Finite Group Databasebeta

← D3×#5526 #11901080

Subgroups — D3×#5526 #11901080

Order 1152.

3159 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×D3×#117C211yesmaximal, characteristic, complemented
6#10594866C211yesmaximal, characteristic, complemented
7#10594856C211yesmaximal, characteristic, complemented
8D3×#897C214yesmaximal, complemented
9#10594380C214yesmaximal, complemented
10D3×#886C214yesmaximal, complemented
11#10594081C214yesmaximal, complemented
12D3×#875C212yesmaximal, complemented
13#10593894C212yesmaximal, complemented
14#10593893C212yesmaximal, complemented
15D3×#869C212yesmaximal, complemented
16D3×#536—31nomaximal
17C2×#5526—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C2×D3×#67C2212yes—
24C22×#627C2212yescomplemented
25C2×#3804C2212yes—
26C22×D3×Dic3C2212yes—
27D3×#235—28no—
28C2×D3×D12C2211yescharacteristic
29C2×C4×D32C2212yes—
30C2×#3799C2211yescharacteristic
31C2×#3798C2212yes—
32C2×#3795C2211yescharacteristic
33C2×D3×Dic6—28no—
34C2×D3×Dic6C2212yes—
35C2×D3×Dic6C2212yes—
36C2×D3×Dic6C2211yescharacteristic
37C2×D3×Dic6C2212yescomplemented
38C2×D3×Dic6C2212yescomplemented
39C32×#117C2211yescharacteristic, complemented
40#64106C2214yescomplemented
41#64095C2214yescomplemented
42#64084C2212yescomplemented
43#64078C2212yescomplemented
44C3×#926C2211yescharacteristic, complemented
45C3×#897C2214yescomplemented
46C3×#892C2212yescomplemented
47C3×D3×C4⋊C4C2212yes—
48C3×#886C2214yescomplemented
49C3×D3×C22⋊C4C2212yes—
50C3×#877C2212yescomplemented
51C3×#875C2212yescomplemented
52C3×#872C2212yescomplemented
53C3×C42×D3C2212yes—
54C3×#869C2212yescomplemented
55#63966C2214yescomplemented
56#63962C2214yescomplemented
57D3×(C2×D3)⋊C4C2218yes—
58#63918C2218yescomplemented
59#63895C2218yescomplemented
60#63893C2218yescomplemented
61#63891C2218yescomplemented
62#63890C2218yescomplemented
63D3×C4⋊Dic3C2218yes—
64#63871C2214yescomplemented
65#63866C2212yescomplemented
66#63866C2212yescomplemented
67#63864C2212yescomplemented
68#63860C2212yescomplemented
69#63857C2214yescomplemented
70#63852C2218yescomplemented
71C2×D3×#41—31no—
72C22×D3×Q8—31no—
73C22×#235—31no—
74C23×Dic6—31no—
75C3×#536—31no—
76C2×C3×#117—31no—
77#5825—31no—
78#5816—31no—
79#5724—32no—
80D3×C4⋊Q8—32no—
81#5675—32no—
82D3×#124—32no—
83D3×#123—34no—
84#5648—34no—
85#5628—34no—
86D3×C22⋊Q8—34no—
87#5526—31no—
88#5526—31no—
89#5526—31no—
90#5526—31no—
91#5526—34no—
92#5526—34no—
93#5526—32no—
94#5526—32no—
95#5526—61no—
96#5526D311yescharacteristic, direct product factor
97D3×#117D311yescharacteristic, complemented
98C2×#897—34no—
99C2×#886—34no—
100C2×#875—32no—
101C2×#869—32no—
102C23×C3×D3C2311yescharacteristic
103C22×D32C2312yes—
104C22×C32×C4C2311yescharacteristic
105C2×#638C2312yes—
106C22×C3⋊Dic3C2312yes—
107#3828—24no—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3C2312yes—
