Finite Group Databasebeta

← #67×#217 #11804764

Subgroups — #67×#217 #11804764

Order 1152.

2757 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C212yesmaximal, complemented
4C2×D3×#217C211yesmaximal, characteristic, complemented
5#10592946C211yesmaximal, characteristic, complemented
6#10591721C212yesmaximal, complemented
7#10591716C211yesmaximal, characteristic, complemented
8#10591710C212yesmaximal, complemented
9#10591707C212yesmaximal, complemented
10#10591706C211yesmaximal, characteristic, complemented
11Dic3×#217C211yesmaximal, characteristic, complemented
12D4×#217—31nomaximal
13C22⋊C4×#67—31nomaximal
14C25×C32C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic
16C22×C3×#67—28no—
17C22×C3×#67C418yescomplemented
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2212yescomplemented
24C22×D3×Dic3C2212yescomplemented
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2212yescomplemented
28C2×#3757C2212yescomplemented
29C2×C3×#217—24no—
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2212yescomplemented
33Dic3×#67—28no—
34D3×#217—24no—
35C2×Dic3⋊Dic3C2212yescomplemented
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37C2×(C2×D3)⋊Dic3C2212yescomplemented
38C2×(C2×D3)⋊Dic3C2212yescomplemented
39C2×Dic32C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×C3×D4—31no—
43C23×#67D311yescharacteristic
44C22×C3×C22⋊C4—31no—
45C22×#217—31no—
46C22×#217D311yescharacteristic, complemented
47C2×D4×Dic3—32no—
48C2×C4×#67—32no—
49C2×D3×C22⋊C4—31no—
50#5247—31no—
51#5247—31no—
52#5247—31no—
53#5247—61no—
54#5221—32no—
55#5220—32no—
56#5220—32no—
57#5213—32no—
58#5212—31no—
59C4×#217—31no—
60#4957—32no—
61#4956—32no—
62#4955—31no—
63#4942—31no—
64Dic3×C22⋊C4—31no—
65C24×C32—22no—
66C24×C32—24no—
67C24×C32—22no—
68C24×C32—42no—
69C24×C32C2×C414yescomplemented
70C24×C32C2311yescharacteristic
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C23×C3×D3—22no—
74C23×C3×D3—22no—
75C23×C3×D3—24no—
76C23×C3×D3—42no—
77C23×C3×D3C2×C414yescomplemented
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2312yes—
82C2×C3×#67—24no—
83C2×C3×#67—24no—
84C2×C3×#67—232no—
85C2×C3×#67—24no—
86C2×C3×#67C2×C414yes—
87C2×C3×#67C2×C414yescomplemented
88C2×C3×#67C2×C414yescomplemented
89C2×C3×#67C2×C414yescomplemented
90C2×C3×#67D418yes—
91C22×C3×Dic3—24no—
92C22×C3×Dic3—24no—
93C22×C3×Dic3—24no—
94C22×C3×Dic3—42no—
95C22×C3×Dic3C2×C414yescomplemented
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2311yescharacteristic
100C2×D3×Dic3—24no—
101C2×D3×Dic3—24no—
102C2×D3×Dic3—42no—
103#3757—22no—
104#3757—24no—
105#3757—22no—
106#3757—42no—
107C3×#217—22no—
108C3×#217—24no—
109C3×#217D414yescomplemented
110Dic3⋊Dic3—24no—
111(C2×D3)⋊Dic3—24no—
112(C2×D3)⋊Dic3—24no—
113(C2×D3)⋊Dic3—42no—
114Dic32—24no—
115D4×C22⋊C4—91noSylow
116C25×C3—21no—
117C25×C3—31no—
118C25×C3C2×D311yescharacteristic
119C25×C3C2×D311yescharacteristic
120C24×D3C2×D311yescharacteristic
121C22×C3×D4—31no—
122C22×C3×D4—38no—
123C22×C3×D4—31no—
124C22×C3×D4—31no—
125C22×C3×D4—31no—
