Finite Group Databasebeta

← #13177578

Subgroups — #13177578

Order 1728.

1812 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723976C211yesmaximal, characteristic, complemented
2C3×#64146C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4#11723637C211yesmaximal, characteristic, complemented
5#11723634C211yesmaximal, characteristic, complemented
6#11723631C211yesmaximal, characteristic, complemented
7#11723626C211yesmaximal, characteristic, complemented
8C3⋊D3×#217C211yesmaximal, characteristic, complemented
9#11723600C211yesmaximal, characteristic, complemented
10#11723596C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723513C211yesmaximal, characteristic, complemented
13#11723506C211yesmaximal, characteristic, complemented
14#11723502C211yesmaximal, characteristic, complemented
15#11723407C211yesmaximal, characteristic, complemented
16#10596084—31nomaximal
17#10595180—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×#6293C2211yescharacteristic, complemented
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31#88864C2211yescharacteristic
32#88864C2211yescharacteristic
33#88864C2211yescharacteristic, complemented
34#88857C2211yescharacteristic, complemented
35#88857C2211yescharacteristic, complemented
36C3×#3757C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×#217C2211yescharacteristic, complemented
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#121—31no—
54#64148—31no—
55#64147—31no—
56#64146—31no—
57#64146D311yescharacteristic, complemented
58#64145—31no—
59#64144—31no—
60#64144—34no—
61#64144—64no—
62#64138—31no—
63C4×#638—31no—
64#64107—31no—
65#64105—31no—
66#64094—31no—
67#64090—31no—
68C22⋊C4×C3⋊D3—31no—
69#64088—31no—
70C3×#938D314yescomplemented
71C3×#937—34no—
72#63980—34no—
73#63976—34no—
74#67⋊Dic3—34no—
75#63970—34no—
76D3×#217—34no—
77#63959—34no—
78#63959—34no—
79#63956—34no—
80#63905—34no—
81#63899—34no—
82#63879—34no—
83#63858—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3—22no—
87C22×C3×C3⋊D3—41no—
88C22×C3×C3⋊D3—41no—
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×D4—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)—41no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C3×#638—22no—
100C3×#638—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C32×#67—41no—
104C32×#67—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×C4×D3—41no—
109#6293—41no—
110#6290—22no—
111#6290—41no—
112Dic3×C3⋊D3—41no—
113Dic3×C3⋊D3—41no—
114#5613—94no—
115#5593—91no—
116C23×C3⋊D3C2×D311yescharacteristic
117C23×C3×D3—34no—
118C2×C32×D4—24no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4C2×D314yes—
122C2×C32×D4C2×D311yescharacteristic
123C22×C32×C4—31no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638C2×D311yescharacteristic
127C2×#638C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—34no—
130C22×C3⋊Dic3—64no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×#634—31no—
134C2×C3×#67—34no—
135C2×C3×#67—34no—
136C2×C3×#67C2×D314yes—
137C2×C3×#67C2×D314yescomplemented
138C2×C3×C4×D3C2×D314yescomplemented
139C2×#627—34no—
140C2×#625—34no—
141C2×#625—34no—
142C2×D3×Dic3—34no—
143C2×D3×Dic3—34no—
144C32×C4⋊C4—31no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147#3757—31no—
148#3757—31no—
149#3757—31no—
150#3757—34no—
151#3757—34no—
152#3757—34no—
153#3757—31no—
154#3757—31no—
155#3757—64no—
156#3757—64no—
157#3757—64no—
158#3757C2×D311yescharacteristic
159#3752—31no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752C2×D311yescharacteristic
