Finite Group Databasebeta

← D3×#5223 #11808090

Subgroups — D3×#5223 #11808090

Order 1152.

3785 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C22×D3×#67C212yesmaximal, complemented
3C2×D3×#217C212yesmaximal, complemented
4C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#10592922C211yesmaximal, characteristic, complemented
6C3×#5223C211yesmaximal, characteristic, complemented
7#10591724C212yesmaximal, complemented
8#10591723C212yesmaximal, complemented
9#10591391C211yesmaximal, characteristic, complemented
10#10591389C211yesmaximal, characteristic, complemented
11D3×C3⋊#95C211yesmaximal, characteristic, complemented
12C2×#5223—31nomaximal
13D3×#392—31nomaximal
14C24×C3×D3C2212yes—
15C23×D32C2211yescharacteristic
16C22×C32×D4C2211yescharacteristic, complemented
17C22×#638C2212yescomplemented
18C22×C3×#67C2212yescomplemented
19C22×C3×#67C2212yescomplemented
20C2×C3×D3×D4—24no—
21C2×C3×D3×D4—28no—
22C22×C3×D12C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic
24C2×D3×#67—28no—
25C2×D3×#67—28no—
26C2×D3×#67—28no—
27C22×#626C2212yescomplemented
28C22×#625C2212yescomplemented
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2212yes—
31C2×#3757C2212yescomplemented
32C2×#3752C2211yescharacteristic, complemented
33C2×C3×#217C2212yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35D3×#217—28no—
36C2×#3722C2211yescharacteristic, complemented
37C2×(C2×D3)⋊Dic3C2212yescomplemented
38C2×(C2×D3)⋊Dic3C2212yescomplemented
39C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
40D3×(C2×D3)⋊C4—24no—
41#63658C2211yescharacteristic, complemented
42C3×C3⋊#95C2211yescharacteristic, complemented
43#63579C2212yescomplemented
44C23×C3×D4—31no—
45C23×#67—32no—
46C22×D3×D4—32no—
47C22×D3×D4D311yescharacteristic, complemented
48C22×#217—32no—
49C22×(C2×D3)⋊C4—31no—
50C2×D3×C22⋊C4—32no—
51C2×D3×C22⋊C4—31no—
52C3×#392—31no—
53#5223—31no—
54#5223—31no—
55#5223—32no—
56#5223—32no—
57#5223—32no—
58#5223—31no—
59#5223—31no—
60#5223—61no—
61#5223D311yescharacteristic, direct product factor
62C2×C3⋊#95—31no—
63#4960—32no—
64#4960—31no—
65#4671—31no—
66D3×#95—31no—
67C24×C32C2312yes—
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3—24no—
72C23×C3×D3—24no—
73C23×C3×D3—24no—
74C23×C3×D3—24no—
75C23×C3×D3D418yescomplemented
76C23×C3×D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C22×D32—24no—
80C22×D32—24no—
81C22×D32—22no—
82C22×D32—22no—
83C22×D32D414yescomplemented
84C2×C32×D4—24no—
85C2×C32×D4—22no—
86C22×C32×C4C2311yescharacteristic
87C2×#638—24no—
88C2×#638—24no—
89C2×#638—24no—
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2312yes—
92C2×C3×#67—24no—
93C2×C3×#67—24no—
94C2×C3×#67—24no—
95C2×C3×#67—24no—
96C2×C3×#67—24no—
97C2×C3×#67—24no—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2312yes—
100C22×C3×Dic3C2311yescharacteristic
101C3×D3×D4—232no—
102C2×C3×D12—24no—
103C2×C3×D12—22no—
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3D414yescomplemented
106D3×#67—264no—
107C2×#626—24no—
108C2×#626—24no—
109C2×#626—24no—
110C2×#625—24no—
111C2×#625—24no—
112C2×#625—24no—
113C2×D3×Dic3—24no—
114C2×D3×Dic3—24no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—24no—
117C2×D3×Dic3D418yescomplemented
118#3757—24no—
119#3752—22no—
120C3×#217—24no—
121C3×(C2×D3)⋊C4—22no—
