Finite Group Databasebeta

← #13175916

Subgroups — #13175916

Order 1728.

4500 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×#89026C212yesmaximal, complemented
4C22⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C3×#64091C211yesmaximal, characteristic, complemented
6C32×#882C211yesmaximal, characteristic, complemented
7#11723634C211yesmaximal, characteristic, complemented
8#11723629C211yesmaximal, characteristic, complemented
9#11723541C212yesmaximal, complemented
10#11723540C212yesmaximal, complemented
11#11723539C212yesmaximal, complemented
12C3⋊D3×#120—31nomaximal
13#10594258—34nomaximal
14C23×C3⋊(C3⋊D3)C2211yescharacteristic
15C23×C3×C3⋊D3C2211yescharacteristic, complemented
16C23×C32×D3C2211yescharacteristic, complemented
17C22×D3×C3⋊D3—24no—
18C22×D3×C3⋊D3—28no—
19C22×D3×C3⋊D3C2212yes—
20C22×D3×C3⋊D3C2212yescomplemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2212yescomplemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×D12C2212yescomplemented
27#89039—24no—
28C2×#6292C2211yescharacteristic, complemented
29C2×#6291C2211yescharacteristic, complemented
30C2×#6290C2212yescomplemented
31C2×#6290C2212yescomplemented
32C2×#6289C2211yescharacteristic, complemented
33#89026—28no—
34C33×C22⋊C4C2211yescharacteristic, complemented
35#88864C2211yescharacteristic, complemented
36#88859C2212yescomplemented
37C3×#3752C2212yescomplemented
38C32×(C2×D3)⋊C4C2212yescomplemented
39#88803C2212yescomplemented
40(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
41C24×C3⋊D3—31no—
42C23×D32—34no—
43C2×D4×C3⋊D3—31no—
44C2×D4×C3⋊D3—32no—
45C2×#3811—34no—
46C2×#3802—38no—
47C32×#120—31no—
48#64162—31no—
49#64146—32no—
50#64146—31no—
51#64091—32no—
52#64091D311yescharacteristic, complemented
53C22⋊C4×C3⋊D3—31no—
54C22⋊C4×C3⋊D3—32no—
55C22⋊C4×C3⋊D3—34no—
56C22⋊C4×C3⋊D3—64no—
57C3×#882—34no—
58C3×#882D314yescomplemented
59#63976—34no—
60#63976—34no—
61#63922—38no—
62#63922—38no—
63#63921—38no—
64C23×C33C2311yescharacteristic
65C22×C3⋊(C3⋊D3)—24no—
66C22×C3⋊(C3⋊D3)D414yescomplemented
67C22×C3⋊(C3⋊D3)C2311yescharacteristic
68C22×C3⋊(C3⋊D3)C2311yescharacteristic
69C22×C3×C3⋊D3—22no—
70C22×C3×C3⋊D3—24no—
71C22×C3×C3⋊D3C2312yes—
72C22×C3×C3⋊D3C2311yescharacteristic, complemented
73C22×C32×D3—22no—
74C22×C32×D3—24no—
75C22×C32×D3C2312yes—
76C22×C32×D3C2311yescharacteristic, complemented
77C2×D3×C3⋊D3—232no—
78C2×D3×C3⋊D3—24no—
79C2×D3×C3⋊D3—24no—
80C2×D3×C3⋊D3—24no—
81C2×D3×C3⋊D3—24no—
82C2×D3×C3⋊D3—24no—
83C2×D3×C3⋊D3—24no—
84C2×D3×C3⋊D3—22no—
