Finite Group Databasebeta

← #13177577

Subgroups — #13177577

Order 1728.

1740 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723976C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C32×#939C211yesmaximal, characteristic, complemented
4#11723631C211yesmaximal, characteristic, complemented
5#11723631C211yesmaximal, characteristic, complemented
6#11723626C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8Dic3×#638C211yesmaximal, characteristic, complemented
9#11723614C211yesmaximal, characteristic, complemented
10#11723596C211yesmaximal, characteristic, complemented
11#11723594C211yesmaximal, characteristic, complemented
12#11723507C211yesmaximal, characteristic, complemented
13C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#11723427C211yesmaximal, characteristic, complemented
15#11723401C211yesmaximal, characteristic, complemented
16#10596085—31nomaximal
17#10595179—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30#88864C2211yescharacteristic
31#88864C2211yescharacteristic
32#88864C2211yescharacteristic
33#88857C2211yescharacteristic
34#88857C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41#88807C2211yescharacteristic
42#88807C2211yescharacteristic
43#88806C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47#88803C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3×C3⋊Dic3C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×#121—31no—
54#64147—31no—
55#64147—31no—
56#64147D311yescharacteristic, complemented
57#64144—31no—
58#64144—31no—
59#64144—34no—
60#64144—64no—
61D4×C3⋊Dic3—31no—
62C4×#638—31no—
63#64135—31no—
64C4⋊C4×C3⋊D3—31no—
65#64099—31no—
66#64090—31no—
67#64090—31no—
68#64088—31no—
69#64088—31no—
70C3×#939D314yescomplemented
71C3×#938—34no—
72#67⋊Dic3—34no—
73#67⋊Dic3—34no—
74Dic3×#67—34no—
75#63970—34no—
76#63970—34no—
77#63969—34no—
78#63956—34no—
79#63955—34no—
80#63879—34no—
81D3×Dic3⋊C4—34no—
82#63858—34no—
83#63846—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C33×D4—41no—
89C2×C33×C4C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)—41no—
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C3×#638—22no—
96C3×#638—22no—
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4×C3⋊D3—41no—
101C32×#67—22no—
102C32×#67—41no—
103C2×C32×Dic3—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107#6290—22no—
108Dic3×C3⋊D3—22no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—41no—
111#5614—94no—
112#5601—91no—
113C2×C32×D4—24no—
114C2×C32×D4—31no—
115C2×C32×D4—31no—
116C2×C32×D4C2×D314yes—
117C2×C32×D4C2×D311yescharacteristic
118C22×C32×C4—31no—
119C2×#638—31no—
120C2×#638C2×D311yescharacteristic
121C2×#638C2×D311yescharacteristic
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—34no—
124C22×C3⋊Dic3—31no—
125C22×C3⋊Dic3—64no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3C2×D311yescharacteristic
129C2×C3×#67—34no—
130C2×C3×#67—34no—
131C2×C3×#67C2×D314yes—
132C2×C3×#67C2×D314yes—
133C22×C3×Dic3C2×D314yes—
134C2×C3×C4×D3—34no—
135C2×#625—34no—
136C2×D3×Dic3—34no—
137C2×D3×Dic3—34no—
138C2×D3×Dic3—34no—
139C32×C4⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C22⋊C4—31no—
142#3757—31no—
143#3757—31no—
144#3757—31no—
145#3757—34no—
146#3757—34no—
147#3757—34no—
148#3757—31no—
149#3757—31no—
150#3757—64no—
151#3757—64no—
152#3757—64no—
153#3757C2×D311yescharacteristic
154#3757C2×D311yescharacteristic
155#3752—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)C2×D311yescharacteristic
160#3750—31no—
161#3750—31no—
162#3750—34no—
163#3750—34no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—64no—
168#3750—64no—
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—31no—
171C4×C3⋊Dic3—31no—
172C3×#217—34no—
173C3×#217—34no—
174C3×#217C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×C4⋊Dic3—34no—
177C3×Dic3⋊C4C2×D314yes—
178#3724—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187Dic32—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3#4112yes—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C33×C4—21no—
204C3⋊(C3⋊Dic3)—21no—
205C3⋊(C3⋊Dic3)—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3#4112yes—
214C3×#121—34no—
215C3×#121—91no—
216#939—91no—
217#939—91no—
218#939C3⋊D311yescharacteristic, complemented
219#938—34no—
220#938—94no—
221#938—94no—
222#935—94no—
223#935—94no—
224#935—91no—
225#935—184no—
226D4×Dic3—94no—
227D4×Dic3—91no—
228D4×Dic3—91no—
229C4×#67—94no—
230C4×#67—91no—
