Finite Group Databasebeta

← #13177408

Subgroups — #13177408

Order 1728.

2316 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3#11723976C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5#11723631C211yesmaximal, characteristic, complemented
6#11723629C211yesmaximal, characteristic, complemented
7#11723629C211yesmaximal, characteristic, complemented
8#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
9D3×#3757C211yesmaximal, characteristic, complemented
10C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#11723600C211yesmaximal, characteristic, complemented
12#11723506C211yesmaximal, characteristic, complemented
13#11723474C211yesmaximal, characteristic, complemented
14#11723473C211yesmaximal, characteristic, complemented
15#11723415C211yesmaximal, characteristic, complemented
16#10596277—31nomaximal
17#10595150—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C32×D3×D4—24no—
28C2×C32×D12C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic
30C2×#6293C2211yescharacteristic, complemented
31C2×#6290C2211yescharacteristic
32C2×#6290C2211yescharacteristic, complemented
33C2×#6290C2211yescharacteristic, complemented
34C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
35#89029—24no—
36C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic, complemented
39#88864C2211yescharacteristic, complemented
40#88864C2211yescharacteristic, complemented
41#88857C2211yescharacteristic, complemented
42#88857C2211yescharacteristic, complemented
43C3×#3757C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×C32×D4—31no—
56C2×#3830—31no—
57C2×C3×D3×D4D314yescomplemented
58C2×#3805—34no—
59#64162—31no—
60#64162—31no—
61C2×#3757—31no—
62C2×#3757—31no—
63#64148—31no—
64#64148D311yescharacteristic, complemented
65#64147—31no—
66#64145—31no—
67#64144—31no—
68#64144—34no—
69#64144—31no—
70#64144—64no—
71D4×C3⋊Dic3—31no—
72C4×#638—31no—
73#64133—31no—
74C3×#939—34no—
75#63976—34no—
76#63976—34no—
77Dic3×#67—34no—
78#63970—34no—
79D3×#217—34no—
80C2×(C2×D3)⋊Dic3—34no—
81#63959—34no—
82#63885—34no—
83#63884—34no—
84#63879—34no—
85#63851—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—22no—
93C22×C32×D3—41no—
94C22×C32×D3—41no—
95C22×C32×D3C2311yescharacteristic
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)—22no—
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C3×#638—22no—
106C3×#638—41no—
107C2×C3×C3⋊Dic3—41no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C32×#67—22no—
112C32×#67D414yescomplemented
113C2×C32×Dic3C2311yescharacteristic
114C32×D12—22no—
115C32×C4×D3—22no—
116#6293—22no—
117#6290—22no—
118#6290—22no—
119#6290—41no—
120Dic3×C3⋊D3—22no—
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—41no—
123#5806—94no—
124#5610—91no—
125C24×C32—31no—
126C24×C32—31no—
127C23×C3×D3C2×D314yes—
128C23×C3×D3C2×D314yes—
129C2×C32×D4—24no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×C32×D4—64no—
134C2×C32×D4C2×D314yes—
135C2×C32×D4C2×D311yescharacteristic
136C22×C32×C4—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638C2×D311yescharacteristic, complemented
141C2×#638C2×D311yescharacteristic, complemented
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—34no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—64no—
147C22×C3⋊Dic3C2×D311yescharacteristic, complemented
148#3830—64no—
149C2×C4×C3⋊D3—31no—
150C2×#634—31no—
151C2×C3×#67—34no—
152C2×C3×#67—34no—
153C2×C3×#67C2×D314yes—
154C2×C3×#67C2×D314yes—
155C22×C3×Dic3—34no—
156C3×D3×D4—216no—
157C2×C3×D12C2×D314yes—
158C2×C3×C4×D3C2×D314yes—
159C2×#627—34no—
160C2×#625—34no—
161C2×#625—34no—
162C2×#625—34no—
163#3805—616no—
164C2×D3×Dic3—34no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167#3757—31no—
168#3757—31no—
169#3757—31no—
170#3757—34no—
171#3757—34no—
172#3757—34no—
173#3757—31no—
174#3757—31no—
175#3757—31no—
176#3757—31no—
177#3757—31no—
178#3757—31no—
179#3757—31no—
180#3757—64no—
181#3757—64no—
182#3757—64no—
183#3757C2×D311yescharacteristic, complemented
184#3752C2×D311yescharacteristic, complemented
185C4⋊(C3⋊Dic3)—31no—
186#3750—31no—
187#3750—31no—
188#3750—34no—
