Finite Group Databasebeta

← #11809010

Subgroups — #11809010

Order 1152.

3381 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic, complemented
4C2×#63976C211yesmaximal, characteristic, complemented
5C2×#63922C212yesmaximal, complemented
6#10592654C211yesmaximal, characteristic, complemented
7C3×#4958C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591393C212yesmaximal, complemented
10#10591391C212yesmaximal, complemented
11#10591275C212yesmaximal, complemented
12#82604—31nomaximal
13#74884—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic, complemented
16C23×D32C2211yescharacteristic, complemented
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic, complemented
20C22×C3×D12C2212yescomplemented
21C2×#3811—24no—
22C2×#3811—24no—
23C2×#3811—24no—
24C22×#626—28no—
25C22×#626—24no—
26C22×#626C2212yes—
27C22×#626C2212yescomplemented
28C22×#626C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic, complemented
30C22×#625C2212yescomplemented
31C22×#624C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3757C2211yescharacteristic, complemented
34C2×#3752C2212yescomplemented
35C2×#3752C2212yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C3×#882—24no—
39#63976—24no—
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41C2×(C2×D3)⋊Dic3C2212yescomplemented
42#63922—28no—
43C3×C3⋊#95C2212yescomplemented
44#63579C2212yescomplemented
45C23×#67—31no—
46C22×D3×D4—31no—
47C22×D3×D4—31no—
48C23×D12—31no—
49C2×C3×#120—31no—
50C2×#953—31no—
51C2×#937—31no—
52C2×#937—32no—
53C2×#882—32no—
54C2×#882D311yescharacteristic, complemented
55C3×#386—31no—
56#5223—32no—
57#5220—31no—
58#5213—31no—
59#4960—32no—
60#4960—32no—
61#4958D311yescharacteristic, complemented
62#4956—32no—
63#4955—31no—
64#4955—31no—
65#4955—61no—
66#4671—32no—
67#4665—32no—
68C24×C32C2311yescharacteristic
69C23×C3⋊D3—22no—
70C23×C3⋊D3—22no—
71C23×C3⋊D3—24no—
72C23×C3⋊D3—42no—
73C23×C3⋊D3D414yescomplemented
74C23×C3⋊D3C2311yescharacteristic
75C23×C3⋊D3C2311yescharacteristic
76C23×C3×D3—22no—
77C23×C3×D3—24no—
78C23×C3×D3—22no—
79C23×C3×D3—22no—
80C23×C3×D3—42no—
81C23×C3×D3C2311yescharacteristic
82C23×C3×D3C2312yes—
83C23×C3×D3C2311yescharacteristic
84C22×D32—22no—
85C22×D32—22no—
86C22×D32—22no—
87C22×D32—24no—
88C22×D32—42no—
89C22×C32×C4C2312yes—
90C22×C3⋊Dic3C2312yes—
91C2×C3×#67—22no—
92C2×C3×#67—22no—
93C2×C3×#67—22no—
94C2×C3×#67—22no—
95C2×C3×#67D414yescomplemented
96C2×C3×#67D414yescomplemented
97C22×C3×Dic3—22no—
98C22×C3×Dic3—24no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—24no—
103C2×C3×D12—24no—
104C2×C3×D12—42no—
105#3811—232no—
106C2×#626—232no—
107C2×#626—24no—
108C2×#626—24no—
109C2×#626—24no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626—24no—
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—24no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626D418yescomplemented
119C2×#625—24no—
120C2×#625—24no—
121C2×#625—42no—
122C2×#624—22no—
123C2×#624—22no—
124C2×#624—22no—
125C32×C22⋊C4—22no—
126#3757—22no—
127#3752—24no—
128#3752—42no—
129C3×(C2×D3)⋊C4—24no—
130C3×(C2×D3)⋊C4—24no—
131(C2×D3)⋊Dic3—24no—
132(C2×D3)⋊Dic3—24no—
133#2403—91noSylow
134C25×C3—31no—
135C24×D3—31no—
136C24×D3—31no—
137C24×D3—31no—
138C24×D3—31no—
139C24×D3—61no—
140C24×D3C2×D311yescharacteristic, complemented
141C22×C3×D4—31no—
142C22×C3×D4—31no—
143C22×C3×D4—32no—