85C2×D3×C3⋊D3D418yescomplemented
86C2×C33×C4C2312yescomplemented
87C2×C3⋊(C3⋊Dic3)C2312yescomplemented
88C4×C3⋊(C3⋊D3)—24no—
89C3×#638—22no—
90C2×C3×C3⋊Dic3C2311yescharacteristic, complemented
91C3×C4⋊(C3⋊D3)—24no—
92C32×#67—22no—
93C2×C32×Dic3C2311yescharacteristic, complemented
94C32×D12—24no—
95#6292—22no—
96#6291—22no—
97#6290—24no—
98#6290—24no—
99#6289—22no—
100D3×#120—94no—
101D3×#120—91no—
102C24×C32—31no—
103C23×C3⋊D3—31no—
104C23×C3⋊D3—34no—
105C23×C3⋊D3—32no—
106C23×C3⋊D3—32no—
107C23×C3⋊D3—31no—
108C23×C3⋊D3—64no—
109C23×C3⋊D3—68no—
110C23×C3⋊D3—64no—
111C23×C3⋊D3C2×D311yescharacteristic, complemented
112C23×C3×D3—34no—
113C23×C3×D3C2×D314yescomplemented
114C22×D32—38no—
115C22×D32—38no—
116C22×D32—34no—
117C22×D32—632no—
118C22×D32—616no—
119C2×C32×D4—31no—
120C2×C32×D4—32no—
121C2×#638—32no—
122C2×#638—32no—
123C2×#638—31no—
124C2×#638C2×D311yescharacteristic, complemented
125D4×C3⋊D3—68no—
126D4×C3⋊D3—64no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4⋊(C3⋊D3)C2×D312yescomplemented
129C2×C4×C3⋊D3—32no—
130C2×C4×C3⋊D3—38no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—68no—
133C2×C3×#67—34no—
134C2×C3×#67C2×D314yescomplemented
135C2×C3×D12—38no—
136C2×C3×D12C2×D318yescomplemented
137#3811—616no—
138C2×#626—34no—
139C2×#626—34no—
140C2×#625—38no—
141C2×#625—38no—
142C2×#624—34no—
143#3802—632no—
144C32×C22⋊C4—24no—
145C32×C22⋊C4—32no—
146C32×C22⋊C4C2×D314yescomplemented
147C32×C22⋊C4C2×D311yescharacteristic, complemented
148#3757—31no—
149#3757—34no—
150#3757—32no—
151#3757—64no—
152#3752—32no—
153#3752—32no—
154#3752—38no—
155#3752—68no—
156#3752C2×D312yescomplemented
157C3×(C2×D3)⋊C4—38no—
158C3×(C2×D3)⋊C4C2×D318yescomplemented
159(C2×D3)⋊Dic3—38no—
160(C2×D3)⋊Dic3—38no—
161C22×C33—22no—
162C22×C33C2×D412yescomplemented
163C22×C33C2411yescharacteristic
164C2×C3⋊(C3⋊D3)—22no—
165C2×C3⋊(C3⋊D3)—28no—
166C2×C3⋊(C3⋊D3)C2×D412yes—
167C2×C3⋊(C3⋊D3)C2×D414yes—
168C2×C3⋊(C3⋊D3)C2×D412yescomplemented
169C2×C3×C3⋊D3—28no—
170C2×C3×C3⋊D3—22no—
171C2×C3×C3⋊D3—22no—
172C2×C3×C3⋊D3—22no—
173C2×C3×C3⋊D3—21no—
174C2×C3×C3⋊D3C2×D414yescomplemented
175C2×C32×D3—28no—
176C2×C32×D3—22no—
177C2×C32×D3—22no—
178C2×C32×D3—22no—
179C2×C32×D3—21no—
180C2×C32×D3C2×D414yescomplemented
181D3×C3⋊D3—216no—
182D3×C3⋊D3—216no—
183D3×C3⋊D3—44no—
184C33×C4—22no—
185C3⋊(C3⋊Dic3)—22no—
186C3×C3⋊Dic3—21no—
187C32×Dic3—21no—
188C24×D3—94no—
189C24×D3—91no—
190C2×D3×D4—98no—
191C2×D3×D4—94no—
192C2×D3×D4—91no—
193C2×D3×D4—92no—
194C3×#120—34no—
195C3×#120—91no—
196#953—94no—