110C2×#634—24no—
111C2×#634C2312yes—
112C2×#634C2312yes—
113C2×#634C2311yescharacteristic
114C2×C3×#67C2312yes—
115C22×C3×Dic3C2312yes—
116C22×C3×Dic3C2311yescharacteristic
117C3×#235—24no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3D418yes—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×Dic6—24no—
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130D3×#67—28no—
131C2×#627—28no—
132C2×#627C2314yes—
133C2×#627C2314yes—
134C2×#627C2312yes—
135C2×#626C2312yes—
136C2×#626C2312yes—
137C2×#625C2312yes—
138C2×#624C2312yes—
139#3804—28no—
140C2×D3×Dic3—28no—
141C2×D3×Dic3C2314yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2312yes—
145D3×D12—24no—
146C4×D32—28no—
147#3799—24no—
148#3798—28no—
149#3795—24no—
150D3×Dic6—28no—
151D3×Dic6—28no—
152D3×Dic6—28no—
153D3×Dic6—28no—
154D3×Dic6—24no—
155C32×C4⋊C4C2312yes—
156C32×C22⋊C4C2312yes—
157C32×C42C2312yes—
158#3752C2318yes—
159C4⋊(C3⋊Dic3)C2318yes—
160C3×#217C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2318yes—
163C3×C4⋊Dic3C2318yes—
164C3×C4⋊Dic3C2312yes—
165C3×Dic3⋊C4C2314yes—
166C3×C4×Dic3C2314yes—
167C3×C4×Dic3C2312yes—
168Dic3⋊Dic3C2318yes—
169Dic3⋊Dic3C2318yes—
170#3722C2318yes—
171(C2×D3)⋊Dic3C2318yes—
172C2×#536—91noSylow
173C2×C3×#41—31no—
174C22×C3×Q8—31no—
175C23×C3×C4—31no—
176C22×#67—32no—
177C23×Dic3—32no—
178D3×#41—68no—
179C2×#239—31no—
180C2×D3×Q8—32no—
181C2×D3×Q8—32no—
182C2×D3×Q8—31no—
183C2×D3×Q8—32no—
184C2×D3×Q8—32no—
185C2×D3×Q8—68no—
186C2×#237—32no—
187C2×#237—31no—
188C2×D3×D4—32no—
189C2×D3×D4—31no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—32no—
193C2×#235—31no—
194C2×#235—32no—
195C2×#235—32no—
196C2×#235—31no—
197C2×#235—61no—
198C2×#235—68no—
199C2×#235C2×D311yescharacteristic
200C22×D12—31no—
201C22×C4×D3—32no—
202C22×C4×D3—32no—
203C22×C4×D3—32no—
204C22×C4×D3C2×D311yescharacteristic
205C22×Dic6—31no—
206C22×Dic6—31no—
207C22×Dic6—32no—
208C22×Dic6—32no—
209C22×Dic6—32no—
210C22×Dic6—32no—
211C22×Dic6—31no—
212C22×Dic6—32no—
213C22×Dic6—32no—
214C22×Dic6—61no—
215C22×Dic6—68no—
216C22×Dic6C2×D311yescharacteristic, complemented
217C3×C4⋊Q8—32no—
218C3×#124—32no—
219C3×#123—34no—
220C3×C22⋊Q8—34no—
221C3×#117—21no—
222C3×#117—31no—
223C3×#117—32no—
224C3×#117—32no—
225C3×#117—32no—
226C3×#117C2×D311yescharacteristic, complemented
227C3×#117C2×D311yescharacteristic, complemented
228C2×C3×C4⋊C4—32no—
229C2×C3×C22⋊C4—32no—
230C2×C3×C42—32no—
231#947—32no—
232#946—34no—
233#944—32no—
234#944—32no—
235#936—32no—
236#935—34no—
237#929—34no—
238C2×(C2×D3)⋊C4—38no—
239#926C2×D311yescharacteristic, complemented
240C2×C4⋊Dic3—38no—
241#924—34no—
242#897—34no—
243#897—34no—
244#897—34no—
245#897—34no—
246#897—38no—
247#897—38no—
248#897—64no—
249#897C2×D314yescomplemented
250#896—38no—
251#894—38no—
252#892C2×D312yescomplemented
253D3×C4⋊C4—38no—
254D3×C4⋊C4C2×D312yes—