144C23×C3×C4—31no—
145C22×#67—32no—
146C22×#67—32no—
147C22×#67—32no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—32no—
151C22×#67—68no—
152C22×#67—64no—
153C22×#67C2×D311yescharacteristic
154C22×#67C2×D311yescharacteristic
155C23×Dic3C2×D311yescharacteristic, complemented
156C2×D3×D4—64no—
157C2×D3×D4—64no—
158C2×D3×D4—64no—
159C2×D3×D4—64no—
160C2×D3×D4—64no—
161C2×D3×D4—64no—
162C22×D12—32no—
163C22×D12—31no—
164C22×D12—32no—
165C22×D12—31no—
166C22×D12—68no—
167C22×D12—64no—
168C22×D12C2×D312yescomplemented
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C3×#120—64no—
172C2×C3×C22⋊C4—21no—
173C2×C3×C22⋊C4—32no—
174C2×C3×C22⋊C4—32no—
175C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
176C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
177#953—64no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—32no—
181C2×#217—32no—
182C2×#217—61no—
183#937—68no—
184#937—64no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191C2×(C2×D3)⋊C4—62no—
192C2×(C2×D3)⋊C4—62no—
193C2×(C2×D3)⋊C4C2×D312yescomplemented
194C2×(C2×D3)⋊C4C2×D312yescomplemented
195#882—24no—
196#882—68no—
197C3×#95—32no—
198C3⋊#95—32no—
199C3⋊#95—32no—
200C3⋊#95C2×D312yescomplemented
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⋊D3—28no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—28no—
216C22×C3⋊D3—44no—
217C22×C3⋊D3—48no—
218C22×C3⋊D3—48no—
219C22×C3⋊D3C2×D412yes—
220C22×C3⋊D3C2×D414yes—
221C22×C3⋊D3C2×D412yes—
222C22×C3×D3—28no—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—22no—
230C22×C3×D3—22no—
231C22×C3×D3—22no—
232C22×C3×D3—22no—
233C22×C3×D3—22no—
234C22×C3×D3—22no—
235C22×C3×D3—22no—
236C22×C3×D3—22no—
237C22×C3×D3—48no—
238C22×C3×D3—48no—
239C22×C3×D3—44no—
240C22×C3×D3—44no—
241C22×C3×D3C2×D412yescomplemented
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—
252C2×C3⋊Dic3—22no—
253C2×C3⋊Dic3—22no—
254C2×C3⋊Dic3—22no—
255C3×#67—28no—
256C3×#67—28no—
257C2×C3×Dic3—28no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3C2×D412yescomplemented
265C2×C3×Dic3C2×D414yescomplemented
266C2×C3×Dic3C2×D412yescomplemented
267C3×D12—48no—
268#626—216no—
269#626—28no—
270#626—28no—
271#626—216no—
272#625—48no—
273#624—28no—
274C23×D4—91no—
275C23×D4—91no—
276C2×#120—31no—
277C2×#120—92no—
278C2×#120—91no—
279#392—92no—
280#392—92no—
281#386—31no—
282#386—92no—
283#386—91no—
284#379—91no—
285C24×C3—21no—
286C24×C3—32no—
287C24×C3—31no—
288C24×C3—31no—
289C24×C3—64no—
290C24×C3—62no—
291C24×C3—62no—
292C24×C3—62no—
293C24×C3—122no—
294C24×C3C22×D311yescharacteristic
295C24×C3C22×D311yescharacteristic
296C23×D3—22no—
297C23×D3—24no—
298C23×D3—22no—
299C23×D3—22no—
300C23×D3—31no—
301C23×D3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—34no—
305C23×D3—34no—
306C23×D3—42no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—64no—
310C23×D3—62no—
311C23×D3—62no—
312C23×D3—64no—
313C23×D3—64no—
314C23×D3—62no—
315C23×D3—62no—
316C23×D3—64no—
317C23×D3—64no—
318C23×D3—62no—
319C23×D3—62no—
320C23×D3—62no—
321C23×D3—62no—
322C23×D3—62no—
323C23×D3—62no—
324C23×D3—124no—
325C23×D3—122no—
326C23×D3—122no—
327C23×D3—122no—
328C23×D3—122no—
329C23×D3—122no—
330C23×D3—122no—
331C23×D3—124no—
332C23×D3C22×D311yescharacteristic
333C23×D3C22×D312yes—
334C23×D3C22×D311yescharacteristic
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—64no—
