Finite Group Databasebeta

← C3⋊D3×#882 #13175914

Subgroups — C3⋊D3×#882 #13175914

Order 1728.

4492 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×D12C212yesmaximal, complemented
4#11723923C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6C32×#882C211yesmaximal, characteristic, complemented
7#11723638C211yesmaximal, characteristic, complemented
8#11723630C211yesmaximal, characteristic, complemented
9#11723542C212yesmaximal, complemented
10#11723540C212yesmaximal, complemented
11C3⋊D3×(C2×D3)⋊C4C212yesmaximal, complemented
12C3⋊D3×#120—31nomaximal
13D3×#882—34nomaximal
14C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
15C23×C3×C3⋊D3C2211yescharacteristic
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×#6312C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊(C3⋊D3))C2212yescomplemented
24C2×C3×C4×C3⋊D3C2212yescomplemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×D12C2212yescomplemented
27C3⋊D3×#67—24no—
28C2×#6292C2211yescharacteristic, complemented
29C2×#6291C2212yescomplemented
30C2×#6291C2212yescomplemented
31C2×#6290C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C3⋊D3×D12—28no—
34C33×C22⋊C4C2211yescharacteristic, complemented
35#88859C2212yescomplemented
36C3×#3757C2211yescharacteristic, complemented
37C3×#3752C2212yescomplemented
38C32×(C2×D3)⋊C4C2212yescomplemented
39#88804C2212yescomplemented
40(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
41C24×C3⋊D3—31no—
42C23×D32—34no—
43C2×D4×C3⋊D3—32no—
44C2×D4×C3⋊D3—31no—
45C2×D3×#67—34no—
46C2×D3×D12—38no—
47C32×#120—31no—
48#64162—31no—
49#64146—31no—
50#64146—32no—
51#64091—31no—
52#64091—32no—
53#64091—34no—
54#64091—64no—
55C22⋊C4×C3⋊D3—32no—
56C22⋊C4×C3⋊D3D311yescharacteristic, complemented
57C3×#882D314yescomplemented
58C3×D3×C22⋊C4—34no—
59#63981—34no—
60#63977—34no—
61#63923—38no—
62#63922—38no—
63D3×(C2×D3)⋊C4—38no—
64C23×C33C2311yescharacteristic
65C22×C3⋊(C3⋊D3)—22no—
66C22×C3⋊(C3⋊D3)—24no—
67C22×C3⋊(C3⋊D3)C2312yes—
68C22×C3⋊(C3⋊D3)C2311yescharacteristic, complemented
69C22×C3×C3⋊D3—24no—
70C22×C3×C3⋊D3D414yescomplemented
71C22×C3×C3⋊D3C2311yescharacteristic
72C22×C3×C3⋊D3C2311yescharacteristic
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
87#6312—22no—
88C2×C3⋊(C3⋊Dic3)C2311yescharacteristic, complemented
89C4⋊(C3⋊(C3⋊D3))—24no—
90C2×C3×C3⋊Dic3C2312yescomplemented
91C3×C4×C3⋊D3—24no—
92C32×#67—22no—
93C2×C32×Dic3C2311yescharacteristic, complemented
94C32×D12—24no—
95#6292—22no—
96#6291—24no—
97#6291—24no—
98#6290—22no—
99Dic3×C3⋊D3—22no—
100D3×#120—94no—
101C2×#882—91no—
102C24×C32—31no—
103C23×C3⋊D3—32no—
104C23×C3⋊D3—31no—
105C23×C3⋊D3—34no—
106C23×C3⋊D3—32no—
107C23×C3⋊D3—31no—
108C23×C3⋊D3—68no—
109C23×C3⋊D3—64no—
110C23×C3⋊D3—64no—
111C23×C3⋊D3C2×D311yescharacteristic