122#3722—22no—
123(C2×D3)⋊Dic3—24no—
124(C2×D3)⋊Dic3—22no—
125(C2×D3)⋊Dic3—24no—
126C2×#392—91noSylow
127C25×C3—32no—
128C24×D3—31no—
129C24×D3—31no—
130C24×D3C2×D312yes—
131C22×C3×D4—21no—
132C22×C3×D4—32no—
133C22×C3×D4—32no—
134C22×C3×D4—31no—
135C22×C3×D4—64no—
136C22×C3×D4—68no—
137C22×C3×D4C2×D311yescharacteristic, complemented
138C22×C3×D4C2×D311yescharacteristic, complemented
139C23×C3×C4—31no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—62no—
146C22×#67—68no—
147C22×#67—68no—
148C22×#67—68no—
149C22×#67C2×D312yescomplemented
150C22×#67C2×D312yescomplemented
151C23×Dic3—32no—
152C23×Dic3—31no—
153C2×D3×D4—28no—
154C2×D3×D4—24no—
155C2×D3×D4—68no—
156C2×D3×D4—68no—
157C2×D3×D4—68no—
158C22×D12—32no—
159C22×D12C2×D311yescharacteristic, complemented
160C22×C4×D3—32no—
161C22×C4×D3—31no—
162C22×C4×D3C2×D311yescharacteristic
163C2×C3×C22⋊C4—32no—
164C2×C3×C22⋊C4—31no—
165C2×#217—32no—
166C2×#217—32no—
167C2×#217—31no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—62no—
171C2×#217—68no—
172C2×#217C2×D312yescomplemented
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—61no—
181C2×(C2×D3)⋊C4—64no—
182C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
183D3×C22⋊C4—68no—
184D3×C22⋊C4—64no—
185C3×#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—32no—
189C3⋊#95—32no—
190C3⋊#95—61no—
191C3⋊#95C2×D311yescharacteristic, complemented
192C23×C32—22no—
193C23×C32—22no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32C2×D414yescomplemented
199C23×C32C2411yescharacteristic
200C22×C3⋊D3—21no—
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3C2×D412yescomplemented
205C22×C3×D3—21no—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—216no—
216C22×C3×D3—216no—
217C22×C3×D3—216no—
218C22×C3×D3—48no—
219C22×C3×D3—48no—
220C22×C3×D3—48no—
221C22×C3×D3—48no—
222C22×C3×D3C2×D412yes—
223C22×C3×D3C2×D414yes—
224C22×C3×D3C2×D414yes—
225C22×C3×D3C2×D412yes—
226C22×C3×D3C2×D412yescomplemented
227C22×C3×D3C2×D414yescomplemented
228C22×C3×D3#4112yes—
229C2×D32—216no—
230C2×D32—28no—
231C2×D32—44no—
232C2×D32—48no—
233C2×D32—44no—
234C32×D4—28no—
235C2×C32×C4—22no—
236C2×C32×C4C2×D412yescomplemented
237#638—216no—
238C2×C3⋊Dic3—22no—
239C2×C3⋊Dic3—22no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—22no—
242C2×C3⋊Dic3C2×D414yescomplemented
243C3×#67—216no—
244C3×#67—216no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—22no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D414yescomplemented
251C2×C3×Dic3C2×D412yescomplemented
252C3×D12—28no—
253C3×C4×D3—28no—
254#626—216no—
255#625—216no—
256D3×Dic3—216no—
257D3×Dic3—44no—
258C23×D4—31no—
259C23×D4—92no—
260C22×C22⋊C4—91no—
261C22×C22⋊C4—92no—
262#392—31no—
263#392—91no—
264#392—92no—
265#392—91no—
266#392—92no—
267#392—91no—
268C2×#95—91no—
269C24×C3—22no—
270C24×C3—31no—
271C24×C3—38no—
272C24×C3—32no—
273C24×C3—31no—
274C24×C3—64no—
275C24×C3—64no—
276C24×C3—64no—
277C24×C3—64no—
278C24×C3—64no—
279C24×C3—64no—
280C24×C3C22×D312yes—
281C24×C3C22×D312yes—
282C23×D3—24no—
283C23×D3—24no—
284C23×D3—24no—
285C23×D3—24no—
286C23×D3—24no—
287C23×D3—24no—
288C23×D3—31no—
289C23×D3—31no—
290C23×D3—34no—
291C23×D3—34no—
292C23×D3—61no—
293C23×D3—62no—
294C23×D3—64no—
295C23×D3—64no—
296C23×D3—62no—
297C23×D3—64no—
298C23×D3—62no—
