Finite Group Databasebeta

← D3×#5132 #11857640

Subgroups — D3×#5132 #11857640

Order 1152.

1587 conjugacy classes of subgroups.

The subgroup lattice has 1113 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592831C211yesmaximal, characteristic, complemented
5C3×#5132C211yesmaximal, characteristic, complemented
6#10591078C211yesmaximal, characteristic, complemented
7#10591076C211yesmaximal, characteristic, complemented
8#10591007C212yesmaximal, complemented
9#10591006C212yesmaximal, complemented
10D3×#824C212yesmaximal, complemented
11D3×#823C212yesmaximal, complemented
12C2×#5132—31nomaximal
13D3×#413—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C2×D3×#67C412yes—
18C2×#3804C412yes—
19D3×#235—21no—
20D3×#235—21no—
21D3×#235—21no—
22D3×#235—21no—
23D3×#235—21no—
24D3×#235—21no—
25D3×#235—21no—
26D3×#235—21no—
27C2×D3×D12C2211yescharacteristic
28C2×C4×D32C412yes—
29C2×#3799C2211yescharacteristic
30C2×#3798C412yes—
31C2×#3795C2211yescharacteristic
32C2×D3×Dic6C2211yescharacteristic
33C2×C32×M16C2211yescharacteristic, complemented
34C2×#3748C2211yescharacteristic, complemented
35C2×C3×#208C2211yescharacteristic, complemented
36C2×C3×#208C2211yescharacteristic, complemented
37C3×D3×M16—21no—
38C3×D3×M16—21no—
39C3×D3×M16C2212yes—
40C3×D3×M16C2212yescomplemented
41C2×C3×ΓL(1,𝔽25)—21no—
42C2×C3×D3×C8—21no—
43C2×#3711—21no—
44D3×#208—21no—
45D3×#208—21no—
46D3×#208C2212yes—
47D3×#208C2212yescomplemented
48C2×D3×C3⋊C8—21no—
49#63651C2212yescomplemented
50#63650C2212yescomplemented
51C3×#824C2212yescomplemented
52C3×#823C2212yescomplemented
53#63561C2212yescomplemented
54#63560C2212yescomplemented
55#63559C2212yescomplemented
56#63558C2212yescomplemented
57C2×D3×#41—31no—
58C22×#235—31no—
59C22×C3×M16—31no—
60C22×#208—31no—
61C2×D3×M16—31no—
62C2×D3×M16D311yescharacteristic, complemented
63C3×#413—31no—
64#5237—31no—
65C2×#824—32no—
66#5132—31no—
67#5132—31no—
68#5132—31no—
69#5132—31no—
70#5132—31no—
71#5132—32no—
72#5132—32no—
73#5132—61no—
74#5132D311yescharacteristic, direct product factor
75C2×#823—32no—
76#4751—32no—
77D3×#101—32no—
78#4745—32no—
79D3×#100—32no—
80C23×C3×D3C2×C411yescharacteristic
81C22×D32C2×C412yes—
82C22×C32×C4C2311yescharacteristic
83C2×#638C2×C412yes—
84#3828—21no—
85#3828—21no—
86#3828—21no—
87#3828—21no—
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3C2×C412yes—
90C2×#634C2311yescharacteristic
91C2×C3×#67C2×C412yes—
92C22×C3×Dic3C2×C411yescharacteristic
93C3×#235—21no—
94C3×#235—21no—
95C3×#235—21no—
96C3×#235—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2×C412yes—
99C2×C3×C4×D3C2×C411yescharacteristic
100C2×C3×C4×D3C2×C411yescharacteristic
101C2×C3×C4×D3D411yescharacteristic
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112D3×#67—22no—
113D3×#67—22no—
114D3×#67—22no—
115D3×#67—22no—
116C2×#627C2×C412yes—
117C2×#626C2×C412yes—