255#888—38no—
256#886—34no—
257#886—34no—
258#886—34no—
259#886—34no—
260#886—38no—
261#886—38no—
262#886—64no—
263#886C2×D314yescomplemented
264#885—38no—
265#883—38no—
266D3×C22⋊C4—38no—
267D3×C22⋊C4C2×D312yes—
268#878—38no—
269#877C2×D312yescomplemented
270#875—32no—
271#875—32no—
272#875—32no—
273#875—32no—
274#875—38no—
275#875—62no—
276#875C2×D312yescomplemented
277#872C2×D312yescomplemented
278C42×D3C2×D312yes—
279#869—32no—
280#869—32no—
281#869—32no—
282#869—32no—
283#869—38no—
284#869—62no—
285#869C2×D312yescomplemented
286C23×C32C2411yescharacteristic
287C22×C3⋊D3C2412yes—
288C22×C3×D3—24no—
289C22×C3×D3C2×D414yes—
290C22×C3×D3C2412yes—
291C22×C3×D3C2411yescharacteristic
292C22×C3×D3C2411yescharacteristic
293C2×D32—24no—
294C2×D32—28no—
295C2×C32×C4C2×D414yes—
296C2×C32×C4C2414yes—
297C2×C32×C4C2411yescharacteristic
298C2×C32×C4C2411yescharacteristic
299#638—24no—
300C2×C3⋊Dic3—24no—
301C2×C3⋊Dic3C2414yes—
302C2×C3⋊Dic3C2412yes—
303C4⋊(C3⋊D3)—22no—
304C4×C3⋊D3—24no—
305#634—24no—
306#634—24no—
307#634—22no—
308C3×#67—24no—
309C2×C3×Dic3—24no—
310C2×C3×Dic3C2×D414yes—
311C2×C3×Dic3C2414yes—
312C2×C3×Dic3C2414yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2411yescharacteristic
315C2×C3×Dic3C2411yescharacteristic
316C3×D12—22no—
317C3×C4×D3—28no—
318C3×C4×D3—24no—
319C3×C4×D3C2×D414yes—
320C3×C4×D3C2×D414yes—
321C3×C4×D3C2×D414yes—
322C3×C4×D3C2×D414yes—
323C3×Dic6—24no—
324C3×Dic6—24no—
325C3×Dic6—22no—
326#627—28no—
327#627—28no—
328#627—24no—
329#626—24no—
330#626—24no—
331#625—24no—
332#624—24no—
333D3×Dic3—28no—
334D3×Dic3—28no—
335D3×Dic3—24no—
336D3×Dic3—24no—
337C22×#41—91no—
338C23×Q8—91no—
339#536—31no—
340#536—94no—
341#536—94no—
342#536—92no—
343#536—92no—
344#536—91no—
345#536—91no—
346#536—91no—
347C2×C4⋊Q8—92no—
348C2×#124—92no—
349C2×#123—94no—
350C2×C22⋊Q8—94no—
351C2×#117—31no—
352C24×C3—31no—
353C23×D3—32no—
354C23×D3—32no—
355C23×D3C22×D311yescharacteristic
356C3×#41—64no—
357C2×C3×Q8—31no—
358C2×C3×Q8—32no—
359C2×C3×Q8—32no—
360C2×C3×Q8—64no—
361C2×C3×D4—32no—
362C2×C3×D4—31no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—38no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—32no—
371C22×C3×C4—32no—
372C22×C3×C4—34no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C2×#67—32no—
376C2×#67—32no—
377C2×#67—32no—
378C2×#67—32no—
379C2×#67—32no—
380C2×#67—32no—
381C2×#67—62no—
382C2×#67—68no—
383C2×#67C22×D312yes—
384C22×Dic3—32no—
385C22×Dic3—32no—
386C22×Dic3—32no—
387C22×Dic3—34no—
388C22×Dic3—32no—
389C22×Dic3—34no—
390C22×Dic3—62no—
391C22×Dic3—68no—
392C22×Dic3C22×D312yes—
393C22×Dic3C22×D311yescharacteristic
394#239—64no—
395D3×Q8—68no—
396D3×Q8—68no—
397D3×Q8—68no—
398D3×Q8—68no—
399D3×Q8—64no—
400#237—68no—
401#237—64no—
402D3×D4—68no—
403D3×D4—64no—
404#235—24no—
405#235—64no—
406#235—68no—
407#235—64no—
408#235—68no—
