Finite Group Databasebeta

← #13177601

Subgroups — #13177601

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×#64145C211yesmaximal, characteristic, complemented
3C32×#937C211yesmaximal, characteristic, complemented
4#11723630C211yesmaximal, characteristic, complemented
5#11723628C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#11723616C211yesmaximal, characteristic, complemented
8D3×#3757C211yesmaximal, characteristic, complemented
9#11723603C211yesmaximal, characteristic, complemented
10#11723599C211yesmaximal, characteristic, complemented
11#11723597C211yesmaximal, characteristic, complemented
12#11723521C211yesmaximal, characteristic, complemented
13#11723487C211yesmaximal, characteristic, complemented
14#11723461C211yesmaximal, characteristic, complemented
15#11723428C211yesmaximal, characteristic, complemented
16#10596064—31nomaximal
17#10595184—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C2×C3×#634C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6289C2211yescharacteristic, complemented
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31#88864C2211yescharacteristic
32#88859C2211yescharacteristic, complemented
33#88857C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic, complemented
37C3×#3757C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42#88807C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#120—31no—
54#64162—31no—
55C2×#3757—31no—
56#64148—31no—
57#64148—31no—
58#64148—34no—
59#64148—64no—
60#64147—31no—
61#64145D311yescharacteristic, complemented
62#64144—31no—
63D4×C3⋊Dic3—31no—
64#64094—31no—
65#64092—31no—
66#64090—31no—
67#64088—31no—
68#64088—31no—
69#64087—31no—
70C3×#937D314yescomplemented
71C3×#936—34no—
72#63977—34no—
73#63975—34no—
74#67⋊Dic3—34no—
75#63971—34no—
76D3×#217—34no—
77#63962—34no—
78#63958—34no—
79#63956—34no—
80#63907—34no—
81#63887—34no—
82#63880—34no—
83#63859—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C32×D3—22no—
88C22×C32×D3—41no—
89C22×C32×D3—41no—
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×D4—41no—
93C2×C33×C4C2311yescharacteristic
94#6312—41no—
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)—41no—
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C3×#634—41no—
105C32×#67—22no—
106C32×#67—41no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6291—22no—
110#6291—41no—
111#6289—41no—
112D3×C3⋊Dic3—41no—
113D3×C3⋊Dic3—41no—
114#5678—91no—
115#5593—94no—
116C24×C32—31no—
117C23×C3×D3C2×D314yes—
118C2×C32×D4—24no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4C2×D314yes—
122C2×C32×D4C2×D311yescharacteristic
123C2×#638—31no—
124C2×#638—31no—
125C2×#638—34no—
126C2×#638—34no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—64no—
130C2×#638—64no—
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—34no—
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—64no—
136C2×C4×C3⋊D3—31no—
137C2×#634C2×D311yescharacteristic, complemented
138C2×C3×#67C2×D314yes—
139C2×C3×#67C2×D314yes—
140C2×C3×Dic6—34no—
141C2×#626—34no—
142C2×#626—34no—
143C2×#624—34no—
144C2×D3×Dic3—34no—
145C2×D3×Dic3—34no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149#3757—31no—
150#3757—34no—
151#3757—31no—
152#3757—31no—
153#3757—31no—
154#3757—31no—
155#3757—64no—
156#3757C2×D311yescharacteristic
157#3757C2×D311yescharacteristic
158#3757C2×D311yescharacteristic, complemented
159#3757C2×D311yescharacteristic, complemented
160#3752—31no—
161#3752—34no—
162#3752—31no—
163#3752—64no—
164C4⋊(C3⋊Dic3)—31no—
165C4⋊(C3⋊Dic3)—31no—
166#3750—31no—
167#3750—34no—
168#3750—31no—
169#3750—31no—
170#3750—31no—
171#3750—64no—
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3C2×D311yescharacteristic, complemented
174C3×#217—34no—
175C3×#217—34no—
176C3×#217—34no—
177C3×#217—34no—
178C3×#217C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×(C2×D3)⋊C4C2×D314yes—
181C3×C4×Dic3—34no—
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185Dic3⋊Dic3—34no—
186Dic3⋊Dic3—34no—
187#3722—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—21no—
199C22×C33C2411yescharacteristic
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—44no—
209C2×C32×D3#4112yes—
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—
217C3×C3⋊Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#124—91no—
221C3×#120—34no—
222#953—94no—
223C2×#217—94no—
224#947—91no—
225#946—91no—
226#939—94no—
227#939—94no—
228#939—91no—
229#939—184no—
230#938—94no—
231#937C3⋊D311yescharacteristic, complemented
232#936—34no—
233#935—94no—
234D4×Dic3—94no—
235#886—91no—
236#885—94no—
237#884—91no—
238#884—91no—
239#883—94no—
240#883—91no—
241#882—91no—
