Finite Group Databasebeta

← #13178281

Subgroups — #13178281

Order 1728.

2058 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic
2C22×#6294C211yesmaximal, characteristic, complemented
3C2×C4×#1113C211yesmaximal, characteristic, complemented
4C3×#64090C212yesmaximal, complemented
5C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6#11723726C212yesmaximal, complemented
7#11723700C211yesmaximal, characteristic, complemented
8#11723685C212yesmaximal, complemented
9#11723684C212yesmaximal, complemented
10#11723682C211yesmaximal, characteristic, complemented
11C4×#6294C211yesmaximal, characteristic, complemented
12#10594255—31nomaximal
13D3×#67⋊C4—32nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×#1113C2211yescharacteristic
16C2×C3×#638C2212yes—
17C22×C3×C3⋊Dic3C2212yescomplemented
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2212yescomplemented
21#89049C418yescomplemented
22C2×#6295C2212yes—
23C2×#6294—24no—
24C2×#6294C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2212yescomplemented
28C2×#6294C2212yescomplemented
29C4×#1113—24no—
30C33×C22⋊C4C2211yescharacteristic, complemented
31C3×#3757C2211yescharacteristic, complemented
32C3×#3752C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic, complemented
34C3×#3752C2212yescomplemented
35C3×#3750C2212yescomplemented
36C3×C4×C3⋊Dic3C2212yescomplemented
37#88815C2212yescomplemented
38#88814C2212yescomplemented
39#88813C2212yescomplemented
40C2×#3811—31no—
41C2×D3×#67—32no—
42C22×#624—31no—
43C22×D3×Dic3—32no—
44C2×C4×D32—31no—
45C2×C4×D32—32no—
46#64090D312yescomplemented
47C22⋊C4×C3⋊D3D311yescharacteristic, complemented
48C3×#67⋊C4—32no—
49C3×#67⋊C4—32no—
50C3×#67⋊C4—62no—
51C3×D3×C22⋊C4—32no—
52C3×D3×C22⋊C4—61no—
53#67⋊Dic3—32no—
54Dic3×#67—32no—
55#63952—32no—
56#63921—31no—
57D3×(C2×D3)⋊C4—32no—
58#63904—32no—
59#63902—32no—
60#63883—31no—
61C4×#624—31no—
62#63881—32no—
63#63880—32no—
64#63880—32no—
65#63879—32no—
66D3×Dic3⋊C4—32no—
67C4×D3×Dic3—32no—
68C23×C33C2311yescharacteristic
69C22×C3×C3⋊D3—22no—
70C22×C3×C3⋊D3—22no—
71C22×C3×C3⋊D3C2×C414yescomplemented
72C22×C3×C3⋊D3C2311yescharacteristic
73C22×C3×C3⋊D3C2312yes—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×#1113—22no—
76C2×#1113—22no—
77C2×#1113C2×C414yescomplemented
78C2×C33×C4C2311yescharacteristic
79C2×C33×C4C2311yescharacteristic
80C3×#638C2×C418yescomplemented
81C2×C3×C3⋊Dic3—24no—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C3×C4×C3⋊D3—22no—
88C3×C4×C3⋊D3—22no—
89C3×C4×C3⋊D3—24no—
90#6295C2×C418yescomplemented
91#6294—22no—
92#6294—24no—
93#6294—24no—
94#6294C2×C414yescomplemented
95#6294D414yescomplemented
96C4×D3×D4—92no—
97C2×#67⋊C4—91no—
98C23×C3⋊D3C2×D311yescharacteristic
99C23×C3×D3—32no—
100C23×C3×D3—61no—
101C22×D32—32no—
102C22×D32—31no—
103C2×#638C2×D312yes—
104C22×C3⋊Dic3C2×D312yescomplemented
105C2×C4×C3⋊D3C2×D311yescharacteristic
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×C4×C3⋊D3C2×D312yescomplemented
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C2×C3×#67—62no—
111C22×C3×Dic3—32no—