338C2×C3×D4—64no—
339C2×C3×D4—62no—
340C2×C3×D4—62no—
341C2×C3×D4—62no—
342C2×C3×D4—62no—
343C2×C3×D4—122no—
344C22×C3×C4—22no—
345C22×C3×C4—31no—
346C22×C3×C4—32no—
347C22×C3×C4—31no—
348C22×C3×C4—64no—
349C22×C3×C4—62no—
350C22×C3×C4C22×D312yes—
351C22×C3×C4C22×D312yes—
352C2×#67—22no—
353C2×#67—22no—
354C2×#67—22no—
355C2×#67—22no—
356C2×#67—38no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—64no—
360C2×#67—64no—
361C2×#67—64no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—64no—
365C2×#67—632no—
366C2×#67—64no—
367C2×#67—64no—
368C2×#67—64no—
369C2×#67—64no—
370C2×#67—62no—
371C2×#67—64no—
372C2×#67—62no—
373C2×#67—122no—
374C2×#67—122no—
375C2×#67D1214yescomplemented
376C2×#67#6714yescomplemented
377C22×Dic3—22no—
378C22×Dic3—24no—
379C22×Dic3—32no—
380C22×Dic3—32no—
381C22×Dic3—62no—
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D312yes—
384C22×Dic3C22×D311yescharacteristic
385D3×D4—632no—
386D3×D4—632no—
387C2×D12—24no—
388C2×D12—24no—
389C2×D12—38no—
390C2×D12—42no—
391C2×D12—64no—
392C2×D12—62no—
393C2×D12—62no—
394C2×D12—64no—
395C2×D12—64no—
396C2×D12—64no—
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—632no—
400C2×D12—62no—
401C2×D12—64no—
402C2×D12—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
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—
414#217—62no—
415#217—62no—
416#217—64no—
417#217—64no—
418#217—122no—
419(C2×D3)⋊C4—24no—
420(C2×D3)⋊C4—24no—
421(C2×D3)⋊C4—64no—
422(C2×D3)⋊C4—64no—
423(C2×D3)⋊C4—64no—
424(C2×D3)⋊C4—64no—
425(C2×D3)⋊C4—124no—
426(C2×D3)⋊C4—122no—
427(C2×D3)⋊C4—122no—
428(C2×D3)⋊C4—124no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—24no—
432C22×C32—24no—
433C22×C32#12014yescomplemented
434C22×C32C22×D411yescharacteristic
435C22×C32C22×D411yescharacteristic
436C22×C32C22×D412yes—
437C22×C32C22×D411yescharacteristic
438C22×C32H(5,𝔽2)12yes—
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—24no—
443C2×C3⋊D3—24no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—416no—
447C2×C3⋊D3—42no—
448C2×C3⋊D3—42no—
449C2×C3⋊D3#12014yescomplemented
450C2×C3×D3—24no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—24no—
454C2×C3×D3—24no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—416no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—42no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—42no—
464C2×C3×D3—42no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3—42no—
468D32—416no—
469C32×C4—42no—
470C3⋊Dic3—42no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—24no—
474C25—31no—
475C25—91no—
476C25—91no—
477C22×D4—31no—
478C22×D4—31no—
479C22×D4—32no—
480C22×D4—92no—
481C22×D4—91no—
482C22×D4—92no—
483C22×D4—91no—
484C22×D4—92no—
485C22×D4—188no—
486C22×D4—184no—
487C22×D4—184no—
488C22×D4—184no—
489C22×D4—184no—
490C23×C4—31no—
491C23×C4—91no—
492#120—64no—
493#120—188no—
494#120—184no—
495C2×C22⋊C4—32no—
496C2×C22⋊C4—32no—
497C2×C22⋊C4—92no—
498C2×C22⋊C4—92no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—92no—
501C2×C22⋊C4—92no—
502C2×C22⋊C4D3211yescharacteristic, complemented
503#95—32no—
504#95—92no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—34no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—42no—
517C23×C3—42no—
518C23×C3—68no—
519C23×C3—62no—
520C23×C3—61no—
521C23×C3—62no—
522C23×C3—62no—
523C23×C3—62no—
524C23×C3—62no—
