Finite Group Databasebeta

← #13177615

Subgroups — #13177615

Order 1728.

2020 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723978C211yesmaximal, characteristic, complemented
2C3×#64145C211yesmaximal, characteristic, complemented
3C32×#939C211yesmaximal, characteristic, complemented
4#11723638C211yesmaximal, characteristic, complemented
5#11723627C211yesmaximal, characteristic, complemented
6#11723618C211yesmaximal, characteristic, complemented
7#11723616C211yesmaximal, characteristic, complemented
8#11723614C211yesmaximal, characteristic, complemented
9#11723612C211yesmaximal, characteristic, complemented
10#11723599C211yesmaximal, characteristic, complemented
11#11723596C211yesmaximal, characteristic, complemented
12#11723521C211yesmaximal, characteristic, complemented
13#11723489C211yesmaximal, characteristic, complemented
14#11723461C211yesmaximal, characteristic, complemented
15#11723446C211yesmaximal, characteristic, complemented
16#10596084—31nomaximal
17#10595207—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#634C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31#88864C2211yescharacteristic
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic, complemented
37C3×#3757C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#121—31no—
54#64148—31no—
55#64147—31no—
56#64146—31no—
57#64146—31no—
58#64146—34no—
59#64146—64no—
60#64145D311yescharacteristic, complemented
61#64144—31no—
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×#939D314yescomplemented
71C3×#936—34no—
72#63981—34no—
73#63974—34no—
74#63971—34no—
75#63969—34no—
76#63966—34no—
77#63958—34no—
78#63956—34no—
79#63952—34no—
80#63907—34no—
81#63888—34no—
82#63880—34no—
83#63868—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)—22no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)—41no—
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×D4—41no—
93C2×C33×C4C2311yescharacteristic
94#6312—22no—
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C3×#634—41no—
103C32×#67—41no—
104C32×#67—41no—
105C2×C32×Dic3—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6291—22no—
110#6291—41no—
111#6289—41no—
112#6289—41no—
113D3×C3⋊Dic3—41no—
114#5678—91no—
115#5613—94no—
116C23×C3⋊D3—31no—
117C23×C3⋊D3—34no—
118C23×C3⋊D3—64no—
119C2×C32×D4—24no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4C2×D314yes—
123C2×C32×D4C2×D311yescharacteristic
124C22×C32×C4—31no—
125C2×#638—31no—
126C2×#638—34no—
127C2×#638—31no—
128C2×#638—34no—
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—64no—
132C2×#638—64no—
133C22×C3⋊Dic3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×#634C2×D311yescharacteristic, complemented
137C2×C3×#67C2×D314yes—
138C2×C3×#67C2×D314yescomplemented
139C22×C3×Dic3C2×D314yescomplemented
140C2×C3×Dic6—34no—
141C2×#626—34no—
142C2×#626—34no—
143C2×#624—34no—
144C2×#624—34no—
145C2×D3×Dic3—34no—
146C32×C4⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149#3757—31no—
150#3757—34no—
151#3757—31no—
152#3757—64no—
153#3757C2×D311yescharacteristic
154#3757C2×D311yescharacteristic
155#3757C2×D311yescharacteristic, complemented
156#3757C2×D311yescharacteristic, complemented
157#3752—31no—
158#3752—31no—
159#3752—34no—
160#3752—34no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—64no—
166#3752—64no—
167C4⋊(C3⋊Dic3)—31no—
168#3750—31no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
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×D314yescomplemented
180C3×Dic3⋊C4C2×D314yescomplemented
181C3×C4×Dic3—34no—
182#3724—34no—
183#3724—34no—
184Dic3⋊Dic3—34no—
185Dic3⋊Dic3—34no—
186Dic3⋊Dic3—34no—
