Finite Group Databasebeta

← D3×#5522 #11899965

Subgroups — D3×#5522 #11899965

Order 1152.

3611 conjugacy classes of subgroups.

The subgroup lattice has 1049 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2#10595993C211yesmaximal, characteristic, complemented
3C3×#5522C211yesmaximal, characteristic, complemented
4C3×D3×#117C211yesmaximal, characteristic, complemented
5#10594958C211yesmaximal, characteristic, complemented
6#10594954C211yesmaximal, characteristic, complemented
7C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
8D3×#893C212yesmaximal, complemented
9#10594362C212yesmaximal, complemented
10#10594358C212yesmaximal, complemented
11D3×#887C212yesmaximal, complemented
12D3×#67⋊C4C214yesmaximal, complemented
13#10594048C214yesmaximal, complemented
14D3×#872C212yesmaximal, complemented
15C42×D32C212yesmaximal, complemented
16#10593966C212yesmaximal, complemented
17#10593965C212yesmaximal, complemented
18C4×D3×#41—31nomaximal
19C2×#5522—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×D3×#67C2212yes—
24C2×#3804C2212yes—
25C22×D3×Dic3C2212yes—
26D3×#235C4116yescomplemented
27C2×D3×D12C2211yescharacteristic
28C2×C4×D32C2214yes—
29C2×C4×D32C2212yes—
30C2×#3799C2211yescharacteristic
31C2×#3798C2212yes—
32C2×#3795C2211yescharacteristic
33C2×D3×Dic6C2211yescharacteristic
34C32×#117C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36#64102C2212yescomplemented
37#64096C2212yescomplemented
38#64090C2214yescomplemented
39#64081C2212yescomplemented
40C42×C3⋊D3C2212yescomplemented
41C3×#926C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2211yescharacteristic, complemented
43C3×#893C2212yescomplemented
44C3×#892C2212yescomplemented
45C3×D3×C4⋊C4C2212yes—
46C3×#887C2212yescomplemented
47C3×#67⋊C4C2214yescomplemented
48C3×D3×C22⋊C4C2212yes—
49C3×#877C2212yescomplemented
50C3×#872C2212yescomplemented
51C3×#872C2212yescomplemented
52C3×C42×D3C2212yes—
53C3×C42×D3C2212yescomplemented
54#67⋊Dic3C2214yescomplemented
55C2×Dic32C2212yescomplemented
56#63952C2214yescomplemented
57D3×(C2×D3)⋊C4C2214yes—
58#63904C2214yescomplemented
59#63902C2214yescomplemented
60#63898C2212yescomplemented
61#63894C2212yescomplemented
62C4×#624C2214yescomplemented
63C4×#624C2212yescomplemented
64#63881C2214yescomplemented
65#63881C2214yescomplemented
66#63880C2214yescomplemented
67#63879C2214yescomplemented
68#63877C2214yescomplemented
69D3×Dic3⋊C4C2214yes—
70C4×D3×Dic3C2212yes—
71C4×D3×Dic3C2214yes—
72C4×D3×Dic3C2211yescharacteristic
73C4×D3×Dic3C2211yescharacteristic
74C4×D3×Dic3C2214yescomplemented
75C4×D3×Dic3C2212yescomplemented
76C4×D3×Dic3C2211yescharacteristic, complemented
77C4×D3×Dic3C2211yescharacteristic, complemented
78C4×D3×Dic3C2212yescomplemented
79#63874C2212yescomplemented
80#63855C2212yescomplemented
81#63844C2212yescomplemented
82#63843C2212yescomplemented
83#63838C2214yescomplemented
84#63837C2214yescomplemented
85#63836C2214yescomplemented
86C2×D3×#41—31no—
87C22×#235—31no—
88C3×C4×#41—31no—
89C2×C3×#117—31no—
90Dic3×#41—31no—
91C22×C4×Dic3—31no—
92C4×#239—32no—
93C4×D3×Q8—32no—
94C4×D3×D4—32no—
95C4×D3×D4—34no—
96C4×#237—32no—
97C4×#237—34no—
98#5522—31no—
99#5522—31no—