126C22×C3×D4—68no—
127C23×C3×C4—31no—
128C23×C3×C4—32no—
129C22×#67—28no—
130C22×#67Dic318yescomplemented
131C22×#67C2×D311yescharacteristic
132C22×#67C2×D311yescharacteristic
133C22×#67C2×D311yescharacteristic
134C22×#67C2×D311yescharacteristic
135C23×Dic3—32no—
136C23×Dic3C2×D311yescharacteristic
137C23×Dic3C2×D312yescomplemented
138C22×C4×D3—32no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—64no—
143C2×#217—24no—
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—32no—
149C2×#217—32no—
150C2×#217—32no—
151C2×#217—32no—
152C2×#217—32no—
153C2×#217—32no—
154C2×#217—32no—
155C2×#217—61no—
156C2×#217—61no—
157C2×#217—62no—
158C2×#217—62no—
159C2×#217—64no—
160C2×#217C2×D311yescharacteristic
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D312yescomplemented
163D4×Dic3—68no—
164C4×#67—68no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—32no—
167C2×(C2×D3)⋊C4—32no—
168C2×C4⋊Dic3—32no—
169C2×Dic3⋊C4—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172D3×C22⋊C4—64no—
173C3⋊#95—32no—
174C3⋊#95—32no—
175C3⋊#95—32no—
176C3⋊#95—32no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32—28no—
184C23×C32—28no—
185C23×C32—21no—
186C23×C32—22no—
187C23×C32—21no—
188C23×C32—44no—
189C23×C32—48no—
190C23×C32—48no—
191C23×C32C22×C412yes—
192C23×C32C22×C412yes—
193C23×C32C22×C412yes—
194C23×C32C2×D414yes—
195C23×C32C2×D412yes—
196C23×C32#4112yes—
197C23×C32C2411yescharacteristic
198C22×C3×D3—21no—
199C22×C3×D3—21no—
200C22×C3×D3—22no—
201C22×C3×D3—28no—
202C22×C3×D3—21no—
203C22×C3×D3—22no—
204C22×C3×D3—21no—
205C22×C3×D3—22no—
206C22×C3×D3—28no—
207C22×C3×D3—44no—
208C22×C3×D3—48no—
209C22×C3×D3—48no—
210C22×C3×D3C22×C412yes—
211C22×C3×D3C22×C412yes—
212C22×C3×D3C2×D414yes—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C3×#67—28no—
220C3×#67—28no—
221C3×#67—28no—
222C3×#67C22⋊C4116yescomplemented
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—28no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—48no—
231C2×C3×Dic3C22×C412yes—
232C2×C3×Dic3C22×C412yes—
233C2×C3×Dic3C2×D414yes—
234C2×C3×Dic3C2×D414yescomplemented
235D3×Dic3—48no—
236C23×D4—31no—
237C2×C4×D4—92no—
238C22×C22⋊C4—31no—
239C22×C22⋊C4—91no—
240#390—92no—
241#386—92no—
242#386—92no—
243#380—91no—
244#379—91no—
245#379—91no—
246C4×C22⋊C4—91no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—24no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—24no—
253C24×C3—24no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—31no—
258C24×C3—31no—
259C24×C3—34no—
260C24×C3—42no—
261C24×C3—42no—
262C24×C3—44no—
263C24×C3—42no—
264C24×C3—42no—
265C24×C3—44no—
266C24×C3—64no—
267C24×C3—62no—
268C24×C3—62no—
269C24×C3—122no—
270C24×C3C4×D314yescomplemented
271C24×C3C2×Dic314yescomplemented
272C24×C3C22×D311yescharacteristic
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C24×C3C22×D311yescharacteristic
276C24×C3C22×D311yescharacteristic
277C24×C3C22×D311yescharacteristic
278C23×D3—22no—
279C23×D3—22no—
280C23×D3—24no—
281C23×D3—42no—
282C23×D3C2×Dic314yescomplemented