118C2×#626C2×C412yes—
119C2×#625C2×C412yes—
120C2×#624C2×C412yes—
121#3804—22no—
122#3804—22no—
123#3804—22no—
124#3804—22no—
125C2×D3×Dic3C2×C412yes—
126C2×D3×Dic3C2×C412yes—
127D3×D12—21no—
128D3×D12—21no—
129D3×D12—21no—
130D3×D12—21no—
131C4×D32—22no—
132C4×D32—22no—
133C4×D32—22no—
134C4×D32—22no—
135#3799—21no—
136#3799—21no—
137#3799—21no—
138#3799—21no—
139#3798—22no—
140#3798—22no—
141#3798—22no—
142#3798—22no—
143#3795—21no—
144#3795—21no—
145#3795—21no—
146#3795—21no—
147D3×Dic6—21no—
148D3×Dic6—21no—
149D3×Dic6—21no—
150D3×Dic6—21no—
151C32×M16—21no—
152C32×M16C2312yes—
153C2×C32×C8—21no—
154#3748—21no—
155#3748C2312yes—
156C2×C3⋊(C3⋊C8)—21no—
157C3×#208—21no—
158C3×#208—21no—
159C3×#208C2312yes—
160C3×#208C2312yes—
161C2×C3×C3⋊C8—21no—
162C2×C3×C3⋊C8—21no—
163C3×ΓL(1,𝔽25)—22no—
164C3×ΓL(1,𝔽25)—22no—
165C3×D3×C8—22no—
166C3×D3×C8—22no—
167#3711—22no—
168#3711—22no—
169D3×C3⋊C8—22no—
170D3×C3⋊C8—22no—
171C2×#413—91noSylow
172C2×C3×#41—31no—
173C23×C3×C4—31no—
174C22×#67—32no—
175D3×#41—61no—
176D3×#41—61no—
177D3×#41—61no—
178D3×#41—61no—
179D3×#41—61no—
180D3×#41—61no—
181D3×#41—61no—
182D3×#41—61no—
183C2×#239—31no—
184C2×D3×Q8—31no—
185C2×#237—32no—
186C2×#237—31no—
187C2×D3×D4—32no—
188C2×D3×D4—31no—
189C2×#235—31no—
190C2×#235—31no—
191C2×#235—32no—
192C2×#235—31no—
193C2×#235—32no—
194C2×#235—32no—
195C2×#235—31no—
196C2×#235—61no—
197C2×#235—61no—
198C2×#235—61no—
199C2×#235—61no—
200C2×#235—61no—
201C2×#235—61no—
202C2×#235—61no—
203C2×#235—61no—
204C2×#235—61no—
205C2×#235C2×D311yescharacteristic
206C22×D12—31no—
207C22×C4×D3—32no—
208C22×C4×D3—32no—
209C22×C4×D3C2×D311yescharacteristic
210C22×Dic6—31no—
211C2×C3×M16—21no—
212C2×C3×M16—31no—
213C2×C3×M16—31no—
214C2×C3×M16—32no—
215C2×C3×M16—32no—
216C2×C3×M16—61no—
217C2×C3×M16—61no—
218C2×C3×M16—61no—
219C2×C3×M16C2×D311yescharacteristic, complemented
220C2×C3×M16C2×D311yescharacteristic, complemented
221C22×C3×C8—61no—
222C2×#208—31no—
223C2×#208—31no—
224C2×#208—32no—
225C2×#208—32no—
226C2×#208—61no—
227C2×#208—61no—
228C2×#208—61no—
229C2×#208—61no—
230C2×#208C2×D311yescharacteristic, complemented
231C2×#208C2×D311yescharacteristic, complemented
232C22×C3⋊C8—61no—
233D3×M16—21no—
234D3×M16—21no—
235D3×M16—32no—
236D3×M16—32no—
237D3×M16—61no—
238D3×M16—61no—
239D3×M16C2×D312yes—
240D3×M16C2×D312yescomplemented
241C2×ΓL(1,𝔽25)—21no—
242C2×ΓL(1,𝔽25)—61no—
243C2×D3×C8—21no—
244C2×D3×C8—61no—
245C3×#101—32no—
246C3×#100—32no—
247#836—32no—
248#833—32no—
249#824—32no—
250#824—32no—
251#824—32no—
252#824—32no—
253#824—32no—
254#824—62no—
255#824C2×D312yescomplemented
256#823—32no—
257#823—32no—
258#823—32no—
259#823—32no—
260#823—32no—
261#823—62no—
262#823C2×D312yescomplemented
263C23×C32C22×C411yescharacteristic
264C22×C3⋊D3C22×C412yes—
265C22×C3×D3—42no—
266C22×C3×D3C22⋊C411yescharacteristic
