Finite Group Databasebeta

← #13178655

Subgroups — #13178655

Order 1728.

2204 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89049C212yesmaximal, complemented
3C2×C4⋊#1113C211yesmaximal, characteristic, complemented
4C3×#64149C211yesmaximal, characteristic, complemented
5C3×#64147C211yesmaximal, characteristic, complemented
6#11723729C212yesmaximal, complemented
7#11723727C212yesmaximal, complemented
8#11723725C212yesmaximal, complemented
9#11723696C211yesmaximal, characteristic, complemented
10C4×#6295C211yesmaximal, characteristic, complemented
11#11723691C211yesmaximal, characteristic, complemented
12#10595297—31nomaximal
13#10595293—31nomaximal
14#10595288—31nomaximal
15C23×C3×C3⋊D3C2212yescomplemented
16C22×#1113C2212yescomplemented
17C2×C33×D4C2211yescharacteristic, complemented
18C2×C3×#638C2212yescomplemented
19C2×C3×#638C2212yescomplemented
20C2×C3×#638C2212yescomplemented
21C2×C3×#638C2212yescomplemented
22C3×D4×C3⋊D3—24no—
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27#89049—28no—
28C2×#6295C2211yescharacteristic
29C2×#6295C2212yescomplemented
30C2×#6295C2212yescomplemented
31C2×#6294C2212yescomplemented
32C4⋊#1113—24no—
33C3×#3757C2212yescomplemented
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88814C2212yescomplemented
38#88814C2211yescharacteristic, complemented
39#88814C2211yescharacteristic, complemented
40#88814C2212yescomplemented
41C2×D4×C3⋊D3D311yescharacteristic, complemented
42C2×C3×D3×D4—31no—
43C2×C3×D3×D4—31no—
44C2×C3×D3×D4—61no—
45C2×#3811—32no—
46C2×D3×#67—32no—
47C2×D3×#67—32no—
48C2×#3802—31no—
49C2×D3×D12—31no—
50C2×D3×D12—31no—
51#64149D311yescharacteristic, complemented
52#64147D311yescharacteristic, complemented
53C3×#940—31no—
54C3×#940—31no—
55C3×#940—61no—
56C3×#938—31no—
57C3×#938—31no—
58C3×#938—61no—
59#63983—32no—
60#63983—32no—
61#63983—32no—
62#63981—32no—
63#63977—32no—
64#63976—32no—
65#63971—32no—
66#63970—32no—
67#63958—32no—
68#63916—31no—
69#63909—31no—
70#63908—31no—
71C4×#626—31no—
72C4×#626—31no—
73C4×#625—31no—
74#63898—31no—
75#63894—31no—
76Dic3×D12—31no—
77C23×C33C2312yes—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3—24no—
80C22×C3×C3⋊D3—42no—
81C22×C3×C3⋊D3C2312yes—
82C22×C3×C3⋊D3C2311yescharacteristic
83C22×C3×C3⋊D3C2312yes—
84C22×C3×C3⋊D3C2311yescharacteristic
85C2×#1113—24no—
86C2×#1113—24no—
87C2×#1113—42no—
88C33×D4—22no—
89C2×C33×C4C2311yescharacteristic
90C3×#638—24no—
91C3×#638—24no—
92C3×#638—24no—
93C3×#638—42no—
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2312yes—
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×C4⋊(C3⋊D3)—22no—
100C3×C4⋊(C3⋊D3)D414yescomplemented
101C3×C4×C3⋊D3—22no—
102C3×C4×C3⋊D3—22no—
103#6295—24no—
104#6295—24no—
105#6295D414yescomplemented
106#6294—24no—
107D4×#67—91no—
108#5717—91no—
109#5609—91no—
110C23×C3⋊D3C2×D312yescomplemented
111C23×C3×D3—32no—
112C23×C3×D3—32no—
113C23×C3×D3—62no—
114C22×D32—32no—
115C22×D32—32no—
116C22×D32—32no—
117C2×C32×D4—21no—
118C2×C32×D4—21no—
119C2×C32×D4—21no—
120C2×C32×D4—41no—