100#5522—31no—
101#5522—31no—
102#5522—32no—
103#5522—32no—
104#5522—34no—
105#5522—32no—
106#5522—32no—
107#5522—32no—
108#5522—61no—
109#5522D311yescharacteristic, direct product factor
110D3×#117—32no—
111D3×#117D311yescharacteristic, complemented
112C2×#893—32no—
113C2×#887—32no—
114C2×#67⋊C4—34no—
115C4×#235—31no—
116C4×#235—32no—
117C2×#872—32no—
118C2×C42×D3—31no—
119C2×C42×D3—32no—
120C2×C42×D3—32no—
121C23×C3×D3C2311yescharacteristic
122C22×D32C2312yes—
123C22×C32×C4C2311yescharacteristic
124C2×#638C2312yes—
125C22×C3⋊Dic3C2312yes—
126#3828C2×C418yescomplemented
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2314yes—
129C2×C4×C3⋊D3C2312yes—
130C2×#634C2311yescharacteristic
131C2×C3×#67C2312yes—
132C22×C3×Dic3C2312yes—
133C22×C3×Dic3C2311yescharacteristic
134C3×#235C2×C418yescomplemented
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2×C418yescomplemented
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2314yes—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×C4×D3C2312yes—
144C2×C3×Dic6C2311yescharacteristic
145D3×#67C2×C4116yescomplemented
146C2×#627C2312yes—
147C2×#626C2312yes—
148C2×#626C2312yes—
149C2×#625C2312yes—
150C2×#624C2314yes—
151C2×#624C2312yes—
152#3804C2×C4116yescomplemented
153C2×D3×Dic3—28no—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2312yes—
156C2×D3×Dic3C2312yes—
157C2×D3×Dic3C2312yes—
158C2×D3×Dic3C2312yes—
159C2×D3×Dic3C2312yes—
160C2×D3×Dic3C2312yes—
161D3×D12C2×C418yescomplemented
162C4×D32—216no—
163C4×D32C2×C4116yescomplemented
164#3799C2×C418yescomplemented
165#3798C2×C4116yescomplemented
166#3795C2×C418yescomplemented
167D3×Dic6C2×C418yescomplemented
168C32×C4⋊C4C2312yes—
169C32×C22⋊C4C2312yes—
170C32×C42C2312yes—
171#3752C2314yes—
172#3750C2314yes—
173C4×C3⋊Dic3C2311yescharacteristic
174C4×C3⋊Dic3C2314yes—
175C4×C3⋊Dic3C2311yescharacteristic
176C4×C3⋊Dic3C2312yes—
177C3×#217C2312yes—
178C3×(C2×D3)⋊C4C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×C4⋊Dic3C2312yes—
181C3×Dic3⋊C4C2314yes—
182C3×Dic3⋊C4C2314yes—
183C3×C4×Dic3C2314yes—
184C3×C4×Dic3C2314yes—
185C3×C4×Dic3C2312yes—
186C3×C4×Dic3C2311yescharacteristic
187C3×C4×Dic3C2311yescharacteristic
188C3×C4×Dic3C2312yes—
189#3724C2314yes—
190Dic3⋊Dic3C2314yes—
191#3722C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193Dic32C2312yes—
194Dic32C2312yes—
195Dic32C2314yes—
196Dic32C2312yes—
197Dic32C2314yes—
198Dic32C2312yes—
199C2×C4×#41—91noSylow
200C2×C3×#41—31no—
201C23×C3×C4—31no—
202C22×#67—32no—
203C23×Dic3—32no—
204D3×#41—316no—
205C2×#239—31no—
206C2×D3×Q8—31no—
207C2×#237—32no—
208C2×#237—31no—
209C2×D3×D4—32no—
210C2×D3×D4—31no—
211C2×#235—31no—
212C2×#235—31no—
213C2×#235—32no—
214C2×#235—316no—
215C2×#235—31no—
216C2×#235—32no—
217C2×#235—32no—
218C2×#235—31no—
219C2×#235—61no—
220C2×#235C2×D311yescharacteristic
221C22×D12—31no—
222C22×C4×D3—32no—
223C22×C4×D3—32no—
224C22×C4×D3—32no—
225C22×C4×D3—34no—
226C22×C4×D3—34no—
227C22×C4×D3C2×D311yescharacteristic
228C22×Dic6—31no—
229C3×C4×Q8—32no—
230C3×C4×D4—32no—
231C3×C4×D4—34no—
232C3×#117—21no—
233C3×#117—31no—
234C3×#117—32no—
235C3×#117—32no—
236C3×#117—32no—
237C3×#117—32no—
238C3×#117C2×D311yescharacteristic, complemented
