Finite Group Databasebeta

← #13175341

Subgroups — #13175341

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C3⋊(C3⋊D3))C211yesmaximal, characteristic, complemented
2C3×#64085C211yesmaximal, characteristic, complemented
3C32×#872C211yesmaximal, characteristic, complemented
4#11723527C211yesmaximal, characteristic, complemented
5#11723525C211yesmaximal, characteristic, complemented
6#11723523C211yesmaximal, characteristic, complemented
7#11723514C211yesmaximal, characteristic, complemented
8#11723510C211yesmaximal, characteristic, complemented
9#11723486C211yesmaximal, characteristic, complemented
10#11723472C211yesmaximal, characteristic, complemented
11#11723471C211yesmaximal, characteristic, complemented
12#11723470C211yesmaximal, characteristic, complemented
13#11723453C211yesmaximal, characteristic, complemented
14#11723420C211yesmaximal, characteristic, complemented
15#11723400C211yesmaximal, characteristic, complemented
16#10596001—31nomaximal
17#10593937—34nomaximal
18C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C33×C42C2211yescharacteristic
31#88859C2211yescharacteristic
32#88859C2211yescharacteristic
33C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×C4×Dic3C2211yescharacteristic
45#88807C2211yescharacteristic
46#88806C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×#117—31no—
54#64139—31no—
55C4×#638—31no—
56#64104—31no—
57#64102—31no—
58C4⋊C4×C3⋊D3—31no—
59#64099—31no—
60#64093—31no—
61#64093—31no—
62#64092—31no—
63#64092—31no—
64#64085—31no—
65#64085D311yescharacteristic, complemented
66C4×C4⋊(C3⋊D3)—31no—
67C4×C4⋊(C3⋊D3)—31no—
68C4×C4⋊(C3⋊D3)—34no—
69C4×C4⋊(C3⋊D3)—64no—
70C3×#876—34no—
71C3×#872D314yescomplemented
72#63912—34no—
73#63910—34no—
74#63910—34no—
75#63906—34no—
76#63904—34no—
77#63891—34no—
78#63883—34no—
79#63881—34no—
80#63880—34no—
81#63868—34no—
82#63853—34no—
83#63845—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C4⋊(C3⋊(C3⋊D3))—22no—
94C4×C3⋊(C3⋊D3)—41no—
95C4×C3⋊(C3⋊D3)—41no—
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C32×C4×D3—22no—
103#6292—22no—
104#6292—22no—
105#6291—22no—
106#6291—41no—
107#6290—41no—
108#6289—22no—
109#6289—41no—
110Dic3×C3⋊D3—41no—
111#5709—91no—
112#5530—94no—
113C22×C32×C4—31no—
114C2×#638—31no—
115C2×#638—31no—
116C2×#638—31no—
117C2×C4⋊(C3⋊D3)—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4⋊(C3⋊D3)—34no—
121C2×C4⋊(C3⋊D3)—64no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—34no—
127C2×C4×C3⋊D3—34no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—64no—
130C2×C4×C3⋊D3—64no—
131C2×C3×C4×D3C2×D314yes—
132C2×#626—34no—
133C2×#626—34no—
134C2×#626—34no—
135C2×#626—34no—
136C2×#625—34no—
137C2×#624—34no—
138C2×#624—34no—
139C2×D3×Dic3—34no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C22⋊C4—31no—
143C32×C22⋊C4—31no—
144C32×C42—24no—
145C32×C42—31no—
146C32×C42C2×D314yes—
147C32×C42C2×D311yescharacteristic
148#3757—31no—
149#3752—31no—
150#3752—31no—
151#3752—34no—
152#3752—34no—
153#3752—31no—
154#3752—31no—
155#3752—64no—
156#3752—64no—
157#3752C2×D311yescharacteristic
158#3752C2×D311yescharacteristic
159#3752C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—34no—
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)—31no—
164C4⋊(C3⋊Dic3)—64no—
165#3750—31no—
166#3750—31no—
167#3750C2×D311yescharacteristic