112C22×C3×Dic3—32no—
113C22×C3×Dic3—62no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—61no—
119C2×C3×C4×D3—61no—
120C2×C3×C4×D3—62no—
121#3811—38no—
122D3×#67—316no—
123C2×#626—32no—
124C2×#626—32no—
125C2×#625—32no—
126C2×#624—31no—
127C2×#624—31no—
128C2×#624—32no—
129C2×#624—32no—
130C2×#624—31no—
131C2×#624—64no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—32no—
136C2×D3×Dic3—32no—
137C2×D3×Dic3—32no—
138C2×D3×Dic3—32no—
139C2×D3×Dic3—68no—
140C4×D32—68no—
141C4×D32—64no—
142C32×C22⋊C4—21no—
143C32×C22⋊C4—22no—
144C32×C22⋊C4—41no—
145C32×C22⋊C4C2×D312yescomplemented
146C32×C22⋊C4C2×D311yescharacteristic, complemented
147#3757C2×D311yescharacteristic, complemented
148#3752C2×D311yescharacteristic, complemented
149#3752C2×D311yescharacteristic, complemented
150#3752C2×D312yescomplemented
151#3750C2×D312yescomplemented
152C4×C3⋊Dic3C2×D312yescomplemented
153C3×#217—32no—
154C3×#217—61no—
155C3×(C2×D3)⋊C4—32no—
156C3×(C2×D3)⋊C4—32no—
157C3×(C2×D3)⋊C4—32no—
158C3×(C2×D3)⋊C4—32no—
159C3×(C2×D3)⋊C4—61no—
160C3×(C2×D3)⋊C4—61no—
161C3×(C2×D3)⋊C4—62no—
162C3×Dic3⋊C4—32no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—62no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—32no—
167C3×C4×Dic3—62no—
168#3724—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171#3722—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—32no—
177C22×C33—21no—
178C22×C33—21no—
179C22×C33C22×C412yescomplemented
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—28no—
186C2×C3×C3⋊D3C22×C412yes—
187C2×C3×C3⋊D3C22×C412yescomplemented
188C2×C3×C3⋊D3C22×C414yescomplemented
189C2×C3×C3⋊D3C2×D412yes—
190C2×C3×C3⋊D3#4112yes—
191#1113—28no—
192C33×C4—21no—
193C33×C4—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3C22×C414yescomplemented
198C3×C3⋊Dic3C2×D414yescomplemented
199C22×#67—91no—
200C23×Dic3—91no—
201C2×D3×D4—92no—
202C22×C4×D3—91no—
203C22×C4×D3—92no—
204C22×C4×D3—92no—
205C3×C4×D4—92no—
206C2×C3×C22⋊C4—91no—
207D4×Dic3—92no—
208C4×#67—92no—
209C4×#67—92no—
210C2×(C2×D3)⋊C4—91no—
211C2×Dic3⋊C4—91no—
212C2×C4×Dic3—91no—
213#893—92no—
214D3×C4⋊C4—92no—
215#67⋊C4—32no—
216#67⋊C4—32no—
217#67⋊C4—62no—
218#67⋊C4—92no—
219#67⋊C4—92no—
220#67⋊C4—92no—
221#67⋊C4—92no—
222D3×C22⋊C4—32no—
223D3×C22⋊C4—61no—
224D3×C22⋊C4—92no—
225C4×D12—92no—
226C42×D3—92no—
227C23×C32—21no—
228C23×C32—22no—
229C23×C32—41no—
230C23×C32C22×D312yes—
231C23×C32C22×D311yescharacteristic
232C22×C3⋊D3—22no—
233C22×C3⋊D3—22no—
234C22×C3⋊D3C4×D314yescomplemented
235C22×C3⋊D3C22×D312yes—
236C22×C3⋊D3C22×D311yescharacteristic
237C22×C3⋊D3C22×D311yescharacteristic
238C22×C3×D3—32no—
239C22×C3×D3—38no—
240C22×C3×D3—32no—
241C22×C3×D3—32no—
242C22×C3×D3—32no—
243C22×C3×D3—61no—
244C22×C3×D3—61no—
245C22×C3×D3—64no—
246C22×C3×D3—62no—
247C22×C3×D3—64no—
248C22×C3×D3—64no—
249C22×C3×D3—122no—
250C22×C3×D3—122no—
251C2×D32—34no—
252C2×D32—38no—
253C2×D32—64no—
254C2×D32—64no—
255C2×D32—62no—
256C2×D32—62no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—41no—