239C3×#117C2×D311yescharacteristic, complemented
240C2×C3×C4⋊C4—32no—
241C2×C3×C22⋊C4—32no—
242C2×C3×C42—31no—
243C2×C3×C42—32no—
244C2×C3×C42—32no—
245Q8×Dic3—32no—
246D4×Dic3—34no—
247D4×Dic3—32no—
248C4×#67—34no—
249C4×#67—34no—
250C4×#67—34no—
251C2×(C2×D3)⋊C4—34no—
252#926—32no—
253#926C2×D311yescharacteristic, complemented
254C2×Dic3⋊C4—34no—
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3—32no—
258C2×C4×Dic3—32no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3—34no—
261C2×C4×Dic3—32no—
262C2×C4×Dic3—34no—
263C2×C4×Dic3—31no—
264C2×C4×Dic3—32no—
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267C2×C4×Dic3—32no—
268C2×C4×Dic3—61no—
269C2×C4×Dic3C2×D311yescharacteristic, complemented
270#893—32no—
271#893—34no—
272#893—32no—
273#893—32no—
274#893—34no—
275#893—34no—
276#893—32no—
277#893—62no—
278#893C2×D312yescomplemented
279#892—34no—
280#892C2×D312yescomplemented
281D3×C4⋊C4—34no—
282D3×C4⋊C4C2×D312yes—
283#887—32no—
284#887—32no—
285#887—32no—
286#887—34no—
287#887—34no—
288#887—34no—
289#887—32no—
290#887—62no—
291#887C2×D312yescomplemented
292#67⋊C4—34no—
293#67⋊C4—34no—
294#67⋊C4—34no—
295#67⋊C4—34no—
296#67⋊C4—34no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—34no—
300#67⋊C4—34no—
301#67⋊C4—34no—
302#67⋊C4—64no—
303#67⋊C4C2×D314yescomplemented
304D3×C22⋊C4—34no—
305D3×C22⋊C4C2×D312yes—
306#877—34no—
307#877C2×D312yescomplemented
308C4×D12—34no—
309C4×D12—32no—
310#872—32no—
311#872—32no—
312#872—32no—
313#872—34no—
314#872—34no—
315#872—32no—
316#872—32no—
317#872—62no—
318#872C2×D312yescomplemented
319#872C2×D312yescomplemented
320C42×D3—31no—
321C42×D3—31no—
322C42×D3—31no—
323C42×D3—34no—
324C42×D3—32no—
325C42×D3—31no—
326C42×D3—32no—
327C42×D3—34no—
328C42×D3—32no—
329C42×D3—32no—
330C42×D3—32no—
331C42×D3—32no—
332C42×D3—34no—
333C42×D3—32no—
334C42×D3—34no—
335C42×D3—62no—
336C42×D3C2×D312yes—
337C42×D3C2×D312yescomplemented
338C4×Dic6—32no—
339C4×Dic6—34no—
340C23×C32C2411yescharacteristic
341C22×C3⋊D3C2412yes—
342C22×C3×D3—24no—
343C22×C3×D3C22×C414yes—
344C22×C3×D3C2412yes—
345C22×C3×D3C2411yescharacteristic
346C22×C3×D3C2411yescharacteristic
347C2×D32—28no—
348C2×D32C22×C418yes—
349C2×C32×C4C22×C414yescomplemented
350C2×C32×C4C2414yes—
351C2×C32×C4C2411yescharacteristic
352C2×C32×C4C2411yescharacteristic
353#638C22×C418yescomplemented
354C2×C3⋊Dic3—24no—
355C2×C3⋊Dic3C2412yes—
356C2×C3⋊Dic3C2412yes—
357C2×C3⋊Dic3C2412yes—
358C4⋊(C3⋊D3)C22×C414yescomplemented
359C4×C3⋊D3—28no—
360C4×C3⋊D3C22×C418yescomplemented
361#634C22×C414yescomplemented
362C3×#67C22×C418yescomplemented
363C2×C3×Dic3—24no—
364C2×C3×Dic3C22×C414yescomplemented
365C2×C3×Dic3C2414yes—
366C2×C3×Dic3C2412yes—
367C2×C3×Dic3C2411yescharacteristic
368C2×C3×Dic3C2411yescharacteristic
369C2×C3×Dic3C2412yes—
370C2×C3×Dic3C2412yes—
371C3×D12C22×C414yescomplemented
372C3×C4×D3—28no—
373C3×C4×D3—28no—
374C3×C4×D3C22×C414yes—
375C3×C4×D3C22×C414yes—
376C3×C4×D3C22×C414yescomplemented
377C3×C4×D3C22×C414yescomplemented
378C3×C4×D3C22×C418yescomplemented
379C3×Dic6C22×C414yescomplemented
380#627C22×C418yescomplemented
381#626C22×C418yescomplemented
382#626C22×C418yescomplemented