267C22×C3×D3C22⋊C411yescharacteristic
268C22×C3×D3C22⋊C411yescharacteristic
269C22×C3×D3C22⋊C411yescharacteristic
270C22×C3×D3C22×C411yescharacteristic
271C22×C3×D3C22×C412yes—
272C22×C3×D3C22×C411yescharacteristic
273C2×D32—22no—
274C2×D32—22no—
275C2×D32—44no—
276C2×C32×C4C22×C411yescharacteristic
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2×D411yescharacteristic
279C2×C32×C4C2×D411yescharacteristic
280C2×C32×C4C2×D411yescharacteristic
281C2×C32×C4C2411yescharacteristic
282#638—22no—
283#638—22no—
284C2×C3⋊Dic3C22×C412yes—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4×C3⋊D3—22no—
288C4×C3⋊D3—22no—
289#634—21no—
290#634—21no—
291C3×#67—22no—
292C3×#67—22no—
293C2×C3×Dic3C22⋊C411yescharacteristic
294C2×C3×Dic3C22⋊C411yescharacteristic
295C2×C3×Dic3C22⋊C411yescharacteristic
296C2×C3×Dic3C22⋊C411yescharacteristic
297C2×C3×Dic3C22×C412yes—
298C2×C3×Dic3C22×C411yescharacteristic
299C2×C3×Dic3C22×C411yescharacteristic
300C3×D12—21no—
301C3×D12—21no—
302C3×C4×D3—22no—
303C3×C4×D3—22no—
304C3×C4×D3C22⋊C411yescharacteristic
305C3×C4×D3C22⋊C411yescharacteristic
306C3×C4×D3C22⋊C411yescharacteristic
307C3×C4×D3C22⋊C411yescharacteristic
308C3×C4×D3C22⋊C411yescharacteristic
309C3×C4×D3C22⋊C411yescharacteristic
310C3×C4×D3C22⋊C411yescharacteristic
311C3×C4×D3C22⋊C411yescharacteristic
312C3×C4×D3C2×D411yescharacteristic
313C3×C4×D3C2×D411yescharacteristic
314C3×C4×D3C2×D411yescharacteristic
315C3×C4×D3C2×D411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×C4×D3C2×D411yescharacteristic
319C3×C4×D3C2×D411yescharacteristic
320C3×Dic6—21no—
321C3×Dic6—21no—
322#627—22no—
323#627—22no—
324#626—22no—
325#626—22no—
326#626—22no—
327#626—22no—
328#625—22no—
329#625—22no—
330#624—22no—
331#624—22no—
332D3×Dic3—22no—
333D3×Dic3—22no—
334D3×Dic3—22no—
335D3×Dic3—22no—
336C32×C8—22no—
337C3⋊(C3⋊C8)—22no—
338C3×C3⋊C8—22no—
339C3×C3⋊C8—22no—
340C22×#41—91no—
341C22×M16—31no—
342C22×M16—91no—
343#413—31no—
344#413—92no—
345#413—92no—
346#413—91no—
347#413—91no—
348#413—91no—
349C2×#101—92no—
350C2×#100—92no—
351C24×C3—31no—
352C23×D3—32no—
353C23×D3—32no—
354C23×D3C4×D311yescharacteristic
355C3×#41—61no—
356C3×#41—61no—
357C3×#41—61no—
358C3×#41—61no—
359C2×C3×Q8—31no—
360C2×C3×D4—32no—
361C2×C3×D4—31no—
362C22×C3×C4—21no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—32no—
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C2×#67—32no—
380C2×#67—32no—
381C2×#67—32no—
382C2×#67—32no—
383C2×#67—32no—
384C2×#67—32no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67C4×D312yes—
391C22×Dic3—32no—
392C22×Dic3—32no—
393C22×Dic3C4×D311yescharacteristic
394#239—61no—
395#239—61no—
396#239—61no—
397#239—61no—
398D3×Q8—61no—
399D3×Q8—61no—
400D3×Q8—61no—
401D3×Q8—61no—
402#237—62no—
403#237—62no—
404#237—62no—
405#237—62no—
406#237—61no—
407#237—61no—
408#237—61no—
409#237—61no—
