Finite Group Databasebeta

← #13177640

Subgroups — #13177640

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723980C211yesmaximal, characteristic, complemented
2C3×#64146C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4#11723642C211yesmaximal, characteristic, complemented
5#11723636C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7#11723623C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9#11723605C211yesmaximal, characteristic, complemented
10C2×#88803C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723504C211yesmaximal, characteristic, complemented
13#11723438C211yesmaximal, characteristic, complemented
14#11723416C211yesmaximal, characteristic, complemented
15#11723407C211yesmaximal, characteristic, complemented
16#10596031—31nomaximal
17#10595123—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6289C2211yescharacteristic, complemented
31#88864C2211yescharacteristic, complemented
32#88859C2211yescharacteristic, complemented
33#88857C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic, complemented
39C32×C4⋊Dic3C2211yescharacteristic, complemented
40C32×C4×Dic3C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C4×D4—31no—
54#64148—31no—
55#64148—34no—
56#64148—64no—
57#64146D311yescharacteristic, complemented
58#64139—31no—
59#64138—31no—
60C4×#638—31no—
61C2×#3752—31no—
62#64107—31no—
63#64103—31no—
64#64094—31no—
65#64093—31no—
66#64091—31no—
67#64087—31no—
68#64085—31no—
69#64084—31no—
70C3×#937—34no—
71C3×D4×Dic3D314yescomplemented
72#63982—34no—
73#63978—34no—
74#63977—34no—
75#63961—34no—
76C2×(C2×D3)⋊Dic3—34no—
77#63959—34no—
78#63958—34no—
79#63952—34no—
80#63859—34no—
81#63858—34no—
82#63854—34no—
83#63852—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3—22no—
88C22×C3×C3⋊D3—41no—
89C22×C3×C3⋊D3—41no—
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C33×D4—22no—
93C2×C33×C4C2311yescharacteristic
94#6312—22no—
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)—41no—
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C3×#638—41no—
101C3×#638—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C32×Dic3—41no—
105C2×C32×Dic3—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110#6293—41no—
111#6292—41no—
112#6292—41no—
113#6289—41no—
114#5593—91no—
115#5560—94no—
116C23×C3⋊D3C2×D311yescharacteristic
117C23×C3×D3—34no—
118C2×C32×D4—24no—
119C2×C32×D4C2×D314yes—
120C2×C32×D4C2×D311yescharacteristic
121C22×C32×C4—31no—
122C22×C32×C4—31no—
123C2×#638—31no—
124C2×#638—34no—
125C2×#638—31no—
126C2×#638—34no—
127C2×#638—64no—
128C2×#638—64no—
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—34no—
133C22×C3⋊Dic3—64no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4×C3⋊D3—31no—
137C2×#634—31no—
138C2×C3×#67—34no—
139C2×C3×#67—34no—
140C22×C3×Dic3C2×D314yes—
141C22×C3×Dic3C2×D314yescomplemented
142C2×#627—34no—
143C2×#626—34no—
144C2×#626—34no—
145C2×#624—34no—
146C32×C4⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C42—31no—
150#3757—31no—
151#3757—34no—
152#3757—64no—
153#3757C2×D311yescharacteristic
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3752—31no—
160#3752—31no—
161#3752—34no—
162#3752—31no—
163#3752—64no—
164#3752C2×D311yescharacteristic
165#3752C2×D311yescharacteristic
166C4⋊(C3⋊Dic3)—31no—
167#3750—31no—
168#3750—34no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
172#3750—64no—
173C4×C3⋊Dic3—31no—
174C3×#217—34no—
175C3×#217C2×D314yes—
176C3×#217C2×D314yescomplemented
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4—34no—
179C3×C4⋊Dic3C2×D314yescomplemented
180C3×C4×Dic3C2×D314yescomplemented