164#3752C2×D311yescharacteristic
165C4⋊(C3⋊Dic3)—31no—
166#3750—31no—
167#3750—31no—
168#3750—34no—
169#3750—34no—
170#3750—31no—
171#3750—31no—
172#3750—64no—
173#3750—64no—
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C3×#217—34no—
177C3×#217C2×D314yes—
178C3×#217C2×D314yescomplemented
179C3×(C2×D3)⋊C4—34no—
180C3×(C2×D3)⋊C4—34no—
181C3×C4⋊Dic3C2×D314yescomplemented
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191Dic32—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—44no—
206C2×C3×C3⋊D3#4112yes—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C33×C4—21no—
211C3⋊(C3⋊Dic3)—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#121—34no—
221C3×#120—91no—
222#953—91no—
223C2×#217—91no—
224#939—94no—
225#939—91no—
226#939—91no—
227#938—94no—
228#938C3⋊D311yescharacteristic, complemented
229#937—34no—
230#937—94no—
231#936—94no—
232#936—91no—
233#935—94no—
234#935—91no—
235#935—184no—
236D4×Dic3—91no—
237#929—94no—
238C4×#67—94no—
239#898—94no—
240#896—94no—
241#885—94no—
242#885—91no—
243#883—91no—
244#67⋊C4—94no—
245#67⋊C4—91no—
246D3×C22⋊C4—94no—
247#879—94no—
248#879—91no—
249#879—91no—
250#878—91no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—31no—
254C23×C32C22×D314yes—
255C23×C32C22×D314yes—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—22no—
259C22×C3⋊D3—41no—
260C22×C3⋊D3—41no—
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3—34no—
265C22×C3×D3—68no—
266C22×C3×D3—124no—
267C22×C3×D3—124no—
268C22×C3×D3C22×D314yes—
269C32×D4—41no—
270C32×D4—44no—
271C32×D4—48no—
272C32×D4—121no—
273C32×D4—121no—
274C2×C32×C4—24no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—121no—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D311yescharacteristic
281#638—22no—
282#638—41no—
283#638—62no—
284#638—121no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—34no—
291C2×C3⋊Dic3—34no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—121no—
298C2×C3⋊Dic3—124no—
299C2×C3⋊Dic3—128no—
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C4×C3⋊D3—121no—
303C4×C3⋊D3—121no—
304#634—121no—
305C3×#67—44no—
306C3×#67—44no—
307C3×#67—68no—
308C3×#67—124no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3C22×D314yes—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C3×C4×D3—44no—
315#627—124no—
316#625—68no—
317#625—124no—
318D3×Dic3—124no—
319D3×Dic3—124no—
320#538—271noSylow
321C2×C33—41no—
322C2×C33—41no—
323C2×C33C2×#4111yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C3×C3⋊D3—22no—
327C3×C3⋊D3—41no—
328C32×D3—41no—
329C24×C3—91no—
330C23×D3—34no—
331C2×C3×D4—24no—
332C2×C3×D4—34no—
333C2×C3×D4—34no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4D3214yes—
337C2×C3×D4C2×C3⋊D311yescharacteristic
338C22×C3×C4—34no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—94no—
342C2×#67—91no—
343C2×#67—94no—
344C2×#67—91no—
345C2×#67C2×C3⋊D311yescharacteristic
346C2×#67C2×C3⋊D311yescharacteristic, complemented
347C22×Dic3—94no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—184no—
352C2×C4×D3—94no—
353C2×C4×D3—94no—
354C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
355C2×Dic6—94no—
356C2×Dic6—91no—
357C3×C4⋊C4—34no—
358C3×C22⋊C4—34no—
359C3×C22⋊C4—34no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363#217—34no—
364#217—94no—
365#217—94no—
366#217—94no—
367#217—94no—
368#217—94no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—184no—
377#217—184no—
378#217—184no—
379#217C2×C3⋊D311yescharacteristic
380#217C2×C3⋊D311yescharacteristic, complemented