410D3×D4—62no—
411D3×D4—62no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—61no—
415D3×D4—61no—
416D3×D4—61no—
417D3×D4—61no—
418#235—21no—
419#235—21no—
420#235—21no—
421#235—21no—
422#235—61no—
423#235—61no—
424#235—61no—
425#235—61no—
426#235—62no—
427#235—62no—
428#235—62no—
429#235—62no—
430#235—61no—
431#235—61no—
432#235—61no—
433#235—61no—
434#235—62no—
435#235—62no—
436#235—62no—
437#235—62no—
438#235—61no—
439#235—61no—
440#235—61no—
441#235—61no—
442#235—61no—
443#235—61no—
444#235—61no—
445#235—61no—
446#235—62no—
447#235—62no—
448#235—62no—
449#235—62no—
450#235—121no—
451#235—121no—
452#235—121no—
453#235—121no—
454C2×D12—32no—
455C2×D12—32no—
456C2×D12—31no—
457C2×D12—31no—
458C2×D12—61no—
459C2×D12—61no—
460C2×D12—61no—
461C2×D12—61no—
462C2×D12—61no—
463C2×D12C22×D311yescharacteristic
464C2×C4×D3—32no—
465C2×C4×D3—32no—
466C2×C4×D3—32no—
467C2×C4×D3—32no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—62no—
471C2×C4×D3—62no—
472C2×C4×D3—62no—
473C2×C4×D3—62no—
474C2×C4×D3—62no—
475C2×C4×D3—62no—
476C2×C4×D3—62no—
477C2×C4×D3—62no—
478C2×C4×D3—62no—
479C2×C4×D3C4×D312yes—
480C2×C4×D3C4×D311yescharacteristic
481C2×C4×D3C4×D311yescharacteristic
482C2×C4×D3D1211yescharacteristic
483C2×C4×D3D1211yescharacteristic
484C2×C4×D3D1211yescharacteristic
485C2×C4×D3D1211yescharacteristic
486C2×C4×D3#6711yescharacteristic
487C2×C4×D3#6711yescharacteristic
488C2×C4×D3#6711yescharacteristic
489C2×C4×D3#6711yescharacteristic
490C2×C4×D3C22×D311yescharacteristic
491C2×C4×D3C22×D311yescharacteristic
492C2×Dic6—31no—
493C2×Dic6—31no—
494C2×Dic6—32no—
495C2×Dic6—32no—
496C2×Dic6—61no—
497C2×Dic6—61no—
498C2×Dic6—61no—
499C2×Dic6—61no—
500C2×Dic6—61no—
501C2×Dic6C22×D311yescharacteristic
502C3×M16—21no—
503C3×M16—21no—
504C3×M16—22no—
505C3×M16—32no—
506C3×M16—32no—
507C3×M16—41no—
508C3×M16—62no—
509C3×M16—62no—
510C3×M16—61no—
511C3×M16—61no—
512C3×M16C22×D312yes—
513C3×M16C22×D312yes—
514C2×C3×C8—21no—
515C2×C3×C8—21no—
516C2×C3×C8—41no—
517C2×C3×C8—62no—
518C2×C3×C8—62no—
519C2×C3×C8—61no—
520C2×C3×C8—61no—
521#208—21no—
522#208—21no—
523#208—32no—
524#208—32no—
525#208—62no—
526#208—62no—
527#208—62no—
528#208—61no—
529#208—61no—
530#208—121no—
531#208C22×D312yes—
532#208C22×D312yes—
533C2×C3⋊C8—21no—
534C2×C3⋊C8—21no—
535C2×C3⋊C8—62no—
536C2×C3⋊C8—62no—
537C2×C3⋊C8—61no—
538C2×C3⋊C8—61no—
539C2×C3⋊C8—121no—
540ΓL(1,𝔽25)—22no—
541ΓL(1,𝔽25)—22no—
542ΓL(1,𝔽25)—62no—
543ΓL(1,𝔽25)—62no—
544D3×C8—22no—
545D3×C8—22no—
546D3×C8—62no—
547D3×C8—62no—
548C22×C32—41no—
549C22×C32C2×C22⋊C411yescharacteristic
550C22×C32C2×C22⋊C411yescharacteristic
551C22×C32C23×C411yescharacteristic
552C2×C3⋊D3—22no—
553C2×C3⋊D3—42no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—41no—
559C2×C3×D3—41no—
560C2×C3×D3—41no—
561C2×C3×D3—42no—
562C2×C3×D3C2×C22⋊C411yescharacteristic