187#3722—34no—
188#3722—34no—
189#3722—34no—
190#3722—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×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×#124—91no—
221C3×#121—34no—
222#947—91no—
223#946—91no—
224#939—94no—
225#939C3⋊D311yescharacteristic, complemented
226#938—94no—
227#937—94no—
228#937—94no—
229#937—91no—
230#937—184no—
231#936—34no—
232#935—94no—
233#929—94no—
234C4×#67—94no—
235#898—94no—
236#896—94no—
237#886—91no—
238#885—94no—
239#884—91no—
240#884—91no—
241#883—91no—
242#882—91no—
243#67⋊C4—94no—
244#67⋊C4—91no—
245D3×C22⋊C4—94no—
246D3×C22⋊C4—91no—
247#879—94no—
248#879—91no—
249#876—91no—
250C4×D12—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—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—34no—
261C22×C3⋊D3—34no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3—64no—
264C22×C3⋊D3—62no—
265C22×C3⋊D3—68no—
266C22×C3⋊D3—128no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3—124no—
270C22×C3⋊D3—124no—
271C22×C3⋊D3—128no—
272C22×C3⋊D3—128no—
273C22×C3×D3C22×D314yes—
274C32×D4—41no—
275C32×D4—44no—
276C32×D4—48no—
277C32×D4—121no—
278C32×D4—121no—
279C2×C32×C4—24no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—121no—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D311yescharacteristic
286#638—62no—
287#638—62no—
288#638—68no—
289#638—128no—
290#638—121no—
291#638—121no—
292#638—124no—
293#638—128no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—34no—
297C2×C3⋊Dic3—34no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3—64no—
300C2×C3⋊Dic3—121no—
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C4×C3⋊D3—121no—
306C4×C3⋊D3—121no—
307#634—41no—
308C3×#67—44no—
309C3×#67—44no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318C3×Dic6—124no—
319#626—68no—
320#626—124no—
321#624—124no—
322#624—124no—
323D3×Dic3—124no—
324#538—271noSylow
325C2×C33—41no—
326C2×C33—41no—
327C2×C33C2×#4111yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C2×C33H(5,𝔽2)11yescharacteristic
330C3⋊(C3⋊D3)—22no—
331C3⋊(C3⋊D3)—41no—
332C32×D3—41no—
333C23×D3—94no—
334C23×D3—91no—
335C23×D3—184no—
336C2×C3×Q8—91no—
337C2×C3×D4—24no—
338C2×C3×D4—34no—
339C2×C3×D4—34no—
340C2×C3×D4D3214yes—
341C2×C3×D4C2×C3⋊D311yescharacteristic
342C22×C3×C4—34no—
343C2×#67—94no—
344C2×#67—94no—
345C2×#67—94no—
346C2×#67—91no—
347C2×#67—94no—
348C2×#67—91no—
349C2×#67—184no—
350C2×#67—184no—
351C2×#67C2×C3⋊D311yescharacteristic
352C2×#67C2×C3⋊D311yescharacteristic, complemented
353C22×Dic3—94no—
354C22×Dic3C2×C3⋊D311yescharacteristic, complemented
355C2×D12—91no—
356C2×D12—91no—
357C2×C4×D3—94no—
358C2×C4×D3—94no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×Dic6—34no—
363C3×C4⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4—91no—
370C3×C42—91no—
371#217—34no—
372#217—34no—
373#217—34no—
374#217—34no—
375#217—94no—
376#217—94no—
377#217—91no—
378#217—184no—
379#217C2×C3⋊D311yescharacteristic
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—184no—
394(C2×D3)⋊C4—184no—
395(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
396C4⋊Dic3—94no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399Dic3⋊C4—94no—
400Dic3⋊C4—94no—
401Dic3⋊C4—94no—
402Dic3⋊C4—94no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
407C4×Dic3—34no—
408C4×Dic3—94no—
409C4×Dic3—91no—
410C22×C32—28no—
411C22×C32—21no—
412C22×C32—24no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—24no—
423C22×C32—24no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—44no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32C23×D314yes—
433C22×C32C23×D311yescharacteristic
434C2×C3⋊D3—32no—
435C2×C3⋊D3—38no—