181#3724—34no—
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—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—
191(C2×D3)⋊Dic3—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33#4112yes—
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—21no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—44no—
210C33×C4—21no—
211C3⋊(C3⋊Dic3)—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#120—91no—
221C3×C4×D4—34no—
222#953—91no—
223C2×#217—91no—
224#939—94no—
225#939—91no—
226#939—91no—
227#939—184no—
228#938—91no—
229#937—34no—
230#936—91no—
231#935—91no—
232D4×Dic3C3⋊D311yescharacteristic, complemented
233#930—94no—
234#929—94no—
235C4×#67—94no—
236C2×(C2×D3)⋊C4—94no—
237#898—94no—
238#894—94no—
239#885—94no—
240#885—91no—
241#884—94no—
242#883—91no—
243#882—94no—
244#67⋊C4—91no—
245#879—91no—
246#879—91no—
247#878—94no—
248#878—91no—
249#876—94no—
250#875—94no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32C22×D314yes—
254C23×C32C22×D314yes—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—22no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—34no—
260C22×C3⋊D3—41no—
261C22×C3⋊D3—41no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—34no—
266C22×C3×D3—34no—
267C22×C3×D3—68no—
268C22×C3×D3—124no—
269C22×C3×D3—124no—
270C32×D4—22no—
271C32×D4—28no—
272C32×D4—48no—
273C2×C32×C4—24no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—121no—
279C2×C32×C4—121no—
280C2×C32×C4C22×D314yes—
281C2×C32×C4C22×D311yescharacteristic
282#638—41no—
283#638—41no—
284#638—62no—
285#638—68no—
286#638—128no—
287#638—121no—
288#638—124no—
289#638—128no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—34no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—64no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3—121no—
300C2×C3⋊Dic3—124no—
301C2×C3⋊Dic3—128no—
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C4⋊(C3⋊D3)—121no—
305C4⋊(C3⋊D3)—121no—
306C4×C3⋊D3—121no—
307#634—121no—
308C3×#67—124no—
309C3×#67—124no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3C22×D314yes—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318#627—124no—
319#626—124no—
320#626—124no—
321#624—124no—
322#538—271noSylow
323C2×C33—22no—
324C2×C33—41no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C3⋊(C3⋊D3)—41no—
329C3×C3⋊D3—41no—
330C3×C3⋊D3—41no—
331C24×C3—91no—
332C23×D3—34no—
333C2×C3×D4—24no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4D3214yes—
337C2×C3×D4C2×C3⋊D311yescharacteristic
338C22×C3×C4—34no—
339C22×C3×C4—34no—
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—94no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—184no—
349C2×#67—184no—
350C22×Dic3—94no—
351C22×Dic3—91no—
352C22×Dic3—184no—
353C22×Dic3C2×C3⋊D311yescharacteristic
354C22×Dic3C2×C3⋊D311yescharacteristic, complemented
355C2×D12—94no—
356C2×D12—94no—
357C2×C4×D3—94no—
358C2×C4×D3—91no—
359C2×Dic6—94no—
360C2×Dic6—91no—
361C3×C4⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C42—34no—
368#217—34no—
369#217—94no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—184no—
378#217C2×C3⋊D311yescharacteristic
379#217C2×C3⋊D311yescharacteristic, complemented
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—94no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—184no—
393C4⋊Dic3—94no—
394C4⋊Dic3—91no—
395C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
396Dic3⋊C4—94no—
397Dic3⋊C4—94no—
398Dic3⋊C4—94no—
399Dic3⋊C4—94no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—184no—
405C4×Dic3—94no—
406C4×Dic3—91no—
407C4×Dic3C2×C3⋊D311yescharacteristic, complemented