168#3750C2×D311yescharacteristic
169#3750C2×D311yescharacteristic
170C4×C3⋊Dic3—31no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×Dic3⋊C4—34no—
177C3×Dic3⋊C4—34no—
178C3×Dic3⋊C4—34no—
179C3×Dic3⋊C4C2×D314yes—
180C3×Dic3⋊C4C2×D314yes—
181C3×C4×Dic3C2×D314yes—
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185Dic3⋊Dic3—34no—
186#3722—34no—
187#3722—34no—
188(C2×D3)⋊Dic3—34no—
189Dic32—34no—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)—21no—
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)#4112yes—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3#4112yes—
214C3×#126—91no—
215C3×#117—34no—
216#930—94no—
217C4×#67—94no—
218#898—91no—
219#895—94no—
220#895—91no—
221#894—91no—
222#893—94no—
223#893—91no—
224D3×C4⋊C4—94no—
225D3×C4⋊C4—91no—
226#890—94no—
227#889—91no—
228#886—91no—
229#884—94no—
230#884—94no—
231#884—91no—
232#884—91no—
233#884—91no—
234#883—94no—
235#883—94no—
236#67⋊C4—91no—
237#67⋊C4—91no—
238#876—34no—
239#876—94no—
240C4×D12—94no—
241C4×D12—94no—
242C4×D12—91no—
243C4×D12—184no—
244#872C3⋊D311yescharacteristic, complemented
245C23×C32—31no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—34no—
249C22×C3⋊D3—34no—
250C22×C3⋊D3—64no—
251C22×C3⋊D3—64no—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3C22×D314yes—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—62no—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—62no—
269#638—121no—
270#638—121no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—34no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—64no—
276C2×C3⋊Dic3—64no—
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D311yescharacteristic
279C2×C3⋊Dic3C22×D311yescharacteristic
280C4⋊(C3⋊D3)—62no—
281C4⋊(C3⋊D3)—68no—
282C4⋊(C3⋊D3)—616no—
283C4⋊(C3⋊D3)—62no—
284C4⋊(C3⋊D3)—62no—
285C4×C3⋊D3—62no—
286C4×C3⋊D3—121no—
287C4×C3⋊D3—121no—
288C4×C3⋊D3—121no—
289C4×C3⋊D3—124no—
290C4×C3⋊D3—124no—
291C4×C3⋊D3—121no—
292C4×C3⋊D3—128no—
293C4×C3⋊D3—128no—
294C2×C3×Dic3—34no—
295C2×C3×Dic3—34no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3C22×D314yes—
298C2×C3×Dic3C22×D314yes—
299C2×C3×Dic3C22×D314yes—
300C3×C4×D3—28no—
301#626—68no—
302#626—68no—
303#626—68no—
304#626—124no—
305#625—124no—
306#624—68no—
307#624—124no—
308D3×Dic3—124no—
309#553—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C3⋊(C3⋊D3)—22no—
314C3⋊(C3⋊D3)—41no—
315C3×C3⋊D3—41no—
316C32×D3—41no—
317C22×C3×C4—34no—
318C2×#67—94no—
319C2×#67—94no—
320C2×#67—94no—
321C2×#67—91no—
322C2×#67—91no—
323C2×#67—91no—
324C22×Dic3—91no—
325C2×D12—94no—
326C2×D12—94no—
327C2×D12—91no—
328C2×D12—94no—
329C2×D12—91no—
330C2×D12—91no—
331C2×D12—184no—
332C2×C4×D3—94no—
333C2×C4×D3—91no—
334C2×C4×D3—94no—
335C2×C4×D3—94no—
336C2×C4×D3—94no—
337C2×C4×D3—94no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—184no—
342C2×C4×D3—184no—
343C2×C4×D3C2×C3⋊D311yescharacteristic
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4—91no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4—91no—
354C3×C42—24no—
355C3×C42—34no—
356C3×C42D3214yes—
357C3×C42C2×C3⋊D311yescharacteristic
358#217—94no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—34no—
361(C2×D3)⋊C4—34no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—94no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—184no—
372(C2×D3)⋊C4—184no—
