Finite Group Databasebeta

← C2×#11723726 #13178790

Subgroups — C2×#11723726 #13178790

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic
2C23×C3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C22×#6294C211yesmaximal, characteristic, complemented
4C2×C3×#3757C211yesmaximal, characteristic, complemented
5#11723726C218yesmaximal, direct product factor
6C2×#88815C211yesmaximal, characteristic, complemented
7C2×#88814C211yesmaximal, characteristic, complemented
8C2×#88813C211yesmaximal, characteristic, complemented
9C2×#67⋊Dic3—31nomaximal
10C2×Dic3×#67—31nomaximal
11C2×#63952—31nomaximal
12C24×C33C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C2×C3×#638C418yescomplemented
15C2×C3×#638C2214yes—
16C22×C3×C3⋊Dic3—24no—
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2214yescomplemented
23C2×#6294—24no—
24C2×#6294C2214yescomplemented
25C3×#3757C2214yescomplemented
26#88815C2214yescomplemented
27#88814C2214yescomplemented
28#88813C2214yescomplemented
29C22×#638D311yescharacteristic
30C23×C3⋊Dic3D311yescharacteristic, complemented
31C22×C3×#67—31no—
32C22×C3×#67—31no—
33C22×C3×#67—61no—
34C23×C3×Dic3—31no—
35C23×C3×Dic3—31no—
36C23×C3×Dic3—61no—
37C22×#624—31no—
38C22×D3×Dic3—31no—
39C22×D3×Dic3—31no—
40C2×#3757D311yescharacteristic, complemented
41C2×C3×#217—31no—
42C2×C3×#217—31no—
43C2×C3×#217—61no—
44#67⋊Dic3—38no—
45Dic3×#67—38no—
46C2×#3724—31no—
47C2×Dic3⋊Dic3—31no—
48C2×Dic3⋊Dic3—31no—
49C2×#3722—31no—
50C2×(C2×D3)⋊Dic3—31no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×Dic32—31no—
53C2×Dic32—31no—
54C2×Dic32—31no—
55#63952—38no—
56C23×C33—22no—
57C23×C33—22no—
58C23×C33C2×C414yescomplemented
59C23×C33C2312yes—
60C23×C33C2311yescharacteristic
61C22×C3×C3⋊D3—22no—
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3C2×C414yescomplemented
64C22×C3×C3⋊D3C2312yes—
65C3×#638C2×C4116yescomplemented
66C2×C3×C3⋊Dic3—22no—
67C2×C3×C3⋊Dic3—22no—
68C2×C3×C3⋊Dic3—22no—
69C2×C3×C3⋊Dic3—28no—
70C2×C3×C3⋊Dic3C2×C414yescomplemented
71C2×C3×C3⋊Dic3D414yescomplemented
72C2×C3×C3⋊Dic3C2312yes—
73C2×C3×C3⋊Dic3C2312yes—
74C2×C3×C3⋊Dic3C2312yes—
75C2×C3×C3⋊Dic3C2312yes—
76C2×C3×C3⋊Dic3C2312yes—
77#6294—28no—
78C2×D4×Dic3—91no—
79C2×C4×#67—91no—
80C2×#67⋊C4—91no—
81C24×C32—21no—
82C24×C32—21no—
83C24×C32—21no—
84C24×C32—41no—
85C24×C32C2×D311yescharacteristic
86C24×C32C2×D311yescharacteristic
87C24×C32C2×D311yescharacteristic
88C23×C3⋊D3C2×D311yescharacteristic
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—61no—
92C2×#638Dic318yescomplemented
93C2×#638C2×D314yes—
94C22×C3⋊Dic3—24no—
95C22×C3⋊Dic3C2×D311yescharacteristic
96C22×C3⋊Dic3C2×D311yescharacteristic
97C22×C3⋊Dic3C2×D311yescharacteristic
98C22×C3⋊Dic3C2×D311yescharacteristic
99C22×C3⋊Dic3C2×D311yescharacteristic
100C22×C3⋊Dic3C2×D314yescomplemented
101C2×C3×#67—38no—
102C2×C3×#67—38no—
103C2×C3×#67—34no—
104C2×C3×#67—34no—
105C2×C3×#67—68no—