197#953—91no—
198#937—98no—
199#937—94no—
200#937—91no—
201#937—92no—
202#882—34no—
203#882—98no—
204#882—92no—
205#882C3⋊D311yescharacteristic, complemented
206D3×C22⋊C4—98no—
207D3×C22⋊C4—94no—
208D3×C22⋊C4—91no—
209D3×C22⋊C4—92no—
210D3×C22⋊C4—184no—
211C23×C32—24no—
212C23×C32—32no—
213C23×C32—31no—
214C23×C32—64no—
215C23×C32—62no—
216C23×C32C22×D314yes—
217C23×C32C22×D311yescharacteristic
218C22×C3⋊D3—22no—
219C22×C3⋊D3—24no—
220C22×C3⋊D3—31no—
221C22×C3⋊D3—34no—
222C22×C3⋊D3—31no—
223C22×C3⋊D3—38no—
224C22×C3⋊D3—34no—
225C22×C3⋊D3—316no—
226C22×C3⋊D3—34no—
227C22×C3⋊D3—64no—
228C22×C3⋊D3—64no—
229C22×C3⋊D3—616no—
230C22×C3⋊D3—64no—
231C22×C3⋊D3—64no—
232C22×C3⋊D3—64no—
233C22×C3⋊D3—64no—
234C22×C3⋊D3—62no—
235C22×C3⋊D3—64no—
236C22×C3⋊D3—632no—
237C22×C3⋊D3—64no—
238C22×C3⋊D3—64no—
239C22×C3⋊D3—616no—
240C22×C3⋊D3—1216no—
241C22×C3⋊D3C22×D312yes—
242C22×C3⋊D3C22×D311yescharacteristic, complemented
243C22×C3×D3—28no—
244C22×C3×D3—216no—
245C22×C3×D3—38no—
246C22×C3×D3—34no—
247C22×C3×D3—616no—
248C22×C3×D3—68no—
249C22×C3×D3C22×D318yes—
250C22×C3×D3C22×D314yescomplemented
251C2×D32—332no—
252C2×D32—616no—
253C2×D32—616no—
254C2×D32—616no—
255C2×D32—616no—
256C2×D32—6128no—
257C2×D32—616no—
258C2×D32—616no—
259C2×D32—68no—
260C32×D4—64no—
261C32×D4—62no—
262C2×C32×C4—28no—
263C2×C32×C4—31no—
264C2×C32×C4C22×D318yescomplemented
265C2×C32×C4C22×D312yescomplemented
266#638—22no—
267#638—62no—
268#638—64no—
269#638—64no—
270C2×C3⋊Dic3—32no—
271C2×C3⋊Dic3—38no—
272C2×C3⋊Dic3—68no—
273C2×C3⋊Dic3C22×D311yescharacteristic, complemented
274C4⋊(C3⋊D3)—24no—
275C4⋊(C3⋊D3)—62no—
276C4×C3⋊D3—62no—
277C4×C3⋊D3—64no—
278C4×C3⋊D3—616no—
279C4×C3⋊D3—1216no—
280C3×#67—28no—
281C3×#67—68no—
282C2×C3×Dic3—34no—
283C2×C3×Dic3C22×D314yescomplemented
284C3×D12—216no—
285C3×D12—616no—
286#626—68no—
287#626—68no—
288#625—616no—
289#625—616no—
290#624—68no—
291C2×#120—271noSylow
292C2×C33—22no—
293C2×C33C22×D411yescharacteristic
294C2×C33C22×D412yes—
295C3⋊(C3⋊D3)—22no—
296C3⋊(C3⋊D3)#12014yescomplemented
297C3×C3⋊D3—24no—
298C3×C3⋊D3—41no—
299C32×D3—24no—
300C32×D3—41no—
301C24×C3—34no—
302C24×C3—91no—
303C23×D3—34no—
304C23×D3—98no—
305C23×D3—98no—
306C23×D3—94no—
307C23×D3—94no—
308C23×D3—91no—
309C23×D3—92no—
310C23×D3—92no—
311C23×D3—91no—
312C23×D3—184no—
313C23×D3—184no—
314C23×D3—188no—
315C23×D3—1832no—
316C23×D3—1816no—
317C23×D3C2×C3⋊D311yescharacteristic, complemented
318C2×C3×D4—34no—
319C2×C3×D4—38no—
320C2×C3×D4—91no—
321C2×C3×D4—92no—
322C2×#67—34no—
323C2×#67—94no—