299C23×D3—62no—
300C23×D3—64no—
301C23×D3#6718yescomplemented
302C23×D3C22×D311yescharacteristic
303C23×D3C22×D312yes—
304C23×D3C22×D311yescharacteristic
305C2×C3×D4—24no—
306C2×C3×D4—24no—
307C2×C3×D4—22no—
308C2×C3×D4—22no—
309C2×C3×D4—42no—
310C2×C3×D4—44no—
311C2×C3×D4—64no—
312C2×C3×D4—64no—
313C2×C3×D4—64no—
314C2×C3×D4—632no—
315C2×C3×D4—64no—
316C2×C3×D4—64no—
317C2×C3×D4—64no—
318C2×C3×D4—64no—
319C2×C3×D4—62no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—32no—
323C22×C3×C4—34no—
324C22×C3×C4—31no—
325C22×C3×C4—64no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—24no—
329C2×#67—24no—
330C2×#67—24no—
331C2×#67—24no—
332C2×#67—24no—
333C2×#67—24no—
334C2×#67—64no—
335C2×#67—64no—
336C2×#67—64no—
337C2×#67—64no—
338C2×#67—64no—
339C2×#67—64no—
340C2×#67—664no—
341C2×#67—64no—
342C2×#67—64no—
343C2×#67—64no—
344C2×#67—64no—
345C2×#67—64no—
346C2×#67—64no—
347C2×#67—64no—
348C2×#67—64no—
349C2×#67—64no—
350C2×#67—124no—
351C2×#67—124no—
352C2×#67—124no—
353C22×Dic3—32no—
354C22×Dic3—32no—
355C22×Dic3—38no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—62no—
359C22×Dic3—61no—
360C22×Dic3—64no—
361C22×Dic3—64no—
362C22×Dic3—62no—
363C22×Dic3—64no—
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D312yes—
366C22×Dic3C22×D311yescharacteristic
367D3×D4—232no—
368D3×D4—664no—
369C2×D12—24no—
370C2×D12—22no—
371C2×D12—64no—
372C2×D12—64no—
373C2×D12—64no—
374C2×C4×D3—24no—
375C2×C4×D3—38no—
376C2×C4×D3—64no—
377C2×C4×D3—64no—
378C2×C4×D3—64no—
379C2×C4×D3—62no—
380C2×C4×D3#6714yescomplemented
381C3×C22⋊C4—64no—
382C3×C22⋊C4—62no—
383#217—24no—
384#217—64no—
385#217—64no—
386#217—64no—
387#217—64no—
388#217—62no—
389#217—124no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—64no—
393(C2×D3)⋊C4—64no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—122no—
399C22×C32—24no—
400C22×C32—24no—
401C22×C32—24no—
402C22×C32—42no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—42no—
406C22×C32C22×D411yescharacteristic
407C22×C32C22×D412yes—
408C22×C32C22×D412yes—
409C22×C32C22×D411yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C2×C3⋊D3—24no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—42no—
415C2×C3⋊D3—41no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—24no—
419C2×C3×D3—22no—
420C2×C3×D3—24no—
421C2×C3×D3—41no—
422C2×C3×D3—42no—
423C2×C3×D3—42no—
424C2×C3×D3—42no—
425C2×C3×D3—42no—
426C2×C3×D3—41no—
427C2×C3×D3—42no—
428C2×C3×D3—432no—
429C2×C3×D3#12018yes—
430C2×C3×D3#12014yes—
431C2×C3×D3#12114yes—
432C2×C3×D3#12118yes—
433C2×C3×D3#12714yes—
434D32—416no—
435C32×C4—22no—
436C3⋊Dic3—24no—
437C3⋊Dic3—41no—
438C3×Dic3—24no—
439C3×Dic3—22no—
440C3×Dic3—41no—
441C25—32no—
442C25—91no—
443C22×D4—32no—
444C22×D4—32no—
445C22×D4—31no—
446C22×D4—64no—
447C22×D4—68no—
448C22×D4—92no—
449C22×D4—92no—
450C22×D4—92no—
451C22×D4—188no—
452C22×D4—188no—
453C22×D4—188no—
454C22×D4D3211yescharacteristic, complemented
455C23×C4—31no—
456C23×C4—92no—
457C23×C4—91no—
458C2×C22⋊C4—32no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—92no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—92no—
464C2×C22⋊C4—92no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—184no—
467C2×C22⋊C4—188no—
468#95—31no—
469#95—92no—
470#95—91no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—21no—