106C2×C3×#67—64no—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—34no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—34no—
119C22×C3×Dic3—64no—
120C22×C3×Dic3—64no—
121C22×C3×Dic3—61no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—64no—
124C22×C3×Dic3—61no—
125C22×C3×Dic3—68no—
126C22×C3×Dic3—61no—
127C22×C3×Dic3—61no—
128C2×#624—34no—
129C2×#624—64no—
130C2×D3×Dic3—34no—
131C2×D3×Dic3—34no—
132C2×D3×Dic3—64no—
133C2×D3×Dic3—64no—
134#3757C2×D314yescomplemented
135C3×#217—34no—
136C3×#217—34no—
137C3×#217—64no—
138#3724—34no—
139Dic3⋊Dic3—34no—
140Dic3⋊Dic3—34no—
141#3722—34no—
142(C2×D3)⋊Dic3—34no—
143(C2×D3)⋊Dic3—34no—
144Dic32—34no—
145Dic32—34no—
146Dic32—34no—
147C22×C33—28no—
148C22×C33—22no—
149C22×C33—22no—
150C22×C33C22×C412yes—
151C22×C33C22×C414yescomplemented
152C22×C33C2×D412yes—
153C22×C33#4112yes—
154C22×C33C2411yescharacteristic
155C2×C3×C3⋊D3—28no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—22no—
158C2×C3×C3⋊D3C22×C414yescomplemented
159C3×C3⋊Dic3—22no—
160C3×C3⋊Dic3—22no—
161C3×C3⋊Dic3—22no—
162C3×C3⋊Dic3C22×C414yescomplemented
163C3×C3⋊Dic3C2×D414yescomplemented
164C22×C3×D4—91no—
165C23×C3×C4—91no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—61no—
169C23×Dic3—31no—
170C23×Dic3—31no—
171C23×Dic3—61no—
172C23×Dic3—91no—
173C22×C4×D3—91no—
174C22×C4×D3—91no—
175C2×C3×C22⋊C4—91no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—61no—
179C2×#217—91no—
180D4×Dic3—98no—
181C4×#67—98no—
182C2×(C2×D3)⋊C4—91no—
183C2×(C2×D3)⋊C4—91no—
184C2×C4⋊Dic3—91no—
185C2×Dic3⋊C4—91no—
186C2×Dic3⋊C4—91no—
187C2×C4×Dic3—91no—
188C2×C4×Dic3—91no—
189C2×C4×Dic3—91no—
190#67⋊C4—98no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—24no—
194C23×C32—24no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—24no—
200C23×C32—24no—
201C23×C32—24no—
202C23×C32—21no—
203C23×C32—22no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32—44no—
209C23×C32—42no—
210C23×C32—41no—
211C23×C32—42no—
212C23×C32—42no—
213C23×C32—42no—
214C23×C32—42no—
215C23×C32—44no—
216C23×C32—44no—
217C23×C32C4×D314yescomplemented
218C23×C32C4×D314yescomplemented
219C23×C32C2×Dic314yescomplemented
220C23×C32C22×D312yes—
221C23×C32C22×D312yes—
222C23×C32C22×D312yes—
223C23×C32C22×D311yescharacteristic
224C23×C32C22×D311yescharacteristic
225C23×C32C22×D311yescharacteristic
226C22×C3⋊D3—22no—
227C22×C3⋊D3—22no—
228C22×C3⋊D3C2×Dic314yescomplemented
229C22×C3⋊D3C22×D312yes—
230C22×C3×D3—34no—
231C22×C3×D3—34no—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—64no—
235C22×C3×D3—62no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—62no—
239C22×C3×D3—62no—
240C22×C3×D3—122no—
241C22×C3×D3—122no—
242#638C2×Dic3116yescomplemented
243C2×C3⋊Dic3—22no—
244C2×C3⋊Dic3—28no—
245C2×C3⋊Dic3—22no—
246C2×C3⋊Dic3—22no—
247C2×C3⋊Dic3C2×Dic314yescomplemented
248C2×C3⋊Dic3#6714yescomplemented
249C2×C3⋊Dic3C22×D312yes—
250C2×C3⋊Dic3C22×D312yes—
251C2×C3⋊Dic3C22×D312yes—
252C2×C3⋊Dic3C22×D312yes—
253C2×C3⋊Dic3C22×D312yes—