283C23×D3C22×D311yescharacteristic
284C23×D3C22×D311yescharacteristic
285C2×C3×D4—34no—
286C2×C3×D4—38no—
287C2×C3×D4—34no—
288C2×C3×D4—34no—
289C2×C3×D4—34no—
290C2×C3×D4—64no—
291C2×C3×D4—632no—
292C2×C3×D4—64no—
293C2×C3×D4—64no—
294C22×C3×C4—31no—
295C22×C3×C4—34no—
296C22×C3×C4—31no—
297C22×C3×C4—32no—
298C22×C3×C4—32no—
299C22×C3×C4—64no—
300C22×C3×C4—64no—
301C22×C3×C4—64no—
302C22×C3×C4—122no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—232no—
306C2×#67—24no—
307C2×#67C2×Dic314yes—
308C2×#67C2×Dic314yescomplemented
309C2×#67C2×Dic314yescomplemented
310C2×#67C2×Dic314yescomplemented
311C2×#67#6718yes—
312C22×Dic3—24no—
313C22×Dic3—24no—
314C22×Dic3—24no—
315C22×Dic3—32no—
316C22×Dic3—32no—
317C22×Dic3—32no—
318C22×Dic3—32no—
319C22×Dic3—42no—
320C22×Dic3—62no—
321C22×Dic3—62no—
322C22×Dic3—64no—
323C22×Dic3—64no—
324C22×Dic3—122no—
325C22×Dic3C2×Dic314yescomplemented
326C22×Dic3C22×D312yes—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D312yes—
329C22×Dic3C22×D311yescharacteristic
330C2×C4×D3—64no—
331C2×C4×D3—64no—
332C2×C4×D3—122no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—64no—
335C3×C22⋊C4—62no—
336#217—22no—
337#217—24no—
338#217—64no—
339#217—62no—
340#217—62no—
341#217—64no—
342#217—62no—
343#217—64no—
344#217—62no—
345#217—64no—
346#217—122no—
347#217—122no—
348#217—124no—
349#217—122no—
350#217—122no—
351#217—122no—
352#217—124no—
353#217#6714yesdirect product factor
354(C2×D3)⋊C4—64no—
355(C2×D3)⋊C4—64no—
356(C2×D3)⋊C4—122no—
357C4⋊Dic3—64no—
358Dic3⋊C4—64no—
359C4×Dic3—64no—
360C4×Dic3—64no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—24no—
367C22×C32—24no—
368C22×C32—24no—
369C22×C32—24no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—416no—
373C22×C32—42no—
374C22×C32—42no—
375C22×C32C2×C22⋊C414yescomplemented
376C22×C32C4×D414yescomplemented
377C22×C32C23×C411yescharacteristic
378C22×C32C22×D412yes—
379C22×C32C22×D411yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32H(5,𝔽2)12yes—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3—24no—
385C2×C3×D3—24no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—416no—
390C2×C3×D3—42no—
391C2×C3×D3—42no—
392C2×C3×D3C2×C22⋊C414yescomplemented
393C3⋊Dic3—42no—
394C3⋊Dic3—42no—
395C3×Dic3—22no—
396C3×Dic3—24no—
397C3×Dic3—42no—
398C3×Dic3C2×C22⋊C414yescomplemented
399C25—31no—
400C25D3211yescharacteristic
401C22×D4—31no—
402C22×D4—38no—
403C22×D4—31no—
404C22×D4—31no—
405C22×D4—31no—
406C22×D4—68no—
407C23×C4—31no—
408C23×C4—32no—
409C23×C4—92no—
410C4×D4—188no—
411C2×C4⋊C4—92no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—64no—
416C2×C22⋊C4—92no—
417C2×C22⋊C4—92no—
418C2×C22⋊C4—91no—
419C2×C22⋊C4—92no—
420C2×C22⋊C4—91no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—92no—
423C2×C22⋊C4—184no—
424C2×C42—92no—
425#95—92no—
426#95—92no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—22no—
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—24no—
438C23×C3—28no—
439C23×C3—28no—
440C23×C3—28no—