436C2×C3⋊D3—68no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—68no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—64no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—124no—
449C2×C3⋊D3—124no—
450C2×C3⋊D3—124no—
451C2×C3⋊D3—124no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—1216no—
454C2×C3⋊D3—1232no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C32×C4—21no—
459C32×C4—24no—
460C32×C4—44no—
461C32×C4—61no—
462C32×C4—61no—
463C32×C4—61no—
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3⋊Dic3—21no—
468C3⋊Dic3—61no—
469C3⋊Dic3—61no—
470C3⋊Dic3—64no—
471C3⋊Dic3—64no—
472C3⋊Dic3—124no—
473C3⋊Dic3—124no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476C3×Dic3—24no—
477C3×Dic3—64no—
478C3×Dic3—64no—
479C3×Dic3—64no—
480C3×Dic3—64no—
481#126—271no—
482#126—271no—
483#124—91no—
484#124—271no—
485#123—271no—
486#123—271no—
487C22⋊Q8—271no—
488#121—31no—
489#121—271no—
490#121—271no—
491#120—271no—
492#120—271no—
493C4×D4—271no—
494C4×D4—271no—
495C2×C22⋊C4—271no—
496C33#53811yescharacteristic, complemented, Sylow
497C23×C3—24no—
498C23×C3—24no—
499C23×C3—34no—
500C23×C3C2×D3214yes—
501C23×C3C2×D3214yes—
502C23×C3C22×C3⋊D311yescharacteristic
503C23×C3C22×C3⋊D311yescharacteristic
504C22×D3—94no—
505C22×D3—91no—
506C22×D3—94no—
507C22×D3—91no—
508C22×D3—184no—
509C22×D3—184no—
510C22×D3—182no—
511C22×D3—188no—
512C22×D3—368no—
513C22×D3—364no—
514C22×D3—364no—
515C22×D3—361no—
516C22×D3—361no—
517C22×D3—368no—
518C22×D3—368no—
519C22×D3C22×C3⋊D311yescharacteristic
520C3×Q8—361no—
521C3×D4—44no—
522C3×D4—41no—
523C3×D4—48no—
524C3×D4—124no—
525C3×D4—124no—
526C2×C3×C4—24no—
527C2×C3×C4—34no—
528C2×C3×C4—34no—
529C2×C3×C4—34no—
530C2×C3×C4—91no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—124no—
535C2×C3×C4C2×D3214yes—
536C2×C3×C4C22×C3⋊D311yescharacteristic
537#67—41no—
538#67—41no—
539#67—188no—
540#67—182no—
541#67—188no—
542#67—368no—
543#67—364no—
544#67—364no—
545#67—361no—
546#67—368no—
547C2×Dic3—34no—
548C2×Dic3—34no—
549C2×Dic3—34no—
550C2×Dic3—34no—
551C2×Dic3—41no—
552C2×Dic3—94no—
553C2×Dic3—94no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—184no—
557C2×Dic3—184no—
558C2×Dic3—364no—
559C2×Dic3C22×C3⋊D311yescharacteristic
560C2×Dic3C22×C3⋊D311yescharacteristic
561C2×Dic3C22×C3⋊D311yescharacteristic
562D12—182no—
563D12—361no—
564C4×D3—361no—
565C4×D3—361no—
566C4×D3—364no—
567C4×D3—364no—
568C4×D3—361no—
569Dic6—124no—
570C2×C32—24no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—48no—
574C2×C32—41no—
575C2×C32—41no—
576C2×C32—44no—
577C2×C32—44no—
578C2×C32—84no—
579C2×C32—121no—
580C2×C32#100414yes—
581C2×C32#100414yes—
582C2×C32#100411yescharacteristic
583C2×C32D3×#4114yes—
584C2×C32D3×#4111yescharacteristic
585C2×C32#100911yescharacteristic
586C3⋊D3—62no—
587C3⋊D3—68no—
588C3⋊D3—128no—
589C3⋊D3—128no—
590C3⋊D3—121no—
591C3⋊D3—124no—
592C3×D3—44no—
593C24—271no—
594C2×Q8—91no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—271no—
598C2×D4—271no—
599C2×D4—271no—
600C2×D4—271no—
601C2×D4D3×C3⋊D311yescharacteristic
602C22×C4—31no—
603C22×C4—271no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—271no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C42—91no—
627C42—271no—
628C22×C3—28no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—24no—
634C22×C3—24no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—24no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—64no—
648C22×C3—64no—
649C22×C3—64no—
650C22×C3C22×D3214yes—
651C22×C3C23×C3⋊D311yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—98no—
656C2×D3—92no—
657C2×D3—188no—
658C2×D3—184no—
