Finite Group Databasebeta

← #11809012

Subgroups — #11809012

Order 1152.

3271 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C23×#625C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic, complemented
4C2×#63977C211yesmaximal, characteristic, complemented
5C2×#63922C212yesmaximal, complemented
6#10592657C211yesmaximal, characteristic, complemented
7C3×#4955C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591393C212yesmaximal, complemented
10#10591389C212yesmaximal, complemented
11#10591363C212yesmaximal, complemented
12#82604—31nomaximal
13#73852—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic, complemented
16C23×D32C2211yescharacteristic, complemented
17C22×#638C2211yescharacteristic
18C23×C3⋊Dic3C2211yescharacteristic, complemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2212yescomplemented
21C2×D3×#67—24no—
22C2×D3×#67—24no—
23C2×D3×#67—24no—
24C22×#626C2211yescharacteristic, complemented
25C22×#626C2212yescomplemented
26C22×#625—28no—
27C22×#625—24no—
28C22×#625C2212yes—
29C22×#625C2212yescomplemented
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3752C2212yescomplemented
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C3×#882—24no—
39#63977—24no—
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41C2×(C2×D3)⋊Dic3C2212yescomplemented
42#63922—28no—
43#63658C2212yescomplemented
44#63579C2212yescomplemented
45C23×#67—31no—
46C23×#67—31no—
47C23×#67—31no—
48C22×D3×D4—31no—
49C2×C3×#120—31no—
50C2×#953—31no—
51C2×#937—32no—
52C2×#882—31no—
53C2×#882—32no—
54C2×#882D311yescharacteristic, complemented
55C3×#379—31no—
56#5223—32no—
57#5220—31no—
58#4960—32no—
59#4960—32no—
60#4960—32no—
61#4958—31no—
62#4958—31no—
63#4958—31no—
64#4958—32no—
65#4958—61no—
66#4956—32no—
67#4955D311yescharacteristic, complemented
68C24×C32C2311yescharacteristic
69C23×C3⋊D3C2311yescharacteristic
70C23×C3×D3—22no—
71C23×C3×D3—22no—
72C23×C3×D3—22no—
73C23×C3×D3—24no—
74C23×C3×D3—24no—
75C23×C3×D3—22no—
76C23×C3×D3—22no—
77C23×C3×D3—42no—
78C23×C3×D3—42no—
79C23×C3×D3D414yescomplemented
80C23×C3×D3C2311yescharacteristic
81C23×C3×D3C2312yes—
82C23×C3×D3C2311yescharacteristic
83C23×C3×D3C2311yescharacteristic
84C22×D32—22no—
85C22×D32—22no—
86C22×D32—22no—
87C22×D32—24no—
88C22×D32—42no—
89C22×C32×C4C2312yes—
90C2×#638—22no—
91C2×#638—22no—
92C2×#638D414yescomplemented
93C22×C3⋊Dic3—22no—
94C22×C3⋊Dic3—24no—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2312yes—
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67D414yescomplemented
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—24no—
103C2×C3×D12—24no—
104C2×C3×D12—42no—
105D3×#67—232no—
106C2×#626—22no—
107C2×#626—22no—
108C2×#626—22no—
109C2×#626—24no—
110C2×#626—24no—
111C2×#626—42no—
112C2×#625—232no—
113C2×#625—24no—
114C2×#625—24no—
115C2×#625—24no—
116C2×#625—22no—
117C2×#625—24no—
118C2×#625—22no—
119C2×#625—24no—
120C2×#625—22no—
121C2×#625D418yescomplemented
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C32×C22⋊C4—22no—
126#3752—24no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—24no—
129C3×(C2×D3)⋊C4—24no—
130C3×(C2×D3)⋊C4—42no—
131(C2×D3)⋊Dic3—24no—
132(C2×D3)⋊Dic3—24no—
133#2403—91noSylow
134C25×C3—31no—
135C25×C3—31no—
136C24×D3—31no—
137C24×D3—31no—
138C24×D3C2×D311yescharacteristic
139C24×D3C2×D311yescharacteristic, complemented
