Finite Group Databasebeta

← #13177230

Subgroups — #13177230

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6312C211yesmaximal, characteristic, complemented
2C2×C3×#3752C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4#11723641C211yesmaximal, characteristic, complemented
5#11723636C211yesmaximal, characteristic, complemented
6#11723635C211yesmaximal, characteristic, complemented
7#11723634C211yesmaximal, characteristic, complemented
8#11723530C211yesmaximal, characteristic, complemented
9#11723527C211yesmaximal, characteristic, complemented
10#11723514C211yesmaximal, characteristic, complemented
11#11723513C211yesmaximal, characteristic, complemented
12#11723438C211yesmaximal, characteristic, complemented
13#11723433C211yesmaximal, characteristic, complemented
14#11723421C211yesmaximal, characteristic, complemented
15#11723416C211yesmaximal, characteristic, complemented
16#10596031—31nomaximal
17#10595036—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31#88864C2211yescharacteristic
32#88859C2211yescharacteristic, complemented
33#88857C2211yescharacteristic, complemented
34C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C32×C4×D4—31no—
54#64148—31no—
55#64146—31no—
56#64139—31no—
57#64138—31no—
58C4×#638—31no—
59C4×#638—34no—
60C4×#638—64no—
61C2×#3752D311yescharacteristic, complemented
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×C4×#67D314yescomplemented
71C2×C3×(C2×D3)⋊C4—34no—
72#63978—34no—
73#63977—34no—
74#63976—34no—
75#63964—34no—
76#63915—34no—
77#63912—34no—
78#63906—34no—
79#63905—34no—
80#63862—34no—
81#63859—34no—
82#63853—34no—
83#63852—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
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
92C2×C33×C4—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95#6312—22no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C4×C3⋊(C3⋊D3)—41no—
100C2×C3×C3⋊Dic3—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C32×#67—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C32×C4×D3—41no—
108#6293—41no—
109#6292—41no—
110#6292—41no—
111#6291—41no—
112#6290—41no—
113#6290—41no—
114#5560—94no—
115#5494—91no—
116C23×C3⋊D3C2×D311yescharacteristic
117C23×C3×D3—34no—
118C2×C32×D4—31no—
119C22×C32×C4—24no—
120C22×C32×C4—31no—
121C22×C32×C4C2×D314yes—
122C22×C32×C4C2×D311yescharacteristic
123C2×#638—31no—
124C2×#638—34no—
125C2×#638—31no—
126C2×#638—31no—
127C2×#638—31no—
128C2×#638—64no—
129C22×C3⋊Dic3C2×D311yescharacteristic
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—34no—
134C2×C4×C3⋊D3—64no—
135C2×#634—31no—
136C2×C3×#67C2×D314yes—
137C22×C3×Dic3—34no—
138C2×C3×C4×D3C2×D314yescomplemented
139C2×#627—34no—
140C2×#626—34no—
141C2×#626—34no—
142C2×#626—34no—
143C2×#625—34no—
144C2×#625—34no—
145C32×C4⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C42—31no—
149#3757—31no—
150#3757—34no—
151#3757—31no—
152#3757—64no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—34no—
159#3752—31no—
160#3752—64no—
161#3752C2×D311yescharacteristic
162#3752C2×D311yescharacteristic
163#3752C2×D311yescharacteristic
164#3752C2×D311yescharacteristic
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⋊Dic3—34no—
174C4×C3⋊Dic3—64no—
175C3×#217C2×D314yes—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4—34no—
179C3×(C2×D3)⋊C4—34no—
180C3×(C2×D3)⋊C4C2×D314yescomplemented
181C3×Dic3⋊C4C2×D314yescomplemented
182C3×C4×Dic3C2×D314yescomplemented
183#3724—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—
192(C2×D3)⋊Dic3—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
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—44no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C33×C4—21no—
211C33×C4—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×C4×D4—34no—
221C2×C3×C22⋊C4—91no—
222#953—91no—
223#953—91no—
224#939—94no—
225#937—94no—
226#930—94no—
227#930—91no—
228#929—94no—
229C4×#67—94no—
230C4×#67—91no—
231C4×#67—184no—
232C4×#67C3⋊D311yescharacteristic, complemented
233C2×(C2×D3)⋊C4—34no—
234#924—91no—
235#898—94no—
236#894—94no—
237#885—94no—
238#885—91no—
239#885—91no—
240#884—94no—
241#884—91no—
242#884—91no—
243#883—91no—
244#883—91no—
245#882—94no—
246#879—91no—
247#879—91no—
248#878—94no—
249#876—94no—
250#875—94no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—22no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—41no—
259C22×C3⋊D3—41no—
260C22×C3⋊D3—64no—
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—62no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—41no—
276C2×C32×C4—44no—
277C2×C32×C4—48no—