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—31no—
122C2×#638—34no—
123C2×#638—31no—
124C2×#638—32no—
125C2×#638—32no—
126C2×#638—64no—
127D4×C3⋊D3—68no—
128D4×C3⋊D3—64no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—32no—
131C2×C4⋊(C3⋊D3)—38no—
132C2×C4⋊(C3⋊D3)—68no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3C2×D312yescomplemented
135C2×C3×#67C2×D314yescomplemented
136C2×C3×D12C2×D318yescomplemented
137C2×C3×C4×D3—38no—
138D3×#67—616no—
139C2×#626—38no—
140C2×#626—38no—
141C2×#626—34no—
142C2×#625—34no—
143C2×D3×Dic3—34no—
144D3×D12—632no—
145C32×C22⋊C4—24no—
146C32×C22⋊C4—32no—
147C32×C22⋊C4C2×D314yescomplemented
148C32×C22⋊C4C2×D311yescharacteristic, complemented
149#3757—32no—
150#3757C2×D311yescharacteristic, complemented
151#3752—32no—
152#3752—38no—
153#3752—32no—
154#3752—68no—
155#3752C2×D312yescomplemented
156C3×#217—34no—
157C3×(C2×D3)⋊C4—38no—
158C3×(C2×D3)⋊C4C2×D318yescomplemented
159#3722—38no—
160(C2×D3)⋊Dic3—38no—
161C22×C33—22no—
162C22×C33C2×D412yescomplemented
163C22×C33C2411yescharacteristic
164C2×C3⋊(C3⋊D3)—28no—
165C2×C3⋊(C3⋊D3)—22no—
166C2×C3⋊(C3⋊D3)—22no—
167C2×C3⋊(C3⋊D3)—22no—
168C2×C3⋊(C3⋊D3)—21no—
169C2×C3⋊(C3⋊D3)C2×D414yescomplemented
170C2×C3×C3⋊D3—22no—
171C2×C3×C3⋊D3—28no—
172C2×C3×C3⋊D3C2×D412yes—
173C2×C3×C3⋊D3C2×D414yes—
174C2×C3×C3⋊D3C2×D412yescomplemented
175C2×C32×D3—28no—
176C2×C32×D3—22no—
177C2×C32×D3—22no—
178C2×C32×D3—21no—
179C2×C32×D3—22no—
180C2×C32×D3C2×D414yescomplemented
181D3×C3⋊D3—216no—
182D3×C3⋊D3—216no—
183D3×C3⋊D3—44no—
184C33×C4—22no—
185C3⋊(C3⋊Dic3)—21no—
186C3×C3⋊Dic3—22no—
187C32×Dic3—21no—
188C24×D3—94no—
189C24×D3—91no—
190C22×#67—91no—
191C2×D3×D4—98no—
192C2×D3×D4—94no—
193C22×D12—92no—
194C3×#120—34no—
195C2×C3×C22⋊C4—91no—
196#953—94no—
197#937—98no—
198#937—94no—
199C2×(C2×D3)⋊C4—92no—
200#882—98no—
201#882—91no—
202#882—91no—
203#882—92no—
204#882—94no—
205#882—91no—
206#882—92no—
207#882—184no—
208#882C3⋊D311yescharacteristic, direct product factor
209D3×C22⋊C4—34no—
210D3×C22⋊C4—98no—
211C23×C32—24no—
212C23×C32—32no—
213C23×C32—31no—
214C23×C32—64no—
215C23×C32—62no—
216C23×C32C22×D314yes—
217C23×C32C22×D311yescharacteristic
218C22×C3⋊D3—24no—
219C22×C3⋊D3—32no—
220C22×C3⋊D3—38no—
221C22×C3⋊D3—31no—
222C22×C3⋊D3—38no—
223C22×C3⋊D3—34no—
224C22×C3⋊D3—68no—
225C22×C3⋊D3—64no—
226C22×C3⋊D3—64no—
227C22×C3⋊D3—64no—
228C22×C3⋊D3—632no—
229C22×C3⋊D3—64no—
230C22×C3⋊D3—62no—
231C22×C3⋊D3—64no—
232C22×C3⋊D3—64no—
233C22×C3⋊D3—64no—
234C22×C3⋊D3—62no—
235C22×C3⋊D3—64no—
236C22×C3⋊D3—616no—
237C22×C3⋊D3—68no—
238C22×C3⋊D3—1216no—
239C22×C3⋊D3—128no—
240C22×C3⋊D3D1214yescomplemented
241C22×C3⋊D3C22×D311yescharacteristic
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3×D3—28no—
244C22×C3×D3—216no—
245C22×C3×D3—34no—
246C22×C3×D3—316no—
247C22×C3×D3—34no—