262C2×C32×C4—41no—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D312yes—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D312yes—
267#638C4×D318yescomplemented
268C2×C3⋊Dic3—24no—
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D312yes—
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D312yes—
273C2×C3⋊Dic3C22×D312yes—
274C4×C3⋊D3—22no—
275C4×C3⋊D3—22no—
276C4×C3⋊D3—24no—
277C3×#67—38no—
278C3×#67—38no—
279C3×#67—68no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3—61no—
293C2×C3×Dic3—64no—
294C2×C3×Dic3—64no—
295C2×C3×Dic3—124no—
296C3×C4×D3—64no—
297C3×C4×D3—64no—
298C3×C4×D3—64no—
299C3×C4×D3—64no—
300C3×C4×D3—124no—
301C3×C4×D3—122no—
302C3×C4×D3—122no—
303#626—38no—
304#626—38no—
305#625—38no—
306#624—34no—
307#624—34no—
308#624—64no—
309#624—64no—
310#624—62no—
311D3×Dic3—38no—
312D3×Dic3—38no—
313D3×Dic3—64no—
314D3×Dic3—64no—
315D3×Dic3—64no—
316D3×Dic3—64no—
317D3×Dic3—64no—
318C2×C4×D4—271noSylow
319C2×C33—22no—
320C2×C33C23×C411yescharacteristic
321C2×C33C22×D411yescharacteristic
322C2×C33C2×#4111yescharacteristic
323C3×C3⋊D3—24no—
324C3×C3⋊D3—22no—
325C3×C3⋊D3C4×D414yescomplemented
326C24×C3—91no—
327C23×D3—32no—
328C23×D3—61no—
329C23×D3—92no—
330C23×D3—91no—
331C2×C3×D4—92no—
332C22×C3×C4—92no—
333C22×C3×C4—91no—
334C22×C3×C4—91no—
335C22×C3×C4—92no—
336C2×#67—32no—
337C2×#67—32no—
338C2×#67—62no—
339C2×#67—92no—
340C2×#67—92no—
341C2×#67—98no—
342C22×Dic3—32no—
343C22×Dic3—32no—
344C22×Dic3—62no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C22×Dic3—92no—
348C22×Dic3—92no—
349C22×Dic3—91no—
350C22×Dic3—184no—
351D3×D4—916no—
352C2×D12—92no—
353C2×C4×D3—32no—
354C2×C4×D3—32no—
355C2×C4×D3—32no—
356C2×C4×D3—32no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—62no—
360C2×C4×D3—92no—
361C2×C4×D3—92no—
362C2×C4×D3—92no—
363C2×C4×D3—92no—
364C2×C4×D3—92no—
365C2×C4×D3—92no—
366C2×C4×D3—92no—
367C2×C4×D3—188no—
368C2×C4×D3—184no—
369C2×C4×D3—188no—
370C3×C4⋊C4—92no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—22no—
373C3×C22⋊C4—41no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—92no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4D3212yescomplemented
379C3×C22⋊C4D3211yescharacteristic, complemented
380C3×C42—92no—
381#217—32no—
382#217—61no—
383#217—92no—
384(C2×D3)⋊C4—32no—
385(C2×D3)⋊C4—32no—
386(C2×D3)⋊C4—32no—
387(C2×D3)⋊C4—32no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—92no—
392(C2×D3)⋊C4—92no—
393C4⋊Dic3—92no—
394Dic3⋊C4—32no—
395Dic3⋊C4—32no—
396Dic3⋊C4—62no—
397Dic3⋊C4—92no—
398Dic3⋊C4—92no—
399C4×Dic3—32no—
400C4×Dic3—32no—
401C4×Dic3—62no—
402C4×Dic3—92no—
403C4×Dic3—92no—
404C4×Dic3—92no—
405C22×C32—21no—
406C22×C32—22no—
407C22×C32—21no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—21no—
411C22×C32—24no—
412C22×C32—22no—
413C22×C32—41no—
414C22×C32—42no—
415C22×C32—42no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—42no—
419C22×C32—81no—
420C22×C32—81no—
421C22×C32C2×C4×D312yescomplemented
422C22×C32C2×C4×D314yescomplemented
423C22×C32C23×D311yescharacteristic
424C22×C32C23×D312yes—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—28no—