525C23×C3—62no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—61no—
533C23×C3—128no—
534C23×C3—128no—
535C23×C3—124no—
536C23×C3—124no—
537C23×C3C2×D1212yes—
538C23×C3D3×D412yes—
539C23×C3D3×D412yes—
540C23×C3D3×D412yes—
541C23×C3D3×D412yes—
542C23×C3C2×#6712yes—
543C23×C3C23×D311yescharacteristic
544C23×C3C23×D311yescharacteristic
545C22×D3—28no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—34no—
561C22×D3—34no—
562C22×D3—32no—
563C22×D3—32no—
564C22×D3—32no—
565C22×D3—32no—
566C22×D3—48no—
567C22×D3—48no—
568C22×D3—44no—
569C22×D3—44no—
570C22×D3—64no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—68no—
574C22×D3—68no—
575C22×D3—68no—
576C22×D3—68no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—62no—
581C22×D3—62no—
582C22×D3—61no—
583C22×D3—64no—
584C22×D3—68no—
585C22×D3—68no—
586C22×D3—61no—
587C22×D3—62no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—62no—
593C22×D3—61no—
594C22×D3—128no—
595C22×D3—121no—
596C22×D3—122no—
597C22×D3—121no—
598C22×D3—121no—
599C22×D3—122no—
600C22×D3—121no—
601C22×D3—128no—
602C22×D3—128no—
603C22×D3—128no—
604C22×D3—124no—
605C22×D3—124no—
606C22×D3—128no—
607C22×D3—128no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3—124no—
612C22×D3—128no—
613C22×D3—128no—
614C22×D3—128no—
615C22×D3—128no—
616C22×D3—128no—
617C22×D3—1216no—
618C22×D3—1216no—
619C22×D3C2×D1212yescomplemented
620C22×D3D3×D414yescomplemented
621C22×D3C2×#6712yescomplemented
622C3×D4—68no—
623C3×D4—68no—
624C3×D4—128no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—32no—
632C2×C3×C4—34no—
633C2×C3×C4—32no—
634C2×C3×C4—42no—
635C2×C3×C4—42no—
636C2×C3×C4—42no—
637C2×C3×C4—68no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—62no—
642C2×C3×C4—62no—
643C2×C3×C4—61no—
644#67—28no—
645#67—28no—
646#67—616no—
647#67—68no—
648#67—68no—
649#67—616no—
650#67—128no—
651#67—128no—
652C2×Dic3—28no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—122no—
666C2×Dic3—122no—
667C2×Dic3—122no—
668C2×Dic3C2×D1212yescomplemented
669C2×Dic3D3×D414yescomplemented
670C2×Dic3C2×#6712yescomplemented
671D12—48no—
672D12—616no—
673D12—616no—
674D12—68no—
675D12—68no—
676C4×D3—68no—
677C4×D3—68no—
678C2×C32—24no—
679C2×C32C2×#12011yescharacteristic
680C2×C32C2×#12011yescharacteristic
681C2×C32#53411yescharacteristic
682C2×C32D4212yes—
683C2×C32D4212yes—
684C3⋊D3—24no—
685C3⋊D3—42no—
686C3×D3—42no—
687C3×D3—42no—
688C3×D3—44no—
689C24—31no—
690C24—32no—
691C24—31no—
692C24—64no—
693C24—62no—
694C24—62no—
695C24—62no—
696C24—91no—
697C24—91no—
698C24—94no—
699C24—122no—
700C24—184no—
701C24—182no—
702C24—182no—
703C24—182no—
704C24—184no—
705C24—182no—
706C24—182no—
707C24—362no—
708C24—362no—
709C24C2×D3211yescharacteristic
710C2×D4—34no—
711C2×D4—34no—
712C2×D4—64no—
713C2×D4—64no—
714C2×D4—62no—
715C2×D4—62no—
716C2×D4—62no—
717C2×D4—62no—
718C2×D4—98no—
719C2×D4—122no—
720C2×D4—182no—
721C2×D4—184no—
722C2×D4—182no—
723C2×D4—182no—
724C2×D4—184no—
725C2×D4—182no—
726C2×D4—184no—
727C2×D4—184no—
728C2×D4—182no—
729C2×D4—182no—
730C2×D4—184no—
731C2×D4—1832no—
732C2×D4—1832no—
733C2×D4—184no—
734C2×D4—184no—
735C2×D4—362no—
736C22×C4—31no—
737C22×C4—32no—
738C22×C4—31no—
739C22×C4—64no—
740C22×C4—62no—
741C22×C4—92no—
742C22×C4—182no—
743C22×C4—182no—
744C22×C4—182no—
745C22×C4C2×D3212yes—
746C22⋊C4—22no—
747C22⋊C4—64no—