324C2×#67—98no—
325C2×#67—98no—
326C2×#67—92no—
327C2×#67—92no—
328C2×#67—91no—
329C2×#67C2×C3⋊D311yescharacteristic, complemented
330D3×D4—188no—
331D3×D4—1832no—
332D3×D4—184no—
333D3×D4—1816no—
334C2×D12—38no—
335C2×D12—94no—
336C2×D12—91no—
337C2×D12C2×C3⋊D312yescomplemented
338C2×C4×D3—94no—
339C2×C4×D3—98no—
340C2×C4×D3—92no—
341C2×C4×D3—91no—
342C2×C4×D3—188no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—38no—
345C3×C22⋊C4—92no—
346C3×C22⋊C4D3214yescomplemented
347C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
348#217—98no—
349#217—94no—
350#217—91no—
351#217—92no—
352#217—184no—
353(C2×D3)⋊C4—38no—
354(C2×D3)⋊C4—98no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—98no—
357(C2×D3)⋊C4—92no—
358(C2×D3)⋊C4—188no—
359(C2×D3)⋊C4C2×C3⋊D312yescomplemented
360C22×C32—22no—
361C22×C32—24no—
362C22×C32—28no—
363C22×C32—28no—
364C22×C32—34no—
365C22×C32—48no—
366C22×C32—68no—
367C22×C32—62no—
368C22×C32—62no—
369C22×C32—61no—
370C22×C32—62no—
371C22×C32D3×D418yescomplemented
372C22×C32D3×D412yescomplemented
373C22×C32C23×D314yes—
374C22×C32C23×D311yescharacteristic
375C2×C3⋊D3—28no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3—22no—
379C2×C3⋊D3—21no—
380C2×C3⋊D3—32no—
381C2×C3⋊D3—34no—
382C2×C3⋊D3—32no—
383C2×C3⋊D3—38no—
384C2×C3⋊D3—316no—
385C2×C3⋊D3—38no—
386C2×C3⋊D3—616no—
387C2×C3⋊D3—68no—
388C2×C3⋊D3—68no—
389C2×C3⋊D3—616no—
390C2×C3⋊D3—616no—
391C2×C3⋊D3—68no—
392C2×C3⋊D3—62no—
393C2×C3⋊D3—632no—
394C2×C3⋊D3—68no—
395C2×C3⋊D3—1232no—
396C2×C3⋊D3—128no—
397C2×C3⋊D3—124no—
398C2×C3⋊D3D3×D414yescomplemented
399C2×C3×D3—232no—
400C2×C3×D3—28no—
401C2×C3×D3—28no—
402C2×C3×D3—28no—
403C2×C3×D3—24no—
404C2×C3×D3—316no—
405C2×C3×D3—632no—
406C2×C3×D3—68no—
407C2×C3×D3—68no—
408C2×C3×D3—68no—
409C2×C3×D3—64no—
410C2×C3×D3D3×D4116yescomplemented
411D32—664no—
412D32—664no—
413D32—1216no—
414C32×C4—22no—
415C32×C4—28no—
416C32×C4—48no—
417C32×C4—61no—
418C3⋊Dic3—21no—
419C3⋊Dic3—62no—
420C3⋊Dic3—68no—
421C3⋊Dic3—128no—
422C3×Dic3—24no—
423C3×Dic3—64no—
424C25—271no—
425C22×D4—271no—
426C22×D4—272no—
427#120—31no—
428#120—91no—
429#120—272no—
430#120—272no—
431#120—271no—
432#120—271no—
433C2×C22⋊C4—272no—
434C2×C22⋊C4—271no—
435C33C2×#12011yescharacteristic, complemented, Sylow
436C23×C3—24no—
437C23×C3—38no—
438C23×C3—34no—
439C23×C3—616no—
440C23×C3—68no—
441C23×C3—92no—
442C23×C3—91no—
443C23×C3—184no—
444C23×C3—182no—
445C23×C3C2×D3214yes—
446C23×C3C22×C3⋊D311yescharacteristic
447C22×D3—22no—
448C22×D3—24no—
449C22×D3—38no—