383#625C22×C418yescomplemented
384#624—28no—
385#624C22×C418yescomplemented
386D3×Dic3—24no—
387D3×Dic3—28no—
388D3×Dic3—24no—
389D3×Dic3—24no—
390D3×Dic3C22×C418yes—
391D3×Dic3C22×C418yescomplemented
392D3×Dic3#4118yescomplemented
393C22×#41—91no—
394C4×#41—31no—
395C4×#41—91no—
396C4×#41—92no—
397C4×#41—92no—
398C4×#41—94no—
399C4×#41—92no—
400C4×#41—92no—
401C4×#41—91no—
402C4×#41—91no—
403C2×C4×Q8—92no—
404C2×C4×D4—94no—
405C2×C4×D4—92no—
406C2×#117—31no—
407C2×#117—92no—
408C22×C42—92no—
409C22×C42—91no—
410C24×C3—31no—
411C23×D3—32no—
412C23×D3—32no—
413C23×D3C22×D311yescharacteristic
414C3×#41—38no—
415C2×C3×Q8—31no—
416C2×C3×D4—32no—
417C2×C3×D4—31no—
418C22×C3×C4—21no—
419C22×C3×C4—31no—
420C22×C3×C4—38no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—32no—
426C22×C3×C4—32no—
427C22×C3×C4—34no—
428C22×C3×C4—34no—
429C22×C3×C4C22×D311yescharacteristic
430C22×C3×C4C22×D311yescharacteristic
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—316no—
436C2×#67—32no—
437C2×#67—32no—
438C2×#67—62no—
439C2×#67C22×D312yes—
440C22×Dic3—32no—
441C22×Dic3—32no—
442C22×Dic3—32no—
443C22×Dic3—32no—
444C22×Dic3—32no—
445C22×Dic3—32no—
446C22×Dic3—32no—
447C22×Dic3—34no—
448C22×Dic3—32no—
449C22×Dic3—62no—
450C22×Dic3—68no—
451C22×Dic3C22×D312yes—
452C22×Dic3C22×D311yescharacteristic
453#239—38no—
454D3×Q8—38no—
455#237—316no—
456#237—38no—
457D3×D4—316no—
458D3×D4—38no—
459#235—38no—
460#235—38no—
461#235—316no—
462#235—38no—
463#235—316no—
464#235—316no—
465#235—38no—
466#235—68no—
467#235C4×D318yescomplemented
468C2×D12—32no—
469C2×D12—32no—
470C2×D12—31no—
471C2×D12—31no—
472C2×D12—38no—
473C2×D12—61no—
474C2×D12C22×D311yescharacteristic
475C2×C4×D3—32no—
476C2×C4×D3—32no—
477C2×C4×D3—32no—
478C2×C4×D3—32no—
479C2×C4×D3—32no—
480C2×C4×D3—32no—
481C2×C4×D3—32no—
482C2×C4×D3—316no—
483C2×C4×D3—316no—
484C2×C4×D3—32no—
485C2×C4×D3—32no—
486C2×C4×D3—34no—
487C2×C4×D3—32no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—62no—
493C2×C4×D3—64no—
494C2×C4×D3—616no—
495C2×C4×D3—616no—
496C2×C4×D3—68no—
497C2×C4×D3C4×D318yescomplemented
498C2×C4×D3C22×D314yes—
499C2×C4×D3C22×D314yes—
500C2×C4×D3C22×D311yescharacteristic
501C2×C4×D3C22×D311yescharacteristic
502C2×C4×D3C22×D311yescharacteristic
503C2×C4×D3C22×D311yescharacteristic
504C2×C4×D3C22×D312yes—
505C2×Dic6—31no—
506C2×Dic6—31no—
507C2×Dic6—32no—
508C2×Dic6—32no—
509C2×Dic6—38no—
510C2×Dic6—61no—
511C2×Dic6C22×D311yescharacteristic
512C3×C4⋊C4—22no—
513C3×C4⋊C4—34no—
514C3×C4⋊C4—32no—
515C3×C4⋊C4—34no—
516C3×C4⋊C4C22×D312yes—
517C3×C4⋊C4C22×D312yes—
518C3×C22⋊C4—22no—
519C3×C22⋊C4—32no—
520C3×C22⋊C4—34no—
521C3×C22⋊C4—34no—
522C3×C22⋊C4C22×D312yes—
523C3×C22⋊C4C22×D312yes—
524C3×C42—22no—
525C3×C42—34no—
526C3×C42—32no—
527C3×C42—31no—
528C3×C42—34no—
529C3×C42—31no—
530C3×C42—32no—
531C3×C42C22×D312yes—
532C3×C42C22×D312yes—
533#217—34no—
534#217C22×D312yes—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—64no—
541(C2×D3)⋊C4C22×D314yes—
542(C2×D3)⋊C4C22×D314yes—
543C4⋊Dic3—34no—
544C4⋊Dic3C22×D312yes—
545Dic3⋊C4—34no—
546Dic3⋊C4—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—64no—
551Dic3⋊C4C22×D314yes—