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—24no—
414C22×C32—28no—
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#23518yes—
426C22×C32#23712yes—
427C22×C32C23×D314yes—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—21no—
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—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—64no—
442C2×C3⋊D3—124no—
443C2×C3⋊D3—124no—
444C2×C3⋊D3—124no—
445C2×C3×D3—64no—
446C2×C3×D3—64no—
447C2×C3×D3—64no—
448C2×C3×D3—64no—
449C2×C3×D3—64no—
450C2×C3×D3—64no—
451C2×C3×D3—1216no—
452C32×C4—21no—
453C32×C4—24no—
454C32×C4—44no—
455C32×C4—61no—
456C32×C4—61no—
457C32×C4—61no—
458C32×C4—61no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—68no—
462C3⋊Dic3—61no—
463C3⋊Dic3—61no—
464C3⋊Dic3—61no—
465C3⋊Dic3—64no—
466C3⋊Dic3—64no—
467C3⋊Dic3—64no—
468C3⋊Dic3—124no—
469C3⋊Dic3—124no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3—24no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476#126—271no—
477#126—271no—
478#124—271no—
479#124—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485#121—271no—
486#120—91no—
487#120—271no—
488C4×D4—31no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C33#53811yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—91no—
495C23×C3—91no—
496C23×C3—182no—
497C23×C3—361no—
498C23×C3—361no—
499C23×C3C2×D3214yes—
500C23×C3C2×D3214yes—
501C23×C3C22×C3⋊D311yescharacteristic
502C23×C3C22×C3⋊D311yescharacteristic
503C22×D3—34no—
504C22×D3—34no—
505C22×D3—68no—
506C22×D3—94no—
507C22×D3—91no—
508C22×D3—124no—
509C22×D3—124no—
510C22×D3—184no—
511C3×D4—28no—
512C3×D4—22no—
513C3×D4—48no—
514C3×D4—361no—
515C3×D4—361no—
516C2×C3×C4—24no—
517C2×C3×C4—34no—
518C2×C3×C4—34no—
519C2×C3×C4—34no—
520C2×C3×C4—34no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—124no—
524C2×C3×C4—124no—
525C2×C3×C4C2×D3214yes—
526C2×C3×C4C22×C3⋊D311yescharacteristic
527#67—124no—
528#67—124no—
529#67—188no—
530#67—182no—
531#67—368no—
532#67—361no—
533#67—361no—
534#67—364no—
535#67—361no—
536#67—368no—
537C2×Dic3—34no—
538C2×Dic3—34no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—94no—
542C2×Dic3—94no—
543C2×Dic3—94no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—184no—
548C2×Dic3—184no—
549C2×Dic3—184no—
550C2×Dic3—364no—
551C2×Dic3—361no—
552C2×Dic3—368no—
553C2×Dic3C22×C3⋊D311yescharacteristic
554C2×Dic3C22×C3⋊D311yescharacteristic
555C2×Dic3C22×C3⋊D311yescharacteristic
556C2×Dic3C22×C3⋊D311yescharacteristic
557D12—364no—
558D12—364no—
559C4×D3—361no—
560C4×D3—364no—
561Dic6—361no—
562Dic6—364no—
563C2×C32—22no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—24no—
567C2×C32—28no—
568C2×C32—48no—
569C2×C32—41no—
570C2×C32—44no—
571C2×C32—84no—
572C2×C32C2×#23514yes—
573C2×C32C2×#23711yescharacteristic
574C2×C32#100414yes—
575C2×C32#100411yescharacteristic
576C2×C32#100411yescharacteristic
577C2×C32#100914yes—
578C3⋊D3—41no—
579C3⋊D3—41no—
580C3⋊D3—121no—
581C3⋊D3—124no—
582C3⋊D3—244no—
583C3×D3—124no—
584C3×D3—124no—
585C24—91no—
586C2×Q8—271no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4D3×C3⋊D311yescharacteristic
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C42—31no—
619C42—271no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—24no—
631C22×C3—28no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—44no—
637C22×C3—181no—
638C22×C3—181no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—364no—
644C22×C3#380418yes—
645C22×C3#382812yes—
646C22×C3C22×D3214yes—
647C22×C3C23×C3⋊D311yescharacteristic
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—1216no—