242#67⋊C4—94no—
243#67⋊C4—91no—
244D3×C22⋊C4—91no—
245#879—94no—
246#879—94no—
247#879—91no—
248#878—94no—
249#876—91no—
250C4×D12—91no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32—62no—
256C23×C32—121no—
257C23×C32—121no—
258C23×C32C22×D314yes—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3⋊D3—34no—
264C22×C3⋊D3—64no—
265C22×C3×D3—28no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3C22×D314yes—
269C22×C3×D3C22×D314yes—
270C32×D4—41no—
271C32×D4—44no—
272C32×D4—48no—
273C32×D4—62no—
274C32×D4—121no—
275C2×C32×C4—24no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4C22×D314yes—
279C2×C32×C4C22×D311yescharacteristic
280#638—62no—
281#638—121no—
282#638—121no—
283#638—121no—
284#638—124no—
285#638—124no—
286#638—128no—
287#638—128no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—34no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—121no—
298C2×C3⋊Dic3—121no—
299C2×C3⋊Dic3—121no—
300C2×C3⋊Dic3—124no—
301C2×C3⋊Dic3—128no—
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C4×C3⋊D3—121no—
307#634—41no—
308C3×#67—28no—
309C3×#67—44no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3C22×D314yes—
315C2×C3×Dic3C22×D314yes—
316C3×Dic6—124no—
317#626—68no—
318#626—124no—
319#624—124no—
320D3×Dic3—124no—
321D3×Dic3—124no—
322#538—271noSylow
323C2×C33—41no—
324C2×C33—41no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C3⋊(C3⋊D3)—41no—
329C32×D3—22no—
330C32×D3—41no—
331C24×C3—34no—
332C23×D3C2×C3⋊D311yescharacteristic
333C2×C3×Q8—91no—
334C2×C3×D4—24no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4D3214yes—
338C2×C3×D4C2×C3⋊D311yescharacteristic
339C2×#67—94no—
340C2×#67—94no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—184no—
346C2×#67—184no—
347C2×#67C2×C3⋊D311yescharacteristic
348C2×#67C2×C3⋊D311yescharacteristic
349C22×Dic3—94no—
350C22×Dic3—94no—
351C22×Dic3—94no—
352C22×Dic3—91no—
353C22×Dic3—184no—
354C2×D12—91no—
355C2×D12—91no—
356C2×C4×D3—94no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×Dic6—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C42—91no—
369#217—34no—
370#217—34no—
371#217—34no—
372#217—34no—
373#217—94no—
374#217—94no—
375#217—94no—
376#217—94no—
377#217—94no—
378#217—91no—
379#217—184no—
380#217C2×C3⋊D311yescharacteristic
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—184no—
390(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
391(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
392C4⋊Dic3—94no—
393C4⋊Dic3—94no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
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—34no—
406C4×Dic3—94no—
407C4×Dic3—91no—
408C22×C32—28no—
409C22×C32—24no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—32no—
423C22×C32—44no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—124no—
434C22×C32C23×D314yes—
435C22×C32C23×D311yescharacteristic
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—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C2×C3×D3—24no—
450C2×C3×D3—416no—
451C2×C3×D3#23718yes—
452C32×C4—21no—
453C32×C4—24no—
454C32×C4—44no—
455C32×C4—61no—
456C32×C4—61no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—68no—
462C3⋊Dic3—64no—
463C3⋊Dic3—61no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—64no—
467C3⋊Dic3—64no—
468C3⋊Dic3—124no—
469C3⋊Dic3—124no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—64no—
473C3×Dic3—64no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476#126—271no—
477#126—271no—
478#124—91no—
479#124—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485#121—271no—
486#120—31no—
487#120—271no—
488C4×D4—271no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C33#53811yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—34no—
495C23×C3—34no—
496C23×C3—68no—
497C23×C3—124no—
498C23×C3—124no—
499C23×C3C2×D3214yes—
500C23×C3C2×D3214yes—
501C23×C3C22×C3⋊D311yescharacteristic
502C23×C3C22×C3⋊D311yescharacteristic
503C22×D3—22no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—94no—
507C22×D3—91no—
508C22×D3—184no—
509C22×D3C22×C3⋊D311yescharacteristic
510C22×D3C22×C3⋊D311yescharacteristic
511C3×Q8—361no—
512C3×D4—44no—
513C3×D4—41no—
514C3×D4—48no—
515C3×D4—68no—
516C3×D4—124no—
517C2×C3×C4—24no—
518C2×C3×C4—34no—
519C2×C3×C4—34no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4C2×D3214yes—
525C2×C3×C4C22×C3⋊D311yescharacteristic
526#67—22no—
527#67—41no—
528#67—188no—
529#67—364no—
530#67—364no—
531#67—364no—
532#67—361no—
533#67—361no—
534#67—368no—
535#67—368no—
536C2×Dic3—34no—
537C2×Dic3—34no—
538C2×Dic3—34no—
539C2×Dic3—34no—
540C2×Dic3—94no—
541C2×Dic3—94no—
542C2×Dic3—94no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—184no—