254C3×#67—316no—
255C3×#67—316no—
256C3×#67—616no—
257C2×C3×Dic3—34no—
258C2×C3×Dic3—34no—
259C2×C3×Dic3—34no—
260C2×C3×Dic3—34no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—64no—
272C2×C3×Dic3—64no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3—68no—
279C2×C3×Dic3—68no—
280C2×C3×Dic3—616no—
281C2×C3×Dic3—64no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—122no—
289C2×C3×Dic3—122no—
290#624—68no—
291D3×Dic3—68no—
292D3×Dic3—68no—
293C2×C4×D4—271noSylow
294C2×C33—24no—
295C2×C33C4×D414yescomplemented
296C2×C33C23×C411yescharacteristic
297C2×C33C22×D411yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C3×C3⋊D3—24no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—21no—
303C24×C3—41no—
304C24×C3—91no—
305C24×C3D3211yescharacteristic
306C24×C3D3211yescharacteristic
307C24×C3D3211yescharacteristic
308C23×D3—31no—
309C23×D3—31no—
310C23×D3—61no—
311C2×C3×D4—98no—
312C2×C3×D4—94no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×C3×C4—91no—
317C22×C3×C4—91no—
318C22×C3×C4—94no—
319C22×C3×C4—184no—
320C2×#67—38no—
321C2×#67—38no—
322C2×#67—34no—
323C2×#67—34no—
324C2×#67—68no—
325C2×#67—64no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—34no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—34no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—64no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—64no—
345C22×Dic3—64no—
346C22×Dic3—68no—
347C22×Dic3—94no—
348C22×Dic3—184no—
349C2×C4×D3—94no—
350C2×C4×D3—94no—
351C2×C4×D3—184no—
352C2×C4×D3—184no—
353C3×C22⋊C4—94no—
354#217—34no—
355#217—34no—
356#217—64no—
357#217—94no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360C4⋊Dic3—94no—
361Dic3⋊C4—94no—
362Dic3⋊C4—94no—
363C4×Dic3—94no—
364C4×Dic3—94no—
365C4×Dic3—94no—
366C22×C32—28no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—24no—
370C22×C32—24no—
371C22×C32—216no—
372C22×C32—28no—
373C22×C32—28no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32—24no—
384C22×C32—24no—
385C22×C32—22no—
386C22×C32—22no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—24no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—42no—
394C22×C32—44no—
395C22×C32—42no—
396C22×C32—42no—
397C22×C32—41no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32—42no—
402C22×C32—48no—
403C22×C32—48no—
404C22×C32—44no—
405C22×C32—416no—
406C22×C32—44no—
407C22×C32C2×C4×D312yes—
408C22×C32C2×C4×D312yes—
409C22×C32C2×C4×D314yescomplemented
410C22×C32C2×C4×D314yescomplemented
411C22×C32#23512yes—
412C22×C32D3×D412yes—
413C22×C32D3×D412yes—
414C22×C32#23712yes—
415C22×C32#23712yes—
416C22×C32C22×Dic312yes—
417C22×C32C22×Dic314yescomplemented
418C22×C32C2×#6712yes—
419C22×C32C23×D311yescharacteristic
420C22×C32C23×D311yescharacteristic
421C22×C32C23×D311yescharacteristic
422C2×C3⋊D3—28no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3C22×Dic314yescomplemented
426C2×C3×D3—34no—
427C2×C3×D3—34no—
428C2×C3×D3—64no—