140C22×C3×D4—31no—
141C22×C3×D4—32no—
142C22×#67—31no—
143C22×#67—31no—
144C22×#67—32no—
145C22×#67—32no—
146C22×#67—31no—
147C22×#67—32no—
148C22×#67—31no—
149C22×#67—32no—
150C22×#67—31no—
151C22×#67—32no—
152C22×#67—61no—
153C22×#67—64no—
154C22×#67—64no—
155C22×#67—68no—
156C22×#67—68no—
157C22×#67—64no—
158C22×#67—64no—
159C22×#67—64no—
160C22×#67C2×D311yescharacteristic
161C23×Dic3—31no—
162C23×Dic3—31no—
163C23×Dic3—31no—
164C23×Dic3—61no—
165C2×D3×D4—64no—
166C2×D3×D4—64no—
167C2×D3×D4—64no—
168C22×D12—31no—
169C22×D12—32no—
170C22×D12C2×D312yescomplemented
171C22×C4×D3—31no—
172C3×#120—64no—
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—32no—
176C2×C3×C22⋊C4—32no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
179C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
180#953—64no—
181C2×#217—32no—
182C2×#217—32no—
183C2×#217C2×D311yescharacteristic, complemented
184#937—68no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—62no—
190C2×(C2×D3)⋊C4C2×D312yescomplemented
191C2×(C2×D3)⋊C4C2×D312yescomplemented
192C2×(C2×D3)⋊C4C2×D312yescomplemented
193#882—24no—
194#882—68no—
195#882—64no—
196C3⋊#95—32no—
197C3⋊#95—32no—
198C3⋊#95—32no—
199C3⋊#95—32no—
200C3⋊#95—62no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32C2×D412yes—
204C23×C32C2×D412yes—
205C23×C32C2×D412yes—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3C2×D412yescomplemented
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—28no—
216C22×C3×D3—28no—
217C22×C3×D3—22no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—22no—
228C22×C3×D3—22no—
229C22×C3×D3—22no—
230C22×C3×D3—22no—
231C22×C3×D3—28no—
232C22×C3×D3—44no—
233C22×C3×D3—48no—
234C22×C3×D3—48no—
235C22×C3×D3—48no—
236C22×C3×D3—48no—
237C22×C3×D3—44no—
238C22×C3×D3—44no—
239C22×C3×D3C2×D412yes—
240C22×C3×D3C2×D412yes—
241C22×C3×D3C2×D414yes—
242C22×C3×D3C2×D414yescomplemented
243C22×C3×D3C2×D412yescomplemented
244C2×D32—28no—
245C2×D32—48no—
246C2×D32—48no—
247C2×D32—44no—
248C2×D32—44no—
249C2×C32×C4—22no—
250C2×C32×C4—22no—
251C2×C32×C4—22no—
252#638—28no—
253C2×C3⋊Dic3—28no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—22no—
257C2×C3⋊Dic3—22no—
258C2×C3⋊Dic3C2×D412yescomplemented
259C2×C3⋊Dic3C2×D414yescomplemented
260C3×#67—28no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3C2×D412yescomplemented
267C3×D12—48no—
268#626—28no—
269#626—48no—
270#625—216no—
271#625—28no—
272#625—216no—
273D3×Dic3—28no—
274C23×D4—91no—
275C23×D4—91no—
276C2×#120—31no—
277C2×#120—92no—
278C2×#120—91no—
279#392—92no—
280#392—92no—
281#386—92no—
282#386—91no—
283#386—91no—
284#379—31no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3—32no—
288C24×C3—31no—
289C24×C3—31no—
290C24×C3—34no—
291C24×C3—64no—
292C24×C3—64no—
293C24×C3—62no—
294C24×C3—62no—
295C24×C3—62no—
296C24×C3—62no—
297C24×C3—62no—
298C24×C3—122no—
299C24×C3—122no—
300C24×C3C22×D311yescharacteristic
301C24×C3C22×D311yescharacteristic
302C23×D3—22no—
303C23×D3—22no—
304C23×D3—22no—
305C23×D3—24no—
306C23×D3—24no—
307C23×D3—22no—
308C23×D3—22no—
309C23×D3—31no—
310C23×D3—31no—
311C23×D3—42no—
312C23×D3—42no—
313C23×D3—61no—
314C23×D3—62no—
315C23×D3—62no—
316C23×D3—62no—
317C23×D3—62no—
318C23×D3—64no—
319C23×D3—62no—
320C23×D3—62no—
321C23×D3—64no—
322C23×D3—122no—
323C23×D3—122no—
324C23×D3D1214yescomplemented