441C23×C3—28no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—22no—
445C23×C3—21no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—21no—
449C23×C3—22no—
450C23×C3—21no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—24no—
456C23×C3—22no—
457C23×C3—32no—
458C23×C3—34no—
459C23×C3—32no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—42no—
468C23×C3—48no—
469C23×C3—48no—
470C23×C3—44no—
471C23×C3—44no—
472C23×C3—48no—
473C23×C3—48no—
474C23×C3—48no—
475C23×C3—48no—
476C23×C3—48no—
477C23×C3—416no—
478C23×C3—416no—
479C23×C3—68no—
480C23×C3—61no—
481C23×C3—62no—
482C23×C3—61no—
483C23×C3—68no—
484C23×C3—61no—
485C23×C3—62no—
486C23×C3—62no—
487C23×C3—61no—
488C23×C3—124no—
489C23×C3—128no—
490C23×C3—128no—
491C23×C3C2×C4×D312yes—
492C23×C3C2×C4×D312yes—
493C23×C3C2×C4×D312yes—
494C23×C3#23512yes—
495C23×C3D3×D414yes—
496C23×C3D3×D412yes—
497C23×C3#23712yes—
498C23×C3C22×Dic312yes—
499C23×C3C22×Dic312yes—
500C23×C3C22×Dic312yes—
501C23×C3C2×#6712yes—
502C23×C3C2×#6714yes—
503C23×C3C23×D311yescharacteristic
504C23×C3C23×D311yescharacteristic
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—22no—
508C22×D3—28no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—28no—
514C22×D3—44no—
515C22×D3—48no—
516C22×D3—48no—
517C22×D3C22×Dic312yes—
518C22×D3C22×Dic312yes—
519C22×D3C2×#6714yes—
520C3×D4—316no—
521C3×D4—68no—
522C3×D4—68no—
523C3×D4—68no—
524C2×C3×C4—32no—
525C2×C3×C4—34no—
526C2×C3×C4—32no—
527C2×C3×C4—34no—
528C2×C3×C4—68no—
529C2×C3×C4—62no—
530C2×C3×C4—62no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—128no—
536#67—28no—
537#67—28no—
538#67—28no—
539#67#217116yesdirect product factor
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—28no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—48no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—122no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3—122no—
565C2×Dic3—122no—
566C2×Dic3—128no—
567C2×Dic3C22×Dic312yes—
568C2×Dic3C22×Dic312yes—
569C2×Dic3C2×#6714yes—
570C2×Dic3C2×#6714yescomplemented
571C4×D3—128no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—42no—
575C2×C32C22×C22⋊C411yescharacteristic
576C2×C32C2×C4×D411yescharacteristic
577C2×C32#51811yescharacteristic
578C2×C32D4212yes—
579C2×C32#54612yes—
580C3×D3—24no—
581C3×D3—42no—
582C24—22no—
583C24—22no—
584C24—24no—
585C24—31no—
586C24—31no—
587C24—34no—
588C24—42no—
589C24—64no—
590C24—62no—
591C24—62no—
592C24—122no—
593C24D3×Dic314yescomplemented
594C24C2×D3211yescharacteristic
595C24C2×D3211yescharacteristic
596C24C2×D3211yescharacteristic
597C2×D4—34no—
598C2×D4—38no—
599C2×D4—34no—
600C2×D4—34no—
601C2×D4—34no—
602C2×D4—64no—
603C2×D4—632no—
604C2×D4—64no—
605C2×D4—64no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—32no—
609C22×C4—34no—
610C22×C4—32no—
611C22×C4—64no—
612C22×C4—64no—
613C22×C4—64no—
614C22×C4—92no—
615C22×C4—92no—
616C22×C4—122no—
617C22×C4—184no—
618C22×C4—184no—
619C22×C4—362no—
620C4⋊C4—184no—
621C22⋊C4—34no—
622C22⋊C4—64no—
623C22⋊C4—62no—
624C22⋊C4—184no—
625C22⋊C4—184no—
626C22⋊C4—182no—