409#235—64no—
410#235—64no—
411#235—68no—
412#235—124no—
413C2×D12—32no—
414C2×D12—32no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—61no—
418C2×D12—64no—
419C2×D12C22×D311yescharacteristic
420C2×C4×D3—34no—
421C2×C4×D3—34no—
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—62no—
429C2×C4×D3—68no—
430C2×C4×D3—68no—
431C2×C4×D3—68no—
432C2×C4×D3D1218yes—
433C2×C4×D3C22×D314yes—
434C2×C4×D3C22×D312yes—
435C2×C4×D3C22×D311yescharacteristic
436C2×C4×D3C22×D311yescharacteristic
437C2×C4×D3C22×D311yescharacteristic
438C2×C4×D3C22×D311yescharacteristic
439C2×Dic6—24no—
440C2×Dic6—31no—
441C2×Dic6—32no—
442C2×Dic6—31no—
443C2×Dic6—32no—
444C2×Dic6—32no—
445C2×Dic6—32no—
446C2×Dic6—32no—
447C2×Dic6—34no—
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—32no—
451C2×Dic6—34no—
452C2×Dic6—61no—
453C2×Dic6—62no—
454C2×Dic6—62no—
455C2×Dic6—68no—
456C2×Dic6—68no—
457C2×Dic6—68no—
458C2×Dic6—68no—
459C2×Dic6—64no—
460C2×Dic6—68no—
461C2×Dic6—64no—
462C2×Dic6—64no—
463C2×Dic6—68no—
464C2×Dic6—124no—
465C2×Dic6C22×D311yescharacteristic
466C2×Dic6C22×D312yes—
467C2×Dic6C22×D312yes—
468C3×C4⋊C4—22no—
469C3×C4⋊C4—38no—
470C3×C4⋊C4—34no—
471C3×C4⋊C4—32no—
472C3×C4⋊C4C22×D312yes—
473C3×C4⋊C4C22×D312yes—
474C3×C22⋊C4—22no—
475C3×C22⋊C4—32no—
476C3×C22⋊C4—38no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4C22×D312yes—
479C3×C22⋊C4C22×D312yes—
480C3×C42—22no—
481C3×C42—34no—
482C3×C42—32no—
483C3×C42C22×D312yes—
484C3×C42C22×D312yes—
485#217—38no—
486#217C22×D312yes—
487(C2×D3)⋊C4—38no—
488(C2×D3)⋊C4—38no—
489(C2×D3)⋊C4—38no—
490(C2×D3)⋊C4—38no—
491(C2×D3)⋊C4—38no—
492(C2×D3)⋊C4—68no—
493(C2×D3)⋊C4C22×D314yes—
494(C2×D3)⋊C4C22×D318yes—
495C4⋊Dic3—38no—
496C4⋊Dic3—38no—
497C4⋊Dic3—38no—
498C4⋊Dic3—38no—
499C4⋊Dic3—68no—
500C4⋊Dic3C22×D318yes—
501C4⋊Dic3C22×D312yes—
502Dic3⋊C4—38no—
503Dic3⋊C4—38no—
504Dic3⋊C4C22×D314yes—
505C4×Dic3C22×D312yes—
506C4×Dic3C22×D314yes—
507C22×C32—22no—
508C22×C32C22×D412yes—
509C22×C32C2511yescharacteristic
510C2×C3⋊D3—22no—
511C2×C3⋊D3—24no—
512C2×C3×D3—22no—
513C2×C3×D3—28no—
514C2×C3×D3—22no—
515C2×C3×D3—24no—
516C2×C3×D3C22×D412yes—
517C2×C3×D3C22×D412yes—
518C2×C3×D32−1+414yes—
519D32—48no—
520C32×C4—24no—
521C32×C4C22×D412yes—
522C32×C4C22×D412yes—
523C3⋊Dic3—22no—
524C3⋊Dic3—24no—
525C3×Dic3—24no—
526C3×Dic3—22no—
527C3×Dic3—24no—
528C3×Dic3C22×D412yes—
529C3×Dic3C22×D412yes—
530C2×#41—31no—
531C2×#41—92no—
532C2×#41—92no—
533C2×#41—91no—
534C2×#41—91no—
535C2×#41—91no—
536C2×#41—188no—
537C22×Q8—31no—
538C22×Q8—92no—
539C22×Q8—92no—
540C22×Q8—92no—
541C22×Q8—91no—
542C22×Q8—92no—
543C22×Q8—92no—
544C22×Q8—91no—
545C22×Q8—188no—
546C22×D4—91no—
547C22×D4—92no—
548C23×C4—31no—
549C23×C4—92no—
550C23×C4—92no—
551C4⋊Q8—32no—
552C4⋊Q8—98no—
553C4⋊Q8—92no—
554C4⋊Q8—92no—
555C4⋊Q8—92no—
556#124—32no—
557#124—98no—
558#124—92no—
559#124—92no—