373(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
374(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
375C4⋊Dic3—94no—
376C4⋊Dic3—94no—
377C4⋊Dic3—94no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380C4⋊Dic3—184no—
381Dic3⋊C4—34no—
382Dic3⋊C4—34no—
383Dic3⋊C4—34no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4C2×C3⋊D311yescharacteristic
390Dic3⋊C4C2×C3⋊D311yescharacteristic
391C4×Dic3—94no—
392C4×Dic3—91no—
393C4×Dic3C2×C3⋊D311yescharacteristic
394C22×C32—24no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D314yes—
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—32no—
404C2×C3⋊D3—38no—
405C2×C3⋊D3—68no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—68no—
409C2×C3⋊D3—64no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—64no—
414C2×C3⋊D3—64no—
415C2×C3⋊D3—64no—
416C2×C3⋊D3—64no—
417C2×C3⋊D3—124no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3—124no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C32×C4—28no—
428C32×C4—28no—
429C32×C4—24no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—24no—
433C32×C4—21no—
434C32×C4—24no—
435C32×C4—32no—
436C32×C4—44no—
437C32×C4—61no—
438C32×C4—61no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3⋊Dic3—64no—
445C3⋊Dic3—64no—
446C3⋊Dic3—124no—
447C3⋊Dic3—124no—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452C3×Dic3—64no—
453C3×Dic3#23518yes—
454#126—91no—
455#126—271no—
456#125—271no—
457#123—271no—
458#123—271no—
459#121—271no—
460#121—271no—
461#121—271no—
462#121—271no—
463C4×D4—271no—
464C4×D4—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—31no—
468C2×C4⋊C4—271no—
469C33#55311yescharacteristic, complemented, Sylow
470C23×C3—34no—
471C23×C3—91no—
472C22×D3—34no—
473C22×D3—94no—
474C22×D3—91no—
475C22×D3—94no—
476C22×D3—91no—
477C22×D3—184no—
478C22×D3—184no—
479C22×D3C22×C3⋊D311yescharacteristic
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—68no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4C2×D3214yes—
491C2×C3×C4C2×D3214yes—
492C2×C3×C4C2×D3214yes—
493C2×C3×C4C22×C3⋊D311yescharacteristic
494C2×C3×C4C22×C3⋊D311yescharacteristic
495C2×C3×C4C22×C3⋊D311yescharacteristic
496#67—182no—
497#67—188no—
498#67—182no—
499#67—364no—
500#67—361no—
501#67—364no—
502C2×Dic3—34no—
503C2×Dic3—34no—
504C2×Dic3—34no—
505C2×Dic3—94no—
506C2×Dic3—94no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—184no—
510C2×Dic3—184no—
511C2×Dic3—361no—
512C2×Dic3C22×C3⋊D311yescharacteristic
513C2×Dic3C22×C3⋊D311yescharacteristic
514C2×Dic3C22×C3⋊D311yescharacteristic
515D12—188no—
516D12—182no—
517D12—1816no—
518D12—188no—
519D12—188no—
520D12—182no—
521D12—361no—
522C4×D3—22no—
523C4×D3—188no—
524C4×D3—182no—
525C4×D3—361no—
526C4×D3—364no—
527C4×D3—364no—
528C4×D3—364no—
529C4×D3—361no—
530C4×D3—361no—
531C4×D3—364no—
532C4×D3—368no—
533C4×D3—368no—
534C2×C32—24no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—121no—
538C2×C32C2×#23514yes—
539C2×C32D3×#4114yes—
540C2×C32D3×#4111yescharacteristic
541C2×C32D3×#4111yescharacteristic
542C2×C32#100914yes—
543C2×C32#100911yescharacteristic
544C3⋊D3—41no—
545C3⋊D3—62no—
546C3⋊D3—68no—
547C3⋊D3—128no—
548C3⋊D3—128no—
549C3⋊D3—121no—
550C3⋊D3—124no—
551C3×D3—44no—
552C3×D3—124no—
553C2×D4—271no—
554C2×D4—271no—
555C2×D4—271no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C42—31no—
586C42—271no—