231#926—94no—
232C2×Dic3⋊C4—91no—
233#898—91no—
234D3×C4⋊C4—94no—
235#890—94no—
236#889—91no—
237#883—91no—
238#67⋊C4—94no—
239#67⋊C4—94no—
240#67⋊C4—91no—
241#879—94no—
242#879—94no—
243#879—91no—
244#877—91no—
245C23×C32—24no—
246C23×C32—24no—
247C23×C32—31no—
248C23×C32C22×D314yes—
249C23×C32C22×D314yes—
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3C22×D314yes—
255C32×D4—41no—
256C32×D4—44no—
257C32×D4—48no—
258C32×D4—62no—
259C32×D4—121no—
260C2×C32×C4—24no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—62no—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D311yescharacteristic
267#638—22no—
268#638—22no—
269#638—62no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3—121no—
284C2×C3⋊Dic3—124no—
285C2×C3⋊Dic3—128no—
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C4×C3⋊D3—41no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—121no—
292C3×#67—28no—
293C3×#67—44no—
294C3×#67—68no—
295C3×#67—68no—
296C2×C3×Dic3—28no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C2×C3×Dic3C22×D314yes—
303C3×C4×D3—124no—
304#625—68no—
305D3×Dic3—68no—
306D3×Dic3—124no—
307D3×Dic3—124no—
308#553—271noSylow
309C2×C33—41no—
310C2×C33—41no—
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C2×C33H(5,𝔽2)11yescharacteristic
314C3×C3⋊D3—22no—
315C32×D3—41no—
316C2×C3×D4—24no—
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C2×C3×D4—91no—
320C2×C3×D4—91no—
321C2×C3×D4D3214yes—
322C2×C3×D4C2×C3⋊D311yescharacteristic
323C22×C3×C4—34no—
324C22×C3×C4—91no—
325C2×#67—34no—
326C2×#67—34no—
327C2×#67—94no—
328C2×#67—91no—
329C2×#67C2×C3⋊D311yescharacteristic
330C2×#67C2×C3⋊D311yescharacteristic
331C22×Dic3—94no—
332C22×Dic3—94no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—184no—
337C22×Dic3C2×C3⋊D311yescharacteristic
338C2×C4×D3—34no—
339C2×C4×D3—94no—
340C2×C4×D3—94no—
341C2×C4×D3—91no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—91no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348#217—34no—
349#217—34no—
350#217—94no—
351#217—94no—
352#217—94no—
353#217—94no—
354#217—94no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—184no—
360#217—184no—
361#217—184no—
362#217C2×C3⋊D311yescharacteristic
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
367C4⋊Dic3—34no—
368C4⋊Dic3—94no—
369C4⋊Dic3—94no—
370C4⋊Dic3—94no—
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373Dic3⋊C4—94no—
374Dic3⋊C4—94no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—184no—
385Dic3⋊C4—184no—
386Dic3⋊C4C2×C3⋊D311yescharacteristic
387C4×Dic3—94no—
388C4×Dic3—94no—
389C4×Dic3—94no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C22×C32—28no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—24no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—44no—
408C22×C32—44no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32—61no—
413C22×C32—61no—
414C22×C32—61no—
415C22×C32C23×D314yes—
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3#23712yes—
420C2×C3×D3—24no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—38no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—32no—
429C32×C4—44no—
430C32×C4—61no—
431C32×C4—61no—
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—61no—
436C3⋊Dic3—61no—
437C3⋊Dic3—61no—
438C3⋊Dic3—61no—
439C3⋊Dic3—64no—
440C3⋊Dic3—64no—
441C3⋊Dic3—64no—
442C3⋊Dic3—64no—
443C3⋊Dic3—124no—
444C3⋊Dic3—124no—
445C3⋊Dic3—124no—
446C3⋊Dic3—124no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—64no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452C3×Dic3#23718yes—
453#126—271no—
454#126—271no—
455#125—271no—
456#123—271no—
457#123—271no—
458#121—31no—
459#121—91no—
460#121—271no—
461#121—271no—
462C4×D4—271no—
463C4×D4—271no—
464C4×D4—271no—
465C4×D4—271no—
466#117—271no—
467C2×C4⋊C4—271no—
468C33#55311yescharacteristic, complemented, Sylow
469C23×C3—24no—
470C23×C3—24no—
471C23×C3—34no—
472C23×C3—91no—
473C23×C3C2×D3214yes—
474C23×C3C2×D3214yes—
475C23×C3C22×C3⋊D311yescharacteristic
476C23×C3C22×C3⋊D311yescharacteristic
477C22×D3—34no—
478C22×D3C22×C3⋊D311yescharacteristic
479C3×D4—44no—
480C3×D4—41no—
481C3×D4—48no—
482C3×D4—68no—
483C3×D4—124no—
484C3×D4—182no—
485C3×D4—182no—
486C2×C3×C4—24no—
487C2×C3×C4—34no—
488C2×C3×C4—34no—
489C2×C3×C4—34no—
490C2×C3×C4—68no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—361no—
495C2×C3×C4C2×D3214yes—
496C2×C3×C4C22×C3⋊D311yescharacteristic
497#67—22no—
498#67—41no—
499#67—68no—