484C23×C3—24no—
485C23×C3—34no—
486C23×C3—32no—
487C23×C3—32no—
488C23×C3—34no—
489C23×C3—32no—
490C23×C3—32no—
491C23×C3—34no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—42no—
498C23×C3—616no—
499C23×C3—616no—
500C23×C3—616no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—62no—
505C23×C3—62no—
506C23×C3—62no—
507C23×C3—61no—
508C23×C3—62no—
509C23×C3—61no—
510C23×C3—62no—
511C23×C3—128no—
512C23×C3—128no—
513C23×C3—128no—
514C23×C3—128no—
515C23×C3D3×D414yescomplemented
516C23×C3C2×#6714yescomplemented
517C23×C3C23×D311yescharacteristic
518C23×C3C23×D311yescharacteristic
519C22×D3—21no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—21no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—216no—
530C22×D3—216no—
531C22×D3—216no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—48no—
535C22×D3—48no—
536C22×D3—48no—
537C22×D3—48no—
538C22×D3—62no—
539C22×D3—616no—
540C22×D3—68no—
541C22×D3—61no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—62no—
549C22×D3—616no—
550C22×D3—68no—
551C22×D3—121no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—121no—
555C22×D3—124no—
556C22×D3—124no—
557C22×D3—128no—
558C22×D3—128no—
559C22×D3—124no—
560C22×D3—124no—
561C22×D3D3×D412yes—
562C22×D3D3×D414yes—
563C22×D3D3×D412yescomplemented
564C22×D3#23712yes—
565C22×D3C2×#6714yes—
566C22×D3C2×#6712yes—
567C22×D3C2×#6714yescomplemented
568C3×D4—28no—
569C3×D4—28no—
570C3×D4—48no—
571C3×D4—68no—
572C3×D4—616no—
573C3×D4—616no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—32no—
578C2×C3×C4—34no—
579C2×C3×C4—42no—
580C2×C3×C4—68no—
581C2×C3×C4—62no—
582C2×C3×C4—62no—
583C2×C3×C4—62no—
584C2×C3×C4—62no—
585C2×C3×C4—61no—
586C2×C3×C4D3×D412yescomplemented
587C2×C3×C4C2×#6712yescomplemented
588#67—216no—
589#67—216no—
590#67—616no—
591#67—616no—
592#67—616no—
593#67—616no—
594#67—616no—
595#67—1216no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—21no—
600C2×Dic3—22no—
601C2×Dic3—34no—
602C2×Dic3—34no—
603C2×Dic3—64no—
604C2×Dic3—616no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—61no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—61no—
613C2×Dic3—122no—
614C2×Dic3—122no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3—124no—
618C2×Dic3D3×D414yescomplemented
619C2×Dic3C2×#6712yescomplemented
620D12—28no—
621D12—616no—
622C4×D3—28no—
623C4×D3—616no—
624C4×D3—124no—
625C2×C32—44no—
626C2×C32C2×#12012yes—
627C2×C32C2×#12011yescharacteristic
628C2×C32C2×#12111yescharacteristic
629C2×C32C2×#12112yes—
630C2×C32C2×#12711yescharacteristic
631C3⋊D3—42no—
632C3×D3—42no—
633C3×D3—44no—
634C3×D3#39218yescomplemented
635C24—31no—
636C24—31no—
637C24—32no—
638C24—38no—
639C24—64no—
640C24—64no—
641C24—64no—
642C24—64no—
643C24—64no—
644C24—64no—
645C24—94no—
646C24—91no—
647C24—182no—
648C24—184no—
649C24—184no—
650C24—182no—
651C24C2×D3212yes—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—64no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—632no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—64no—
661C2×D4—64no—
662C2×D4—62no—
663C2×D4—184no—
664C2×D4—184no—
665C2×D4—184no—
666C2×D4—184no—
667C2×D4—184no—
668C2×D4—1864no—
669C2×D4—184no—
670C2×D4—184no—
671C2×D4—184no—
672C2×D4—184no—
673C22×C4—32no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—31no—