627C22⋊C4—182no—
628C22⋊C4—184no—
629C22⋊C4—362no—
630C22⋊C4—362no—
631C42—184no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—24no—
636C22×C3—24no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—24no—
642C22×C3—24no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—24no—
647C22×C3—22no—
648C22×C3—24no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—34no—
663C22×C3—42no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—416no—
674C22×C3—416no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—432no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—62no—
683C22×C3—64no—
684C22×C3—62no—
685C22×C3—64no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—1216no—
690C22×C3—122no—
691C22×C3—122no—
692C22×C3D3×C22⋊C414yescomplemented
693C22×C3C4×#6714yescomplemented
694C22×C3D4×Dic314yescomplemented
695C22×C3C2×#21714yescomplemented
696C22×C3C22×C4×D311yescharacteristic
697C22×C3C2×#23511yescharacteristic
698C22×C3C2×D3×D412yes—
699C22×C3C2×D3×D411yescharacteristic
700C22×C3C2×#23711yescharacteristic
701C22×C3#100412yes—
702C22×C3#100412yes—
703C22×C3C23×Dic311yescharacteristic
704C22×C3C22×#6711yescharacteristic
705C22×C3C22×#6712yes—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—24no—
709C2×D3—24no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—416no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3C2×#21714yescomplemented
717C3×C4—34no—
718C3×C4—62no—
719C3×C4—64no—
720C3×C4—122no—
721Dic3—24no—
722Dic3—22no—
723Dic3—42no—
724Dic3—122no—
725Dic3—122no—
726Dic3—122no—
727Dic3—122no—
728Dic3—242no—
729Dic3—242no—
730Dic3C2×#21714yescomplemented
731C32D4×C22⋊C411yescharacteristic, complemented, Sylow
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—28no—
742C23—28no—
743C23—32no—
744C23—34no—
745C23—32no—
746C23—44no—
747C23—48no—
748C23—48no—
749C23—68no—
750C23—61no—
751C23—61no—
752C23—62no—
753C23—61no—
754C23—61no—
755C23—62no—
756C23—62no—
757C23—68no—
758C23—124no—
759C23—128no—
760C23—128no—
761C23C2×D3×Dic312yes—
762C23C2×D3×Dic312yes—
763C23C2×D3×Dic312yes—
764C23#380412yes—
765C23D3×#6714yes—
766C23D3×#6712yes—
767C23C22×D3211yescharacteristic
768D4—316no—
769D4—68no—
770D4—68no—
771D4—68no—
772C2×C4—32no—
773C2×C4—34no—
774C2×C4—32no—
775C2×C4—34no—
776C2×C4—68no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—128no—
784C2×C4—182no—
785C2×C4—182no—
786C2×C4—182no—
787C2×C4—182no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—368no—
791C2×C3—24no—
792C2×C3—24no—
793C2×C3—24no—
794C2×C3—24no—
795C2×C3—21no—
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—22no—
800C2×C3—44no—
801C2×C3—44no—
802C2×C3—44no—
803C2×C3—42no—
804C2×C3—42no—
805C2×C3—64no—
806C2×C3—122no—
807C2×C3C2×D3×C22⋊C411yescharacteristic
808C2×C3#548611yescharacteristic
809C2×C3#549012yes—
810C2×C3C2×C4×#6711yescharacteristic
811C2×C3C2×D4×Dic311yescharacteristic
812C2×C3#579811yescharacteristic
813C2×C3D4×#6712yes—
814C2×C3D4×#6712yes—
815C2×C3#580612yes—
816C2×C3C22×#21711yescharacteristic
817D3—24no—