659C2×D3—184no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—188no—
663C2×D3—184no—
664C2×D3—184no—
665C2×D3—184no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—364no—
670C2×D3—364no—
671C2×D3—364no—
672C2×D3—364no—
673C2×D3—3616no—
674C2×D3—364no—
675C2×D3—3632no—
676C3×C4—24no—
677C3×C4—21no—
678C3×C4—44no—
679C3×C4—64no—
680C3×C4—64no—
681C3×C4—64no—
682C3×C4—181no—
683C3×C4—181no—
684C3×C4—181no—
685C3×C4—181no—
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—64no—
690Dic3—64no—
691Dic3—64no—
692Dic3—64no—
693Dic3—184no—
694Dic3—184no—
695Dic3—181no—
696Dic3—181no—
697Dic3—364no—
698Dic3—364no—
699C32—24no—
700C32#561314yescomplemented
701C32#567811yescharacteristic, complemented
702C23—31no—
703C23—271no—
704C23—271no—
705C23—542no—
706C23—1081no—
707C23—1081no—
708C23C2×D3×C3⋊D311yescharacteristic
709C23C2×D3×C3⋊D311yescharacteristic
710Q8—361no—
711D4—41no—
712D4—121no—
713D4—121no—
714D4—542no—
715D4—542no—
716D4—1081no—
717D4—1081no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—271no—
727C2×C4—271no—
728C2×C4—1081no—
729C2×C4—1081no—
730C2×C4—1081no—
731C2×C4C2×D3×C3⋊D311yescharacteristic
732C2×C3—24no—
733C2×C3—24no—
734C2×C3—24no—
735C2×C3—48no—
736C2×C3—44no—
737C2×C3—44no—
738C2×C3—41no—
739C2×C3—41no—
740C2×C3—84no—
741C2×C3—124no—
742C2×C3#6431214yes—
743C2×C3#6431414yes—
744C2×C3#6433014yes—
745C2×C3#6436111yescharacteristic
746C2×C3#6436111yescharacteristic
747C2×C3#41×C3⋊D311yescharacteristic
748D3—41no—
749D3—188no—
750D3—182no—
751D3—368no—
752D3—368no—
753D3—364no—
754D3—361no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—272no—
765C22—541no—
766C22—541no—
767C22—541no—
768C22—541no—
769C22—541no—
770C22—1084no—
771C22C22×D3×C3⋊D311yescharacteristic
772C4—21no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—181no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—541no—
781C4—541no—
782C3—24no—
783C3#1059520714yescomplemented
784C3#1059608411yescharacteristic, complemented
785C2—41no—
786C2—41no—
787C2—121no—
788C2—542no—
789C2—1081no—
790C2#1172458611yescharacteristic
791C2#1172458811yescharacteristic
792C2#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. #11723978C2semidirect
2. C3×#64145C2semidirect
3. C32×#939C2semidirect
4. #11723638C2semidirect
5. #11723627C2semidirect
6. #11723618C2semidirect
7. #11723616C2semidirect
8. #11723614C2semidirect
9. #11723612C2semidirect
10. #11723599C2semidirect
11. #11723596C2semidirect
12. #11723521C2semidirect
13. #11723489C2semidirect
14. #11723461C2semidirect
15. #11723446C2semidirect
22. C2×C3×#634C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
36. C3×#3757C22semidirect
37. C3×#3757C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88807C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
60. #64145D3semidirect
70. C3×#939D3semidirect
136. C2×#634C2×D3semidirect
138. C2×C3×#67C2×D3semidirect
139. C22×C3×Dic3C2×D3semidirect
155. #3757C2×D3semidirect
156. #3757C2×D3semidirect
173. C4×C3⋊Dic3C2×D3semidirect
179. C3×(C2×D3)⋊C4C2×D3semidirect
180. C3×Dic3⋊C4C2×D3semidirect
225. #939C3⋊D3semidirect
352. C2×#67C2×C3⋊D3semidirect
354. C22×Dic3C2×C3⋊D3semidirect
395. (C2×D3)⋊C4C2×C3⋊D3semidirect
406. Dic3⋊C4C2×C3⋊D3semidirect
496. C33#538semidirect
700. C32#5613semidirect
701. C32#5678semidirect
783. C3#10595207semidirect
784. C3#10596084semidirect

Maximal subgroups

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

subgroupindex
#117239782
C3×#641452
C32×#9392
#117236382
#117236272
#117236182
#117236162
#117236142
#117236122
#117235992
#117235962
#117235212
#117234892
#117234612
#117234462
#105960843
#105952073