748C22⋊C4—64no—
749C22⋊C4—184no—
750C22⋊C4—184no—
751C22⋊C4—184no—
752C22⋊C4—182no—
753C22⋊C4—362no—
754C22×C3—22no—
755C22×C3—24no—
756C22×C3—24no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—24no—
761C22×C3—24no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—21no—
767C22×C3—24no—
768C22×C3—42no—
769C22×C3—44no—
770C22×C3—44no—
771C22×C3—42no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—64no—
775C22×C3—64no—
776C22×C3—64no—
777C22×C3—64no—
778C22×C3—64no—
779C22×C3—1216no—
780C22×C3—121no—
781C22×C3—122no—
782C22×C3—122no—
783C22×C3—122no—
784C22×C3—122no—
785C22×C3—122no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—122no—
790C22×C3#88214yescomplemented
791C22×C3#93714yescomplemented
792C22×C3C22×D1211yescharacteristic
793C22×C3C2×D3×D411yescharacteristic
794C22×C3C2×D3×D411yescharacteristic
795C22×C3C2×D3×D411yescharacteristic
796C22×C3C2×D3×D412yes—
797C22×C3C2×D3×D412yes—
798C22×C3C2×D3×D411yescharacteristic
799C22×C3#100412yes—
800C22×C3#100912yes—
801C22×C3C22×#6711yescharacteristic
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—24no—
805C2×D3—24no—
806C2×D3—24no—
807C2×D3—24no—
808C2×D3—24no—
809C2×D3—34no—
810C2×D3—34no—
811C2×D3—416no—
812C2×D3—41no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—42no—
818C2×D3—41no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—64no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—64no—
827C2×D3—64no—
828C2×D3—62no—
829C2×D3—64no—
830C2×D3—64no—
831C2×D3—64no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—124no—
839C2×D3—124no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—1216no—
845C2×D3—1216no—
846C2×D3—1216no—
847C2×D3—1216no—
848C2×D3—124no—
849C2×D3—124no—
850C2×D3—1232no—
851C2×D3—122no—
852C2×D3—122no—
853C2×D3—122no—
854C2×D3—122no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—64no—
860C3×C4—82no—
861Dic3—22no—
862Dic3—22no—
863Dic3—24no—
864Dic3—122no—
865Dic3—122no—
866Dic3—242no—
867C32#240311yescharacteristic, complemented, Sylow
868C23—22no—
869C23—22no—
870C23—32no—
871C23—34no—
872C23—32no—
873C23—68no—
874C23—62no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—61no—
888C23—92no—
889C23—94no—
890C23—92no—
891C23—128no—
892C23—128no—
893C23—124no—
894C23—124no—
895C23—188no—
896C23—188no—
897C23—181no—
898C23—182no—
899C23—181no—
900C23—181no—
901C23—182no—
902C23—182no—
903C23—181no—
904C23—188no—
905C23—364no—
906C23—368no—
907C23—368no—
908C23—368no—
909C23—368no—
910C23—364no—
911C23—364no—
912C23D3×D1212yes—
913C23#380212yes—
914C23D3×#6712yes—
915C23C22×D3211yescharacteristic
916D4—68no—
917D4—68no—
918D4—128no—
919D4—1816no—
920D4—1816no—
921D4—188no—
922D4—188no—
923D4—368no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—32no—
928C2×C4—34no—
929C2×C4—32no—
930C2×C4—68no—
931C2×C4—61no—
932C2×C4—62no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—62no—
936C2×C4—61no—
937C2×C4—188no—
938C2×C4—182no—
939C2×C4—182no—
940C2×C4—182no—
941C2×C3—24no—
942C2×C3—24no—
943C2×C3—21no—
944C2×C3—22no—
945C2×C3—22no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—44no—
949C2×C3—122no—
950C2×C3—124no—
951C2×C3—122no—
952C2×C3C2×#88211yescharacteristic
953C2×C3D4×D1212yes—
954C2×C3D3×#12011yescharacteristic
955C2×C3D3×#12011yescharacteristic
956C2×C3#558911yescharacteristic
957C2×C3#559012yes—
958C2×C3#560912yes—