563C2×C3×D3C2×C22⋊C411yescharacteristic
564C2×C3×D3C2×C22⋊C411yescharacteristic
565C2×C3×D3C2×C22⋊C411yescharacteristic
566D32—44no—
567D32—44no—
568C32×C4C2×C22⋊C411yescharacteristic
569C32×C4C2×C22⋊C411yescharacteristic
570C32×C4C22×D411yescharacteristic
571C32×C4C22×D411yescharacteristic
572C3⋊Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3C2×C22⋊C411yescharacteristic
575C3×Dic3C2×C22⋊C411yescharacteristic
576C3×Dic3C2×C22⋊C411yescharacteristic
577C3×Dic3C2×C22⋊C411yescharacteristic
578C2×#41—31no—
579C2×#41—92no—
580C2×#41—91no—
581C2×#41—92no—
582C2×#41—91no—
583C2×#41—91no—
584C2×#41—181no—
585C2×#41—181no—
586C2×#41—181no—
587C2×#41—181no—
588C2×#41—181no—
589C2×#41—181no—
590C2×#41—181no—
591C2×#41—181no—
592C22×Q8—91no—
593C22×D4—91no—
594C22×D4—92no—
595C23×C4—31no—
596C23×C4—92no—
597C2×M16—31no—
598C2×M16—31no—
599C2×M16—32no—
600C2×M16—32no—
601C2×M16—61no—
602C2×M16—61no—
603C2×M16—61no—
604C2×M16—92no—
605C2×M16—92no—
606C2×M16—91no—
607C2×M16—181no—
608C2×M16—181no—
609C2×M16—181no—
610C2×M16D3211yescharacteristic, complemented
611C22×C8—61no—
612C22×C8—181no—
613#101—32no—
614#101—92no—
615#101—92no—
616#101—92no—
617#100—32no—
618#100—92no—
619#100—92no—
620#100—92no—
621C23×C3—21no—
622C23×C3—31no—
623C23×C3—31no—
624C23×C3—31no—
625C23×C3—31no—
626C23×C3—31no—
627C23×C3—31no—
628C23×C3—32no—
629C23×C3—122no—
630C23×C3C2×C4×D311yescharacteristic
631C23×C3C2×C4×D311yescharacteristic
632C22×D3—32no—
633C22×D3—32no—
634C22×D3—42no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3(C2×D3)⋊C411yescharacteristic
643C22×D3(C2×D3)⋊C411yescharacteristic
644C22×D3(C2×D3)⋊C411yescharacteristic
645C22×D3(C2×D3)⋊C411yescharacteristic
646C22×D3C2×C4×D311yescharacteristic
647C22×D3C2×C4×D312yes—
648C22×D3C2×C4×D311yescharacteristic
649C3×Q8—61no—
650C3×Q8—61no—
651C3×D4—62no—
652C3×D4—62no—
653C3×D4—61no—
654C3×D4—61no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—32no—
684C2×C3×C4—62no—
685C2×C3×C4—62no—
686C2×C3×C4C2×C4×D311yescharacteristic
687C2×C3×C4C2×C4×D311yescharacteristic
688C2×C3×C4C2×D1211yescharacteristic
689C2×C3×C4C2×D1211yescharacteristic
690C2×C3×C4D3×D411yescharacteristic
691C2×C3×C4D3×D411yescharacteristic
692C2×C3×C4D3×D411yescharacteristic
693C2×C3×C4D3×D411yescharacteristic
694C2×C3×C4C2×#6711yescharacteristic
695C2×C3×C4C2×#6711yescharacteristic
696C2×C3×C4C23×D311yescharacteristic
697C2×C3×C4C23×D311yescharacteristic
698#67—22no—
699#67—22no—
700#67—62no—
701#67—62no—
702#67—62no—
703#67—62no—
704#67—62no—
705#67—62no—
706#67—62no—
707#67—62no—
708#67—62no—
709#67—62no—
710#67—62no—
711#67—62no—
712#67—122no—
713#67—122no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3(C2×D3)⋊C411yescharacteristic
722C2×Dic3(C2×D3)⋊C411yescharacteristic
723C2×Dic3(C2×D3)⋊C411yescharacteristic
724C2×Dic3(C2×D3)⋊C411yescharacteristic
725C2×Dic3C2×C4×D312yes—