450C22×D3—34no—
451C22×D3—616no—
452C22×D3—68no—
453C22×D3—932no—
454C22×D3—94no—
455C22×D3—91no—
456C22×D3—94no—
457C22×D3—91no—
458C22×D3—916no—
459C22×D3—94no—
460C22×D3—98no—
461C22×D3—184no—
462C22×D3—184no—
463C22×D3—1816no—
464C22×D3—184no—
465C22×D3—184no—
466C22×D3—184no—
467C22×D3—184no—
468C22×D3—182no—
469C22×D3—184no—
470C22×D3—1832no—
471C22×D3—1816no—
472C22×D3—1816no—
473C22×D3—1816no—
474C22×D3—1816no—
475C22×D3—188no—
476C22×D3—1816no—
477C22×D3—1816no—
478C22×D3—18128no—
479C22×D3—184no—
480C22×D3—1816no—
481C22×D3—184no—
482C22×D3—3616no—
483C22×D3C22×C3⋊D312yes—
484C22×D3C22×C3⋊D311yescharacteristic, complemented
485C3×D4—616no—
486C3×D4—68no—
487C3×D4—184no—
488C3×D4—182no—
489C2×C3×C4—28no—
490C2×C3×C4—34no—
491C2×C3×C4—91no—
492C2×C3×C4C2×D3218yescomplemented
493C2×C3×C4C22×C3⋊D312yescomplemented
494#67—22no—
495#67—68no—
496#67—182no—
497#67—188no—
498#67—184no—
499#67—1816no—
500#67—1816no—
501#67—184no—
502C2×Dic3—34no—
503C2×Dic3—98no—
504C2×Dic3—92no—
505C2×Dic3—188no—
506C2×Dic3C22×C3⋊D311yescharacteristic, complemented
507D12—24no—
508D12—616no—
509D12—188no—
510D12—182no—
511C4×D3—182no—
512C4×D3—188no—
513C4×D3—184no—
514C4×D3—1816no—
515C4×D3—3616no—
516C2×C32—22no—
517C2×C32—24no—
518C2×C32—28no—
519C2×C32—28no—
520C2×C32—48no—
521C2×C32—64no—
522C2×C32—121no—
523C2×C32C2×D3×D414yes—
524C2×C32C2×D3×D418yes—
525C2×C32C2×D3×D411yescharacteristic
526C2×C32C2×D3×D412yes—
527C3⋊D3—24no—
528C3⋊D3—34no—
529C3⋊D3—316no—
530C3⋊D3—41no—
531C3⋊D3—616no—
532C3⋊D3—62no—
533C3⋊D3—68no—
534C3⋊D3—128no—
535C3×D3—216no—
536C3×D3—44no—
537C3×D3—616no—
538C3×D3—124no—
539C24—31no—
540C24—91no—
541C24—272no—
542C24—272no—
543C24—271no—
544C24—271no—
545C24—548no—
546C24—544no—
547C2×D4—31no—
548C2×D4—32no—
549C2×D4—91no—
550C2×D4—92no—
551C2×D4—271no—
552C2×D4—271no—
553C2×D4—272no—
554C2×D4—272no—
555C2×D4—548no—
556C2×D4—544no—
557C22×C4—271no—
558C22×C4—272no—
559C22⋊C4—32no—
560C22⋊C4—92no—
561C22⋊C4—272no—
562C22⋊C4—272no—
563C22⋊C4—271no—
564C22⋊C4—272no—
565C22⋊C4D3×C3⋊D311yescharacteristic, complemented
566C22×C3—28no—
567C22×C3—22no—
568C22×C3—24no—
569C22×C3—28no—
570C22×C3—316no—
571C22×C3—48no—
572C22×C3—632no—
573C22×C3—68no—
574C22×C3—68no—
575C22×C3—64no—
576C22×C3—68no—
577C22×C3—94no—
578C22×C3—188no—
579C22×C3—182no—
580C22×C3—182no—
581C22×C3—181no—
582C22×C3—182no—
583C22×C3#380218yescomplemented
584C22×C3D4×C3⋊D312yescomplemented
585C22×C3C22×D3214yes—
586C22×C3C23×C3⋊D311yescharacteristic
587C2×D3—28no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—21no—