560#124—92no—
561#123—34no—
562#123—98no—
563#123—98no—
564#123—94no—
565#123—94no—
566#123—94no—
567C22⋊Q8—34no—
568C22⋊Q8—98no—
569C22⋊Q8—98no—
570C22⋊Q8—94no—
571C22⋊Q8—94no—
572C22⋊Q8—94no—
573#117—31no—
574#117—32no—
575#117—32no—
576#117—32no—
577#117D3211yescharacteristic, complemented
578C2×C4⋊C4—32no—
579C2×C4⋊C4—98no—
580C2×C22⋊C4—32no—
581C2×C22⋊C4—98no—
582C2×C42—32no—
583C23×C3—21no—
584C23×C3—31no—
585C23×C3—34no—
586C23×C3—31no—
587C23×C3—32no—
588C23×C3—64no—
589C23×C3C23×D311yescharacteristic
590C23×C3C23×D311yescharacteristic
591C22×D3—24no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—62no—
595C22×D3—64no—
596C22×D3—68no—
597C22×D3—64no—
598C22×D3—68no—
599C22×D3C2×D1214yes—
600C22×D3C23×D312yes—
601C22×D3C23×D311yescharacteristic
602C22×D3C23×D311yescharacteristic
603C3×Q8—64no—
604C3×Q8—64no—
605C3×Q8—62no—
606C3×D4—64no—
607C3×D4—62no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—24no—
611C2×C3×C4—24no—
612C2×C3×C4—34no—
613C2×C3×C4—31no—
614C2×C3×C4—31no—
615C2×C3×C4—34no—
616C2×C3×C4—34no—
617C2×C3×C4—34no—
618C2×C3×C4—34no—
619C2×C3×C4—32no—
620C2×C3×C4—34no—
621C2×C3×C4—34no—
622C2×C3×C4—68no—
623C2×C3×C4—64no—
624C2×C3×C4—64no—
625C2×C3×C4C2×D1214yes—
626C2×C3×C4D3×D414yes—
627C2×C3×C4C23×D314yes—
628C2×C3×C4C23×D314yes—
629C2×C3×C4C23×D311yescharacteristic
630C2×C3×C4C23×D311yescharacteristic
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D311yescharacteristic
633#67—24no—
634#67—64no—
635#67—64no—
636#67—64no—
637#67—64no—
638#67—64no—
639#67—64no—
640#67—124no—
641C2×Dic3—24no—
642C2×Dic3—32no—
643C2×Dic3—34no—
644C2×Dic3—32no—
645C2×Dic3—34no—
646C2×Dic3—62no—
647C2×Dic3—64no—
648C2×Dic3—68no—
649C2×Dic3—68no—
650C2×Dic3—64no—
651C2×Dic3—64no—
652C2×Dic3—64no—
653C2×Dic3—64no—
654C2×Dic3—124no—
655C2×Dic3C2×D1214yes—
656C2×Dic3C23×D314yes—
657C2×Dic3C23×D312yes—
658C2×Dic3C23×D314yes—
659C2×Dic3C23×D311yescharacteristic
660C2×Dic3C23×D311yescharacteristic
661D12—22no—
662D12—64no—
663D12—64no—
664D12—62no—
665D12—62no—
666D12—122no—
667C4×D3—28no—
668C4×D3—24no—
669C4×D3—64no—
670C4×D3—64no—
671C4×D3—64no—
672C4×D3—68no—
673C4×D3—68no—
674C4×D3—64no—
675C4×D3—64no—
676C4×D3—64no—
677C4×D3—124no—
678C4×D3C2×D1214yes—
679C4×D3C2×D1214yes—
680C4×D3C2×D1214yes—
681C4×D3C2×D1214yes—
682Dic6—24no—
683Dic6—24no—
684Dic6—22no—
685Dic6—68no—
686Dic6—68no—
687Dic6—64no—
688Dic6—64no—
689Dic6—64no—
690Dic6—62no—
691Dic6—64no—
692Dic6—64no—
693Dic6—62no—
694Dic6—68no—
695Dic6—68no—
696Dic6—64no—
697Dic6—124no—
698Dic6—124no—
699Dic6—122no—
700C2×C32—22no—
701C2×C32C23×D411yescharacteristic
702C2×C32C2×2−1+412yes—
703C3⋊D3—42no—
704C3×D3—22no—
705C3×D3—42no—
706C3×D3#53614yescomplemented
707C24—31no—
708C24—92no—
709#41—64no—
710#41—188no—
711#41—188no—
712#41—184no—
713#41—184no—
714#41—184no—
715C2×Q8—32no—
716C2×Q8—32no—
717C2×Q8—31no—