552Dic3⋊C4C22×D314yes—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—31no—
556C4×Dic3—34no—
557C4×Dic3—34no—
558C4×Dic3—32no—
559C4×Dic3—31no—
560C4×Dic3—32no—
561C4×Dic3—34no—
562C4×Dic3—32no—
563C4×Dic3—32no—
564C4×Dic3—32no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3—34no—
568C4×Dic3—34no—
569C4×Dic3—34no—
570C4×Dic3—32no—
571C4×Dic3—32no—
572C4×Dic3—32no—
573C4×Dic3—61no—
574C4×Dic3—64no—
575C4×Dic3—61no—
576C4×Dic3—62no—
577C4×Dic3C22×D311yescharacteristic
578C4×Dic3C22×D312yes—
579C4×Dic3C22×D314yes—
580C4×Dic3C22×D314yes—
581C4×Dic3C22×D311yescharacteristic
582C4×Dic3C22×D312yes—
583C22×C32—22no—
584C22×C32C23×C412yes—
585C22×C32C2511yescharacteristic
586C2×C3⋊D3—24no—
587C2×C3⋊D3C23×C414yes—
588C2×C3×D3—22no—
589C2×C3×D3—24no—
590C2×C3×D3—28no—
591C2×C3×D3C23×C414yes—
592C2×C3×D3C23×C412yes—
593C2×C3×D3C23×C412yes—
594C2×C3×D3C2×#4114yes—
595D32—216no—
596C32×C4—24no—
597C32×C4C23×C412yes—
598C32×C4C23×C412yes—
599C3⋊Dic3—22no—
600C3⋊Dic3C23×C414yes—
601C3⋊Dic3C2×#4114yescomplemented
602C3×Dic3—22no—
603C3×Dic3—24no—
604C3×Dic3C23×C414yes—
605C3×Dic3C23×C412yes—
606C3×Dic3C23×C412yes—
607C3×Dic3C2×#4114yescomplemented
608C2×#41—31no—
609C2×#41—92no—
610C2×#41—92no—
611C2×#41—91no—
612C2×#41—91no—
613C2×#41—916no—
614C2×#41—91no—
615C22×Q8—91no—
616C22×D4—91no—
617C22×D4—92no—
618C23×C4—31no—
619C23×C4—92no—
620C23×C4—94no—
621C23×C4—92no—
622C4×Q8—32no—
623C4×Q8—94no—
624C4×Q8—92no—
625C4×Q8—94no—
626C4×Q8—92no—
627C4×Q8—92no—
628C4×D4—32no—
629C4×D4—34no—
630C4×D4—94no—
631C4×D4—92no—
632C4×D4—94no—
633C4×D4—94no—
634C4×D4—94no—
635C4×D4—94no—
636C4×D4—94no—
637C4×D4—94no—
638C4×D4—94no—
639C4×D4—92no—
640C4×D4—92no—
641C4×D4—94no—
642#117—31no—
643#117—32no—
644#117—32no—
645#117—32no—
646#117—32no—
647#117—92no—
648#117—94no—
649#117—94no—
650#117—92no—
651#117—92no—
652#117D3211yescharacteristic, complemented
653C2×C4⋊C4—32no—
654C2×C4⋊C4—94no—
655C2×C22⋊C4—32no—
656C2×C22⋊C4—94no—
657C2×C42—31no—
658C2×C42—32no—
659C2×C42—32no—
660C2×C42—94no—
661C2×C42—92no—
662C2×C42—91no—
663C2×C42—92no—
664C2×C42—94no—
665C2×C42—94no—
666C2×C42—92no—
667C2×C42—91no—
668C2×C42—92no—
669C2×C42—91no—
670C2×C42—91no—
671C2×C42—92no—
672C2×C42—91no—
673C2×C42—92no—
674C23×C3—21no—
675C23×C3—31no—
676C23×C3—34no—
677C23×C3—32no—
678C23×C3—31no—
679C23×C3—64no—
680C23×C3C23×D311yescharacteristic
681C23×C3C23×D311yescharacteristic
682C22×D3—24no—
683C22×D3—32no—
684C22×D3—32no—
685C22×D3—38no—
686C22×D3—38no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—68no—
690C22×D3C2×C4×D314yes—
691C22×D3C23×D312yes—
692C22×D3C23×D311yescharacteristic
693C22×D3C23×D311yescharacteristic
694C3×Q8—34no—
695C3×D4—38no—
696C3×D4—34no—
697C2×C3×C4—21no—
698C2×C3×C4—24no—
699C2×C3×C4—21no—
700C2×C3×C4—24no—
701C2×C3×C4—34no—
702C2×C3×C4—31no—
703C2×C3×C4—32no—
704C2×C3×C4—31no—
705C2×C3×C4—32no—
706C2×C3×C4—34no—
707C2×C3×C4—34no—
708C2×C3×C4—38no—
709C2×C3×C4—34no—
710C2×C3×C4—34no—
711C2×C3×C4—34no—
712C2×C3×C4—32no—
713C2×C3×C4—68no—
714C2×C3×C4—68no—
715C2×C3×C4—64no—
716C2×C3×C4C2×C4×D314yescomplemented
717C2×C3×C4C2×C4×D314yescomplemented
718C2×C3×C4C23×D314yes—
719C2×C3×C4C23×D314yes—