121C2×C32×D4C2×D311yescharacteristic, complemented
122C2×C32×D4C2×D311yescharacteristic, complemented
123C2×C32×D4C2×D311yescharacteristic, complemented
124C2×#638C2×D312yescomplemented
125C2×#638C2×D312yescomplemented
126C2×#638C2×D312yescomplemented
127C2×#638C2×D312yescomplemented
128D4×C3⋊D3—24no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
131C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
132C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
133C2×C3×#67—32no—
134C2×C3×#67—32no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—32no—
140C2×C3×#67—32no—
141C2×C3×#67—62no—
142C2×C3×#67—62no—
143C2×C3×#67—62no—
144C2×C3×#67—62no—
145C3×D3×D4—64no—
146C3×D3×D4—64no—
147C3×D3×D4—68no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—31no—
151C2×C3×D12—31no—
152C2×C3×D12—61no—
153C2×C3×D12—61no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—61no—
159C2×C3×C4×D3—61no—
160#3811—68no—
161D3×#67—68no—
162D3×#67—68no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—32no—
166C2×#626—32no—
167C2×#626—32no—
168C2×#626—32no—
169C2×#625—31no—
170C2×#625—32no—
171C2×#625—32no—
172C2×#624—32no—
173C2×D3×Dic3—32no—
174C2×D3×Dic3—32no—
175#3802—64no—
176D3×D12—64no—
177D3×D12—64no—
178#3757C2×D312yescomplemented
179C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
180C4×C3⋊Dic3C2×D311yescharacteristic, complemented
181C3×#217—32no—
182C3×#217—32no—
183C3×#217—62no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—61no—
187C3×C4×Dic3—31no—
188C3×C4×Dic3—31no—
189C3×C4×Dic3—61no—
190#3724—31no—
191Dic3⋊Dic3—31no—
192Dic3⋊Dic3—31no—
193#3722—32no—
194#3722—31no—
195#3722—31no—
196#3722—32no—
197(C2×D3)⋊Dic3—32no—
198(C2×D3)⋊Dic3—32no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—32no—
204(C2×D3)⋊Dic3—32no—
205C22×C33—22no—
206C22×C33—22no—
207C22×C33—22no—
208C22×C33C2411yescharacteristic
209C2×C3×C3⋊D3—21no—
210C2×C3×C3⋊D3—22no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—22no—
215C2×C3×C3⋊D3—22no—
216C2×C3×C3⋊D3—22no—
217C2×C3×C3⋊D3—22no—
218C2×C3×C3⋊D3—48no—
219C2×C3×C3⋊D3C2×D412yescomplemented
220C2×C3×C3⋊D3C2×D412yescomplemented
221C2×C3×C3⋊D3C2×D414yescomplemented
222#1113—48no—
223C33×C4C2×D412yescomplemented
224C3×C3⋊Dic3—21no—
225C3×C3⋊Dic3—22no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C3×C3⋊Dic3C2×D412yescomplemented
229C22×C3×D4—91no—
230C22×#67—92no—
231C2×D3×D4—31no—
232C2×D3×D4—31no—
233C2×D3×D4—61no—
234C2×D3×D4—91no—
235C2×D3×D4—91no—
236C2×D3×D4—92no—
237C2×D3×D4—92no—
238C22×D12—91no—
239C3×#127—91no—
240C3×#121—91no—
241#953—92no—
242#940—31no—
243#940—31no—
244#940—61no—
245#939—92no—
246#938—31no—
247#938—31no—
248#938—61no—
249#938—91no—
250#938—92no—
251#937—92no—
252#937—92no—
253#937—92no—
254#937—92no—
255D4×Dic3—91no—
256#930—91no—
257C4×#67—91no—
258C4×#67—91no—
259#895—91no—
260#893—91no—
261#884—92no—
262#882—92no—
263C4×D12—91no—
264C4×D12—91no—
265C23×C32—22no—
266C23×C32—22no—
267C23×C32—22no—
268C23×C32—42no—
269C23×C32C22×D312yes—
270C23×C32C22×D312yes—
271C23×C32C22×D312yes—
