924no—
341D3×D4—924no—
342D3×D4—924no—
343D3×D4—924no—
344D3×D4—948no—
345D3×D4—924no—
346D3×D4—912no—
347D3×D4—924no—
348D3×D4—96no—
349D3×D4—912no—
350D3×D4—96no—
351D3×D4—96no—
352D3×D4—1824no—
353D3×D4C2×C3⋊D316yescomplemented
354#235—312no—
355#235—924no—
356#235—924no—
357#235—912no—
358#235—93no—
359#235—96no—
360#235—93no—
361#235—96no—
362#235—93no—
363#235—1812no—
364#235C2×C3⋊D313yescomplemented
365C2×D12—924no—
366C2×D12—96no—
367C2×D12—912no—
368C2×D12—93no—
369C2×D12—93no—
370C2×D12—96no—
371C2×D12—96no—
372C2×D12—96no—
373C2×D12—1812no—
374C2×D12C2×C3⋊D313yescomplemented
375C2×C4×D3—312no—
376C2×C4×D3—924no—
377C2×C4×D3—96no—
378C2×Dic6—91no—
379C22×C32—212no—
380C22×C32—36no—
381C22×C32—126no—
382C22×C32C23×D3112yes—
383C22×C32C23×D313yes—
384C2×C3⋊D3—26no—
385C2×C3⋊D3—36no—
386C2×C3⋊D3—324no—
387C2×C3⋊D3—624no—
388C2×C3⋊D3—612no—
389C2×C3⋊D3—1212no—
390C2×C3⋊D3—126no—
391C2×C3⋊D3—1224no—
392C2×C3⋊D3—2424no—
393C2×C3⋊D3C23×D313yes—
394C2×C3⋊D3C23×D311yescharacteristic
395C2×C3×D3—34no—
396C2×C3×D3—312no—
397C2×C3×D3—424no—
398C2×C3×D3—624no—
399C2×C3×D3C23×D3124yes—
400D32—648no—
401D32—1248no—
402C32×C4—24no—
403C32×C4—212no—
404C32×C4—32no—
405C32×C4C23×D3112yes—
406C32×C4C23×D314yes—
407C32×C4C23×D311yescharacteristic
408C32×C4C23×D313yes—
409C3⋊Dic3—32no—
410C3⋊Dic3—38no—
411C3⋊Dic3—68no—
412C3⋊Dic3C23×D311yescharacteristic
413C3⋊Dic3C23×D313yes—
414C3×Dic3—312no—
415C3×Dic3—34no—
416C3×Dic3C23×D318yes—
417H(5,𝔽2)—31no—
418H(5,𝔽2)—276no—
419H(5,𝔽2)—273no—
420H(5,𝔽2)—272no—
421H(5,𝔽2)—273no—
422H(5,𝔽2)—271no—
423C2×#41—91no—
424C2×#41—273no—
425C2×#41—272no—
426C22×D4—273no—
427C22×D4—276no—
428C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
429C23×C3—324no—
430C23×C3—93no—
431C22×D3—312no—
432C22×D3—924no—
433C22×D3—948no—
434C22×D3—924no—
435C22×D3—96no—
436C22×D3—96no—
437C22×D3—912no—
438C22×D3—1824no—
439C22×D3—3612no—
440C22×D3—3648no—
441C22×D3C22×C3⋊D316yescomplemented
442C3×Q8—24no—
443C3×Q8—34no—
444C3×Q8—93no—
445C3×Q8C2×D3214yescomplemented
446C3×Q8C22×C3⋊D311yescharacteristic, complemented
447C3×D4—212no—
448C3×D4—324no—
449C3×D4—324no—
450C3×D4—312no—
451C3×D4—96no—
452C3×D4—93no—
453C3×D4C2×D32112yescomplemented
454C3×D4C22×C3⋊D313yescomplemented
455C2×C3×C4—212no—
456C2×C3×C4—324no—
457C2×C3×C4—93no—
458C2×C3×C4—91no—
459C2×C3×C4—93no—
460C2×C3×C4—93no—
461C2×C3×C4—93no—
462C2×C3×C4C2×D32112yescomplemented
463C2×C3×C4C22×C3⋊D313yescomplemented