592C2×D3—316no—
593C2×D3—632no—
594C2×D3—68no—
595C2×D3—68no—
596C2×D3—64no—
597C2×D3—68no—
598C2×D3—98no—
599C2×D3—916no—
600C2×D3—92no—
601C2×D3—94no—
602C2×D3—98no—
603C2×D3—92no—
604C2×D3—1816no—
605C2×D3—188no—
606C2×D3—188no—
607C2×D3—1816no—
608C2×D3—1816no—
609C2×D3—1864no—
610C2×D3—1864no—
611C2×D3—188no—
612C2×D3—1832no—
613C2×D3—188no—
614C2×D3—182no—
615C2×D3—3632no—
616C2×D3—368no—
617C2×D3—364no—
618C2×D3—3616no—
619C2×D3D4×C3⋊D314yescomplemented
620C3×C4—28no—
621C3×C4—22no—
622C3×C4—48no—
623C3×C4—64no—
624C3×C4—181no—
625Dic3—21no—
626Dic3—64no—
627Dic3—188no—
628Dic3—182no—
629Dic3—368no—
630C32—24no—
631C32D3×#12014yescomplemented
632C32D3×#12011yescharacteristic, complemented
633C23—32no—
634C23—31no—
635C23—64no—
636C23—62no—
637C23—92no—
638C23—91no—
639C23—184no—
640C23—182no—
641C23—278no—
642C23—271no—
643C23—271no—
644C23—274no—
645C23—544no—
646C23—544no—
647C23—544no—
648C23—544no—
649C23—544no—
650C23—544no—
651C23—542no—
652C23—544no—
653C23—5432no—
654C23C2×D3×C3⋊D311yescharacteristic
655D4—64no—
656D4—62no—
657D4—184no—
658D4—182no—
659D4—542no—
660D4—542no—
661D4—544no—
662D4—544no—
663C2×C4—31no—
664C2×C4—91no—
665C2×C4—272no—
666C2×C4—544no—
667C2×C4—542no—
668C2×C4C2×D3×C3⋊D312yescomplemented
669C2×C3—28no—
670C2×C3—22no—
671C2×C3—24no—
672C2×C3—28no—
673C2×C3—48no—
674C2×C3—616no—
675C2×C3—124no—
676C2×C3—184no—
677C2×C3—361no—
678C2×C3C2×#380214yes—
679C2×C3D32×D418yes—
680C2×C3C2×D4×C3⋊D311yescharacteristic
681C2×C3C2×D4×C3⋊D312yes—
682D3—24no—
683D3—41no—
684D3—616no—
685D3—916no—
686D3—94no—
687D3—124no—
688D3—1816no—
689D3—188no—
690D3—182no—
691D3—368no—
692C22—22no—
693C22—34no—
694C22—68no—
695C22—62no—
696C22—62no—
697C22—61no—
698C22—62no—
699C22—94no—
700C22—188no—
701C22—182no—
702C22—182no—
703C22—181no—
704C22—182no—
705C22—272no—
706C22—274no—
707C22—272no—
708C22—548no—
709C22—5416no—
710C22—5416no—
711C22—542no—
712C22—1084no—
713C22#8902612yescomplemented
714C22C22×D3×C3⋊D311yescharacteristic
715C4—22no—
716C4—61no—
717C4—181no—
718C4—542no—
719C3—24no—
720C3#1059425814yescomplemented
721C3C3⋊D3×#12011yescharacteristic, complemented
722C2—22no—
723C2—64no—
724C2—121no—
725C2—184no—
726C2—274no—
727C2—361no—
728C2—542no—
729C2C2×#8902611yescharacteristic
730C2D3×D4×C3⋊D312yes—
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×#120
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×C3⋊D3C2semidirect
2. C2×#89039C2semidirect
3. C2×#89026C2semidirect