189#3750—34no—
190#3750—64no—
191#3750—64no—
192#3750C2×D311yescharacteristic, complemented
193C4×C3⋊Dic3—31no—
194C3×#217—34no—
195C3×(C2×D3)⋊C4—34no—
196C3×Dic3⋊C4—34no—
197Dic3⋊Dic3—34no—
198(C2×D3)⋊Dic3—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33C2×D412yes—
212C22×C33C2411yescharacteristic
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—44no—
224C2×C32×D3—44no—
225C2×C32×D3C2×D412yes—
226C2×C32×D3#4112yescomplemented
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3—21no—
235C32×Dic3C2×D412yes—
236C22×C3×D4—34no—
237C2×#237—94no—
238C2×#237—91no—
239C2×D3×D4C3⋊D311yescharacteristic, complemented
240C3×#121—91no—
241#953—94no—
242#953—94no—
243C2×#217—94no—
244C2×#217—94no—
245#939—34no—
246#939—94no—
247#939—91no—
248#938—94no—
249#937—91no—
250#937—91no—
251#936—94no—
252#935—94no—
253#935—94no—
254#935—91no—
255#935—184no—
256D4×Dic3—94no—
257C4×#67—94no—
258C4×#67—91no—
259C2×(C2×D3)⋊C4—91no—
260#924—94no—
261#896—91no—
262#894—91no—
263#885—91no—
264#884—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32—31no—
271C23×C32—31no—
272C23×C32—62no—
273C23×C32—62no—
274C23×C32—62no—
275C23×C32—62no—
276C23×C32—121no—
277C23×C32—121no—
278C23×C32C22×D314yes—
279C23×C32C22×D314yes—
280C23×C32C22×D311yescharacteristic
281C23×C32C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—28no—
284C22×C3×D3—28no—
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—34no—
288C22×C3×D3—44no—
289C22×C3×D3—44no—
290C22×C3×D3C22×D314yes—
291C22×C3×D3C22×D314yes—
292C22×C3×D3C22×D314yes—
293C32×D4—22no—
294C32×D4—28no—
295C32×D4—34no—
296C32×D4—48no—
297C32×D4—62no—
298C32×D4—62no—
299C2×C32×C4—24no—
300C2×C32×C4—31no—
301C2×C32×C4—62no—
302C2×C32×C4C22×D314yes—
303C2×C32×C4C22×D311yescharacteristic
304#638—22no—
305#638—41no—
306#638—62no—
307#638—62no—
308#638—121no—
309C2×C3⋊Dic3—31no—
310C2×C3⋊Dic3—31no—
311C2×C3⋊Dic3—31no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—34no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—34no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—41no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—62no—
323C2×C3⋊Dic3—62no—
324C2×C3⋊Dic3—68no—
325C2×C3⋊Dic3—128no—
326C2×C3⋊Dic3—121no—
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4×C3⋊D3—62no—
331#634—62no—
332C3×#67—28no—
333C3×#67—68no—
334C3×#67—124no—
335C3×#67#67116yescomplemented
336C2×C3×Dic3—34no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—124no—
340C2×C3×Dic3C22×D314yes—
341C3×D12—28no—
342C3×C4×D3—28no—
343#627—68no—
344#625—68no—
345#625—68no—
346#625—124no—
347D3×Dic3—68no—
348D3×Dic3—68no—
349D3×Dic3—124no—
350#546—271noSylow
351C2×C33—22no—
352C2×C33—41no—
353C2×C33C22×D411yescharacteristic
354C2×C33C2×#4111yescharacteristic
355C2×C33H(5,𝔽2)11yescharacteristic
356C3×C3⋊D3—41no—
357C32×D3—22no—
358C32×D3—22no—
359C32×D3—41no—
360C24×C3—34no—
361C24×C3—34no—
362C23×D3C2×C3⋊D311yescharacteristic
363C23×D3C2×C3⋊D311yescharacteristic
364C2×C3×D4—24no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—616no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4D3214yes—
372C2×C3×D4C2×C3⋊D311yescharacteristic
373C22×C3×C4—34no—
374C22×C3×C4—91no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—94no—
382C2×#67—91no—
383C2×#67C2×C3⋊D311yescharacteristic
384C2×#67C2×C3⋊D311yescharacteristic
385C22×Dic3—34no—
386C22×Dic3—94no—
387C22×Dic3—94no—
388C22×Dic3—94no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—184no—
392#237—1816no—
393#237—184no—
394D3×D4—24no—
395C2×D12C2×C3⋊D311yescharacteristic
396C2×C4×D3—94no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3C2×C3⋊D311yescharacteristic
400C2×Dic6—94no—
401C2×Dic6—91no—
402C3×C4⋊C4—91no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—91no—
405#217—34no—
406#217—94no—
407#217—94no—
408#217—94no—
409#217—94no—
410#217—94no—
411#217—94no—
412#217—94no—
413#217—94no—
414#217—94no—
415#217—94no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—184no—
420#217—184no—
421#217—184no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430C4⋊Dic3—94no—
431Dic3⋊C4—34no—
432Dic3⋊C4—94no—