464#67—324no—
465#67—948no—
466#67—924no—
467#67—924no—
468#67—924no—
469#67—96no—
470#67—96no—
471#67—96no—
472#67—1824no—
473#67C22×C3⋊D316yescomplemented
474C2×Dic3—312no—
475C2×Dic3—924no—
476C2×Dic3—92no—
477D12—312no—
478D12—924no—
479D12—96no—
480D12—912no—
481D12—924no—
482D12—912no—
483D12—93no—
484D12—96no—
485D12—1812no—
486D12—1824no—
487D12C22×C3⋊D313yescomplemented
488D12C22×C3⋊D316yescomplemented
489C4×D3—34no—
490C4×D3—312no—
491C4×D3—312no—
492C4×D3—312no—
493C4×D3—924no—
494C4×D3—98no—
495C4×D3—96no—
496C4×D3—924no—
497C4×D3—96no—
498C4×D3—96no—
499C4×D3—1824no—
500C4×D3C22×C3⋊D316yescomplemented
501Dic6—312no—
502Dic6—98no—
503Dic6—94no—
504Dic6—91no—
505Dic6—92no—
506Dic6—184no—
507Dic6C22×C3⋊D311yescharacteristic, complemented
508C2×C32—23no—
509C2×C32—24no—
510C2×C32—212no—
511C2×C32—412no—
512C2×C32—66no—
513C2×C32C24×D314yes—
514C2×C32C24×D311yescharacteristic
515C3⋊D3—23no—
516C3⋊D3—66no—
517C3⋊D3—624no—
518C3⋊D3—1224no—
519C3⋊D3#100912yesdirect product factor
520C3×D3—224no—
521C3×D3—38no—
522C3×D3—612no—
523C24—276no—
524#41—32no—
525#41—33no—
526#41—91no—
527#41—93no—
528#41—93no—
529#41—276no—
530#41—276no—
531#41—276no—
532#41—273no—
533#41—273no—
534#41—276no—
535#41—272no—
536#41—273no—
537#41D3×C3⋊D311yescharacteristic, complemented
538C2×Q8—91no—
539C2×Q8—271no—
540C2×D4—36no—
541C2×D4—33no—
542C2×D4—93no—
543C2×D4—276no—
544C2×D4—273no—
545C2×D4—276no—
546C2×D4—276no—
547C2×D4—276no—
548C2×D4—276no—
549C2×D4—2712no—
550C2×D4—276no—
551C2×D4—276no—
552C2×D4—2712no—
553C2×D4—276no—
554C2×D4—273no—
555C22×C4—93no—
556C22×C4—276no—
557C22×C3—212no—
558C22×C3—324no—
559C22×C3—91no—
560C22×C3—93no—
561C22×C3—1224no—
562C22×C3—186no—
563C22×C3C22×D32112yes—
564C22×C3C23×C3⋊D313yes—
565C2×D3—34no—
566C2×D3—312no—
567C2×D3—46no—
568C2×D3—624no—
569C2×D3—924no—
570C2×D3—96no—
571C2×D3—1824no—
572C2×D3—1812no—
573C2×D3—1848no—
574C2×D3—3612no—
575C2×D3—3648no—
576C2×D3—366no—
577C2×D3—3624no—
578C2×D3—7224no—
579C2×D3C23×C3⋊D316yes—
580C3×C4—24no—
581C3×C4—212no—
582C3×C4—38no—
583C3×C4—91no—
584C3×C4—93no—
585C3×C4C22×D32112yes—
586C3×C4C22×D3214yes—
587C3×C4C23×C3⋊D311yescharacteristic
588C3×C4C23×C3⋊D313yes—
589Dic3—312no—
590Dic3—34no—
591Dic3—98no—
592Dic3—92no—
593Dic3—188no—
594Dic3C23×C3⋊D312yes—
595C32—24no—
596C32C2×#100911yescharacteristic, complemented
597C32D3×H(5,𝔽2)14yescomplemented
598C23—36no—
599C23—93no—
600C23—276no—
601C23—2712no—
602C23—276no—