726C2×Dic3C2×C4×D311yescharacteristic
727C2×Dic3C2×C4×D311yescharacteristic
728D12—21no—
729D12—21no—
730D12—62no—
731D12—62no—
732D12—62no—
733D12—62no—
734D12—61no—
735D12—61no—
736D12—61no—
737D12—61no—
738D12—121no—
739D12—121no—
740C4×D3—22no—
741C4×D3—22no—
742C4×D3—62no—
743C4×D3—62no—
744C4×D3—62no—
745C4×D3—62no—
746C4×D3—62no—
747C4×D3—62no—
748C4×D3—62no—
749C4×D3—62no—
750C4×D3—62no—
751C4×D3—62no—
752C4×D3—62no—
753C4×D3—62no—
754C4×D3—122no—
755C4×D3—122no—
756C4×D3(C2×D3)⋊C411yescharacteristic
757C4×D3(C2×D3)⋊C411yescharacteristic
758C4×D3(C2×D3)⋊C411yescharacteristic
759C4×D3(C2×D3)⋊C411yescharacteristic
760C4×D3(C2×D3)⋊C411yescharacteristic
761C4×D3(C2×D3)⋊C411yescharacteristic
762C4×D3(C2×D3)⋊C411yescharacteristic
763C4×D3(C2×D3)⋊C411yescharacteristic
764C4×D3C2×D1211yescharacteristic
765C4×D3C2×D1211yescharacteristic
766C4×D3C2×D1211yescharacteristic
767C4×D3C2×D1211yescharacteristic
768C4×D3C2×#6711yescharacteristic
769C4×D3C2×#6711yescharacteristic
770C4×D3C2×#6711yescharacteristic
771C4×D3C2×#6711yescharacteristic
772Dic6—21no—
773Dic6—21no—
774Dic6—62no—
775Dic6—62no—
776Dic6—61no—
777Dic6—61no—
778Dic6—61no—
779Dic6—61no—
780Dic6—62no—
781Dic6—62no—
782Dic6—121no—
783Dic6—121no—
784C3×C8—22no—
785C3×C8—22no—
786C3×C8—42no—
787C3×C8—62no—
788C3×C8—62no—
789C3⋊C8—22no—
790C3⋊C8—22no—
791C3⋊C8—62no—
792C3⋊C8—62no—
793C3⋊C8—122no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32C22×C22⋊C411yescharacteristic
798C3⋊D3—42no—
799C3×D3—21no—
800C3×D3—21no—
801C3×D3—21no—
802C3×D3—42no—
803C3×D3#41312yescomplemented
804C24—31no—
805C24—92no—
806#41—61no—
807#41—61no—
808#41—61no—
809#41—61no—
810#41—182no—
811#41—182no—
812#41—182no—
813#41—182no—
814#41—182no—
815#41—182no—
816#41—182no—
817#41—182no—
818#41—181no—
819#41—181no—
820#41—181no—
821#41—181no—
822#41—181no—
823#41—181no—
824#41—181no—
825#41—181no—
826#41—181no—
827#41—181no—
828#41—181no—
829#41—181no—
830C2×Q8—31no—
831C2×Q8—92no—
832C2×Q8—91no—
833C2×Q8—181no—
834C2×Q8—181no—
835C2×Q8—181no—
836C2×Q8—181no—
837C2×D4—32no—
838C2×D4—31no—
839C2×D4—92no—
840C2×D4—92no—
841C2×D4—92no—
842C2×D4—92no—
843C2×D4—91no—
844C2×D4—181no—
845C2×D4—181no—
846C2×D4—181no—
847C2×D4—181no—
848C2×D4—182no—
849C2×D4—182no—
850C2×D4—182no—
851C2×D4—182no—
852C22×C4—31no—
853C22×C4—31no—
854C22×C4—31no—
855C22×C4—31no—
856C22×C4—31no—
857C22×C4—31no—
858C22×C4—31no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—31no—
862C22×C4—31no—
863C22×C4—31no—
864C22×C4—31no—
865C22×C4—32no—
866C22×C4—92no—
867C22×C4—92no—
868C22×C4—92no—
869C22×C4—92no—
870C22×C4—182no—
871C22×C4—182no—
872C22×C4—182no—
873C22×C4—182no—
874C22×C4C2×D3211yescharacteristic
875M16—21no—
876M16—32no—
877M16—32no—
878M16—62no—
879M16—62no—
880M16—61no—
881M16—61no—
882M16—92no—
883M16—182no—
884M16—182no—
885M16—181no—
886M16C2×D3212yes—