587C42D3×C3⋊D311yescharacteristic
588C22×C3—24no—
589C22×C3—64no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3C22×D3214yes—
596C22×C3C23×C3⋊D311yescharacteristic
597C2×D3—21no—
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—64no—
603C2×D3—98no—
604C2×D3—92no—
605C2×D3—188no—
606C2×D3—184no—
607C2×D3—184no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—188no—
611C2×D3—184no—
612C2×D3—184no—
613C2×D3—184no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—364no—
618C2×D3—364no—
619C2×D3—364no—
620C2×D3—364no—
621C3×C4—28no—
622C3×C4—28no—
623C3×C4—24no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—38no—
630C3×C4—44no—
631C3×C4—64no—
632C3×C4—64no—
633C3×C4—181no—
634C3×C4—181no—
635C3×C4—181no—
636Dic3—21no—
637Dic3—21no—
638Dic3—64no—
639Dic3—64no—
640Dic3—64no—
641Dic3—184no—
642Dic3—184no—
643Dic3—181no—
644Dic3—181no—
645Dic3—364no—
646Dic3—364no—
647Dic3#382812yes—
648C32—24no—
649C32#553014yescomplemented
650C32#570911yescharacteristic, complemented
651C23—31no—
652C23—91no—
653C23—271no—
654C23—271no—
655D4—542no—
656D4—542no—
657D4—542no—
658D4—542no—
659D4—1081no—
660D4—1081no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—62no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—542no—
671C2×C4—1081no—
672C2×C4—1081no—
673C2×C4—1081no—
674C2×C4—1081no—
675C2×C4C2×D3×C3⋊D311yescharacteristic
676C2×C4C2×D3×C3⋊D311yescharacteristic
677C2×C4C2×D3×C3⋊D311yescharacteristic
678C2×C3—24no—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—124no—
682C2×C3—361no—
683C2×C3D3×#23514yes—
684C2×C3#6430614yes—
685C2×C3#6430814yes—
686C2×C3C2×#382811yescharacteristic
687C2×C3#41×C3⋊D311yescharacteristic
688C2×C3#6436611yescharacteristic
689D3—41no—
690D3—124no—
691D3—188no—
692D3—182no—
693D3—368no—
694D3—368no—
695D3—364no—
696D3—361no—
697C22—61no—
698C22—61no—
699C22—61no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—272no—
704C22—541no—
705C22—541no—
706C22—541no—
707C22—541no—
708C22—541no—
709C22C22×D3×C3⋊D311yescharacteristic
710C4—21no—
711C4—21no—
712C4—21no—
713C4—32no—
714C4—61no—
715C4—61no—
716C4—181no—
717C4—181no—
718C4—181no—
719C4—541no—
720C4—541no—
721C3—24no—
722C3#1059393714yescomplemented
723C3#1059600111yescharacteristic, complemented
724C2—121no—
725C2—361no—
726C2—542no—
727C2—1081no—
728C2D3×#382811yescharacteristic
729C2#1172457811yescharacteristic
730C2#1172458111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
hypercenterC42D3×C3⋊D3
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C3⋊(C3⋊D3))C2semidirect
2. C3×#64085C2semidirect
3. C32×#872C2semidirect
4. #11723527C2semidirect
5. #11723525C2semidirect
6. #11723523C2semidirect
7. #11723514C2semidirect
8. #11723510C2semidirect
9. #11723486C2semidirect
10. #11723472C2semidirect
11. #11723471C2semidirect
12. #11723470C2semidirect
13. #11723453C2semidirect
14. #11723420C2semidirect
15. #11723400C2semidirect
65. #64085D3semidirect
71. C3×#872D3semidirect
244. #872C3⋊D3semidirect
469. C33#553semidirect
649. C32#5530semidirect
650. C32#5709semidirect
722. C3#10593937semidirect
723. C3#10596001semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C3⋊(C3⋊D3))2
C3×#640852
C32×#8722
#117235272
#117235252
#117235232
#117235142
#117235102
#117234862
#117234722
#117234712
#117234702
#117234532
#117234202
#117234002
#105960013
#105939373