272C22×C3⋊D3—24no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—42no—
275C22×C3⋊D3C22×D312yes—
276C22×C3⋊D3C22×D311yescharacteristic
277C22×C3⋊D3C22×D311yescharacteristic
278C22×C3⋊D3C22×D312yes—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—32no—
282C22×C3×D3—32no—
283C22×C3×D3—31no—
284C22×C3×D3—31no—
285C22×C3×D3—32no—
286C22×C3×D3—32no—
287C22×C3×D3—61no—
288C22×C3×D3—62no—
289C22×C3×D3—61no—
290C22×C3×D3—62no—
291C22×C3×D3—64no—
292C22×C3×D3—64no—
293C22×C3×D3—64no—
294C22×C3×D3—64no—
295C22×C3×D3—68no—
296C22×C3×D3—124no—
297C22×C3×D3—122no—
298C22×C3×D3—122no—
299C22×C3×D3—124no—
300C2×D32—64no—
301C2×D32—64no—
302C2×D32—64no—
303C2×D32—64no—
304C2×D32—64no—
305C2×D32—64no—
306C2×D32—122no—
307C2×D32—122no—
308C2×D32—122no—
309C32×D4—22no—
310C32×D4—24no—
311C32×D4—22no—
312C32×D4—22no—
313C32×D4—42no—
314C32×D4—42no—
315C32×D4—44no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—21no—
319C2×C32×C4—41no—
320C2×C32×C4C22×D311yescharacteristic
321C2×C32×C4C22×D311yescharacteristic
322C2×C32×C4C22×D311yescharacteristic
323#638—24no—
324#638—24no—
325#638—24no—
326#638—42no—
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D312yes—
330C2×C3⋊Dic3C22×D311yescharacteristic
331C2×C3⋊Dic3C22×D311yescharacteristic
332C4⋊(C3⋊D3)—22no—
333C4⋊(C3⋊D3)#6714yescomplemented
334C4×C3⋊D3—22no—
335C4×C3⋊D3—22no—
336C3×#67—64no—
337C3×#67—64no—
338C3×#67—64no—
339C3×#67—64no—
340C3×#67—64no—
341C3×#67—64no—
342C3×#67—68no—
343C3×#67—124no—
344C3×#67—124no—
345C3×#67—122no—
346C3×#67—122no—
347C3×#67—124no—
348C2×C3×Dic3—31no—
349C2×C3×Dic3—31no—
350C2×C3×Dic3—31no—
351C2×C3×Dic3—31no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—31no—
354C2×C3×Dic3—32no—
355C2×C3×Dic3—32no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—61no—
359C2×C3×Dic3—61no—
360C2×C3×Dic3—61no—
361C2×C3×Dic3—62no—
362C2×C3×Dic3—61no—
363C3×D12—34no—
364C3×D12—34no—
365C3×D12—64no—
366C3×D12—62no—
367C3×D12—62no—
368C3×D12—122no—
369C3×C4×D3—64no—
370C3×C4×D3—62no—
371C3×C4×D3—62no—
372C3×C4×D3—62no—
373C3×C4×D3—62no—
374C3×C4×D3—122no—
375#626—34no—
376#626—34no—
377#626—64no—
378#626—64no—
379#626—64no—
380#626—64no—
381#625—34no—
382#625—64no—
383#625—64no—
384#624—64no—
385D3×Dic3—64no—
386D3×Dic3—64no—
387D42—271noSylow
388C2×C33—42no—
389C2×C33C22×D411yescharacteristic
390C2×C33C22×D411yescharacteristic
391C2×C33H(5,𝔽2)11yescharacteristic
392C3×C3⋊D3—22no—
393C3×C3⋊D3—22no—
394C3×C3⋊D3—24no—
395C3×C3⋊D3—42no—
396C24×C3—92no—
397C23×D3—32no—
398C23×D3—32no—
399C23×D3—62no—
400C23×D3—92no—
401C23×D3—92no—
402C23×D3—92no—
403C2×C3×D4—21no—
404C2×C3×D4—21no—
405C2×C3×D4—21no—
406C2×C3×D4—41no—
407C2×C3×D4—92no—
408C2×C3×D4—92no—
409C2×C3×D4—92no—
410C2×C3×D4—92no—
411C2×C3×D4—91no—
412C2×C3×D4—91no—
413C2×C3×D4—184no—
414C2×C3×D4D3211yescharacteristic, complemented
415C2×C3×D4D3211yescharacteristic, complemented
416C2×C3×D4D3211yescharacteristic, complemented
417C22×C3×C4—91no—
418C22×C3×C4—91no—
419C2×#67—32no—
420C2×#67—32no—
421C2×#67—32no—
422C2×#67—32no—
423C2×#67—32no—