603C23—10812no—
604Q8—31no—
605Q8—93no—
606Q8—272no—
607Q8—271no—
608Q8C2×D3×C3⋊D311yescharacteristic, complemented
609D4—36no—
610D4—36no—
611D4—33no—
612D4—96no—
613D4—93no—
614D4—276no—
615D4—276no—
616D4—2712no—
617D4—276no—
618D4—276no—
619D4—276no—
620D4—273no—
621D4C2×D3×C3⋊D313yescomplemented
622C2×C4—36no—
623C2×C4—93no—
624C2×C4—91no—
625C2×C4—93no—
626C2×C4—93no—
627C2×C4—93no—
628C2×C4—276no—
629C2×C4—272no—
630C2×C4—276no—
631C2×C4—276no—
632C2×C4C2×D3×C3⋊D313yescomplemented
633C2×C3—212no—
634C2×C3—23no—
635C2×C3—24no—
636C2×C3—412no—
637C2×C3—624no—
638C2×C3—92no—
639C2×C3—183no—
640C2×C3C23×D3214yes—
641C2×C3C24×C3⋊D311yescharacteristic
642D3—26no—
643D3—38no—
644D3—612no—
645D3—1824no—
646D3—186no—
647D3—3624no—
648C22—36no—
649C22—91no—
650C22—93no—
651C22—126no—
652C22—186no—
653C22—276no—
654C22—5412no—
655C22—1086no—
656C22—10812no—
657C22C22×D3×C3⋊D313yes—
658C4—32no—
659C4—91no—
660C4—93no—
661C4—272no—
662C4C22×D3×C3⋊D313yes—
663C4C22×D3×C3⋊D311yescharacteristic
664C3—24no—
665C3D3×#100914yescomplemented
666C3C3⋊D3×H(5,𝔽2)11yescharacteristic, complemented
667C2—23no—
668C2—66no—
669C2—92no—
670C2—183no—
671C2—546no—
672C2C23×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. #11724684C2semidirect
2. C3×#41×C3⋊D3C2semidirect
3. C32×#1009C2semidirect
4. #11724597C2semidirect
5. C3⋊D3×#239C2semidirect
6. #11724588C2semidirect
7. D3×D4×C3⋊D3C2semidirect
8. #11724581C2semidirect
9. #11724579C2semidirect
10. C3⋊D3×#235C2semidirect
11. C2×C3⋊D3×D12C2semidirect
14. C22×D3×C3⋊D3C22semidirect
15. C33×#41C22semidirect
16. #89080C22semidirect
17. D4×C3⋊(C3⋊D3)C22semidirect
18. #89076C22semidirect
19. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
20. C3×#3832C22semidirect
21. C3×Q8×C3⋊D3C22semidirect
22. C3×#3830C22semidirect
23. C3×D4×C3⋊D3C22semidirect
24. C3×#3828C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
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×#6291C22semidirect
34. #89028C22semidirect
35. #89026C22semidirect
36. C3⋊D3×D12C22semidirect
37. C3⋊D3×D12C22semidirect
38. C3⋊D3×D12C22semidirect
39. C3⋊D3×D12C22semidirect
40. D3×C4⋊(C3⋊D3)C22semidirect
41. C4×D3×C3⋊D3C22semidirect
42. #89022C22semidirect
43. #89020C22semidirect
44. #89018C22semidirect
45. C3⋊D3×Dic6C22semidirect
46. #89015C22semidirect
47. #89014C22semidirect
56. #41×C3⋊D3D3semidirect
61. C3×#1009D3semidirect
71. C22×C3⋊(C3⋊D3)C23semidirect
73. C22×C32×D3C23semidirect