718C2×Q8—64no—
719C2×Q8—94no—
720C2×Q8—94no—
721C2×Q8—92no—
722C2×Q8—92no—
723C2×Q8—92no—
724C2×Q8—91no—
725C2×Q8—188no—
726C2×Q8—188no—
727C2×Q8—188no—
728C2×Q8—188no—
729C2×Q8—188no—
730C2×Q8—184no—
731C2×Q8—184no—
732C2×D4—32no—
733C2×D4—31no—
734C2×D4—92no—
735C2×D4—92no—
736C2×D4—92no—
737C2×D4—92no—
738C2×D4—91no—
739C2×D4—184no—
740C2×D4—188no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—38no—
747C22×C4—32no—
748C22×C4—34no—
749C22×C4—32no—
750C22×C4—92no—
751C22×C4—94no—
752C22×C4—92no—
753C22×C4—92no—
754C22×C4—94no—
755C22×C4—92no—
756C22×C4—92no—
757C22×C4—188no—
758C22×C4—188no—
759C22×C4C2×D3211yescharacteristic
760C4⋊C4—34no—
761C4⋊C4—32no—
762C4⋊C4—38no—
763C4⋊C4—98no—
764C4⋊C4—98no—
765C4⋊C4—98no—
766C4⋊C4C2×D3212yes—
767C22⋊C4—32no—
768C22⋊C4—34no—
769C22⋊C4—38no—
770C22⋊C4—98no—
771C22⋊C4—98no—
772C22⋊C4—98no—
773C22⋊C4C2×D3212yes—
774C42—34no—
775C42—32no—
776C42C2×D3212yes—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—21no—
781C22×C3—32no—
782C22×C3—34no—
783C22×C3—32no—
784C22×C3—42no—
785C22×C3—68no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—64no—
789C22×C3C22×D1212yes—
790C22×C3C2×D3×D412yes—
791C22×C3C24×D311yescharacteristic
792C22×C3C24×D311yescharacteristic
793C2×D3—22no—
794C2×D3—28no—
795C2×D3—22no—
796C2×D3—24no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—64no—
800C2×D3—64no—
801C2×D3—122no—
802C2×D3—124no—
803C2×D3—128no—
804C2×D3—128no—
805C2×D3C22×D1212yes—
806C2×D3C22×D1212yes—
807C2×D3#101014yes—
808C3×C4—24no—
809C3×C4—24no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—32no—
813C3×C4—32no—
814C3×C4—44no—
815C3×C4—64no—
816C3×C4—62no—
817C3×C4—64no—
818C3×C4C22×D1212yes—
819C3×C4C22×D1212yes—
820C3×C4C2×D3×D412yes—
821C3×C4C2×D3×D412yes—
822Dic3—24no—
823Dic3—22no—
824Dic3—24no—
825Dic3—64no—
826Dic3—62no—
827Dic3—64no—
828Dic3—62no—
829Dic3—124no—
830Dic3—122no—
831Dic3C22×D1212yes—
832Dic3C22×D1212yes—
833C32C2×#53611yescharacteristic, complemented, Sylow
834C23—31no—
835C23—34no—
836C23—31no—
837C23—32no—
838C23—64no—
839C23—92no—
840C23—184no—
841C23—188no—
842C23C22×D3211yescharacteristic
843Q8—64no—
844Q8—64no—
845Q8—62no—
846Q8—188no—
847Q8—188no—
848Q8—184no—
849Q8—184no—
850Q8—184no—
851Q8—182no—
852D4—64no—
853D4—62no—
854D4—184no—
855D4—184no—
856D4—184no—
857D4—184no—
858D4—182no—
859C2×C4—34no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—34no—
863C2×C4—34no—
864C2×C4—34no—
865C2×C4—34no—
866C2×C4—34no—
867C2×C4—34no—
868C2×C4—32no—
869C2×C4—68no—
870C2×C4—64no—
871C2×C4—64no—
872C2×C4—94no—
873C2×C4—92no—
874C2×C4—184no—
875C2×C4—184no—
876C2×C4—184no—
877C2×C4—188no—
878C2×C4—188no—
879C2×C4—184no—
880C2×C4—184no—
881C2×C4D3×D1214yes—
882C2×C4C22×D3214yes—
883C2×C4C22×D3211yescharacteristic
884C2×C4C22×D3211yescharacteristic
885C2×C3—22no—
886C2×C3—22no—
887C2×C3—21no—