248C22×C3×D3—616no—
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—64no—
267#638—64no—
268#638—62no—
269#638—62no—
270#638—68no—
271#638—128no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—34no—
274C2×C3⋊Dic3—64no—
275C2×C3⋊Dic3C22×D312yescomplemented
276C4⋊(C3⋊D3)—64no—
277C4⋊(C3⋊D3)—62no—
278C4⋊(C3⋊D3)—616no—
279C4⋊(C3⋊D3)—1216no—
280C4×C3⋊D3—24no—
281C4×C3⋊D3—62no—
282C3×#67—28no—
283C2×C3×Dic3—38no—
284C2×C3×Dic3C22×D314yescomplemented
285C3×D12—216no—
286C3×C4×D3—616no—
287#626—68no—
288#626—616no—
289#626—616no—
290#625—68no—
291D3×Dic3—68no—
292C2×#120—271noSylow
293C2×C33—22no—
294C2×C33C22×D411yescharacteristic
295C2×C33C22×D412yes—
296C3⋊(C3⋊D3)—24no—
297C3⋊(C3⋊D3)—41no—
298C3×C3⋊D3—22no—
299C3×C3⋊D3#12014yescomplemented
300C32×D3—24no—
301C32×D3—41no—
302C24×C3—34no—
303C24×C3—91no—
304C23×D3—34no—
305C23×D3—98no—
306C23×D3—98no—
307C23×D3—94no—
308C23×D3—92no—
309C23×D3—94no—
310C23×D3—91no—
311C23×D3—92no—
312C23×D3—91no—
313C23×D3—184no—
314C23×D3—188no—
315C23×D3—184no—
316C23×D3—1816no—
317C23×D3—1832no—
318C23×D3C2×C3⋊D311yescharacteristic, complemented
319C2×C3×D4—34no—
320C2×C3×D4—38no—
321C22×C3×C4—92no—
322C2×#67—98no—
323C2×#67—98no—
324C2×#67—94no—
325C2×#67—94no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—184no—
330C2×#67—184no—
331C2×#67C2×C3⋊D311yescharacteristic, complemented
332C22×Dic3—91no—
333D3×D4—1832no—
334D3×D4—1816no—
335C2×D12—94no—
336C2×D12—92no—
337C2×D12—92no—
338C2×D12—98no—
339C2×D12—92no—
340C2×D12—188no—
341C2×D12—188no—
342C2×D12C2×C3⋊D312yescomplemented
343C2×C4×D3—38no—
344C2×C4×D3—94no—
345C3×C22⋊C4—24no—
346C3×C22⋊C4—38no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—92no—
349C3×C22⋊C4D3214yescomplemented
350C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
351#217—34no—
352#217—98no—
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—92no—
359(C2×D3)⋊C4—188no—
360(C2×D3)⋊C4C2×C3⋊D312yescomplemented
361C22×C32—22no—
362C22×C32—24no—
363C22×C32—28no—
364C22×C32—28no—
365C22×C32—34no—
366C22×C32—48no—
367C22×C32—68no—
368C22×C32—62no—
369C22×C32—62no—
370C22×C32—61no—
371C22×C32—62no—
372C22×C32C2×D1212yescomplemented
373C22×C32D3×D418yescomplemented
374C22×C32C23×D314yes—
375C22×C32C23×D311yescharacteristic
376C2×C3⋊D3—22no—
377C2×C3⋊D3—28no—
378C2×C3⋊D3—34no—
379C2×C3⋊D3—316no—
380C2×C3⋊D3—616no—
381C2×C3⋊D3—616no—
382C2×C3⋊D3—68no—
383C2×C3⋊D3—62no—
384C2×C3⋊D3—62no—
385C2×C3⋊D3—616no—
386C2×C3⋊D3—61no—
387C2×C3⋊D3—62no—
388C2×C3⋊D3—632no—
389C2×C3⋊D3—68no—
390C2×C3⋊D3—68no—
391C2×C3⋊D3—68no—
392C2×C3⋊D3—64no—
393C2×C3⋊D3—128no—
394C2×C3⋊D3—128no—
395C2×C3⋊D3—1232no—
396C2×C3⋊D3—128no—
397C2×C3⋊D3—124no—
398C2×C3⋊D3—124no—
399C2×C3⋊D3C2×D1212yes—
400C2×C3⋊D3C2×D1212yescomplemented
401C2×C3⋊D3D3×D414yes—
402C2×C3×D3—232no—
403C2×C3×D3—28no—