677C22×C4—64no—
678C22×C4—98no—
679C22×C4—92no—
680C22×C4—91no—
681C22×C4—184no—
682C22×C4—184no—
683C22×C4—184no—
684C22×C4—182no—
685C22×C4C2×D3211yescharacteristic
686C22⋊C4—64no—
687C22⋊C4—62no—
688C22⋊C4—182no—
689C22⋊C4—184no—
690C22⋊C4—182no—
691C22⋊C4—184no—
692C22⋊C4—184no—
693C22⋊C4—182no—
694C22×C3—24no—
695C22×C3—24no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—22no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—22no—
705C22×C3—34no—
706C22×C3—38no—
707C22×C3—34no—
708C22×C3—34no—
709C22×C3—38no—
710C22×C3—44no—
711C22×C3—44no—
712C22×C3—44no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—64no—
722C22×C3—62no—
723C22×C3—64no—
724C22×C3—64no—
725C22×C3—64no—
726C22×C3—82no—
727C22×C3—82no—
728C22×C3—82no—
729C22×C3—82no—
730C22×C3—1232no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—122no—
736C22×C3—122no—
737C22×C3—122no—
738C22×C3C2×D3×D412yes—
739C22×C3C2×D3×D411yescharacteristic
740C22×C3C2×D3×D412yes—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D412yes—
744C22×C3C2×#23711yescharacteristic
745C22×C3D3×#4111yescharacteristic
746C22×C3C22×#6712yes—
747C22×C3C22×#6711yescharacteristic
748C2×D3—24no—
749C2×D3—24no—
750C2×D3—24no—
751C2×D3—24no—
752C2×D3—22no—
753C2×D3—41no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—41no—
759C2×D3—42no—
760C2×D3—432no—
761C2×D3—64no—
762C2×D3—62no—
763C2×D3—64no—
764C2×D3—62no—
765C2×D3—124no—
766C2×D3—122no—
767C2×D3—1216no—
768C2×D3—121no—
769C2×D3—122no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—122no—
774C2×D3—1216no—
775C2×D3—241no—
776C2×D3—242no—
777C2×D3—241no—
778C2×D3#93718yes—
779C2×D3#93814yes—
780C2×D3#93918yes—
781C2×D3#94014yes—
782C2×D3#95314yes—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—42no—
786C3×C4—64no—
787C3×C4—62no—
788C3×C4—121no—
789Dic3—22no—
790Dic3—24no—
791Dic3—41no—
792Dic3—64no—
793Dic3—64no—
794Dic3—124no—
795Dic3—121no—
796Dic3—121no—
797Dic3—241no—
798C32C2×#39211yescharacteristic, complemented, Sylow
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—34no—
806C23—32no—
807C23—32no—
808C23—32no—
809C23—34no—
810C23—32no—
811C23—34no—
812C23—616no—
813C23—616no—
814C23—616no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—61no—
821C23—61no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—92no—
826C23—128no—
827C23—128no—
828C23—128no—
829C23—128no—
830C23—1816no—
831C23—188no—
832C23—182no—
833C23—181no—
834C23—181no—
835C23—182no—
836C23—364no—
837C23—368no—
838C23—364no—
839C23D3×#6714yescomplemented
840C23C22×D3211yescharacteristic
841D4—28no—
842D4—68no—
843D4—616no—
844D4—616no—
845D4—1816no—
846D4—1816no—
847D4—1816no—
848C2×C4—22no—
849C2×C4—34no—
850C2×C4—32no—
851C2×C4—68no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—61no—
857C2×C4—94no—
858C2×C4—1816no—
859C2×C4—182no—
860C2×C4—182no—
861C2×C4—182no—
862C2×C4—181no—
863C2×C4—364no—
864C2×C4D3×#6712yescomplemented
865C2×C3—21no—
866C2×C3—22no—
867C2×C3—21no—
868C2×C3—22no—
869C2×C3—21no—
870C2×C3—38no—
871C2×C3—44no—
872C2×C3—44no—
873C2×C3—84no—
874C2×C3—122no—
875C2×C3—124no—
876C2×C3D3×#12011yescharacteristic
877C2×C3D3×#12012yes—
878C2×C3D3×#12111yescharacteristic
879C2×C3D3×#12112yes—
880C2×C3D3×#12711yescharacteristic
881C2×C3C2×#93712yes—
882C2×C3C2×#93811yescharacteristic