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389C4⋊Dic3—94no—
390C4⋊Dic3—91no—
391C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
392Dic3⋊C4—94no—
393Dic3⋊C4—94no—
394Dic3⋊C4—94no—
395Dic3⋊C4—94no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—184no—
401Dic3⋊C4—184no—
402C4×Dic3—94no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C22×C32—28no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—24no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—44no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32C23×D314yes—
429C22×C32C23×D311yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—44no—
436C2×C3⋊D3#23712yes—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—38no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3—64no—
445C2×C3×D3—64no—
446C2×C3×D3—1216no—
447C32×C4—21no—
448C32×C4—24no—
449C32×C4—44no—
450C32×C4—61no—
451C32×C4—61no—
452C32×C4—61no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—61no—
456C3⋊Dic3—61no—
457C3⋊Dic3—61no—
458C3⋊Dic3—61no—
459C3⋊Dic3—64no—
460C3⋊Dic3—64no—
461C3⋊Dic3—64no—
462C3⋊Dic3—64no—
463C3⋊Dic3—124no—
464C3⋊Dic3—124no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3×Dic3—24no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472#126—271no—
473#126—271no—
474#124—271no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—31no—
480#121—271no—
481#121—271no—
482#120—91no—
483#120—271no—
484C4×D4—271no—
485C4×D4—271no—
486C2×C22⋊C4—271no—
487C33#53811yescharacteristic, complemented, Sylow
488C23×C3—24no—
489C23×C3—24no—
490C23×C3—34no—
491C23×C3—91no—
492C23×C3—91no—
493C23×C3—182no—
494C23×C3—361no—
495C23×C3—361no—
496C23×C3C2×D3214yes—
497C23×C3C2×D3214yes—
498C23×C3C22×C3⋊D311yescharacteristic
499C23×C3C22×C3⋊D311yescharacteristic
500C22×D3—34no—
501C22×D3—34no—
502C22×D3—68no—
503C22×D3—124no—
504C22×D3—124no—
505C22×D3C22×C3⋊D311yescharacteristic
506C3×D4—44no—
507C3×D4—41no—
508C3×D4—48no—
509C3×D4—124no—
510C3×D4—124no—
511C3×D4—182no—
512C3×D4—361no—
513C2×C3×C4—24no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—124no—
520C2×C3×C4C2×D3214yes—
521C2×C3×C4C22×C3⋊D311yescharacteristic
522#67—41no—
523#67—41no—
524#67—68no—
525#67—124no—
526#67—182no—
527#67—188no—
528#67—361no—
529#67—364no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—94no—
533C2×Dic3—94no—
534C2×Dic3—94no—
535C2×Dic3—94no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—184no—
541C2×Dic3—184no—
542C2×Dic3—184no—
543C2×Dic3—184no—
544C2×Dic3—361no—
545C2×Dic3—361no—
546C2×Dic3—364no—
547C2×Dic3—361no—
548C2×Dic3—368no—
549C2×Dic3C22×C3⋊D311yescharacteristic
550C2×Dic3C22×C3⋊D311yescharacteristic
551C2×Dic3C22×C3⋊D311yescharacteristic
552C4×D3—41no—
553C4×D3—364no—
554C4×D3—364no—
555Dic6—361no—
556Dic6—364no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—48no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32—44no—
564C2×C32—44no—
565C2×C32—84no—
566C2×C32—121no—
567C2×C32C2×#23711yescharacteristic
568C2×C32#100414yes—
569C2×C32#100414yes—
570C2×C32#100411yescharacteristic
571C2×C32#100411yescharacteristic
572C2×C32D3×#4114yes—
573C3⋊D3—22no—
574C3⋊D3—41no—
575C3×D3—44no—
576C3×D3—68no—
577C3×D3—124no—
578C24—91no—
579C2×Q8—271no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4D3×C3⋊D311yescharacteristic
587C22×C4—31no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C4⋊C4—31no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C42—271no—
612C42—271no—
613C22×C3—28no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—24no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—92no—