424C2×#67—32no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—62no—
428C2×#67—62no—
429C2×#67—62no—
430C2×#67—62no—
431C2×#67—91no—
432C2×#67—91no—
433C2×#67—92no—
434C2×#67—92no—
435C2×#67—92no—
436C2×#67—92no—
437C2×#67—188no—
438C22×Dic3—92no—
439D3×D4—64no—
440D3×D4—64no—
441D3×D4—68no—
442D3×D4—184no—
443D3×D4—184no—
444D3×D4—188no—
445D3×D4—188no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—31no—
449C2×D12—31no—
450C2×D12—61no—
451C2×D12—61no—
452C2×D12—91no—
453C2×D12—92no—
454C2×D12—92no—
455C2×D12—184no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—61no—
461C2×C4×D3—61no—
462C2×C4×D3—92no—
463C2×C4×D3—92no—
464C3×C4⋊C4—91no—
465C3×C22⋊C4—92no—
466C3×C42—91no—
467#217—32no—
468#217—32no—
469#217—62no—
470#217—91no—
471#217—91no—
472#217—92no—
473#217—92no—
474(C2×D3)⋊C4—92no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—92no—
479(C2×D3)⋊C4—92no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—92no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—61no—
485C4⋊Dic3—91no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488C4×Dic3—31no—
489C4×Dic3—31no—
490C4×Dic3—61no—
491C22×C32—22no—
492C22×C32—24no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—41no—
505C22×C32—42no—
506C22×C32—42no—
507C22×C32—44no—
508C22×C32—42no—
509C22×C32—42no—
510C22×C32—42no—
511C22×C32—42no—
512C22×C32—42no—
513C22×C32—42no—
514C22×C32—82no—
515C22×C32—82no—
516C22×C32C23×D311yescharacteristic
517C22×C32C23×D311yescharacteristic
518C22×C32C23×D311yescharacteristic
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—22no—
526C2×C3⋊D3—22no—
527C2×C3⋊D3—22no—
528C2×C3⋊D3—48no—
529C2×C3⋊D3D3×D412yescomplemented
530C2×C3⋊D3D3×D412yescomplemented
531C2×C3⋊D3C2×#6714yescomplemented
532C2×C3×D3—32no—
533C2×C3×D3—32no—
534C2×C3×D3—32no—
535C2×C3×D3—34no—
536C2×C3×D3—32no—
537C2×C3×D3—34no—
538C2×C3×D3—62no—
539C2×C3×D3—64no—
540C2×C3×D3—62no—
541C2×C3×D3—62no—
542C2×C3×D3—62no—
543C2×C3×D3—62no—
544C2×C3×D3—62no—
545C2×C3×D3—61no—
546C2×C3×D3—61no—
547C2×C3×D3—61no—
548C2×C3×D3—61no—
549C2×C3×D3—61no—
550C2×C3×D3—62no—
551C2×C3×D3—61no—
552C2×C3×D3—62no—
553C2×C3×D3—61no—
554C2×C3×D3—61no—
555C2×C3×D3—62no—
556C2×C3×D3—62no—
557C2×C3×D3—62no—
558C2×C3×D3—62no—
559C2×C3×D3—62no—
560C2×C3×D3—62no—
561C2×C3×D3—121no—
562C2×C3×D3—121no—
563C2×C3×D3—122no—
564C2×C3×D3—122no—
565C2×C3×D3—122no—
566C2×C3×D3—122no—
567C2×C3×D3—122no—
568C2×C3×D3—128no—
569C2×C3×D3—128no—
570C2×C3×D3—1216no—
571D32—128no—
572D32—128no—
573D32—128no—
574C32×C4—22no—
575C32×C4—22no—
576C32×C4—22no—
577C32×C4—42no—
578C32×C4D3×D412yescomplemented
579C32×C4D3×D412yescomplemented
580C32×C4C2×#6712yescomplemented
581C3⋊Dic3—21no—
582C3⋊Dic3—21no—
583C3⋊Dic3—22no—
584C3⋊Dic3—21no—
585C3⋊Dic3D3×D412yescomplemented
586C3×Dic3—32no—
587C3×Dic3—32no—
588C3×Dic3—62no—
589C3×Dic3—62no—
590C3×Dic3—62no—
591C3×Dic3—62no—
592C3×Dic3—62no—
593C3×Dic3—61no—
594C3×Dic3—61no—
595C3×Dic3—61no—
596C3×Dic3—61no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—121no—
600C3×Dic3—122no—