4. C22⋊C4×C3⋊(C3⋊D3)C2semidirect
5. C3×#64091C2semidirect
6. C32×#882C2semidirect
7. #11723634C2semidirect
8. #11723629C2semidirect
9. #11723541C2semidirect
10. #11723540C2semidirect
11. #11723539C2semidirect
15. C23×C3×C3⋊D3C22semidirect
16. C23×C32×D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6290C22semidirect
31. C2×#6290C22semidirect
32. C2×#6289C22semidirect
34. C33×C22⋊C4C22semidirect
35. #88864C22semidirect
36. #88859C22semidirect
37. C3×#3752C22semidirect
38. C32×(C2×D3)⋊C4C22semidirect
39. #88803C22semidirect
40. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. #64091D3semidirect
58. C3×#882D3semidirect
66. C22×C3⋊(C3⋊D3)D4semidirect
72. C22×C3×C3⋊D3C23semidirect
76. C22×C32×D3C23semidirect
85. C2×D3×C3⋊D3D4semidirect
86. C2×C33×C4C23semidirect
87. C2×C3⋊(C3⋊Dic3)C23semidirect
90. C2×C3×C3⋊Dic3C23semidirect
93. C2×C32×Dic3C23semidirect
111. C23×C3⋊D3C2×D3semidirect
113. C23×C3×D3C2×D3semidirect
124. C2×#638C2×D3semidirect
128. C2×C4⋊(C3⋊D3)C2×D3semidirect
134. C2×C3×#67C2×D3semidirect
136. C2×C3×D12C2×D3semidirect
146. C32×C22⋊C4C2×D3semidirect
147. C32×C22⋊C4C2×D3semidirect
156. #3752C2×D3semidirect
158. C3×(C2×D3)⋊C4C2×D3semidirect
162. C22×C33C2×D4semidirect
168. C2×C3⋊(C3⋊D3)C2×D4semidirect
174. C2×C3×C3⋊D3C2×D4semidirect
180. C2×C32×D3C2×D4semidirect
205. #882C3⋊D3semidirect
242. C22×C3⋊D3C22×D3semidirect
250. C22×C3×D3C22×D3semidirect
264. C2×C32×C4C22×D3semidirect
265. C2×C32×C4C22×D3semidirect
273. C2×C3⋊Dic3C22×D3semidirect
283. C2×C3×Dic3C22×D3semidirect
296. C3⋊(C3⋊D3)#120semidirect
317. C23×D3C2×C3⋊D3semidirect
329. C2×#67C2×C3⋊D3semidirect
337. C2×D12C2×C3⋊D3semidirect
346. C3×C22⋊C4D32semidirect
347. C3×C22⋊C4C2×C3⋊D3semidirect
359. (C2×D3)⋊C4C2×C3⋊D3semidirect
371. C22×C32D3×D4semidirect
372. C22×C32D3×D4semidirect
398. C2×C3⋊D3D3×D4semidirect
410. C2×C3×D3D3×D4semidirect
435. C33C2×#120semidirect
484. C22×D3C22×C3⋊D3semidirect
492. C2×C3×C4C2×D32semidirect
493. C2×C3×C4C22×C3⋊D3semidirect
506. C2×Dic3C22×C3⋊D3semidirect
565. C22⋊C4D3×C3⋊D3semidirect
583. C22×C3#3802semidirect
584. C22×C3D4×C3⋊D3semidirect
619. C2×D3D4×C3⋊D3semidirect
631. C32D3×#120semidirect
632. C32D3×#120semidirect
668. C2×C4C2×D3×C3⋊D3semidirect
713. C22#89026semidirect
720. C3#10594258semidirect
721. C3C3⋊D3×#120semidirect

Maximal subgroups

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

subgroupindex
C23×D3×C3⋊D32
C2×#890392
C2×#890262
C22⋊C4×C3⋊(C3⋊D3)2
C3×#640912
C32×#8822
#117236342
#117236292
#117235412
#117235402
#117235392
C3⋊D3×#1203
#105942583