720C2×C3×C4C23×D311yescharacteristic
721C2×C3×C4C23×D311yescharacteristic
722C2×C3×C4C23×D311yescharacteristic
723C2×C3×C4C23×D311yescharacteristic
724#67—38no—
725#67—38no—
726#67—38no—
727#67—38no—
728#67—38no—
729#67—38no—
730#67—68no—
731#67C2×C4×D318yescomplemented
732C2×Dic3—24no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—32no—
737C2×Dic3—38no—
738C2×Dic3—38no—
739C2×Dic3—38no—
740C2×Dic3—32no—
741C2×Dic3—32no—
742C2×Dic3—62no—
743C2×Dic3—62no—
744C2×Dic3—62no—
745C2×Dic3—68no—
746C2×Dic3—64no—
747C2×Dic3—64no—
748C2×Dic3—64no—
749C2×Dic3—64no—
750C2×Dic3—64no—
751C2×Dic3—124no—
752C2×Dic3C2×C4×D314yescomplemented
753C2×Dic3C23×D312yes—
754C2×Dic3C23×D314yes—
755C2×Dic3C23×D311yescharacteristic
756C2×Dic3C23×D311yescharacteristic
757C2×Dic3C23×D312yes—
758C2×Dic3C23×D312yes—
759D12—38no—
760D12—38no—
761D12—34no—
762D12—34no—
763D12—64no—
764D12C2×C4×D314yescomplemented
765C4×D3—28no—
766C4×D3—28no—
767C4×D3—38no—
768C4×D3—38no—
769C4×D3—38no—
770C4×D3—38no—
771C4×D3—38no—
772C4×D3—38no—
773C4×D3—38no—
774C4×D3—68no—
775C4×D3—68no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—64no—
779C4×D3—68no—
780C4×D3—64no—
781C4×D3—64no—
782C4×D3—68no—
783C4×D3—128no—
784C4×D3C2×C4×D314yes—
785C4×D3C2×C4×D314yes—
786C4×D3C2×C4×D318yescomplemented
787C4×D3C2×C4×D314yescomplemented
788C4×D3C2×C4×D314yescomplemented
789Dic6—34no—
790Dic6—34no—
791Dic6—38no—
792Dic6—38no—
793Dic6—64no—
794Dic6C2×C4×D314yescomplemented
795C2×C32—22no—
796C2×C32C24×C411yescharacteristic
797C2×C32C22×#4112yes—
798C3⋊D3—24no—
799C3×D3—24no—
800C3×D3—22no—
801C3×D3C4×#4114yescomplemented
802C24—31no—
803C24—92no—
804#41—38no—
805#41—916no—
806#41—916no—
807#41—98no—
808#41—98no—
809#41—98no—
810C2×Q8—31no—
811C2×Q8—92no—
812C2×Q8—98no—
813C2×Q8—91no—
814C2×D4—32no—
815C2×D4—31no—
816C2×D4—98no—
817C2×D4—92no—
818C2×D4—92no—
819C2×D4—916no—
820C2×D4—92no—
821C2×D4—92no—
822C2×D4—91no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—31no—
827C22×C4—32no—
828C22×C4—31no—
829C22×C4—38no—
830C22×C4—32no—
831C22×C4—34no—
832C22×C4—34no—
833C22×C4—92no—
834C22×C4—916no—
835C22×C4—94no—
836C22×C4—92no—
837C22×C4—92no—
838C22×C4—92no—
839C22×C4—92no—
840C22×C4—92no—
841C22×C4—92no—
842C22×C4—94no—
843C22×C4—92no—
844C22×C4—92no—
845C22×C4—94no—
846C22×C4—1816no—
847C22×C4—188no—
848C22×C4C2×D3211yescharacteristic
849C4⋊C4—34no—
850C4⋊C4—32no—
851C4⋊C4—34no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4—94no—
855C4⋊C4C2×D3212yes—
856C22⋊C4—32no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4C2×D3212yes—
863C42—34no—
864C42—34no—
865C42—32no—
866C42—31no—
867C42—31no—
868C42—32no—
869C42—92no—
870C42—92no—
871C42—92no—
872C42—94no—
873C42—94no—
874C42—92no—
875C42—94no—
876C42—92no—
877C42—91no—
878C42—91no—
879C42C2×D3212yes—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—21no—
884C22×C3—32no—
885C22×C3—34no—
886C22×C3—34no—
887C22×C3—32no—
888C22×C3—42no—
889C22×C3—68no—
890C22×C3—62no—
891C22×C3—64no—
892C22×C3C22×C4×D312yes—
893C22×C3C22×C4×D312yes—
894C22×C3C24×D311yescharacteristic
895C22×C3C24×D311yescharacteristic
896C2×D3—24no—
897C2×D3—22no—
898C2×D3—28no—
899C2×D3—34no—
900C2×D3—34no—