636C22×C3—181no—
637C22×C3—181no—
638C22×C3—181no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3—364no—
642C22×C3C22×D3214yes—
643C22×C3C23×C3⋊D311yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—38no—
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—1216no—
654C3×C4—24no—
655C3×C4—21no—
656C3×C4—44no—
657C3×C4—64no—
658C3×C4—64no—
659C3×C4—64no—
660C3×C4—181no—
661C3×C4—181no—
662Dic3—21no—
663Dic3—21no—
664Dic3—21no—
665Dic3—64no—
666Dic3—64no—
667Dic3—184no—
668Dic3—184no—
669Dic3—184no—
670Dic3—184no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—364no—
676Dic3—364no—
677Dic3—364no—
678Dic3—364no—
679C32—24no—
680C32#559311yescharacteristic, complemented
681C32#561314yescomplemented
682C23—31no—
683C23—91no—
684C23—91no—
685C23—182no—
686C23—361no—
687C23—361no—
688C23C2×D3×C3⋊D311yescharacteristic
689C23C2×D3×C3⋊D311yescharacteristic
690Q8—1081no—
691D4—41no—
692D4—121no—
693D4—121no—
694D4—182no—
695D4—361no—
696D4—542no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—121no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4—1081no—
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—24no—
713C2×C3—24no—
714C2×C3—24no—
715C2×C3—48no—
716C2×C3—44no—
717C2×C3—44no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—84no—
721C2×C3—124no—
722C2×C3—182no—
723C2×C3—361no—
724C2×C3D3×#23714yes—
725C2×C3#6431314yes—
726C2×C3#6433014yes—
727C2×C3#6436111yescharacteristic
728C2×C3#6436111yescharacteristic
729C2×C3#41×C3⋊D311yescharacteristic
730D3—41no—
731D3—68no—
732D3—124no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—92no—
743C22—181no—
744C22—181no—
745C22—181no—
746C22—181no—
747C22—181no—
748C22—364no—
749C22C22×D3×C3⋊D311yescharacteristic
750C4—21no—
751C4—61no—
752C4—61no—
753C4—61no—
754C4—181no—
755C4—181no—
756C4—541no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—24no—
761C3#1059518014yescomplemented
762C3#1059608411yescharacteristic, complemented
763C2—41no—
764C2—41no—
765C2—121no—
766C2—182no—
767C2—361no—
768C2C3⋊D3×#23711yescharacteristic
769C2#1172458711yescharacteristic
770C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#538
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×#64146C2semidirect
3. C32×#938C2semidirect
4. #11723637C2semidirect
5. #11723634C2semidirect
6. #11723631C2semidirect
7. #11723626C2semidirect
8. C3⋊D3×#217C2semidirect
9. #11723600C2semidirect
10. #11723596C2semidirect
11. #11723591C2semidirect
12. #11723513C2semidirect
13. #11723506C2semidirect
14. #11723502C2semidirect
15. #11723407C2semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×#6293C22semidirect
33. #88864C22semidirect
34. #88857C22semidirect
35. #88857C22semidirect
40. C32×#217C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. #64146D3semidirect
70. C3×#938D3semidirect
137. C2×C3×#67C2×D3semidirect
138. C2×C3×C4×D3C2×D3semidirect
178. C3×#217C2×D3semidirect
181. C3×C4⋊Dic3C2×D3semidirect
228. #938C3⋊D3semidirect
346. C2×#67C2×C3⋊D3semidirect
354. C2×C4×D3C2×C3⋊D3semidirect
380. #217C2×C3⋊D3semidirect
391. C4⋊Dic3C2×C3⋊D3semidirect
487. C33#538semidirect
680. C32#5593semidirect
681. C32#5613semidirect
761. C3#10595180semidirect
762. C3#10596084semidirect

Maximal subgroups

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

subgroupindex
#117239762
C3×#641462
C32×#9382
#117236372
#117236342
#117236312
#117236262
C3⋊D3×#2172
#117236002
#117235962
#117235912
#117235132
#117235062
#117235022
#117234072
#105960843
#105951803