325C23×D3C22×D311yescharacteristic
326C23×D3C22×D312yes—
327C23×D3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C2×C3×D4—34no—
330C2×C3×D4—64no—
331C2×C3×D4—64no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C2×C3×D4—122no—
335C22×C3×C4—22no—
336C22×C3×C4—31no—
337C22×C3×C4—32no—
338C22×C3×C4C22×D312yes—
339C22×C3×C4C22×D312yes—
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—34no—
343C2×#67—34no—
344C2×#67—38no—
345C2×#67—38no—
346C2×#67—64no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—64no—
350C2×#67—64no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—64no—
354C2×#67—64no—
355C2×#67—632no—
356C2×#67—62no—
357C2×#67—64no—
358C2×#67—64no—
359C2×#67—62no—
360C2×#67—64no—
361C2×#67—64no—
362C2×#67—632no—
363C2×#67—632no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—64no—
370C2×#67—64no—
371C2×#67—64no—
372C2×#67—64no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—122no—
376C2×#67—122no—
377C2×#67—122no—
378C2×#67#6714yescomplemented
379C22×Dic3—32no—
380C22×Dic3—31no—
381C22×Dic3—32no—
382C22×Dic3—31no—
383C22×Dic3—61no—
384C22×Dic3—62no—
385C22×Dic3—62no—
386C22×Dic3—62no—
387C22×Dic3—64no—
388C22×Dic3—64no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—124no—
393C22×Dic3—122no—
394C22×Dic3C22×D312yes—
395C22×Dic3C22×D311yescharacteristic
396D3×D4—632no—
397C2×D12—24no—
398C2×D12—24no—
399C2×D12—42no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—64no—
404C2×D12—64no—
405C2×D12—122no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—22no—
411C3×C22⋊C4—42no—
412C3×C22⋊C4—64no—
413C3×C22⋊C4—64no—
414C3×C22⋊C4—62no—
415C3×C22⋊C4—122no—
416#217—22no—
417#217—64no—
418#217—64no—
419(C2×D3)⋊C4—24no—
420(C2×D3)⋊C4—24no—
421(C2×D3)⋊C4—42no—
422(C2×D3)⋊C4—64no—
423(C2×D3)⋊C4—64no—
424(C2×D3)⋊C4—64no—
425(C2×D3)⋊C4—64no—
426(C2×D3)⋊C4—124no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32#12014yescomplemented
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C22×D412yes—
435C22×C32C22×D411yescharacteristic
436C22×C32H(5,𝔽2)12yes—
437C2×C3⋊D3—22no—
438C2×C3⋊D3—24no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—42no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—24no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—416no—
455C2×C3×D3—416no—
456C2×C3×D3—41no—
457C2×C3×D3—42no—
458C2×C3×D3—41no—
459C2×C3×D3—42no—
460C2×C3×D3—42no—
461C2×C3×D3—42no—
462C2×C3×D3—42no—
463C2×C3×D3—42no—
464C2×C3×D3—42no—
465C2×C3×D3#12014yescomplemented
466D32—416no—
467C32×C4—42no—
468C3⋊Dic3—22no—
469C3⋊Dic3—24no—
470C3×Dic3—22no—
471C3×Dic3—42no—
472C25—31no—
473C25—31no—
474C25—91no—
475C22×D4—31no—
476C22×D4—32no—
477C22×D4—91no—
478C22×D4—92no—
479C22×D4—92no—
480C22×D4—91no—
481C22×D4—92no—
482C22×D4—91no—
483C22×D4—184no—
484C22×D4—184no—
485C22×D4—184no—
486C22×D4—188no—
487C22×D4—184no—
488C23×C4—91no—
489C23×C4—91no—
490#120—64no—
491#120—188no—
492#120—184no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—32no—
495C2×C22⋊C4—32no—
496C2×C22⋊C4—32no—
497C2×C22⋊C4—92no—
498C2×C22⋊C4—92no—
499C2×C22⋊C4—92no—
500C2×C22⋊C4D3211yescharacteristic, complemented
501#95—92no—
502#95—92no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—21no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—34no—
512C23×C3—32no—
513C23×C3—32no—
514C23×C3—34no—
515C23×C3—32no—