404C2×C3×D3—28no—
405C2×C3×D3—24no—
406C2×C3×D3—28no—
407C2×C3×D3—38no—
408C2×C3×D3—316no—
409C2×C3×D3—38no—
410C2×C3×D3—632no—
411C2×C3×D3—68no—
412C2×C3×D3D3×D4116yescomplemented
413D32—664no—
414D32—664no—
415D32—1216no—
416C32×C4—22no—
417C32×C4—28no—
418C32×C4—48no—
419C32×C4—61no—
420C3⋊Dic3—22no—
421C3⋊Dic3—61no—
422C3⋊Dic3—64no—
423C3⋊Dic3—124no—
424C3×Dic3—24no—
425C3×Dic3—68no—
426C25—271no—
427C22×D4—272no—
428C22×D4—271no—
429#120—31no—
430#120—272no—
431#120—271no—
432#120—272no—
433#120—271no—
434#120—271no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—272no—
437C33C2×#12011yescharacteristic, complemented, Sylow
438C23×C3—24no—
439C23×C3—38no—
440C23×C3—34no—
441C23×C3—616no—
442C23×C3—68no—
443C23×C3—91no—
444C23×C3—91no—
445C23×C3—94no—
446C23×C3—184no—
447C23×C3C2×D3214yes—
448C23×C3C22×C3⋊D311yescharacteristic
449C22×D3—22no—
450C22×D3—24no—
451C22×D3—34no—
452C22×D3—34no—
453C22×D3—316no—
454C22×D3—616no—
455C22×D3—932no—
456C22×D3—98no—
457C22×D3—92no—
458C22×D3—98no—
459C22×D3—94no—
460C22×D3—91no—
461C22×D3—188no—
462C22×D3—184no—
463C22×D3—184no—
464C22×D3—184no—
465C22×D3—184no—
466C22×D3—184no—
467C22×D3—1832no—
468C22×D3—184no—
469C22×D3—182no—
470C22×D3—1816no—
471C22×D3—1816no—
472C22×D3—1816no—
473C22×D3—188no—
474C22×D3—1816no—
475C22×D3—1816no—
476C22×D3—1816no—
477C22×D3—18128no—
478C22×D3—184no—
479C22×D3—1816no—
480C22×D3—188no—
481C22×D3—182no—
482C22×D3—184no—
483C22×D3—3616no—
484C22×D3—368no—
485C22×D3C22×C3⋊D312yes—
486C22×D3C22×C3⋊D311yescharacteristic, complemented
487C3×D4—616no—
488C3×D4—68no—
489C2×C3×C4—28no—
490C2×C3×C4—34no—
491C2×C3×C4—92no—
492C2×C3×C4—184no—
493C2×C3×C4C2×D3218yescomplemented
494C2×C3×C4C22×C3⋊D312yescomplemented
495#67—22no—
496#67—182no—
497#67—1816no—
498#67—1816no—
499#67—182no—
500#67—188no—
501#67—188no—
502#67—182no—
503#67—368no—
504C2×Dic3—38no—
505C2×Dic3—94no—
506C2×Dic3—91no—
507C2×Dic3—184no—
508C2×Dic3—182no—
509C2×Dic3C22×C3⋊D311yescharacteristic, complemented
510D12—24no—
511D12—184no—
512D12—1816no—
513D12—188no—
514D12—184no—
515D12—184no—
516D12—3616no—
517C4×D3—616no—
518C4×D3—188no—
519C2×C32—22no—
520C2×C32—24no—
521C2×C32—28no—
522C2×C32—28no—
523C2×C32—48no—
524C2×C32—64no—
525C2×C32—121no—
526C2×C32C22×D1211yescharacteristic
527C2×C32C2×D3×D414yes—
528C2×C32C2×D3×D418yes—
529C2×C32C2×D3×D412yes—
530C3⋊D3—22no—
531C3⋊D3—64no—
532C3⋊D3—616no—
533C3⋊D3—1216no—
534C3⋊D3—121no—
535C3⋊D3—124no—
536C3⋊D3—244no—
537C3⋊D3#88214yesdirect product factor
538C3×D3—216no—
539C3×D3—316no—
540C3×D3—44no—
541C3×D3—68no—
542C24—31no—
543C24—91no—
544C24—272no—
545C24—272no—
546C24—271no—
547C24—271no—
548C24—544no—
549C24—548no—
550C2×D4—31no—
551C2×D4—32no—
552C2×D4—271no—
553C2×D4—272no—
554C2×D4—272no—
555C2×D4—271no—
556C2×D4—271no—