433Dic3⋊C4—94no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—184no—
438Dic3⋊C4—184no—
439C4×Dic3—94no—
440C4×Dic3—91no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—24no—
447C22×C32—28no—
448C22×C32—24no—
449C22×C32—24no—
450C22×C32—24no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—32no—
454C22×C32—32no—
455C22×C32—44no—
456C22×C32—44no—
457C22×C32—44no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—61no—
463C22×C32—61no—
464C22×C32—61no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—124no—
468C22×C32—124no—
469C22×C32D3×D412yes—
470C22×C32C2×#6718yes—
471C22×C32C23×D314yes—
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—24no—
482C2×C3×D3—24no—
483C2×C3×D3—416no—
484C2×C3×D3—416no—
485C2×C3×D3—64no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3#23718yescomplemented
489C2×C3×D3C2×#6718yes—
490C32×C4—21no—
491C32×C4—24no—
492C32×C4—32no—
493C32×C4—44no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—61no—
498C3⋊Dic3—61no—
499C3⋊Dic3—61no—
500C3⋊Dic3—61no—
501C3⋊Dic3—64no—
502C3⋊Dic3—64no—
503C3⋊Dic3—64no—
504C3⋊Dic3—64no—
505C3⋊Dic3—124no—
506C3⋊Dic3—124no—
507C3⋊Dic3—124no—
508C3⋊Dic3—124no—
509C3×Dic3—64no—
510C3×Dic3—64no—
511C3×Dic3—64no—
512C3×Dic3C2×#6718yes—
513C2×#41—271no—
514C22×D4—31no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—91no—
520#121—271no—
521#121—271no—
522#120—271no—
523#120—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C22⋊C4—271no—
527C2×C22⋊C4—271no—
528C33#54611yescharacteristic, complemented, Sylow
529C23×C3—24no—
530C23×C3—24no—
531C23×C3—34no—
532C23×C3—34no—
533C23×C3—34no—
534C23×C3—68no—
535C23×C3—68no—
536C23×C3—68no—
537C23×C3—68no—
538C23×C3—91no—
539C23×C3—124no—
540C23×C3—124no—
541C23×C3C2×D3214yes—
542C23×C3C2×D3214yes—
543C23×C3C22×C3⋊D311yescharacteristic
544C23×C3C22×C3⋊D311yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—34no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3C22×C3⋊D311yescharacteristic
553C22×D3C22×C3⋊D311yescharacteristic
554C22×D3C22×C3⋊D311yescharacteristic
555C3×D4—28no—
556C3×D4—22no—
557C3×D4—316no—
558C3×D4—48no—
559C3×D4—68no—
560C3×D4—68no—
561C3×D4—182no—
562C3×D4—361no—
563C2×C3×C4—24no—
564C2×C3×C4—34no—
565C2×C3×C4—68no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—361no—
570C2×C3×C4C2×D3214yes—
571C2×C3×C4C22×C3⋊D311yescharacteristic
572#67—22no—
573#67—68no—
574#67—124no—
575#67—188no—
576#67—188no—
577#67—182no—
578#67—182no—
579#67—361no—
580#67—364no—
581#67#63814yescomplemented
582C2×Dic3—34no—
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—94no—
586C2×Dic3—94no—
587C2×Dic3—94no—
588C2×Dic3—94no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—124no—
594C2×Dic3—184no—
595C2×Dic3—184no—
596C2×Dic3—184no—
597C2×Dic3—184no—
598C2×Dic3—188no—
599C2×Dic3—188no—
600C2×Dic3—182no—
601C2×Dic3—182no—
602C2×Dic3—368no—
603C2×Dic3—364no—
604C2×Dic3C22×C3⋊D311yescharacteristic
605D12—22no—
606C4×D3—22no—
607C4×D3—188no—
608C4×D3—182no—
609C4×D3—361no—
610Dic6—188no—
611Dic6—182no—
612C2×C32—22no—
613C2×C32—24no—
614C2×C32—24no—
615C2×C32—24no—
616C2×C32—28no—
617C2×C32—48no—
618C2×C32—41no—
619C2×C32—44no—
620C2×C32—62no—
621C2×C32—62no—
622C2×C32—84no—
623C2×C32—121no—
624C2×C32C2×D3×D411yescharacteristic
625C2×C32C2×#23714yes—
626C2×C32#100414yes—
627C2×C32#100411yescharacteristic
628C2×C32D3×#4111yescharacteristic
629C2×C32C22×#6714yes—
630C3⋊D3—41no—
631C3×D3—28no—
632C3×D3—28no—
633C3×D3—44no—
634C3×D3—124no—
635C24—31no—
636C24—31no—
637#41—544no—
638C2×Q8—271no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—64no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4D3×C3⋊D311yescharacteristic
649C22×C4—31no—
650C22×C4—91no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—91no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C42—271no—
672C22×C3—24no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—24no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—24no—
683C22×C3—28no—
684C22×C3—38no—
685C22×C3—38no—
686C22×C3—44no—
687C22×C3—44no—
688C22×C3—44no—
689C22×C3—44no—
690C22×C3—44no—