516C23×C3—42no—
517C23×C3—42no—
518C23×C3—68no—
519C23×C3—68no—
520C23×C3—61no—
521C23×C3—62no—
522C23×C3—61no—
523C23×C3—68no—
524C23×C3—62no—
525C23×C3—61no—
526C23×C3—62no—
527C23×C3—62no—
528C23×C3—62no—
529C23×C3—61no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—61no—
533C23×C3—62no—
534C23×C3—62no—
535C23×C3—62no—
536C23×C3—62no—
537C23×C3—61no—
538C23×C3—124no—
539C23×C3—128no—
540C23×C3—128no—
541C23×C3—128no—
542C23×C3—128no—
543C23×C3—124no—
544C23×C3—124no—
545C23×C3C2×D1212yes—
546C23×C3D3×D412yes—
547C23×C3D3×D412yes—
548C23×C3D3×D412yes—
549C23×C3D3×D412yes—
550C23×C3C2×#6712yes—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—22no—
556C22×D3—28no—
557C22×D3—28no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—28no—
573C22×D3—32no—
574C22×D3—32no—
575C22×D3—44no—
576C22×D3—48no—
577C22×D3—48no—
578C22×D3—48no—
579C22×D3—48no—
580C22×D3—44no—
581C22×D3—44no—
582C22×D3—62no—
583C22×D3—68no—
584C22×D3—68no—
585C22×D3—61no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—61no—
593C22×D3—122no—
594C22×D3—121no—
595C22×D3—121no—
596C22×D3—122no—
597C22×D3—128no—
598C22×D3—128no—
599C22×D3—128no—
600C22×D3—124no—
601C22×D3—128no—
602C22×D3—124no—
603C22×D3—124no—
604C22×D3—124no—
605C22×D3C2×D1212yes—
606C22×D3C2×D1212yes—
607C22×D3D3×D414yes—
608C22×D3D3×D414yescomplemented
609C22×D3C2×#6712yescomplemented
610C3×D4—68no—
611C3×D4—128no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—32no—
619C2×C3×C4—42no—
620C2×C3×C4—42no—
621C2×C3×C4—42no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627#67—28no—
628#67—68no—
629#67—616no—
630#67—68no—
631#67—616no—
632#67—68no—
633#67—616no—
634#67—68no—
635#67—68no—
636#67—616no—
637#67—128no—
638#67—128no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—32no—
645C2×Dic3—34no—
646C2×Dic3—34no—
647C2×Dic3—32no—
648C2×Dic3—64no—
649C2×Dic3—62no—
650C2×Dic3—68no—
651C2×Dic3—68no—
652C2×Dic3—68no—
653C2×Dic3—61no—
654C2×Dic3—62no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—61no—
661C2×Dic3—122no—
662C2×Dic3—122no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—128no—
666C2×Dic3C2×#6712yescomplemented
667D12—48no—
668D12—68no—
669D12—128no—
670C4×D3—68no—
671C2×C32—24no—
672C2×C32C2×#12011yescharacteristic
673C2×C32C2×#12011yescharacteristic
674C2×C32#53411yescharacteristic
675C2×C32D4212yes—
676C2×C32D4212yes—
677C3⋊D3—42no—
678C3×D3—24no—
679C3×D3—42no—
680C3×D3—42no—
681C3×D3—44no—
682C24—31no—
683C24—31no—
684C24—32no—
685C24—31no—
686C24—34no—
687C24—64no—
688C24—64no—
689C24—62no—
690C24—62no—
691C24—62no—
692C24—62no—
693C24—62no—
694C24—91no—
695C24—122no—
696C24—122no—
697C24—182no—
698C24—182no—
699C24—184no—
700C24—182no—
701C24—362no—
702C24C2×D3211yescharacteristic
703C2×D4—34no—
704C2×D4—64no—
705C2×D4—64no—
706C2×D4—62no—
707C2×D4—62no—
708C2×D4—98no—
709C2×D4—94no—
710C2×D4—122no—
711C2×D4—182no—
712C2×D4—182no—
713C2×D4—182no—
714C2×D4—184no—
715C2×D4—184no—
716C2×D4—182no—
717C2×D4—184no—
718C2×D4—1832no—
719C2×D4—184no—
720C2×D4—182no—
721C2×D4—184no—
722C2×D4—184no—
723C2×D4—184no—
724C2×D4—182no—
725C2×D4—1832no—
726C2×D4—182no—
727C2×D4—182no—
728C2×D4—362no—
729C22×C4—31no—
730C22×C4—32no—
731C22×C4—91no—
732C22×C4—92no—
733C22×C4—182no—
734C22×C4—182no—
735C22×C4—182no—
736C22×C4—184no—
737C22×C4—182no—
738C22×C4C2×D3212yes—