547C2×Dic3—184no—
548C2×Dic3—184no—
549C2×Dic3—364no—
550C2×Dic3—364no—
551C2×Dic3—364no—
552C2×Dic3—361no—
553C2×Dic3—368no—
554C2×Dic3C22×C3⋊D311yescharacteristic
555C2×Dic3C22×C3⋊D311yescharacteristic
556D12—182no—
557D12—361no—
558C4×D3—361no—
559C4×D3—364no—
560C4×D3—361no—
561C4×D3—361no—
562Dic6—124no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—48no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—44no—
570C2×C32—44no—
571C2×C32—62no—
572C2×C32—84no—
573C2×C32—121no—
574C2×C32C2×#23714yes—
575C2×C32#100414yes—
576C2×C32#100414yes—
577C2×C32#100411yescharacteristic
578C2×C32D3×#4111yescharacteristic
579C2×C32#100911yescharacteristic
580C3⋊D3—121no—
581C3⋊D3—124no—
582C3⋊D3—244no—
583C3×D3—28no—
584C3×D3—44no—
585C24—31no—
586C2×Q8—91no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4D3×C3⋊D311yescharacteristic
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C42—91no—
619C42—271no—
620C22×C3—28no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—24no—
634C22×C3—38no—
635C22×C3—44no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—44no—
640C22×C3—64no—
641C22×C3—64no—
642C22×C3—64no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—1216no—
646C22×C3C22×D3214yes—
647C22×C3C23×C3⋊D311yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—44no—
654C2×D3—184no—
655C2×D3—184no—
656C2×D3—184no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—364no—
661C2×D3—364no—
662C2×D3—364no—
663C2×D3#383012yes—
664C3×C4—24no—
665C3×C4—21no—
666C3×C4—44no—
667C3×C4—64no—
668C3×C4—64no—
669C3×C4—181no—
670C3×C4—181no—
671C3×C4—181no—
672C3×C4—181no—
673Dic3—21no—
674Dic3—21no—
675Dic3—64no—
676Dic3—64no—
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#559314yescomplemented
690C32#567811yescharacteristic, complemented
691C23—31no—
692C23—31no—
693C23—62no—
694C23—121no—
695C23—121no—
696C23—271no—
697C23C2×D3×C3⋊D311yescharacteristic
698C23C2×D3×C3⋊D311yescharacteristic
699Q8—361no—
700D4—41no—
701D4—62no—
702D4—121no—
703D4—542no—
704D4—1081no—
705D4—1081no—
706D4—1081no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—271no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—1081no—
717C2×C4—1081no—
718C2×C4—1081no—
719C2×C4—1081no—
720C2×C4C2×D3×C3⋊D311yescharacteristic
721C2×C3—24no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—48no—
725C2×C3—44no—
726C2×C3—44no—
727C2×C3—41no—
728C2×C3—41no—
729C2×C3—68no—
730C2×C3—84no—
731C2×C3—124no—
732C2×C3D3×#23714yes—
733C2×C3#6431414yes—
734C2×C3#6433014yes—
735C2×C3C2×#383011yescharacteristic
736C2×C3#6436111yescharacteristic
737C2×C3#6436111yescharacteristic
738D3—22no—
739D3—41no—
740D3—364no—
741D3—361no—
742D3—724no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—32no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—124no—
756C22—541no—
757C22—541no—
758C22—541no—
759C22C22×D3×C3⋊D311yescharacteristic
760C4—21no—
761C4—61no—
762C4—61no—
763C4—181no—
764C4—181no—
765C4—181no—
766C4—181no—
767C4—541no—
768C4—541no—
769C4—541no—
770C3—24no—
771C3#1059518414yescomplemented
772C3#1059606411yescharacteristic, complemented
773C2—41no—
774C2—41no—
775C2—62no—
776C2—121no—
777C2—1081no—
778C2D3×#383011yescharacteristic
779C2#1172458811yescharacteristic
780C2#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. #11723980C2semidirect
2. C3×#64145C2semidirect
3. C32×#937C2semidirect
4. #11723630C2semidirect
5. #11723628C2semidirect
6. #67⋊(C3⋊Dic3)C2semidirect
7. #11723616C2semidirect
8. D3×#3757C2semidirect
9. #11723603C2semidirect
10. #11723599C2semidirect
11. #11723597C2semidirect
12. #11723521C2semidirect
13. #11723487C2semidirect
14. #11723461C2semidirect
15. #11723428C2semidirect
21. C2×#6312C22semidirect
22. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#634C22semidirect
28. C2×#6289C22semidirect
32. #88859C22semidirect
33. #88857C22semidirect
36. C3×#3757C22semidirect
37. C3×#3757C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
42. #88807C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
61. #64145D3semidirect
70. C3×#937D3semidirect
137. C2×#634C2×D3semidirect
158. #3757C2×D3semidirect
159. #3757C2×D3semidirect
173. C4×C3⋊Dic3C2×D3semidirect
231. #937C3⋊D3semidirect
491. C33#538semidirect
689. C32#5593semidirect
690. C32#5678semidirect
771. C3#10595184semidirect
772. C3#10596064semidirect

Maximal subgroups

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

subgroupindex
#117239802
C3×#641452
C32×#9372
#117236302
#117236282
#67⋊(C3⋊Dic3)2
#117236162
D3×#37572
#117236032
#117235992
#117235972
#117235212
#117234872
#117234612
#117234282
#105960643
#105951843