278C2×C32×C4—121no—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D314yes—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—616no—
284#638—68no—
285#638—62no—
286#638—121no—
287#638—121no—
288#638—121no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—41no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—64no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4⋊(C3⋊D3)—121no—
302C4⋊(C3⋊D3)—121no—
303C4×C3⋊D3—121no—
304C4×C3⋊D3—124no—
305C4×C3⋊D3—128no—
306#634—121no—
307C3×#67—28no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—124no—
311C2×C3×Dic3C22×D314yes—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C3×C4×D3—44no—
315#627—124no—
316#626—124no—
317#626—124no—
318#626—124no—
319#625—124no—
320#625—124no—
321#538—271noSylow
322C2×C33—22no—
323C2×C33C2×#4111yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C3⋊(C3⋊D3)—41no—
327C3×C3⋊D3—41no—
328C3×C3⋊D3—41no—
329C32×D3—41no—
330C24×C3—91no—
331C23×D3—34no—
332C2×C3×D4—34no—
333C22×C3×C4—24no—
334C22×C3×C4—34no—
335C22×C3×C4—91no—
336C22×C3×C4D3214yes—
337C22×C3×C4C2×C3⋊D311yescharacteristic
338C2×#67—94no—
339C2×#67—94no—
340C2×#67—91no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—184no—
348C2×#67C2×C3⋊D311yescharacteristic
349C22×Dic3—34no—
350C2×D12—94no—
351C2×D12—94no—
352C2×D12—91no—
353C2×C4×D3—94no—
354C2×C4×D3—91no—
355C2×C4×D3—184no—
356C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
357C2×Dic6—94no—
358C2×Dic6—91no—
359C3×C4⋊C4—34no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C42—34no—
367#217—94no—
368#217—94no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—184no—
375#217C2×C3⋊D311yescharacteristic
376(C2×D3)⋊C4—34no—
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—34no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
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, complemented
391C4⋊Dic3—94no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394Dic3⋊C4—94no—
395Dic3⋊C4—94no—
396Dic3⋊C4—94no—
397Dic3⋊C4—94no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—184no—
402Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—184no—
406C4×Dic3C2×C3⋊D311yescharacteristic, complemented
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—24no—
410C22×C32—28no—
411C22×C32—24no—
412C22×C32—24no—
413C22×C32—44no—
414C22×C32—44no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32#23518yes—
419C22×C32#23512yes—
420C22×C32C23×D314yes—
421C22×C32C23×D311yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—44no—
429C2×C3⋊D3—68no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—64no—
435C2×C3⋊D3—64no—
436C2×C3⋊D3—124no—
437C2×C3⋊D3—124no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3—64no—
445C2×C3×D3—64no—
446C2×C3×D3—64no—
447C2×C3×D3—1216no—
448C32×C4—28no—
449C32×C4—24no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—24no—
453C32×C4—44no—
454C32×C4—61no—
455C32×C4—61no—
456C32×C4—61no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—68no—
460C3⋊Dic3—64no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—61no—
464C3⋊Dic3—64no—
465C3⋊Dic3—64no—
466C3⋊Dic3—124no—
467C3⋊Dic3—124no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—64no—
472C3×Dic3—64no—
473#126—271no—
474#126—271no—
475#124—271no—
476#124—271no—
477#123—271no—
478#123—271no—
479C22⋊Q8—271no—
480#121—271no—
481#121—271no—
482#121—271no—
483#120—271no—
484#120—271no—
485C4×D4—31no—
486C4×D4—271no—
487C2×C22⋊C4—91no—
488C33#53811yescharacteristic, complemented, Sylow
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×C3C22×C3⋊D311yescharacteristic
498C22×D3—34no—
499C22×D3—34no—
500C22×D3—68no—
501C22×D3—94no—
502C22×D3—91no—
503C22×D3—124no—
504C22×D3—124no—
505C22×D3—184no—
506C22×D3C22×C3⋊D311yescharacteristic
507C3×D4—68no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—34no—
513C2×C3×C4—44no—
514C2×C3×C4—41no—
515C2×C3×C4—48no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—124no—
519C2×C3×C4—361no—
520C2×C3×C4C2×D3214yes—
521C2×C3×C4C2×D3214yes—
522C2×C3×C4C22×C3⋊D311yescharacteristic
523C2×C3×C4C22×C3⋊D311yescharacteristic
524#67—22no—
525#67—1816no—
526#67—188no—
527#67—182no—
528#67—361no—
529#67—361no—
530#67—364no—
531#67—361no—
532#67—361no—
533#67—364no—
534#67—364no—
535C2×Dic3—34no—
536C2×Dic3—34no—
537C2×Dic3—94no—
538C2×Dic3—94no—
539C2×Dic3—94no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—124no—
544C2×Dic3—184no—
545C2×Dic3—184no—
546C2×Dic3—184no—
547C2×Dic3C22×C3⋊D311yescharacteristic
548C2×Dic3C22×C3⋊D311yescharacteristic
549C2×Dic3C22×C3⋊D311yescharacteristic
550D12—364no—
551D12—364no—
552D12—361no—
553C4×D3—41no—
554C4×D3—364no—
555C4×D3—361no—
556C4×D3—368no—