601C22×D4—91no—
602C22×D4—271no—
603C22×D4—272no—
604#127—91no—
605#121—91no—
606#121—272no—
607#121—271no—
608#120—272no—
609#120—272no—
610C4×D4—271no—
611C4×D4—271no—
612C33D4211yescharacteristic, complemented, Sylow
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—42no—
617C23×C3—92no—
618C23×C3—91no—
619C23×C3—91no—
620C23×C3—92no—
621C23×C3—184no—
622C23×C3—184no—
623C23×C3—362no—
624C23×C3C2×D3212yes—
625C23×C3C2×D3212yes—
626C23×C3C2×D3212yes—
627C22×D3—31no—
628C22×D3—31no—
629C22×D3—31no—
630C22×D3—31no—
631C22×D3—32no—
632C22×D3—32no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—64no—
640C22×D3—64no—
641C22×D3—64no—
642C22×D3—64no—
643C22×D3—68no—
644C22×D3—124no—
645C22×D3—122no—
646C22×D3—122no—
647C22×D3—124no—
648C22×D3—184no—
649C22×D3—184no—
650C22×D3—184no—
651C22×D3—184no—
652C22×D3—184no—
653C22×D3—184no—
654C22×D3—362no—
655C22×D3—362no—
656C22×D3—362no—
657C3×D4—24no—
658C3×D4—22no—
659C3×D4—22no—
660C3×D4—22no—
661C3×D4—42no—
662C3×D4—42no—
663C3×D4—44no—
664C3×D4—94no—
665C3×D4—184no—
666C3×D4—184no—
667C3×D4—184no—
668C3×D4—182no—
669C3×D4—362no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—41no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—91no—
678C2×C3×C4—92no—
679C2×C3×C4—182no—
680C2×C3×C4—182no—
681C2×C3×C4C2×D3211yescharacteristic
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C2×D3211yescharacteristic
684#67—64no—
685#67—64no—
686#67—64no—
687#67—64no—
688#67—64no—
689#67—64no—
690#67—68no—
691#67—94no—
692#67—94no—
693#67—124no—
694#67—124no—
695#67—122no—
696#67—122no—
697#67—124no—
698#67—184no—
699#67—184no—
700#67—184no—
701#67—184no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—62no—
716C2×Dic3—61no—
717C2×Dic3—184no—
718D12—34no—
719D12—34no—
720D12—64no—
721D12—62no—
722D12—62no—
723D12—94no—
724D12—122no—
725D12—184no—
726D12—184no—
727C4×D3—64no—
728C4×D3—62no—
729C4×D3—62no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—122no—
733C4×D3—184no—
734C4×D3—184no—
735C2×C32—21no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—41no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—42no—
748C2×C32—44no—
749C2×C32—42no—
750C2×C32—42no—
751C2×C32—82no—
752C2×C32—82no—
753C2×C32—84no—
754C2×C32C2×D3×D411yescharacteristic
755C2×C32C2×D3×D411yescharacteristic
756C2×C32C2×D3×D411yescharacteristic
757C2×C32C2×D3×D411yescharacteristic
758C2×C32C2×D3×D411yescharacteristic
759C2×C32#100411yescharacteristic
760C2×C32#100411yescharacteristic
761C2×C32#100911yescharacteristic
762C2×C32C22×#6711yescharacteristic
763C3⋊D3—22no—
764C3⋊D3—24no—
765C3⋊D3—22no—
766C3⋊D3—42no—
767C3×D3—64no—
768C3×D3—62no—
769C3×D3—64no—
770C3×D3—62no—
771C3×D3—62no—
772C3×D3—64no—
773C3×D3—62no—
774C3×D3—122no—
775C3×D3—124no—
776C3×D3—122no—
777C3×D3—122no—
778C3×D3—242no—
779C24—92no—
780C24—272no—
781C2×D4—92no—
782C2×D4—92no—
783C2×D4—92no—
784C2×D4—92no—
785C2×D4—91no—
786C2×D4—91no—
787C2×D4—184no—
788C2×D4—271no—
789C2×D4—272no—
790C2×D4—272no—
791C2×D4—544no—
792C2×D4—548no—
793C2×D4#111311yescharacteristic, complemented