557C2×D4—272no—
558C2×D4—548no—
559C2×D4—544no—
560C22×C4—92no—
561C22×C4—271no—
562C22⋊C4—32no—
563C22⋊C4—91no—
564C22⋊C4—92no—
565C22⋊C4—272no—
566C22⋊C4—272no—
567C22⋊C4—272no—
568C22⋊C4D3×C3⋊D311yescharacteristic, complemented
569C22×C3—28no—
570C22×C3—22no—
571C22×C3—24no—
572C22×C3—28no—
573C22×C3—316no—
574C22×C3—48no—
575C22×C3—632no—
576C22×C3—68no—
577C22×C3—68no—
578C22×C3—64no—
579C22×C3—68no—
580C22×C3—92no—
581C22×C3—94no—
582C22×C3—92no—
583C22×C3—188no—
584C22×C3—182no—
585C22×C3D3×D1218yescomplemented
586C22×C3D4×C3⋊D312yescomplemented
587C22×C3C22×D3214yes—
588C22×C3C23×C3⋊D311yescharacteristic
589C2×D3—28no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—21no—
594C2×D3—38no—
595C2×D3—316no—
596C2×D3—38no—
597C2×D3—632no—
598C2×D3—68no—
599C2×D3—916no—
600C2×D3—94no—
601C2×D3—1816no—
602C2×D3—1816no—
603C2×D3—1816no—
604C2×D3—1864no—
605C2×D3—1864no—
606C2×D3—188no—
607C2×D3—1832no—
608C2×D3—188no—
609C2×D3—188no—
610C2×D3—182no—
611C2×D3—182no—
612C2×D3—184no—
613C2×D3—188no—
614C2×D3—182no—
615C2×D3—181no—
616C2×D3—368no—
617C2×D3—368no—
618C2×D3—3632no—
619C2×D3—368no—
620C2×D3—364no—
621C2×D3—3616no—
622C2×D3—364no—
623C2×D3D4×C3⋊D314yescomplemented
624C3×C4—28no—
625C3×C4—22no—
626C3×C4—48no—
627C3×C4—64no—
628C3×C4—182no—
629Dic3—21no—
630Dic3—68no—
631Dic3—184no—
632Dic3—181no—
633Dic3—364no—
634C32—24no—
635C32C2×#88211yescharacteristic, complemented
636C32D3×#12014yescomplemented
637C23—32no—
638C23—31no—
639C23—64no—
640C23—62no—
641C23—91no—
642C23—91no—
643C23—94no—
644C23—184no—
645C23—278no—
646C23—272no—
647C23—271no—
648C23—544no—
649C23—544no—
650C23—544no—
651C23—544no—
652C23—544no—
653C23—542no—
654C23—544no—
655C23—544no—
656C23—5432no—
657C23—542no—
658C23C2×D3×C3⋊D311yescharacteristic
659D4—64no—
660D4—62no—
661D4—544no—
662D4—542no—
663D4—544no—
664D4—544no—
665D4—542no—
666D4—542no—
667C2×C4—31no—
668C2×C4—92no—
669C2×C4—184no—
670C2×C4—271no—
671C2×C4—542no—
672C2×C4C2×D3×C3⋊D312yescomplemented
673C2×C3—28no—
674C2×C3—22no—
675C2×C3—24no—
676C2×C3—28no—
677C2×C3—48no—
678C2×C3—616no—
679C2×C3—94no—
680C2×C3—124no—
681C2×C3—182no—
682C2×C3C2×D3×D1214yes—
683C2×C3D32×D418yes—
684C2×C3C2×D4×C3⋊D311yescharacteristic
685C2×C3C2×D4×C3⋊D312yes—
686D3—24no—
687D3—316no—
688D3—41no—
689D3—68no—
690D3—1816no—
691D3—184no—
692D3—3616no—
693D3—364no—
694D3—361no—
695D3—724no—
696C22—22no—
697C22—34no—
698C22—68no—
699C22—62no—
700C22—62no—
701C22—61no—
702C22—62no—
703C22—92no—
704C22—94no—
705C22—92no—
706C22—188no—
707C22—182no—
708C22—274no—
709C22—548no—
710C22—5416no—
711C22—5416no—
712C22—542no—
713C22—542no—
714C22—541no—
715C22—542no—
716C22—1084no—
717C22C3⋊D3×D1212yescomplemented
718C22C22×D3×C3⋊D311yescharacteristic
719C4—22no—
720C4—61no—
721C4—182no—
722C4—541no—
723C3—24no—