901C2×D3—64no—
902C2×D3—616no—
903C2×D3—64no—
904C2×D3—64no—
905C2×D3—616no—
906C2×D3—124no—
907C2×D3C22×C4×D314yes—
908C2×D3C22×C4×D312yes—
909C2×D3C22×C4×D312yes—
910C2×D3D3×#4114yes—
911C3×C4—24no—
912C3×C4—24no—
913C3×C4—22no—
914C3×C4—22no—
915C3×C4—32no—
916C3×C4—34no—
917C3×C4—32no—
918C3×C4—34no—
919C3×C4—44no—
920C3×C4—64no—
921C3×C4—62no—
922C3×C4C22×C4×D312yes—
923C3×C4C22×C4×D312yes—
924C3×C4C22×C4×D312yes—
925C3×C4C22×C4×D312yes—
926Dic3—24no—
927Dic3—22no—
928Dic3—34no—
929Dic3—34no—
930Dic3—34no—
931Dic3—34no—
932Dic3—64no—
933Dic3—64no—
934Dic3—62no—
935Dic3—62no—
936Dic3—122no—
937Dic3C22×C4×D312yes—
938Dic3C22×C4×D314yes—
939Dic3C22×C4×D312yes—
940Dic3D3×#4114yescomplemented
941C32C2×C4×#4111yescharacteristic, complemented, Sylow
942C23—31no—
943C23—34no—
944C23—31no—
945C23—32no—
946C23—64no—
947C23—98no—
948C23—92no—
949C23—188no—
950C23C22×D3211yescharacteristic
951Q8—34no—
952Q8—98no—
953Q8—94no—
954D4—38no—
955D4—34no—
956D4—98no—
957D4—98no—
958D4—98no—
959D4—98no—
960D4—94no—
961C2×C4—34no—
962C2×C4—31no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—31no—
966C2×C4—34no—
967C2×C4—34no—
968C2×C4—34no—
969C2×C4—34no—
970C2×C4—38no—
971C2×C4—34no—
972C2×C4—32no—
973C2×C4—68no—
974C2×C4—68no—
975C2×C4—64no—
976C2×C4—98no—
977C2×C4—98no—
978C2×C4—98no—
979C2×C4—98no—
980C2×C4—92no—
981C2×C4—92no—
982C2×C4—98no—
983C2×C4—92no—
984C2×C4—188no—
985C2×C4—188no—
986C2×C4—184no—
987C2×C4—188no—
988C2×C4—184no—
989C2×C4—184no—
990C2×C4—184no—
991C2×C4C4×D3214yescomplemented
992C2×C4C22×D3214yes—
993C2×C4C22×D3211yescharacteristic
994C2×C4C22×D3211yescharacteristic
995C2×C3—22no—
996C2×C3—22no—
997C2×C3—21no—
998C2×C3—22no—
999C2×C3—34no—
1000C2×C3—42no—
1001C2×C3—62no—
1002C2×C3—64no—
1003C2×C3C23×C4×D311yescharacteristic
1004C2×C3C23×C4×D311yescharacteristic
1005C2×C3C2×D3×#4112yes—
1006C2×C3C2×D3×#4112yes—
1007D3—24no—
1008D3—22no—
1009D3—64no—
1010D3—64no—
1011D3—124no—
1012D3#552214yesdirect product factor
1013C22—22no—
1014C22—32no—
1015C22—34no—
1016C22—32no—
1017C22—34no—
1018C22—68no—
1019C22—64no—
1020C22—62no—
1021C22—94no—
1022C22—1816no—
1023C22—184no—
1024C22C2×C4×D3212yes—
1025C22C23×D3211yescharacteristic
1026C4—24no—
1027C4—32no—
1028C4—32no—
1029C4—34no—
1030C4—34no—
1031C4—64no—
1032C4—62no—
1033C4—94no—
1034C4—94no—
1035C4—182no—
1036C4C2×C4×D3212yes—
1037C4C2×C4×D3212yes—
1038C3—21no—
1039C3C2×#552211yescharacteristic, complemented
1040C3C4×D3×#4111yescharacteristic, complemented
1041C2—22no—
1042C2—34no—
1043C2—62no—
1044C2—64no—
1045C2—184no—
1046C2C22×C4×D3211yescharacteristic
1047C2D32×#4112yes—
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC2×D3×#235C2
hypercenter#117D32
hypocenterC32C2×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595993C2semidirect
3. C3×#5522C2semidirect
4. C3×D3×#117C2semidirect
5. #10594958C2semidirect
6. #10594954C2semidirect
7. C2×C4×D3×Dic3C2semidirect
8. D3×#893C2semidirect
9. #10594362C2semidirect
10. #10594358C2semidirect
11. D3×#887C2semidirect
12. D3×#67⋊C4C2semidirect
13. #10594048C2semidirect
14. D3×#872C2semidirect
15. C42×D32C2semidirect
16. #10593966C2semidirect
17. #10593965C2semidirect