430C2×C3⋊D3C2×C4×D312yes—
431C2×C3⋊D3C2×C4×D312yescomplemented
432C2×C3⋊D3C2×C4×D314yescomplemented
433C2×C3⋊D3D3×D412yes—
434C2×C3⋊D3#23712yes—
435C2×C3×D3—34no—
436C2×C3×D3—34no—
437C2×C3×D3—34no—
438C2×C3×D3—34no—
439C2×C3×D3—34no—
440C2×C3×D3—34no—
441C2×C3×D3—62no—
442C2×C3×D3—62no—
443C2×C3×D3—62no—
444C2×C3×D3—64no—
445C2×C3×D3—62no—
446C2×C3×D3—616no—
447C2×C3×D3—62no—
448C2×C3×D3—62no—
449C2×C3×D3—62no—
450C2×C3×D3—62no—
451C2×C3×D3—62no—
452C2×C3×D3—62no—
453C2×C3×D3—128no—
454C2×C3×D3—122no—
455C2×C3×D3—122no—
456C2×C3×D3—121no—
457C2×C3×D3—121no—
458D32—616no—
459D32—68no—
460C32×C4—21no—
461C32×C4—22no—
462C32×C4—21no—
463C32×C4—22no—
464C32×C4—42no—
465C32×C4—41no—
466C32×C4—41no—
467C32×C4—42no—
468C32×C4—81no—
469C32×C4—81no—
470C3⋊Dic3—21no—
471C3⋊Dic3—22no—
472C3⋊Dic3—21no—
473C3⋊Dic3C2×C4×D314yescomplemented
474C3⋊Dic3D3×D414yescomplemented
475C3×Dic3—34no—
476C3×Dic3—34no—
477C3×Dic3—34no—
478C3×Dic3—34no—
479C3×Dic3—64no—
480C3×Dic3—64no—
481C3×Dic3—62no—
482C3×Dic3—62no—
483C3×Dic3—62no—
484C3×Dic3—62no—
485C3×Dic3—121no—
486C3×Dic3—121no—
487C3×Dic3—122no—
488C22×D4—271no—
489C23×C4—271no—
490C23×C4—271no—
491C4×D4—92no—
492C4×D4—272no—
493C4×D4—272no—
494C4×D4—272no—
495C2×C4⋊C4—271no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—271no—
498C2×C42—271no—
499C33C2×C4×D411yescharacteristic, complemented, Sylow
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—41no—
503C23×C3—91no—
504C23×C3—92no—
505C23×C3—91no—
506C23×C3—94no—
507C23×C3—182no—
508C23×C3—182no—
509C23×C3C2×D3212yes—
510C23×C3C2×D3211yescharacteristic
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—32no—
514C22×D3—32no—
515C22×D3—38no—
516C22×D3—61no—
517C22×D3—64no—
518C22×D3—61no—
519C22×D3—62no—
520C22×D3—64no—
521C22×D3—64no—
522C22×D3—98no—
523C22×D3—94no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—184no—
527C22×D3—184no—
528C22×D3—182no—
529C22×D3—182no—
530C3×D4—98no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—92no—
538C2×C3×C4—92no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—92no—
542C2×C3×C4—184no—
543C2×C3×C4—182no—
544C2×C3×C4—182no—
545C2×C3×C4—184no—
546C2×C3×C4C2×D3211yescharacteristic
547C2×C3×C4C2×D3212yes—
548C2×C3×C4C2×D3211yescharacteristic
549C2×C3×C4C2×D3212yes—
550#67—38no—
551#67—38no—
552#67—68no—
553#67—98no—
554#67—98no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—62no—
564C2×Dic3—62no—
565C2×Dic3—62no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—64no—
569C2×Dic3—64no—
570C2×Dic3—94no—
571C2×Dic3—94no—
572C2×Dic3—124no—
573C2×Dic3—184no—
574C2×Dic3—184no—
575C2×Dic3—182no—
576D12—98no—
577C4×D3—64no—
578C4×D3—64no—
579C4×D3—64no—
580C4×D3—64no—
581C4×D3—98no—
582C4×D3—98no—
583C4×D3—124no—
584C4×D3—122no—
585C4×D3—122no—
586C4×D3—184no—
587C4×D3—184no—
588C4×D3—184no—
589C4×D3—184no—
590C4×D3—184no—
591C2×C32—22no—
592C2×C32—24no—
593C2×C32—22no—
594C2×C32—21no—
595C2×C32—22no—
596C2×C32—21no—
597C2×C32—22no—
598C2×C32—21no—
599C2×C32—41no—
600C2×C32—41no—
601C2×C32—41no—
602C2×C32—42no—
603C2×C32—44no—