76. C2×D3×C3⋊D3C23semidirect
77. C33×Q8C23semidirect
78. C33×D4C23semidirect
79. C2×C33×C4C23semidirect
80. #6312C23semidirect
81. C4⋊(C3⋊(C3⋊D3))C23semidirect
82. C4⋊(C3⋊(C3⋊D3))C23semidirect
83. C4×C3⋊(C3⋊D3)C23semidirect
84. #6308C23semidirect
85. C3×#638C23semidirect
86. C2×C3×C3⋊Dic3C23semidirect
87. C3×C4⋊(C3⋊D3)C23semidirect
90. C3×C4×C3⋊D3C23semidirect
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. #6291C23semidirect
102. #6290C23semidirect
103. #6289C23semidirect
105. D3×C3⋊Dic3C23semidirect
113. C32×#41C2×D3semidirect
114. C32×#41C2×D3semidirect
123. #3832C2×D3semidirect
125. Q8×C3⋊D3C2×D3semidirect
129. #3830C2×D3semidirect
140. D4×C3⋊D3C2×D3semidirect
146. #3828C2×D3semidirect
152. C2×C4×C3⋊D3C2×D3semidirect
154. C3×#239C2×D3semidirect
158. C3×D3×D4C2×D3semidirect
160. C3×#235C2×D3semidirect
161. C2×C3×D12C2×D3semidirect
208. #1009C3⋊D3direct (N × H)
229. C22×C3×D3C22×D3semidirect
235. C32×Q8C22×D3semidirect
236. C32×Q8C22×D3semidirect
241. C32×D4C22×D3semidirect
242. C32×D4C22×D3semidirect
245. C2×C32×C4C22×D3semidirect
246. C2×C32×C4C22×D3semidirect
253. #638C22×D3semidirect
255. C2×C3⋊Dic3C22×D3semidirect
263. C4⋊(C3⋊D3)C22×D3semidirect
271. C4×C3⋊D3C22×D3semidirect
272. C4×C3⋊D3C22×D3semidirect
277. #634C22×D3semidirect
279. C3×#67C22×D3semidirect
282. C3×D12C22×D3semidirect
283. C3×D12C22×D3semidirect
288. C3×C4×D3C22×D3semidirect
290. C3×Dic6C22×D3semidirect
304. C3×C3⋊D3H(5,𝔽2)semidirect
314. C3×#41D32semidirect
315. C3×#41C2×C3⋊D3semidirect
331. #239C2×C3⋊D3semidirect
353. D3×D4C2×C3⋊D3semidirect
364. #235C2×C3⋊D3semidirect
374. C2×D12C2×C3⋊D3semidirect
428. C33C2×H(5,𝔽2)semidirect
441. C22×D3C22×C3⋊D3semidirect
445. C3×Q8C2×D32semidirect
446. C3×Q8C22×C3⋊D3semidirect
453. C3×D4C2×D32semidirect
454. C3×D4C22×C3⋊D3semidirect
462. C2×C3×C4C2×D32semidirect
463. C2×C3×C4C22×C3⋊D3semidirect
473. #67C22×C3⋊D3semidirect
487. D12C22×C3⋊D3semidirect
488. D12C22×C3⋊D3semidirect
500. C4×D3C22×C3⋊D3semidirect
507. Dic6C22×C3⋊D3semidirect
519. C3⋊D3#1009direct (N × H)
537. #41D3×C3⋊D3semidirect
596. C32C2×#1009semidirect
597. C32D3×H(5,𝔽2)semidirect
608. Q8C2×D3×C3⋊D3semidirect
621. D4C2×D3×C3⋊D3semidirect
632. C2×C4C2×D3×C3⋊D3semidirect
665. C3D3×#1009semidirect
666. 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
#117246842
C3×#41×C3⋊D32
C32×#10092
#117245972
C3⋊D3×#2392
#117245882
D3×D4×C3⋊D32
#117245812
#117245792
C3⋊D3×#2352
C2×C3⋊D3×D122
C3⋊D3×H(5,𝔽2)3
D3×#10093