883C2×C3C2×#93912yes—
884C2×C3C2×#94011yescharacteristic
885C2×C3C2×#95311yescharacteristic
886D3—44no—
887D3—42no—
888D3—122no—
889D3—122no—
890D3—242no—
891D3#522318yesdirect product factor
892C22—24no—
893C22—24no—
894C22—24no—
895C22—34no—
896C22—38no—
897C22—34no—
898C22—38no—
899C22—34no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—64no—
905C22—64no—
906C22—64no—
907C22—62no—
908C22—64no—
909C22—1232no—
910C22—121no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—121no—
917C22—184no—
918C22—182no—
919C22—3616no—
920C22—361no—
921C22—362no—
922C22—361no—
923C22D32×D411yescharacteristic
924C22D32×D412yes—
925C22D3×#23711yescharacteristic
926C22C2×D3×#6712yes—
927C22C2×D3×#6711yescharacteristic
928C4—22no—
929C4—62no—
930C4—64no—
931C4—121no—
932C4—184no—
933C4—361no—
934C3—21no—
935C3D3×#39211yescharacteristic, complemented
936C3C2×#522311yescharacteristic, complemented
937C2—38no—
938C2—44no—
939C2—124no—
940C2—122no—
941C2—362no—
942C2D3×#93712yes—
943C2D3×#93811yescharacteristic
944C2D3×#93912yes—
945C2D3×#94011yescharacteristic
946C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32C2×#392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C22×D3×#67C2semidirect
3. C2×D3×#217C2semidirect
4. C2×D3×(C2×D3)⋊C4C2semidirect
5. #10592922C2semidirect
6. C3×#5223C2semidirect
7. #10591724C2semidirect
8. #10591723C2semidirect
9. #10591391C2semidirect
10. #10591389C2semidirect
11. D3×C3⋊#95C2semidirect
16. C22×C32×D4C22semidirect
17. C22×#638C22semidirect
18. C22×C3×#67C22semidirect
19. C22×C3×#67C22semidirect
22. C22×C3×D12C22semidirect
27. C22×#626C22semidirect
28. C22×#625C22semidirect
31. C2×#3757C22semidirect
32. C2×#3752C22semidirect
33. C2×C3×#217C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×#3722C22semidirect
37. C2×(C2×D3)⋊Dic3C22semidirect
38. C2×(C2×D3)⋊Dic3C22semidirect
39. C2×(C2×D3)⋊Dic3C22semidirect
41. #63658C22semidirect
42. C3×C3⋊#95C22semidirect
43. #63579C22semidirect
47. C22×D3×D4D3semidirect
61. #5223D3direct (N × H)
75. C23×C3×D3D4semidirect
83. C22×D32D4semidirect
105. C2×C3×C4×D3D4semidirect
117. C2×D3×Dic3D4semidirect
137. C22×C3×D4C2×D3semidirect
138. C22×C3×D4C2×D3semidirect
149. C22×#67C2×D3semidirect
150. C22×#67C2×D3semidirect
159. C22×D12C2×D3semidirect
172. C2×#217C2×D3semidirect
182. C2×(C2×D3)⋊C4C2×D3semidirect
191. C3⋊#95C2×D3semidirect
198. C23×C32C2×D4semidirect
204. C22×C3⋊D3C2×D4semidirect
226. C22×C3×D3C2×D4semidirect
227. C22×C3×D3C2×D4semidirect
236. C2×C32×C4C2×D4semidirect
242. C2×C3⋊Dic3C2×D4semidirect
250. C2×C3×Dic3C2×D4semidirect
251. C2×C3×Dic3C2×D4semidirect
301. C23×D3#67semidirect
380. C2×C4×D3#67semidirect
454. C22×D4D32semidirect
515. C23×C3D3×D4semidirect
516. C23×C3C2×#67semidirect
563. C22×D3D3×D4semidirect
567. C22×D3C2×#67semidirect
586. C2×C3×C4D3×D4semidirect
587. C2×C3×C4C2×#67semidirect
618. C2×Dic3D3×D4semidirect
619. C2×Dic3C2×#67semidirect
634. C3×D3#392semidirect
798. C32C2×#392semidirect
839. C23D3×#67semidirect
864. C2×C4D3×#67semidirect
891. D3#5223direct (N × H)
935. C3D3×#392semidirect
936. C3C2×#5223semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C22×D3×#672
C2×D3×#2172
C2×D3×(C2×D3)⋊C42
#105929222
C3×#52232
#105917242
#105917232
#105913912
#105913892
D3×C3⋊#952
C2×#52233
D3×#3923