739C22⋊C4—22no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—62no—
743C22⋊C4—122no—
744C22⋊C4—184no—
745C22⋊C4—184no—
746C22⋊C4—184no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—24no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—24no—
753C22×C3—24no—
754C22×C3—24no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—21no—
760C22×C3—24no—
761C22×C3—34no—
762C22×C3—42no—
763C22×C3—44no—
764C22×C3—44no—
765C22×C3—42no—
766C22×C3—62no—
767C22×C3—64no—
768C22×C3—62no—
769C22×C3—64no—
770C22×C3—64no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—64no—
776C22×C3—64no—
777C22×C3—64no—
778C22×C3—1216no—
779C22×C3—1216no—
780C22×C3—121no—
781C22×C3—122no—
782C22×C3—121no—
783C22×C3—122no—
784C22×C3—122no—
785C22×C3—122no—
786C22×C3—122no—
787C22×C3—122no—
788C22×C3—122no—
789C22×C3#88214yescomplemented
790C22×C3#93714yescomplemented
791C22×C3C22×D1211yescharacteristic
792C22×C3C2×D3×D411yescharacteristic
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×D3×D411yescharacteristic
795C22×C3C2×D3×D412yes—
796C22×C3C2×D3×D412yes—
797C22×C3C2×D3×D411yescharacteristic
798C22×C3#100412yes—
799C22×C3#100412yes—
800C22×C3C22×#6711yescharacteristic
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—24no—
804C2×D3—24no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—24no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—416no—
814C2×D3—416no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—41no—
818C2×D3—42no—
819C2×D3—41no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—64no—
827C2×D3—64no—
828C2×D3—122no—
829C2×D3—124no—
830C2×D3—1216no—
831C2×D3—1216no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—122no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—122no—
838C2×D3—241no—
839C2×D3—242no—
840C2×D3—241no—
841C2×D3#88214yescomplemented
842C3×C4—42no—
843C3×C4—42no—
844C3×C4—62no—
845C3×C4—82no—
846C3×C4—122no—
847Dic3—22no—
848Dic3—42no—
849Dic3—62no—
850Dic3—64no—
851Dic3—62no—
852Dic3—64no—
853Dic3—124no—
854Dic3—122no—
855C32#240311yescharacteristic, complemented, Sylow
856C23—22no—
857C23—22no—
858C23—32no—
859C23—34no—
860C23—32no—
861C23—34no—
862C23—32no—
863C23—68no—
864C23—68no—
865C23—61no—
866C23—62no—
867C23—61no—
868C23—61no—
869C23—62no—
870C23—62no—
871C23—61no—
872C23—61no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—61no—
882C23—68no—
883C23—92no—
884C23—124no—
885C23—128no—
886C23—128no—
887C23—128no—
888C23—128no—
889C23—124no—
890C23—124no—
891C23—188no—
892C23—181no—
893C23—182no—
894C23—182no—
895C23—181no—
896C23—364no—
897C23—368no—
898C23—368no—
899C23—364no—
900C23D3×D1212yes—
901C23#380212yes—
902C23D3×#6712yes—
903C23C22×D3211yescharacteristic
904D4—68no—
905D4—128no—
906D4—188no—
907D4—1816no—
908D4—1816no—
909D4—188no—
910D4—188no—
911D4—368no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—32no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—92no—
922C2×C4—94no—
923C2×C4—188no—
924C2×C4—188no—
925C2×C4—182no—
926C2×C4—181no—
927C2×C4—182no—
928C2×C4—181no—
929C2×C3—24no—
930C2×C3—24no—
931C2×C3—21no—
932C2×C3—22no—
933C2×C3—22no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—44no—
937C2×C3—64no—
938C2×C3—122no—
939C2×C3—124no—
940C2×C3—122no—
941C2×C3C2×#88211yescharacteristic
942C2×C3C2×#88211yescharacteristic
943C2×C3#549311yescharacteristic