888C2×C3—22no—
889C2×C3—34no—
890C2×C3—42no—
891C2×C3—62no—
892C2×C3—122no—
893C2×C3C23×D1211yescharacteristic
894C2×C3C22×D3×D411yescharacteristic
895C2×C3C2×#101012yes—
896C2×C3D3×2−1+412yes—
897D3—22no—
898D3—42no—
899D3—122no—
900D3—122no—
901D3—242no—
902D3#552614yesdirect product factor
903C22—22no—
904C22—32no—
905C22—34no—
906C22—32no—
907C22—68no—
908C22—62no—
909C22—62no—
910C22—64no—
911C22—182no—
912C22—184no—
913C22—368no—
914C22C2×D3×D1212yes—
915C22C23×D3211yescharacteristic
916C4—24no—
917C4—32no—
918C4—32no—
919C4—62no—
920C4—64no—
921C4—64no—
922C4—182no—
923C4—184no—
924C4C2×D3×D1212yes—
925C4C2×D3×D1212yes—
926C3—21no—
927C3C2×#552611yescharacteristic, complemented
928C3D3×#53611yescharacteristic, complemented
929C2—22no—
930C2—34no—
931C2—62no—
932C2—122no—
933C2—362no—
934C2C22×D3×D1211yescharacteristic
935C2D3×#101012yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC2×D3×#235C2
hypercenter#117D32
hypocenterC32C2×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. #10595997C2semidirect
4. C3×#5526C2semidirect
5. C3×D3×#117C2semidirect
6. #10594866C2semidirect
7. #10594856C2semidirect
8. D3×#897C2semidirect
9. #10594380C2semidirect
10. D3×#886C2semidirect
11. #10594081C2semidirect
12. D3×#875C2semidirect
13. #10593894C2semidirect
14. #10593893C2semidirect
15. D3×#869C2semidirect
19. C22×#634C22semidirect
22. C22×C3×Dic6C22semidirect
24. C22×#627C22semidirect
37. C2×D3×Dic6C22semidirect
38. C2×D3×Dic6C22semidirect
39. C32×#117C22semidirect
40. #64106C22semidirect
41. #64095C22semidirect
42. #64084C22semidirect
43. #64078C22semidirect
44. C3×#926C22semidirect
45. C3×#897C22semidirect
46. C3×#892C22semidirect
48. C3×#886C22semidirect
50. C3×#877C22semidirect
51. C3×#875C22semidirect
52. C3×#872C22semidirect
54. C3×#869C22semidirect
55. #63966C22semidirect
56. #63962C22semidirect
58. #63918C22semidirect
59. #63895C22semidirect
60. #63893C22semidirect
61. #63891C22semidirect
62. #63890C22semidirect
64. #63871C22semidirect
65. #63866C22semidirect
66. #63866C22semidirect
67. #63864C22semidirect
68. #63860C22semidirect
69. #63857C22semidirect
70. #63852C22semidirect
96. #5526D3direct (N × H)
97. D3×#117D3semidirect
216. C22×Dic6C2×D3semidirect
226. C3×#117C2×D3semidirect
227. C3×#117C2×D3semidirect
239. #926C2×D3semidirect
249. #897C2×D3semidirect
252. #892C2×D3semidirect
263. #886C2×D3semidirect
269. #877C2×D3semidirect
276. #875C2×D3semidirect
277. #872C2×D3semidirect
285. #869C2×D3semidirect
577. #117D32semidirect
706. C3×D3#536semidirect
833. C32C2×#536semidirect
902. D3#5526direct (N × H)
927. C3C2×#5526semidirect
928. C3D3×#536semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C22×D3×Dic62
#105959972
C3×#55262
C3×D3×#1172
#105948662
#105948562
D3×#8972
#105943802
D3×#8862
#105940812
D3×#8752
#105938942
#105938932
D3×#8692
D3×#5363
C2×#55263