724C3D3×#88214yescomplemented
725C3C3⋊D3×#12011yescharacteristic, complemented
726C2—22no—
727C2—64no—
728C2—94no—
729C2—121no—
730C2—182no—
731C2—544no—
732C2—1081no—
733C2C2×C3⋊D3×D1211yescharacteristic
734C2D3×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×C3⋊D3×#67C2semidirect
3. C2×C3⋊D3×D12C2semidirect
4. #11723923C2semidirect
5. C3×C22⋊C4×C3⋊D3C2semidirect
6. C32×#882C2semidirect
7. #11723638C2semidirect
8. #11723630C2semidirect
9. #11723542C2semidirect
10. #11723540C2semidirect
11. C3⋊D3×(C2×D3)⋊C4C2semidirect
14. C23×C3⋊(C3⋊D3)C22semidirect
16. C23×C32×D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6291C22semidirect
31. C2×#6290C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
34. C33×C22⋊C4C22semidirect
35. #88859C22semidirect
36. C3×#3757C22semidirect
37. C3×#3752C22semidirect
38. C32×(C2×D3)⋊C4C22semidirect
39. #88804C22semidirect
40. (C2×D3)⋊(C3⋊Dic3)C22semidirect
56. C22⋊C4×C3⋊D3D3semidirect
57. C3×#882D3semidirect
68. C22×C3⋊(C3⋊D3)C23semidirect
70. C22×C3×C3⋊D3D4semidirect
76. C22×C32×D3C23semidirect
85. C2×D3×C3⋊D3D4semidirect
86. C2×C33×C4C23semidirect
88. C2×C3⋊(C3⋊Dic3)C23semidirect
90. C2×C3×C3⋊Dic3C23semidirect
93. C2×C32×Dic3C23semidirect
113. C23×C3×D3C2×D3semidirect
134. C2×C4×C3⋊D3C2×D3semidirect
135. C2×C3×#67C2×D3semidirect
136. C2×C3×D12C2×D3semidirect
147. C32×C22⋊C4C2×D3semidirect
148. C32×C22⋊C4C2×D3semidirect
150. #3757C2×D3semidirect
155. #3752C2×D3semidirect
158. C3×(C2×D3)⋊C4C2×D3semidirect
162. C22×C33C2×D4semidirect
169. C2×C3⋊(C3⋊D3)C2×D4semidirect
174. C2×C3×C3⋊D3C2×D4semidirect
180. C2×C32×D3C2×D4semidirect
208. #882C3⋊D3direct (N × H)
240. C22×C3⋊D3D12semidirect
250. C22×C3×D3C22×D3semidirect
264. C2×C32×C4C22×D3semidirect
265. C2×C32×C4C22×D3semidirect
275. C2×C3⋊Dic3C22×D3semidirect
284. C2×C3×Dic3C22×D3semidirect
299. C3×C3⋊D3#120semidirect
318. C23×D3C2×C3⋊D3semidirect
331. C2×#67C2×C3⋊D3semidirect
342. C2×D12C2×C3⋊D3semidirect
349. C3×C22⋊C4D32semidirect
350. C3×C22⋊C4C2×C3⋊D3semidirect
360. (C2×D3)⋊C4C2×C3⋊D3semidirect
372. C22×C32C2×D12semidirect
373. C22×C32D3×D4semidirect
400. C2×C3⋊D3C2×D12semidirect
412. C2×C3×D3D3×D4semidirect
437. C33C2×#120semidirect
486. C22×D3C22×C3⋊D3semidirect
493. C2×C3×C4C2×D32semidirect
494. C2×C3×C4C22×C3⋊D3semidirect
509. C2×Dic3C22×C3⋊D3semidirect
537. C3⋊D3#882direct (N × H)
568. C22⋊C4D3×C3⋊D3semidirect
585. C22×C3D3×D12semidirect
586. C22×C3D4×C3⋊D3semidirect
623. C2×D3D4×C3⋊D3semidirect
635. C32C2×#882semidirect
636. C32D3×#120semidirect
672. C2×C4C2×D3×C3⋊D3semidirect
717. C22C3⋊D3×D12semidirect
724. C3D3×#882semidirect
725. 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×C3⋊D3×#672
C2×C3⋊D3×D122
#117239232
C3×C22⋊C4×C3⋊D32
C32×#8822
#117236382
#117236302
#117235422
#117235402
C3⋊D3×(C2×D3)⋊C42
C3⋊D3×#1203
D3×#8823