944C2×C3D3×#12011yescharacteristic
945C2×C3#558911yescharacteristic
946C2×C3#559012yes—
947C2×C3#559012yes—
948C2×C3#559012yes—
949C2×C3C2×#93711yescharacteristic
950C2×C3D4×#6712yes—
951D3—24no—
952D3—42no—
953D3—44no—
954D3—42no—
955D3—122no—
956D3—122no—
957D3—242no—
958C22—22no—
959C22—24no—
960C22—24no—
961C22—22no—
962C22—34no—
963C22—64no—
964C22—64no—
965C22—62no—
966C22—62no—
967C22—64no—
968C22—62no—
969C22—64no—
970C22—64no—
971C22—64no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—1216no—
976C22—1216no—
977C22—121no—
978C22—122no—
979C22—122no—
980C22—122no—
981C22—122no—
982C22—122no—
983C22—122no—
984C22—121no—
985C22—122no—
986C22—184no—
987C22—182no—
988C22—3616no—
989C22—361no—
990C22—362no—
991C22—361no—
992C22#6392214yescomplemented
993C22C2×D3×D1211yescharacteristic
994C22C2×#380211yescharacteristic
995C22D32×D412yes—
996C22#6431312yes—
997C22C2×D3×#6711yescharacteristic
998C4—42no—
999C4—62no—
1000C4—122no—
1001C4—184no—
1002C4—182no—
1003C3—21no—
1004C3#7385211yescharacteristic, complemented
1005C3#8260411yescharacteristic, complemented
1006C2—24no—
1007C2—64no—
1008C2—124no—
1009C2—122no—
1010C2—122no—
1011C2—362no—
1012C2D3×#88211yescharacteristic
1013C2#1059427112yes—
1014C2#1059429011yescharacteristic
1015C2C2×#6392211yescharacteristic
1016C2#1059528712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2403
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C23×#625C2semidirect
3. C2×C3×#882C2semidirect
4. C2×#63977C2semidirect
5. C2×#63922C2semidirect
6. #10592657C2semidirect
7. C3×#4955C2semidirect
8. #10591713C2semidirect
9. #10591393C2semidirect
10. #10591389C2semidirect
11. #10591363C2semidirect
15. C24×C3×D3C22semidirect
16. C23×D32C22semidirect
18. C23×C3⋊Dic3C22semidirect
20. C22×C3×D12C22semidirect
24. C22×#626C22semidirect
25. C22×#626C22semidirect
29. C22×#625C22semidirect
30. C22×#625C22semidirect
31. C22×D3×Dic3C22semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×#3752C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. C2×(C2×D3)⋊Dic3C22semidirect
43. #63658C22semidirect
44. #63579C22semidirect
54. C2×#882D3semidirect
67. #4955D3semidirect
79. C23×C3×D3D4semidirect
92. C2×#638D4semidirect
99. C2×C3×#67D4semidirect
121. C2×#625D4semidirect
139. C24×D3C2×D3semidirect
170. C22×D12C2×D3semidirect
178. C2×C3×C22⋊C4C2×D3semidirect
179. C2×C3×C22⋊C4C2×D3semidirect
183. C2×#217C2×D3semidirect
190. C2×(C2×D3)⋊C4C2×D3semidirect
191. C2×(C2×D3)⋊C4C2×D3semidirect
192. C2×(C2×D3)⋊C4C2×D3semidirect
211. C22×C3⋊D3C2×D4semidirect
242. C22×C3×D3C2×D4semidirect
243. C22×C3×D3C2×D4semidirect
258. C2×C3⋊Dic3C2×D4semidirect
259. C2×C3⋊Dic3C2×D4semidirect
266. C2×C3×Dic3C2×D4semidirect
324. C23×D3D12semidirect
378. C2×#67#67semidirect
431. C22×C32#120semidirect
465. C2×C3×D3#120semidirect
500. C2×C22⋊C4D32semidirect
608. C22×D3D3×D4semidirect
609. C22×D3C2×#67semidirect
666. C2×Dic3C2×#67semidirect
789. C22×C3#882semidirect
790. C22×C3#937semidirect
841. C2×D3#882semidirect
855. C32#2403semidirect
992. C22#63922semidirect
1004. C3#73852semidirect
1005. C3#82604semidirect

Maximal subgroups

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

subgroupindex
C22×D3×#672
C23×#6252
C2×C3×#8822
C2×#639772
C2×#639222
#105926572
C3×#49552
#105917132
#105913932
#105913892
#105913632
#826043
#738523