500#67—68no—
501#67—182no—
502#67—188no—
503C2×Dic3—22no—
504C2×Dic3—34no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—94no—
508C2×Dic3—94no—
509C2×Dic3—94no—
510C2×Dic3—94no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—184no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—184no—
519C2×Dic3—182no—
520C2×Dic3—361no—
521C2×Dic3—364no—
522C2×Dic3—364no—
523C2×Dic3—361no—
524C2×Dic3—368no—
525C2×Dic3C22×C3⋊D311yescharacteristic
526C2×Dic3C22×C3⋊D311yescharacteristic
527C2×Dic3C22×C3⋊D311yescharacteristic
528C4×D3—124no—
529C4×D3—188no—
530C4×D3—364no—
531C4×D3—361no—
532C2×C32—24no—
533C2×C32—24no—
534C2×C32—24no—
535C2×C32—48no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—44no—
539C2×C32—44no—
540C2×C32—84no—
541C2×C32—121no—
542C2×C32C2×#23714yes—
543C2×C32C2×#23711yescharacteristic
544C2×C32#100414yes—
545C2×C32#100411yescharacteristic
546C2×C32D3×#4114yes—
547C2×C32D3×#4111yescharacteristic
548C3⋊D3—22no—
549C3×D3—44no—
550C3×D3—68no—
551C2×D4—31no—
552C2×D4—31no—
553C2×D4—91no—
554C2×D4—91no—
555C2×D4—271no—
556C2×D4D3×C3⋊D311yescharacteristic
557C22×C4—31no—
558C22×C4—91no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C4⋊C4—31no—
564C4⋊C4—91no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C42—271no—
584C42—271no—
585C42—271no—
586C22×C3—28no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—24no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—64no—
606C22×C3—64no—
607C22×C3—64no—
608C22×C3—92no—
609C22×C3—181no—
610C22×C3—181no—
611C22×C3C22×D3214yes—
612C22×C3C23×C3⋊D311yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—38no—
617C2×D3—64no—
618C2×D3—64no—
619C3×C4—24no—
620C3×C4—21no—
621C3×C4—38no—
622C3×C4—44no—
623C3×C4—64no—
624C3×C4—64no—
625C3×C4—181no—
626C3×C4—181no—
627C3×C4—181no—
628Dic3—21no—
629Dic3—21no—
630Dic3—64no—
631Dic3—64no—
632Dic3—64no—
633Dic3—184no—
634Dic3—184no—
635Dic3—184no—
636Dic3—184no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—364no—
642Dic3—364no—
643Dic3—364no—
644Dic3—364no—
645Dic3#383012yes—
646C32—24no—
647C32#560111yescharacteristic, complemented
648C32#561414yescomplemented
649C23—31no—
650C23—91no—
651C23C2×D3×C3⋊D311yescharacteristic
652C23C2×D3×C3⋊D311yescharacteristic
653D4—41no—
654D4—62no—
655D4—121no—
656D4—182no—
657D4—182no—
658D4—542no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—62no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—271no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—361no—
671C2×C4—542no—
672C2×C4—1081no—
673C2×C4—1081no—
674C2×C4—1081no—
675C2×C4C2×D3×C3⋊D311yescharacteristic
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—48no—
680C2×C3—44no—
681C2×C3—44no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3—84no—
685C2×C3—124no—
686C2×C3—182no—
687C2×C3D3×#23714yes—
688C2×C3D3×#23714yes—
689C2×C3#6433014yes—
690C2×C3C2×#383011yescharacteristic
691C2×C3#6436111yescharacteristic
692C2×C3#41×C3⋊D311yescharacteristic
693D3—41no—
694D3—68no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—61no—
702C22—61no—
703C22—61no—
704C22—92no—
705C22—181no—
706C22—181no—
707C22C22×D3×C3⋊D311yescharacteristic
708C4—21no—
709C4—32no—
710C4—61no—
711C4—61no—
712C4—181no—
713C4—181no—
714C4—181no—
715C4—541no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—24no—
720C3#1059517914yescomplemented
721C3#1059608511yescharacteristic, complemented
722C2—41no—
723C2—41no—
724C2—121no—
725C2—182no—
726C2D3×#383011yescharacteristic
727C2C3⋊D3×#23711yescharacteristic
728C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11723976C2semidirect
2. C3×#64147C2semidirect
3. C32×#939C2semidirect
4. #11723631C2semidirect
5. #11723631C2semidirect
6. #11723626C2semidirect
7. #67⋊(C3⋊Dic3)C2semidirect
8. Dic3×#638C2semidirect
9. #11723614C2semidirect
10. #11723596C2semidirect
11. #11723594C2semidirect
12. #11723507C2semidirect
13. C3⋊D3×Dic3⋊C4C2semidirect
14. #11723427C2semidirect
15. #11723401C2semidirect
56. #64147D3semidirect
70. C3×#939D3semidirect
218. #939C3⋊D3semidirect
468. C33#553semidirect
647. C32#5601semidirect
648. C32#5614semidirect
720. C3#10595179semidirect
721. C3#10596085semidirect

Maximal subgroups

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

subgroupindex
#117239762
C3×#641472
C32×#9392
#117236312
#117236262
#67⋊(C3⋊Dic3)2
Dic3×#6382
#117236142
#117235962
#117235942
#117235072
C3⋊D3×Dic3⋊C42
#117234272
#117234012
#105960853
#105951793