604C2×C32—82no—
605C2×C32C22×C4×D311yescharacteristic
606C2×C32C22×C4×D312yes—
607C2×C32C2×D3×D411yescharacteristic
608C2×C32C2×D3×D412yes—
609C2×C32C2×#23711yescharacteristic
610C2×C32D3×#4112yes—
611C3⋊D3—22no—
612C3⋊D3—24no—
613C3⋊D3#67⋊C414yescomplemented
614C3×D3—38no—
615C3×D3—64no—
616C3×D3—64no—
617C3×D3—64no—
618C3×D3—64no—
619C3×D3—124no—
620C3×D3—122no—
621C24—91no—
622C24—271no—
623C2×D4—92no—
624C2×D4—272no—
625C2×D4—278no—
626C22×C4—92no—
627C22×C4—91no—
628C22×C4—91no—
629C22×C4—92no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C22×C4—272no—
634C22×C4—272no—
635C22×C4—544no—
636C22×C4—544no—
637C4⋊C4—92no—
638C4⋊C4—272no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—91no—
642C22⋊C4—92no—
643C22⋊C4—272no—
644C22⋊C4#111311yescharacteristic, complemented
645C42—92no—
646C42—272no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—24no—
654C22×C3—22no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—41no—
660C22×C3—42no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—92no—
664C22×C3—92no—
665C22×C3—92no—
666C22×C3—92no—
667C22×C3—94no—
668C22×C3—188no—
669C22×C3—181no—
670C22×C3—182no—
671C22×C3—182no—
672C22×C3—181no—
673C22×C3C4×D3212yescomplemented
674C22×C3C4×D3214yescomplemented
675C22×C3C22×D3212yes—
676C22×C3C22×D3211yescharacteristic
677C2×D3—34no—
678C2×D3—34no—
679C2×D3—34no—
680C2×D3—34no—
681C2×D3—34no—
682C2×D3—34no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—64no—
687C2×D3—62no—
688C2×D3—616no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—128no—
696C2×D3—122no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—1816no—
701C2×D3—188no—
702C3×C4—22no—
703C3×C4—21no—
704C3×C4—22no—
705C3×C4—21no—
706C3×C4—42no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—42no—
710C3×C4—81no—
711C3×C4—81no—
712C3×C4—94no—
713C3×C4—94no—
714C3×C4—182no—
715C3×C4—181no—
716C3×C4—181no—
717Dic3—34no—
718Dic3—34no—
719Dic3—34no—
720Dic3—34no—
721Dic3—64no—
722Dic3—64no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—62no—
727Dic3—121no—
728Dic3—121no—
729Dic3—122no—
730C32—22no—
731C32—21no—
732C32—41no—
733C32C2×#67⋊C411yescharacteristic, complemented
734C32C4×D3×D412yescomplemented
735C23—91no—
736C23—91no—
737C23—92no—
738C23—94no—
739C23—182no—
740C23—182no—
741C23—274no—
742C23—542no—
743C23—542no—
744C23C2×#111311yescharacteristic
745D4—98no—
746D4—278no—
747C2×C4—92no—
748C2×C4—92no—
749C2×C4—91no—
750C2×C4—91no—
751C2×C4—92no—
752C2×C4—184no—
753C2×C4—182no—
754C2×C4—182no—
755C2×C4—184no—
756C2×C4—274no—
757C2×C4—274no—
758C2×C4—544no—
759C2×C4—544no—
760C2×C4—542no—
761C2×C4C2×#111311yescharacteristic
762C2×C4C2×#111311yescharacteristic
763C2×C3—24no—
764C2×C3—22no—
765C2×C3—22no—
766C2×C3—21no—
767C2×C3—22no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—22no—
771C2×C3—42no—
772C2×C3—44no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—41no—
776C2×C3—82no—
777C2×C3—94no—
778C2×C3—184no—
779C2×C3—182no—
780C2×C3C2×C4×D3212yes—
781C2×C3C2×C4×D3211yescharacteristic
782C2×C3D32×D412yes—
783C2×C3D32×D411yescharacteristic