26. D3×#235C4semidirect
34. C32×#117C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. #64102C22semidirect
37. #64096C22semidirect
38. #64090C22semidirect
39. #64081C22semidirect
40. C42×C3⋊D3C22semidirect
41. C3×#926C22semidirect
42. C2×C3×C4×Dic3C22semidirect
43. C3×#893C22semidirect
44. C3×#892C22semidirect
46. C3×#887C22semidirect
47. C3×#67⋊C4C22semidirect
49. C3×#877C22semidirect
50. C3×#872C22semidirect
51. C3×#872C22semidirect
53. C3×C42×D3C22semidirect
54. #67⋊Dic3C22semidirect
55. C2×Dic32C22semidirect
56. #63952C22semidirect
58. #63904C22semidirect
59. #63902C22semidirect
60. #63898C22semidirect
61. #63894C22semidirect
62. C4×#624C22semidirect
63. C4×#624C22semidirect
64. #63881C22semidirect
65. #63881C22semidirect
66. #63880C22semidirect
67. #63879C22semidirect
68. #63877C22semidirect
74. C4×D3×Dic3C22semidirect
75. C4×D3×Dic3C22semidirect
76. C4×D3×Dic3C22semidirect
77. C4×D3×Dic3C22semidirect
78. C4×D3×Dic3C22semidirect
79. #63874C22semidirect
80. #63855C22semidirect
81. #63844C22semidirect
82. #63843C22semidirect
83. #63838C22semidirect
84. #63837C22semidirect
85. #63836C22semidirect
109. #5522D3direct (N × H)
111. D3×#117D3semidirect
126. #3828C2×C4semidirect
134. C3×#235C2×C4semidirect
136. C2×C3×C4×D3C2×C4semidirect
145. D3×#67C2×C4semidirect
152. #3804C2×C4semidirect
161. D3×D12C2×C4semidirect
163. C4×D32C2×C4semidirect
164. #3799C2×C4semidirect
165. #3798C2×C4semidirect
166. #3795C2×C4semidirect
167. D3×Dic6C2×C4semidirect
238. C3×#117C2×D3semidirect
239. C3×#117C2×D3semidirect
253. #926C2×D3semidirect
269. C2×C4×Dic3C2×D3semidirect
278. #893C2×D3semidirect
280. #892C2×D3semidirect
291. #887C2×D3semidirect
303. #67⋊C4C2×D3semidirect
307. #877C2×D3semidirect
318. #872C2×D3semidirect
319. #872C2×D3semidirect
337. C42×D3C2×D3semidirect
349. C2×C32×C4C22×C4semidirect
353. #638C22×C4semidirect
358. C4⋊(C3⋊D3)C22×C4semidirect
360. C4×C3⋊D3C22×C4semidirect
361. #634C22×C4semidirect
362. C3×#67C22×C4semidirect
364. C2×C3×Dic3C22×C4semidirect
371. C3×D12C22×C4semidirect
376. C3×C4×D3C22×C4semidirect
377. C3×C4×D3C22×C4semidirect
378. C3×C4×D3C22×C4semidirect
379. C3×Dic6C22×C4semidirect
380. #627C22×C4semidirect
381. #626C22×C4semidirect
382. #626C22×C4semidirect
383. #625C22×C4semidirect
385. #624C22×C4semidirect
391. D3×Dic3C22×C4semidirect
392. D3×Dic3#41semidirect
467. #235C4×D3semidirect
497. C2×C4×D3C4×D3semidirect
601. C3⋊Dic3C2×#41semidirect
607. C3×Dic3C2×#41semidirect
652. #117D32semidirect
716. C2×C3×C4C2×C4×D3semidirect
717. C2×C3×C4C2×C4×D3semidirect
731. #67C2×C4×D3semidirect
752. C2×Dic3C2×C4×D3semidirect
764. D12C2×C4×D3semidirect
786. C4×D3C2×C4×D3semidirect
787. C4×D3C2×C4×D3semidirect
788. C4×D3C2×C4×D3semidirect
794. Dic6C2×C4×D3semidirect
801. C3×D3C4×#41semidirect
940. Dic3D3×#41semidirect
941. C32C2×C4×#41semidirect
991. C2×C4C4×D32semidirect
1012. D3#5522direct (N × H)
1039. C3C2×#5522semidirect
1040. C3C4×D3×#41semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
#105959932
C3×#55222
C3×D3×#1172
#105949582
#105949542
C2×C4×D3×Dic32
D3×#8932
#105943622
#105943582
D3×#8872
D3×#67⋊C42
#105940482
D3×#8722
C42×D322
#105939662
#105939652
C4×D3×#413
C2×#55223