429C2×C3×D3—68no—
430C2×C3×D3—68no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—122no—
436C2×C3×D3—122no—
437C2×C3×D3—128no—
438C3⋊Dic3—22no—
439C3⋊Dic3—22no—
440C3⋊Dic3—22no—
441C3⋊Dic3C22×Dic314yescomplemented
442C3⋊Dic3C2×#6714yescomplemented
443C3×Dic3—34no—
444C3×Dic3—34no—
445C3×Dic3—34no—
446C3×Dic3—34no—
447C3×Dic3—64no—
448C3×Dic3—64no—
449C3×Dic3—64no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—62no—
454C3×Dic3—62no—
455C3×Dic3—62no—
456C3×Dic3—122no—
457C3×Dic3—122no—
458C22×D4—91no—
459C23×C4—91no—
460C23×C4—271no—
461C4×D4—278no—
462C2×C4⋊C4—271no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—271no—
465C2×C42—271no—
466C33C2×C4×D411yescharacteristic, complemented, Sylow
467C23×C3—24no—
468C23×C3—24no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—24no—
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—42no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3—42no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—42no—
492C23×C3—41no—
493C23×C3—92no—
494C23×C3—94no—
495C23×C3—182no—
496C23×C3—182no—
497C23×C3D3×Dic314yescomplemented
498C23×C3D3×Dic314yescomplemented
499C23×C3#62414yescomplemented
500C23×C3C2×D3212yes—
501C23×C3C2×D3212yes—
502C23×C3C2×D3212yes—
503C23×C3C2×D3211yescharacteristic
504C23×C3C2×D3211yescharacteristic
505C23×C3C2×D3211yescharacteristic
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—34no—
509C22×D3—34no—
510C22×D3—64no—
511C22×D3—62no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—122no—
517C22×D3—122no—
518C3×D4—916no—
519C2×C3×C4—92no—
520C2×C3×C4—92no—
521C2×C3×C4—94no—
522C2×C3×C4—94no—
523C2×C3×C4—92no—
524C2×C3×C4—92no—
525C2×C3×C4—92no—
526C2×C3×C4—188no—
527C2×C3×C4—182no—
528C2×C3×C4—182no—
529C2×C3×C4—182no—
530#67—316no—
531#67—316no—
532#67—616no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—34no—
538C2×Dic3—34no—
539C2×Dic3—34no—
540C2×Dic3—34no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—64no—
548C2×Dic3—64no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—68no—
555C2×Dic3—68no—
556C2×Dic3—616no—
557C2×Dic3—64no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—62no—
564C2×Dic3—122no—
565C2×Dic3—122no—
566C2×Dic3—188no—
567C4×D3—188no—
568C4×D3—188no—
569C2×C32—24no—
570C2×C32—28no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—24no—
583C2×C32—24no—
584C2×C32—24no—
585C2×C32—44no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32—41no—
589C2×C32—44no—
590C2×C32—44no—
591C2×C32—48no—
592C2×C32#67⋊C414yescomplemented
593C2×C32C4×#6714yescomplemented
594C2×C32D4×Dic314yescomplemented
595C2×C32C22×C4×D311yescharacteristic
596C2×C32C22×C4×D311yescharacteristic
597C2×C32C2×#23511yescharacteristic
598C2×C32C2×D3×D411yescharacteristic
599C2×C32C2×D3×D411yescharacteristic
600C2×C32C2×#23711yescharacteristic
601C2×C32C2×#23711yescharacteristic
602C2×C32C23×Dic311yescharacteristic
603C2×C32C22×#6711yescharacteristic
604C3⋊D3—24no—