655C2×D3—184no—
656C2×D3—184no—
657C2×D3—184no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—364no—
662C2×D3—364no—
663C2×D3—364no—
664C3×C4—24no—
665C3×C4—21no—
666C3×C4—44no—
667C3×C4—64no—
668C3×C4—64no—
669C3×C4—64no—
670C3×C4—64no—
671C3×C4—181no—
672C3×C4—181no—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—64no—
678Dic3—64no—
679Dic3—188no—
680Dic3—184no—
681Dic3—184no—
682Dic3—184no—
683Dic3—181no—
684Dic3—181no—
685Dic3—181no—
686Dic3—364no—
687Dic3—364no—
688C32—24no—
689C32#556014yescomplemented
690C32#559311yescharacteristic, complemented
691C23—91no—
692C23—91no—
693C23—182no—
694C23—271no—
695C23—361no—
696C23—361no—
697C23C2×D3×C3⋊D311yescharacteristic
698C23C2×D3×C3⋊D311yescharacteristic
699Q8—1081no—
700D4—22no—
701D4—361no—
702D4—361no—
703D4—542no—
704D4—1081no—
705D4—1081no—
706D4—1081no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—271no—
716C2×C4—271no—
717C2×C4—271no—
718C2×C4—1081no—
719C2×C4—1081no—
720C2×C4C2×D3×C3⋊D311yescharacteristic
721C2×C3—28no—
722C2×C3—22no—
723C2×C3—24no—
724C2×C3—24no—
725C2×C3—24no—
726C2×C3—48no—
727C2×C3—44no—
728C2×C3—41no—
729C2×C3—84no—
730C2×C3—361no—
731C2×C3—361no—
732C2×C3#6431314yes—
733C2×C3#6431414yes—
734C2×C3C2×#380414yes—
735C2×C3C2×#382811yescharacteristic
736C2×C3#6436111yescharacteristic
737C2×C3#6436611yescharacteristic
738D3—124no—
739D3—124no—
740D3—364no—
741D3—361no—
742D3—724no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—181no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22—181no—
754C22—364no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22#8903112yes—
759C22C22×D3×C3⋊D311yescharacteristic
760C4—21no—
761C4—61no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—181no—
766C4—181no—
767C4—541no—
768C4—541no—
769C4—541no—
770C3—24no—
771C3#1059512314yescomplemented
772C3#1059603111yescharacteristic, complemented
773C2—22no—
774C2—41no—
775C2—361no—
776C2—361no—
777C2—1081no—
778C2#1172458711yescharacteristic
779C2#1172458911yescharacteristic
780C2C2×#8903111yescharacteristic
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. #11723980C2semidirect
2. C3×#64146C2semidirect
3. C32×D4×Dic3C2semidirect
4. #11723642C2semidirect
5. #11723636C2semidirect
6. #11723632C2semidirect
7. #11723623C2semidirect
8. #11723618C2semidirect
9. #11723605C2semidirect
10. C2×#88803C2semidirect
11. #11723591C2semidirect
12. #11723504C2semidirect
13. #11723438C2semidirect
14. #11723416C2semidirect
15. #11723407C2semidirect
21. C2×#6312C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×#6293C22semidirect
30. C2×#6289C22semidirect
31. #88864C22semidirect
32. #88859C22semidirect
33. #88857C22semidirect
38. C32×#217C22semidirect
39. C32×C4⋊Dic3C22semidirect
40. C32×C4×Dic3C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88804C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. #64146D3semidirect
71. C3×D4×Dic3D3semidirect
141. C22×C3×Dic3C2×D3semidirect
176. C3×#217C2×D3semidirect
179. C3×C4⋊Dic3C2×D3semidirect
180. C3×C4×Dic3C2×D3semidirect
232. D4×Dic3C3⋊D3semidirect
354. C22×Dic3C2×C3⋊D3semidirect
379. #217C2×C3⋊D3semidirect
395. C4⋊Dic3C2×C3⋊D3semidirect
407. C4×Dic3C2×C3⋊D3semidirect
491. C33#538semidirect
689. C32#5560semidirect
690. C32#5593semidirect
771. C3#10595123semidirect
772. C3#10596031semidirect

Maximal subgroups

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

subgroupindex
#117239802
C3×#641462
C32×D4×Dic32
#117236422
#117236362
#117236322
#117236232
#117236182
#117236052
C2×#888032
#117235912
#117235042
#117234382
#117234162
#117234072
#105960313
#105951233