794C22×C4—91no—
795C22×C4—91no—
796C22×C4—272no—
797C4⋊C4—91no—
798C4⋊C4—271no—
799C22⋊C4—92no—
800C22⋊C4—271no—
801C22⋊C4—272no—
802C22⋊C4—271no—
803C22⋊C4—272no—
804C42—91no—
805C22×C3—24no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—44no—
827C22×C3—41no—
828C22×C3—82no—
829C22×C3—82no—
830C22×C3—92no—
831C22×C3—92no—
832C22×C3—94no—
833C22×C3—182no—
834C22×C3—181no—
835C22×C3—182no—
836C22×C3—181no—
837C22×C3—181no—
838C22×C3—181no—
839C22×C3—182no—
840C22×C3—182no—
841C22×C3—182no—
842C22×C3—368no—
843C22×C3C22×D3211yescharacteristic
844C22×C3C22×D3211yescharacteristic
845C22×C3C22×D3211yescharacteristic
846C2×D3—32no—
847C2×D3—32no—
848C2×D3—32no—
849C2×D3—32no—
850C2×D3—34no—
851C2×D3—34no—
852C2×D3—62no—
853C2×D3—64no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—61no—
860C2×D3—62no—
861C2×D3—61no—
862C2×D3—62no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—121no—
876C2×D3—122no—
877C2×D3—122no—
878C2×D3—121no—
879C2×D3—122no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—128no—
883C2×D3—128no—
884C2×D3—1216no—
885C2×D3—368no—
886C2×D3—368no—
887C2×D3—368no—
888C3×C4—22no—
889C3×C4—22no—
890C3×C4—22no—
891C3×C4—42no—
892C3×C4—92no—
893C3×C4—182no—
894C3×C4—181no—
895C3×C4—181no—
896C3×C4—181no—
897C3×C4D3×#6712yescomplemented
898C3×C4D3×#6712yescomplemented
899C3×C4#381112yescomplemented
900Dic3—32no—
901Dic3—32no—
902Dic3—62no—
903Dic3—62no—
904Dic3—62no—
905Dic3—62no—
906Dic3—62no—
907Dic3—61no—
908Dic3—61no—
909Dic3—61no—
910Dic3—61no—
911Dic3—61no—
912Dic3—61no—
913Dic3—121no—
914Dic3—122no—
915C32—21no—
916C32—21no—
917C32—21no—
918C32—41no—
919C32#560911yescharacteristic, complemented
920C32#571711yescharacteristic, complemented
921C32D4×#6711yescharacteristic, complemented
922C23—91no—
923C23—91no—
924C23—92no—
925C23—92no—
926C23—184no—
927C23—184no—
928C23—362no—
929C23—544no—
930C23—544no—
931C23—1082no—
932C23C2×#111312yes—
933D4—22no—
934D4—94no—
935D4—184no—
936D4—184no—
937D4—184no—
938D4—182no—
939D4—274no—
940D4—362no—
941D4—544no—
942D4—544no—
943C2×C4—91no—
944C2×C4—91no—
945C2×C4—91no—
946C2×C4—92no—
947C2×C4—91no—
948C2×C4—182no—
949C2×C4—182no—
950C2×C4—544no—
951C2×C4C2×#111311yescharacteristic
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—21no—
960C2×C3—21no—
961C2×C3—44no—
962C2×C3—42no—
963C2×C3—42no—
964C2×C3—42no—
965C2×C3—41no—
966C2×C3—41no—
967C2×C3—41no—
968C2×C3—82no—
969C2×C3—82no—
970C2×C3—84no—
971C2×C3—182no—
972C2×C3—184no—
973C2×C3—182no—
974C2×C3—362no—
975C2×C3D32×D411yescharacteristic
976C2×C3D32×D411yescharacteristic
977C2×C3D32×D411yescharacteristic
978C2×C3#6431311yescharacteristic
979C2×C3#6431411yescharacteristic
980C2×C3#6431411yescharacteristic
981C2×C3C2×D3×#6711yescharacteristic
982C2×C3C2×D3×#6711yescharacteristic
983C2×C3C2×#381111yescharacteristic
984D3—64no—
985D3—62no—
986D3—64no—
987D3—62no—
988D3—62no—
989D3—64no—
990D3—62no—
991D3—124no—
992D3—122no—
993D3—122no—
994D3—122no—
995D3—242no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—92no—