605C3×D3—64no—
606C3×D3—64no—
607C3×D3—124no—
608C24—91no—
609C24#111311yescharacteristic
610C2×D4—98no—
611C2×D4—94no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—94no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—184no—
619C22×C4—274no—
620C22×C4—544no—
621C4⋊C4—274no—
622C22⋊C4—94no—
623C22⋊C4—274no—
624C42—274no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—216no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—28no—
635C22×C3—28no—
636C22×C3—28no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—48no—
657C22×C3—48no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—416no—
661C22×C3—41no—
662C22×C3—42no—
663C22×C3—44no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—94no—
667C22×C3—182no—
668C22×C3—182no—
669C22×C3—188no—
670C22×C3C2×D3×Dic312yes—
671C22×C3C2×D3×Dic312yes—
672C22×C3C2×D3×Dic314yescomplemented
673C22×C3C2×D3×Dic314yescomplemented
674C22×C3#380412yes—
675C22×C3#380412yes—
676C22×C3#380512yes—
677C22×C3C2×#62412yes—
678C22×C3C2×#62414yescomplemented
679C22×C3D3×#6712yes—
680C22×C3D3×#6712yes—
681C22×C3#381112yes—
682C22×C3C22×D3211yescharacteristic
683C22×C3C22×D3211yescharacteristic
684C22×C3C22×D3211yescharacteristic
685C2×D3—34no—
686C2×D3—34no—
687C2×D3—64no—
688C2×D3—62no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—68no—
693C2×D3—68no—
694C2×D3—122no—
695C2×D3—122no—
696C2×D3—128no—
697C3×C4—94no—
698C3×C4—94no—
699C3×C4—182no—
700C3×C4—182no—
701C3×C4—182no—
702Dic3—34no—
703Dic3—34no—
704Dic3—34no—
705Dic3—34no—
706Dic3—64no—
707Dic3—64no—
708Dic3—64no—
709Dic3—62no—
710Dic3—62no—
711Dic3—62no—
712Dic3—62no—
713Dic3—62no—
714Dic3—62no—
715Dic3—122no—
716Dic3—122no—
717C32—21no—
718C32—21no—
719C32—21no—
720C32—41no—
721C32C2×#67⋊C411yescharacteristic, complemented
722C32C2×C4×#6711yescharacteristic, complemented
723C32C2×D4×Dic311yescharacteristic, complemented
724C23—22no—
725C23—22no—
726C23—92no—
727C23—94no—
728C23—182no—
729C23—182no—
730C23#629414yescomplemented
731C23C2×#111312yes—
732C23C2×#111311yescharacteristic
733D4—916no—
734C2×C4—92no—
735C2×C4—92no—
736C2×C4—94no—
737C2×C4—94no—
738C2×C4—92no—
739C2×C4—92no—
740C2×C4—92no—
741C2×C4—188no—
742C2×C4—182no—
743C2×C4—182no—
744C2×C4—182no—
745C2×C4—548no—
746C2×C3—28no—
747C2×C3—24no—
748C2×C3—24no—
749C2×C3—24no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—24no—
760C2×C3—24no—
761C2×C3—24no—
762C2×C3—44no—
763C2×C3—44no—
764C2×C3—48no—
765C2×C3—41no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—44no—
769C2×C3—184no—
770C2×C3#6395214yescomplemented
771C2×C3Dic3×#6714yescomplemented
772C2×C3#67⋊Dic314yescomplemented
773C2×C3C22×D3×Dic311yescharacteristic
774C2×C3C22×D3×Dic311yescharacteristic
775C2×C3C2×#380411yescharacteristic
776C2×C3C2×#380411yescharacteristic
777C2×C3C2×#380511yescharacteristic
778C2×C3C22×#62411yescharacteristic
779C2×C3C2×D3×#6711yescharacteristic
780C2×C3C2×D3×#6711yescharacteristic