818D3—42no—
819C22—22no—
820C22—24no—
821C22—24no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—24no—
826C22—24no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—34no—
831C22—416no—
832C22—42no—
833C22—42no—
834C22—64no—
835C22—62no—
836C22—62no—
837C22—64no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—1216no—
842C22—122no—
843C22—122no—
844C22D3×#21714yescomplemented
845C22Dic3×#6714yescomplemented
846C22C22×D3×Dic311yescharacteristic
847C22C2×#380411yescharacteristic
848C22C2×D3×#6712yes—
849C22C2×D3×#6711yescharacteristic
850C22#6433012yes—
851C4—34no—
852C4—62no—
853C4—64no—
854C4—122no—
855C4—362no—
856C4—362no—
857C3—21no—
858C3C22⋊C4×#6711yescharacteristic, complemented
859C3D4×#21711yescharacteristic, complemented
860C2—24no—
861C2—24no—
862C2—42no—
863C2—64no—
864C2—122no—
865C2C2×D3×#21711yescharacteristic
866C2#1059549312yes—
867C2C2×Dic3×#6711yescharacteristic
868C2#1059550611yescharacteristic
869C2#67212yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC25×C32C22
socle, cosocleC23×C32C24
prime radicalC23×C3×#67C2
hypercenterC25D32
hypocenterC32D4×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C2×Dic3×#67C2semidirect
4. C2×D3×#217C2semidirect
5. #10592946C2semidirect
6. #10591721C2semidirect
7. #10591716C2semidirect
8. #10591710C2semidirect
9. #10591707C2semidirect
10. #10591706C2semidirect
11. Dic3×#217C2semidirect
17. C22×C3×#67C4semidirect
23. C23×C3×Dic3C22semidirect
24. C22×D3×Dic3C22semidirect
27. C2×#3757C22semidirect
28. C2×#3757C22semidirect
32. C2×C3×#217C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
37. C2×(C2×D3)⋊Dic3C22semidirect
38. C2×(C2×D3)⋊Dic3C22semidirect
39. C2×Dic32C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
46. C22×#217D3semidirect
69. C24×C32C2×C4semidirect
77. C23×C3×D3C2×C4semidirect
87. C2×C3×#67C2×C4semidirect
88. C2×C3×#67C2×C4semidirect
89. C2×C3×#67C2×C4semidirect
95. C22×C3×Dic3C2×C4semidirect
109. C3×#217D4semidirect
130. C22×#67Dic3semidirect
137. C23×Dic3C2×D3semidirect
162. C2×#217C2×D3semidirect
222. C3×#67C22⋊C4semidirect
234. C2×C3×Dic3C2×D4semidirect
270. C24×C3C4×D3semidirect
271. C24×C3C2×Dic3semidirect
282. C23×D3C2×Dic3semidirect
308. C2×#67C2×Dic3semidirect
309. C2×#67C2×Dic3semidirect
310. C2×#67C2×Dic3semidirect
325. C22×Dic3C2×Dic3semidirect
353. #217#67direct (N × H)
375. C22×C32C2×C22⋊C4semidirect
376. C22×C32C4×D4semidirect
392. C2×C3×D3C2×C22⋊C4semidirect
398. C3×Dic3C2×C22⋊C4semidirect
539. #67#217direct (N × H)
570. C2×Dic3C2×#67semidirect
593. C24D3×Dic3semidirect
692. C22×C3D3×C22⋊C4semidirect
693. C22×C3C4×#67semidirect
694. C22×C3D4×Dic3semidirect
695. C22×C3C2×#217semidirect
716. C2×D3C2×#217semidirect
730. Dic3C2×#217semidirect
731. C32D4×C22⋊C4semidirect
844. C22D3×#217semidirect
845. C22Dic3×#67semidirect
858. C3C22⋊C4×#67semidirect
859. C3D4×#217semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C3×#2172
C2×Dic3×#672
C2×D3×#2172
#105929462
#105917212
#105917162
#105917102
#105917072
#105917062
Dic3×#2172
D4×#2173
C22⋊C4×#673