959C2×C3#565311yescharacteristic
960C2×C3C2×#93711yescharacteristic
961C2×C3D4×#6712yes—
962D3—42no—
963D3—44no—
964D3—42no—
965D3—64no—
966D3—64no—
967D3—124no—
968D3—124no—
969D3—122no—
970D3—122no—
971C22—22no—
972C22—24no—
973C22—24no—
974C22—22no—
975C22—64no—
976C22—64no—
977C22—64no—
978C22—64no—
979C22—64no—
980C22—62no—
981C22—62no—
982C22—94no—
983C22—1216no—
984C22—121no—
985C22—121no—
986C22—122no—
987C22—122no—
988C22—122no—
989C22—122no—
990C22—122no—
991C22—122no—
992C22—121no—
993C22—121no—
994C22—184no—
995C22—184no—
996C22—182no—
997C22—182no—
998C22—182no—
999C22—182no—
1000C22—182no—
1001C22—3616no—
1002C22—3616no—
1003C22—362no—
1004C22—362no—
1005C22#6392214yescomplemented
1006C22C2×D3×D1211yescharacteristic
1007C22C2×#380211yescharacteristic
1008C22D32×D412yes—
1009C22#6431412yes—
1010C22C2×D3×#6711yescharacteristic
1011C4—42no—
1012C4—64no—
1013C4—62no—
1014C4—62no—
1015C4—362no—
1016C3—21no—
1017C3#7488411yescharacteristic, complemented
1018C3#8260411yescharacteristic, complemented
1019C2—24no—
1020C2—124no—
1021C2—122no—
1022C2—122no—
1023C2—184no—
1024C2—362no—
1025C2#1059425811yescharacteristic
1026C2#1059427712yes—
1027C2#1059429611yescharacteristic
1028C2C2×#6392211yescharacteristic
1029C2#1059529112yes—
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×#3811C2semidirect
2. C23×#626C2semidirect
3. C2×C3×#882C2semidirect
4. C2×#63976C2semidirect
5. C2×#63922C2semidirect
6. #10592654C2semidirect
7. C3×#4958C2semidirect
8. #10591710C2semidirect
9. #10591393C2semidirect
10. #10591391C2semidirect
11. #10591275C2semidirect
15. C24×C3×D3C22semidirect
16. C23×D32C22semidirect
19. C23×C3×Dic3C22semidirect
20. C22×C3×D12C22semidirect
27. C22×#626C22semidirect
28. C22×#626C22semidirect
29. C22×#626C22semidirect
30. C22×#625C22semidirect
31. C22×#624C22semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×#3757C22semidirect
34. C2×#3752C22semidirect
35. C2×#3752C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. C2×(C2×D3)⋊Dic3C22semidirect
43. C3×C3⋊#95C22semidirect
44. #63579C22semidirect
54. C2×#882D3semidirect
61. #4958D3semidirect
73. C23×C3⋊D3D4semidirect
95. C2×C3×#67D4semidirect
96. C2×C3×#67D4semidirect
118. C2×#626D4semidirect
140. C24×D3C2×D3semidirect
155. C23×Dic3C2×D3semidirect
168. C22×D12C2×D3semidirect
175. C2×C3×C22⋊C4C2×D3semidirect
176. C2×C3×C22⋊C4C2×D3semidirect
193. C2×(C2×D3)⋊C4C2×D3semidirect
194. C2×(C2×D3)⋊C4C2×D3semidirect
200. C3⋊#95C2×D3semidirect
241. C22×C3×D3C2×D4semidirect
242. C22×C3×D3C2×D4semidirect
243. C22×C3×D3C2×D4semidirect
264. C2×C3×Dic3C2×D4semidirect
265. C2×C3×Dic3C2×D4semidirect
266. C2×C3×Dic3C2×D4semidirect
375. C2×#67D12semidirect
376. C2×#67#67semidirect
433. C22×C32#120semidirect
449. C2×C3⋊D3#120semidirect
502. C2×C22⋊C4D32semidirect
619. C22×D3C2×D12semidirect
620. C22×D3D3×D4semidirect
621. C22×D3C2×#67semidirect
668. C2×Dic3C2×D12semidirect
669. C2×Dic3D3×D4semidirect
670. C2×Dic3C2×#67semidirect
790. C22×C3#882semidirect
791. C22×C3#937semidirect
867. C32#2403semidirect
1005. C22#63922semidirect
1017. C3#74884semidirect
1018. C3#82604semidirect

Maximal subgroups

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

subgroupindex
C22×#38112
C23×#6262
C2×C3×#8822
C2×#639762
C2×#639222
#105926542
C3×#49582
#105917102
#105913932
#105913912
#105912752
#826043
#748843