691C22×C3—64no—
692C22×C3—64no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—1216no—
699C22×C3—1216no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3D3×#6718yes—
704C22×C3C2×#63812yes—
705C22×C3C22×D3214yes—
706C22×C3C23×C3⋊D311yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—44no—
715C2×D3—44no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—64no—
719C2×D3#383012yescomplemented
720C2×D3C2×#63812yes—
721C3×C4—24no—
722C3×C4—21no—
723C3×C4—38no—
724C3×C4—44no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728Dic3—64no—
729Dic3—64no—
730Dic3—64no—
731Dic3—184no—
732Dic3—184no—
733Dic3—184no—
734Dic3—184no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739Dic3—364no—
740Dic3—364no—
741Dic3—364no—
742Dic3—364no—
743Dic3C2×#63812yes—
744C32—24no—
745C32#561011yescharacteristic, complemented
746C32#580614yescomplemented
747C23—31no—
748C23—31no—
749C23—31no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—91no—
755C23—121no—
756C23—121no—
757C23C2×D3×C3⋊D311yescharacteristic
758C23C2×D3×C3⋊D311yescharacteristic
759Q8—542no—
760D4—22no—
761D4—34no—
762D4—62no—
763D4—62no—
764D4—182no—
765D4—361no—
766D4—542no—
767D4—542no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—62no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—361no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—1081no—
783C2×C4C2×D3×C3⋊D311yescharacteristic
784C2×C3—28no—
785C2×C3—22no—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—48no—
790C2×C3—44no—
791C2×C3—41no—
792C2×C3—68no—
793C2×C3—68no—
794C2×C3—84no—
795C2×C3—124no—
796C2×C3—361no—
797C2×C3D3×#23714yes—
798C2×C3#6431314yes—
799C2×C3C2×D3×#6714yes—
800C2×C3C2×#383011yescharacteristic
801C2×C3#6436111yescharacteristic
802C2×C3C22×#63811yescharacteristic
803D3—22no—
804D3—22no—
805D3—41no—
806D3—124no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—32no—
813C22—32no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—124no—
822C22—124no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22D3×#63812yes—
827C22C22×D3×C3⋊D311yescharacteristic
828C4—21no—
829C4—32no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—541no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—24no—
838C3#1059515014yescomplemented
839C3#1059627711yescharacteristic, complemented
840C2—22no—
841C2—41no—
842C2—62no—
843C2—62no—
844C2—121no—
845C2—361no—
846C2D3×#383011yescharacteristic
847C2#1172458711yescharacteristic
848C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×#89029C2semidirect
3. #11723976C2semidirect
4. C3×#64148C2semidirect
5. #11723631C2semidirect
6. #11723629C2semidirect
7. #11723629C2semidirect
8. #67×C3⋊Dic3C2semidirect
9. D3×#3757C2semidirect
10. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
11. #11723600C2semidirect
12. #11723506C2semidirect
13. #11723474C2semidirect
14. #11723473C2semidirect
15. #11723415C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
30. C2×#6293C22semidirect
32. C2×#6290C22semidirect
33. C2×#6290C22semidirect
34. C2×Dic3×C3⋊D3C22semidirect
36. C2×D3×C3⋊Dic3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. #88864C22semidirect
39. #88864C22semidirect
40. #88864C22semidirect
41. #88857C22semidirect
42. #88857C22semidirect
43. C3×#3757C22semidirect
44. C3×#3752C22semidirect
45. C3×#3750C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
57. C2×C3×D3×D4D3semidirect
64. #64148D3semidirect
112. C32×#67D4semidirect
140. C2×#638C2×D3semidirect
141. C2×#638C2×D3semidirect
147. C22×C3⋊Dic3C2×D3semidirect
183. #3757C2×D3semidirect
184. #3752C2×D3semidirect
192. #3750C2×D3semidirect
226. C2×C32×D3#41semidirect
239. C2×D3×D4C3⋊D3semidirect
335. C3×#67#67semidirect
488. C2×C3×D3#237semidirect
528. C33#546semidirect
581. #67#638semidirect
719. C2×D3#3830semidirect
745. C32#5610semidirect
746. C32#5806semidirect
838. C3#10595150semidirect
839. C3#10596277semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×#890292
#117239762
C3×#641482
#117236312
#117236292
#67×C3⋊Dic32
D3×#37572
C2×(C2×D3)⋊(C3⋊Dic3)2
#117236002
#117235062
#117234742
#117234732
#117234152
#105962773
#105951503