887C2×C8—21no—
888C2×C8—62no—
889C2×C8—62no—
890C2×C8—61no—
891C2×C8—61no—
892C2×C8—182no—
893C2×C8—182no—
894C2×C8—181no—
895C22×C3—21no—
896C22×C3—21no—
897C22×C3—21no—
898C22×C3—31no—
899C22×C3—31no—
900C22×C3—31no—
901C22×C3—31no—
902C22×C3—41no—
903C22×C3—41no—
904C22×C3—62no—
905C22×C3—62no—
906C22×C3—62no—
907C22×C3—62no—
908C22×C3—81no—
909C22×C3—121no—
910C22×C3—121no—
911C22×C3—121no—
912C22×C3—122no—
913C22×C3D3×C22⋊C411yescharacteristic
914C22×C3D3×C22⋊C411yescharacteristic
915C22×C3C2×(C2×D3)⋊C411yescharacteristic
916C22×C3C2×(C2×D3)⋊C411yescharacteristic
917C22×C3C22×C4×D311yescharacteristic
918C22×C3C22×C4×D311yescharacteristic
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—41no—
924C2×D3—41no—
925C2×D3—41no—
926C2×D3—42no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—122no—
930C2×D3—124no—
931C2×D3—124no—
932C2×D3—124no—
933C2×D3—124no—
934C2×D3—122no—
935C2×D3—122no—
936C2×D3—242no—
937C2×D3C2×(C2×D3)⋊C411yescharacteristic
938C2×D3C2×(C2×D3)⋊C411yescharacteristic
939C2×D3C2×(C2×D3)⋊C411yescharacteristic
940C2×D3C2×(C2×D3)⋊C411yescharacteristic
941C3×C4—21no—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—31no—
946C3×C4—31no—
947C3×C4—31no—
948C3×C4—31no—
949C3×C4—62no—
950C3×C4D3×C22⋊C411yescharacteristic
951C3×C4D3×C22⋊C411yescharacteristic
952C3×C4C2×(C2×D3)⋊C411yescharacteristic
953C3×C4C2×(C2×D3)⋊C411yescharacteristic
954C3×C4C22×D1211yescharacteristic
955C3×C4C2×D3×D411yescharacteristic
956C3×C4C2×D3×D411yescharacteristic
957C3×C4C22×#6711yescharacteristic
958Dic3—22no—
959Dic3—62no—
960Dic3—62no—
961Dic3—122no—
962Dic3C2×(C2×D3)⋊C411yescharacteristic
963Dic3C2×(C2×D3)⋊C411yescharacteristic
964Dic3C2×(C2×D3)⋊C411yescharacteristic
965Dic3C2×(C2×D3)⋊C411yescharacteristic
966C32C2×#41311yescharacteristic, complemented, Sylow
967C23—31no—
968C23—31no—
969C23—31no—
970C23—31no—
971C23—31no—
972C23—31no—
973C23—32no—
974C23—92no—
975C23—122no—
976C23—182no—
977C23—182no—
978C23—364no—
979C23C4×D3211yescharacteristic
980Q8—61no—
981Q8—61no—
982Q8—182no—
983Q8—182no—
984Q8—181no—
985Q8—181no—
986D4—62no—
987D4—62no—
988D4—61no—
989D4—61no—
990D4—182no—
991D4—182no—
992D4—182no—
993D4—182no—
994D4—182no—
995D4—182no—
996D4—182no—
997D4—182no—
998D4—181no—
999D4—181no—
1000C2×C4—31no—
1001C2×C4—31no—
1002C2×C4—31no—
1003C2×C4—31no—
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—31no—
1007C2×C4—31no—
1008C2×C4—31no—
1009C2×C4—31no—
1010C2×C4—31no—
1011C2×C4—31no—
1012C2×C4—31no—
1013C2×C4—31no—
1014C2×C4—31no—
1015C2×C4—31no—
1016C2×C4—31no—
1017C2×C4—31no—
1018C2×C4—31no—
1019C2×C4—31no—
1020C2×C4—31no—
1021C2×C4—31no—
1022C2×C4—32no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—92no—
1026C2×C4—182no—
1027C2×C4—182no—
1028C2×C4—182no—
1029C2×C4—182no—
1030C2×C4—182no—
1031C2×C4—182no—
1032C2×C4—182no—
1033C2×C4—182no—