784C2×C3D3×#23712yes—
785C2×C3#6431211yescharacteristic
786D3—38no—
787D3—64no—
788D3—64no—
789D3—64no—
790D3—64no—
791D3—122no—
792D3—124no—
793C22—21no—
794C22—21no—
795C22—92no—
796C22—92no—
797C22—92no—
798C22—94no—
799C22—92no—
800C22—188no—
801C22—182no—
802C22—181no—
803C22—181no—
804C22—182no—
805C22—548no—
806C22C4×#111312yescomplemented
807C22C22×#111311yescharacteristic
808C4—21no—
809C4—21no—
810C4—94no—
811C4—94no—
812C4—181no—
813C4—182no—
814C4—181no—
815C3—21no—
816C3—22no—
817C3—41no—
818C3D3×#67⋊C412yescomplemented
819C3#1059425511yescharacteristic, complemented
820C2—22no—
821C2—94no—
822C2—182no—
823C2—184no—
824C2C2×C4×#111311yescharacteristic
825C2D4×#111311yescharacteristic
826C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutatorC2×C33C23×C4
FittingC33×C22⋊C4C22
socle, cosocleC22×C33C24
prime radicalC2×#89049C2
hypercenterC22⋊C4#1113
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6294C2semidirect
3. C2×C4×#1113C2semidirect
4. C3×#64090C2semidirect
5. C3×C22⋊C4×C3⋊D3C2semidirect
6. #11723726C2semidirect
7. #11723700C2semidirect
8. #11723685C2semidirect
9. #11723684C2semidirect
10. #11723682C2semidirect
11. C4×#6294C2semidirect
17. C22×C3×C3⋊Dic3C22semidirect
20. C2×C3×C4×C3⋊D3C22semidirect
21. #89049C4semidirect
27. C2×#6294C22semidirect
28. C2×#6294C22semidirect
30. C33×C22⋊C4C22semidirect
31. C3×#3757C22semidirect
32. C3×#3752C22semidirect
33. C3×#3752C22semidirect
34. C3×#3752C22semidirect
35. C3×#3750C22semidirect
36. C3×C4×C3⋊Dic3C22semidirect
37. #88815C22semidirect
38. #88814C22semidirect
39. #88813C22semidirect
46. #64090D3semidirect
47. C22⋊C4×C3⋊D3D3semidirect
71. C22×C3×C3⋊D3C2×C4semidirect
77. C2×#1113C2×C4semidirect
80. C3×#638C2×C4semidirect
90. #6295C2×C4semidirect
94. #6294C2×C4semidirect
95. #6294D4semidirect
104. C22×C3⋊Dic3C2×D3semidirect
107. C2×C4×C3⋊D3C2×D3semidirect
145. C32×C22⋊C4C2×D3semidirect
146. C32×C22⋊C4C2×D3semidirect
147. #3757C2×D3semidirect
148. #3752C2×D3semidirect
149. #3752C2×D3semidirect
150. #3752C2×D3semidirect
151. #3750C2×D3semidirect
152. C4×C3⋊Dic3C2×D3semidirect
179. C22×C33C22×C4semidirect
187. C2×C3×C3⋊D3C22×C4semidirect
188. C2×C3×C3⋊D3C22×C4semidirect
197. C3×C3⋊Dic3C22×C4semidirect
198. C3×C3⋊Dic3C2×D4semidirect
234. C22×C3⋊D3C4×D3semidirect
267. #638C4×D3semidirect
325. C3×C3⋊D3C4×D4semidirect
378. C3×C22⋊C4D32semidirect
379. C3×C22⋊C4D32semidirect
421. C22×C32C2×C4×D3semidirect
422. C22×C32C2×C4×D3semidirect
431. C2×C3⋊D3C2×C4×D3semidirect
432. C2×C3⋊D3C2×C4×D3semidirect
473. C3⋊Dic3C2×C4×D3semidirect
474. C3⋊Dic3D3×D4semidirect
499. C33C2×C4×D4semidirect
613. C3⋊D3#67⋊C4semidirect
644. C22⋊C4#1113semidirect
673. C22×C3C4×D32semidirect
674. C22×C3C4×D32semidirect
733. C32C2×#67⋊C4semidirect
734. C32C4×D3×D4semidirect
806. C22C4×#1113semidirect
818. C3D3×#67⋊C4semidirect
819. C3#10594255semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C22×#62942
C2×C4×#11132
C3×#640902
C3×C22⋊C4×C3⋊D32
#117237262
#117237002
#117236852
#117236842
#117236822
C4×#62942
#105942553
D3×#67⋊C43