1000C22—92no—
1001C22—94no—
1002C22—182no—
1003C22—181no—
1004C22—182no—
1005C22—181no—
1006C22—181no—
1007C22—181no—
1008C22—182no—
1009C22—182no—
1010C22—182no—
1011C22—368no—
1012C22—1088no—
1013C22C22×#111311yescharacteristic
1014C4—92no—
1015C4—182no—
1016C4—181no—
1017C4—181no—
1018C4—181no—
1019C4#8904912yescomplemented
1020C3—21no—
1021C3—21no—
1022C3—21no—
1023C3—41no—
1024C3#1059528811yescharacteristic, complemented
1025C3#1059529311yescharacteristic, complemented
1026C3#1059529711yescharacteristic, complemented
1027C2—42no—
1028C2—182no—
1029C2—184no—
1030C2—182no—
1031C2—362no—
1032C2D4×#111311yescharacteristic
1033C2#1172462311yescharacteristic
1034C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×#89049C2semidirect
3. C2×C4⋊#1113C2semidirect
4. C3×#64149C2semidirect
5. C3×#64147C2semidirect
6. #11723729C2semidirect
7. #11723727C2semidirect
8. #11723725C2semidirect
9. #11723696C2semidirect
10. C4×#6295C2semidirect
11. #11723691C2semidirect
15. C23×C3×C3⋊D3C22semidirect
16. C22×#1113C22semidirect
17. C2×C33×D4C22semidirect
18. C2×C3×#638C22semidirect
19. C2×C3×#638C22semidirect
20. C2×C3×#638C22semidirect
21. C2×C3×#638C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
29. C2×#6295C22semidirect
30. C2×#6295C22semidirect
31. C2×#6294C22semidirect
33. C3×#3757C22semidirect
34. C3×C4⋊(C3⋊Dic3)C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
36. #88815C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
39. #88814C22semidirect
40. #88814C22semidirect
41. C2×D4×C3⋊D3D3semidirect
51. #64149D3semidirect
52. #64147D3semidirect
100. C3×C4⋊(C3⋊D3)D4semidirect
105. #6295D4semidirect
110. C23×C3⋊D3C2×D3semidirect
121. C2×C32×D4C2×D3semidirect
122. C2×C32×D4C2×D3semidirect
123. C2×C32×D4C2×D3semidirect
124. C2×#638C2×D3semidirect
125. C2×#638C2×D3semidirect
126. C2×#638C2×D3semidirect
127. C2×#638C2×D3semidirect
130. C2×C4⋊(C3⋊D3)C2×D3semidirect
131. C2×C4×C3⋊D3C2×D3semidirect
132. C2×C4×C3⋊D3C2×D3semidirect
178. #3757C2×D3semidirect
179. C4⋊(C3⋊Dic3)C2×D3semidirect
180. C4×C3⋊Dic3C2×D3semidirect
219. C2×C3×C3⋊D3C2×D4semidirect
220. C2×C3×C3⋊D3C2×D4semidirect
221. C2×C3×C3⋊D3C2×D4semidirect
223. C33×C4C2×D4semidirect
228. C3×C3⋊Dic3C2×D4semidirect
333. C4⋊(C3⋊D3)#67semidirect
414. C2×C3×D4D32semidirect
415. C2×C3×D4D32semidirect
416. C2×C3×D4D32semidirect
529. C2×C3⋊D3D3×D4semidirect
530. C2×C3⋊D3D3×D4semidirect
531. C2×C3⋊D3C2×#67semidirect
578. C32×C4D3×D4semidirect
579. C32×C4D3×D4semidirect
580. C32×C4C2×#67semidirect
585. C3⋊Dic3D3×D4semidirect
612. C33D42semidirect
793. C2×D4#1113semidirect
897. C3×C4D3×#67semidirect
898. C3×C4D3×#67semidirect
899. C3×C4#3811semidirect
919. C32#5609semidirect
920. C32#5717semidirect
921. C32D4×#67semidirect
1019. C4#89049semidirect
1024. C3#10595288semidirect
1025. C3#10595293semidirect
1026. C3#10595297semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×#890492
C2×C4⋊#11132
C3×#641492
C3×#641472
#117237292
#117237272
#117237252
#117236962
C4×#62952
#117236912
#105952973
#105952933
#105952883