1034C2×C4C4×D3211yescharacteristic
1035C2×C4D3×D1211yescharacteristic
1036C2×C4D3×D1211yescharacteristic
1037C2×C4D3×#6711yescharacteristic
1038C2×C4D3×#6711yescharacteristic
1039C2×C4C22×D3211yescharacteristic
1040C8—22no—
1041C8—62no—
1042C8—62no—
1043C8—182no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—32no—
1052C2×C3—41no—
1053C2×C3—41no—
1054C2×C3—41no—
1055C2×C3—61no—
1056C2×C3—61no—
1057C2×C3—61no—
1058C2×C3—122no—
1059C2×C3C2×D3×C22⋊C411yescharacteristic
1060C2×C3C22×(C2×D3)⋊C411yescharacteristic
1061D3—21no—
1062D3—21no—
1063D3—21no—
1064D3—42no—
1065D3—122no—
1066D3—122no—
1067D3—242no—
1068D3#513212yesdirect product factor
1069C22—31no—
1070C22—31no—
1071C22—31no—
1072C22—31no—
1073C22—41no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—121no—
1079C22—121no—
1080C22—121no—
1081C22—122no—
1082C22—182no—
1083C22—362no—
1084C22—364no—
1085C22—364no—
1086C22D3×(C2×D3)⋊C411yescharacteristic
1087C22D3×(C2×D3)⋊C411yescharacteristic
1088C22C2×C4×D3211yescharacteristic
1089C4—31no—
1090C4—31no—
1091C4—31no—
1092C4—31no—
1093C4—62no—
1094C4—182no—
1095C4D3×(C2×D3)⋊C411yescharacteristic
1096C4D3×(C2×D3)⋊C411yescharacteristic
1097C4C2×D3×D1211yescharacteristic
1098C4C2×D3×#6711yescharacteristic
1099C3—21no—
1100C3D3×#41311yescharacteristic, complemented
1101C3C2×#513211yescharacteristic, complemented
1102C2—21no—
1103C2—21no—
1104C2—21no—
1105C2—32no—
1106C2—61no—
1107C2—61no—
1108C2—61no—
1109C2—122no—
1110C2—362no—
1111C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4D3×(C2×D3)⋊C4
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C22×C22⋊C4
prime radicalC2×D3×#235C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×M16C2semidirect
3. C2×D3×#208C2semidirect
4. #10592831C2semidirect
5. C3×#5132C2semidirect
6. #10591078C2semidirect
7. #10591076C2semidirect
8. #10591007C2semidirect
9. #10591006C2semidirect
10. D3×#824C2semidirect
11. D3×#823C2semidirect
33. C2×C32×M16C22semidirect
34. C2×#3748C22semidirect
35. C2×C3×#208C22semidirect
36. C2×C3×#208C22semidirect
40. C3×D3×M16C22semidirect
47. D3×#208C22semidirect
49. #63651C22semidirect
50. #63650C22semidirect
51. C3×#824C22semidirect
52. C3×#823C22semidirect
53. #63561C22semidirect
54. #63560C22semidirect
55. #63559C22semidirect
56. #63558C22semidirect
62. C2×D3×M16D3semidirect
74. #5132D3direct (N × H)
219. C2×C3×M16C2×D3semidirect
220. C2×C3×M16C2×D3semidirect
230. C2×#208C2×D3semidirect
231. C2×#208C2×D3semidirect
240. D3×M16C2×D3semidirect
255. #824C2×D3semidirect
262. #823C2×D3semidirect
610. C2×M16D32semidirect
803. C3×D3#413semidirect
966. C32C2×#413semidirect
1068. D3#5132direct (N × H)
1100. C3D3×#413semidirect
1101. C3C2×#5132semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×C3×D3×M162
C2×D3×#2082
#105928312
C3×#51322
#105910782
#105910762
#105910072
#105910062
D3×#8242
D3×#8232
C2×#51323
D3×#4133