557Dic6—361no—
558Dic6—364no—
559C2×C32—22no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—24no—
563C2×C32—28no—
564C2×C32—48no—
565C2×C32—121no—
566C2×C32C2×#23514yes—
567C2×C32C2×#23511yescharacteristic
568C2×C32#100414yes—
569C2×C32#100411yescharacteristic
570C2×C32#100411yescharacteristic
571C2×C32#100914yes—
572C3⋊D3—41no—
573C3⋊D3—41no—
574C3⋊D3—128no—
575C3⋊D3—121no—
576C3⋊D3—124no—
577C3×D3—44no—
578C3×D3—124no—
579C3×D3—124no—
580C24—91no—
581C2×Q8—271no—
582C2×D4—31no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—31no—
590C22×C4—91no—
591C22×C4—271no—
592C22×C4D3×C3⋊D311yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—91no—
602C22⋊C4—91no—
603C22⋊C4—91no—
604C22⋊C4—91no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C42—31no—
614C42—271no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—24no—
620C22×C3—28no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—364no—
633C22×C3#379818yes—
634C22×C3#382812yes—
635C22×C3C22×D3214yes—
636C22×C3C23×C3⋊D311yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—1216no—
647C2×D3—188no—
648C2×D3—184no—
649C2×D3—184no—
650C2×D3—184no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—364no—
655C2×D3—364no—
656C3×C4—28no—
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—44no—
662C3×C4—64no—
663C3×C4—64no—
664C3×C4—64no—
665C3×C4—181no—
666C3×C4—181no—
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—64no—
671Dic3—64no—
672Dic3—188no—
673Dic3—184no—
674Dic3—184no—
675Dic3—184no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—364no—
680Dic3—364no—
681C32—24no—
682C32#549411yescharacteristic, complemented
683C32#556014yescomplemented
684C23—31no—
685C23—91no—
686C23—91no—
687C23—182no—
688C23—271no—
689C23—361no—
690C23—361no—
691C23C2×D3×C3⋊D311yescharacteristic
692Q8—1081no—
693D4—62no—
694D4—542no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—41no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—121no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—271no—
710C2×C4—361no—
711C2×C4—1081no—
712C2×C4C2×D3×C3⋊D311yescharacteristic
713C2×C4C2×D3×C3⋊D311yescharacteristic
714C2×C3—22no—
715C2×C3—28no—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3—48no—
720C2×C3—124no—
721C2×C3—361no—
722C2×C3—361no—
723C2×C3C2×#379814yes—
724C2×C3#6430714yes—
725C2×C3#6433014yes—
726C2×C3C2×#382811yescharacteristic
727C2×C3#6436111yescharacteristic
728C2×C3#6436611yescharacteristic
729D3—41no—
730D3—124no—
731D3—124no—
732D3—368no—
733D3—361no—
734D3—364no—
735C22—21no—
736C22—21no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—181no—
746C22—364no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22#8902012yes—
751C22C22×D3×C3⋊D311yescharacteristic
752C4—21no—
753C4—21no—
754C4—61no—
755C4—61no—
756C4—61no—
757C4—181no—
758C4—181no—
759C4—541no—
760C4—541no—
761C4—541no—
762C3—24no—
763C3#1059503614yescomplemented
764C3#1059603111yescharacteristic, complemented
765C2—22no—
766C2—121no—
767C2—361no—
768C2—361no—
769C2—1081no—
770C2C2×#8902011yescharacteristic
771C2#1172458011yescharacteristic
772C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C4×#6312C2semidirect
2. C2×C3×#3752C2semidirect
3. C32×C4×#67C2semidirect
4. #11723641C2semidirect
5. #11723636C2semidirect
6. #11723635C2semidirect
7. #11723634C2semidirect
8. #11723530C2semidirect
9. #11723527C2semidirect
10. #11723514C2semidirect
11. #11723513C2semidirect
12. #11723438C2semidirect
13. #11723433C2semidirect
14. #11723421C2semidirect
15. #11723416C2semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C32×C4×D3C22semidirect
25. C2×#6293C22semidirect
28. C2×#6291C22semidirect
32. #88859C22semidirect
33. #88857C22semidirect
34. C4×C3⋊(C3⋊Dic3)C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×C4×Dic3C22semidirect
43. #88807C22semidirect
44. #88807C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
61. C2×#3752D3semidirect
70. C3×C4×#67D3semidirect
138. C2×C3×C4×D3C2×D3semidirect
180. C3×(C2×D3)⋊C4C2×D3semidirect
181. C3×Dic3⋊C4C2×D3semidirect
182. C3×C4×Dic3C2×D3semidirect
232. C4×#67C3⋊D3semidirect
356. C2×C4×D3C2×C3⋊D3semidirect
390. (C2×D3)⋊C4C2×C3⋊D3semidirect
402. Dic3⋊C4C2×C3⋊D3semidirect
406. C4×Dic3C2×C3⋊D3semidirect
488. C33#538semidirect
682. C32#5494semidirect
683. C32#5560semidirect
763. C3#10595036semidirect
764. C3#10596031semidirect

Maximal subgroups

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

subgroupindex
C4×#63122
C2×C3×#37522
C32×C4×#672
#117236412
#117236362
#117236352
#117236342
#117235302
#117235272
#117235142
#117235132
#117234382
#117234332
#117234212
#117234162
#105960313
#105950363