781C2×C3C2×#381111yescharacteristic
782D3—64no—
783D3—64no—
784D3—124no—
785C22—22no—
786C22—22no—
787C22—28no—
788C22—94no—
789C22—182no—
790C22—182no—
791C22—188no—
792C22C2×#629412yes—
793C22C2×#629414yescomplemented
794C22#8904612yes—
795C22#8904912yes—
796C22C22×#111311yescharacteristic
797C4—94no—
798C4—94no—
799C4—182no—
800C4—182no—
801C4—182no—
802C3—21no—
803C3—21no—
804C3—21no—
805C3—41no—
806C3C2×#6395211yescharacteristic, complemented
807C3C2×Dic3×#6711yescharacteristic, complemented
808C3C2×#67⋊Dic311yescharacteristic, complemented
809C2—24no—
810C2—184no—
811C2#1172372614yesdirect product factor
812C2C22×#629411yescharacteristic
813C2C2×#8904611yescharacteristic
814C2C2×#8904911yescharacteristic
subgroupG/H
centerC23C2×#1113
commutatorC2×C33C23×C4
FrattiniC22C22×#1113
FittingC24×C33C22
socleC23×C33C23
prime radicalC22×C3×#638C2
cosocleC22×C33C24
hypercenterC24#1113
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C23×C3×C3⋊Dic3C2semidirect
3. C22×#6294C2semidirect
4. C2×C3×#3757C2semidirect
5. #11723726C2direct (N × H)
6. C2×#88815C2semidirect
7. C2×#88814C2semidirect
8. C2×#88813C2semidirect
14. C2×C3×#638C4semidirect
22. C22×C3×C3⋊Dic3C22semidirect
24. C2×#6294C22semidirect
25. C3×#3757C22semidirect
26. #88815C22semidirect
27. #88814C22semidirect
28. #88813C22semidirect
30. C23×C3⋊Dic3D3semidirect
40. C2×#3757D3semidirect
58. C23×C33C2×C4semidirect
63. C22×C3×C3⋊D3C2×C4semidirect
65. C3×#638C2×C4semidirect
70. C2×C3×C3⋊Dic3C2×C4semidirect
71. C2×C3×C3⋊Dic3D4semidirect
92. C2×#638Dic3semidirect
100. C22×C3⋊Dic3C2×D3semidirect
134. #3757C2×D3semidirect
151. C22×C33C22×C4semidirect
158. C2×C3×C3⋊D3C22×C4semidirect
162. C3×C3⋊Dic3C22×C4semidirect
163. C3×C3⋊Dic3C2×D4semidirect
217. C23×C32C4×D3semidirect
218. C23×C32C4×D3semidirect
219. C23×C32C2×Dic3semidirect
228. C22×C3⋊D3C2×Dic3semidirect
242. #638C2×Dic3semidirect
247. C2×C3⋊Dic3C2×Dic3semidirect
248. C2×C3⋊Dic3#67semidirect
295. C2×C33C4×D4semidirect
409. C22×C32C2×C4×D3semidirect
410. C22×C32C2×C4×D3semidirect
417. C22×C32C22×Dic3semidirect
425. C2×C3⋊D3C22×Dic3semidirect
441. C3⋊Dic3C22×Dic3semidirect
442. C3⋊Dic3C2×#67semidirect
466. C33C2×C4×D4semidirect
497. C23×C3D3×Dic3semidirect
498. C23×C3D3×Dic3semidirect
499. C23×C3#624semidirect
592. C2×C32#67⋊C4semidirect
593. C2×C32C4×#67semidirect
594. C2×C32D4×Dic3semidirect
672. C22×C3C2×D3×Dic3semidirect
673. C22×C3C2×D3×Dic3semidirect
678. C22×C3C2×#624semidirect
721. C32C2×#67⋊C4semidirect
722. C32C2×C4×#67semidirect
723. C32C2×D4×Dic3semidirect
730. C23#6294semidirect
770. C2×C3#63952semidirect
771. C2×C3Dic3×#67semidirect
772. C2×C3#67⋊Dic3semidirect
793. C22C2×#6294semidirect
806. C3C2×#63952semidirect
807. C3C2×Dic3×#67semidirect
808. C3C2×#67⋊Dic3semidirect
811. C2#11723726direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C23×C3×C3⋊Dic32
C22×#62942
C2×C3×#37572
#117237262
C2×#888152
C2×#888142
C2×#888132
C2×#67⋊Dic33
C2×Dic3×#673
C2×#639523