Finite Group Databasebeta

← #13175427

Subgroups — #13175427

Order 1728.

1792 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723913C211yesmaximal, characteristic, complemented
2C3×#64081C211yesmaximal, characteristic, complemented
3C32×#875C211yesmaximal, characteristic, complemented
4#11723540C211yesmaximal, characteristic
5#11723539C211yesmaximal, characteristic, complemented
6C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11723518C211yesmaximal, characteristic, complemented
8#11723508C211yesmaximal, characteristic, complemented
9#11723477C211yesmaximal, characteristic, complemented
10#11723476C211yesmaximal, characteristic, complemented
11#11723473C211yesmaximal, characteristic, complemented
12#11723461C211yesmaximal, characteristic, complemented
13#11723432C211yesmaximal, characteristic, complemented
14#11723428C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16#10596150—31nomaximal
17#10594016—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C32×D12C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic, complemented
23C2×#6291C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
28C33×C42C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic
31#88857C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C32×#124—31no—
54#64155—31no—
55#64155—31no—
56#64146—31no—
57#64144—31no—
58#64092—31no—
59#64092—31no—
60#64090—31no—
61#64090—31no—
62C22⋊C4×C3⋊D3—31no—
63C22⋊C4×C3⋊D3—31no—
64#64088—31no—
65#64088—31no—
66#64081—31no—
67#64081—34no—
68#64081—64no—
69#64081D311yescharacteristic, complemented
70C3×#875D314yescomplemented
71C3×#872—34no—
72#63922—34no—
73#63921—34no—
74D3×(C2×D3)⋊C4—34no—
75#63905—34no—
76#63902—34no—
77#63888—34no—
78#63887—34no—
79#63884—34no—
80#63880—34no—
81#63862—34no—
82#63859—34no—
83#63853—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4×C3⋊(C3⋊D3)—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—22no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×D12—41no—
105C32×Dic6—41no—
106#6291—22no—
107#6290—22no—
108#6289—41no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—41no—
111#5679—94no—
112#5527—91no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C2×C32×Q8—31no—
116C2×C32×D4—31no—
117C2×#638—31no—
118C2×#638—31no—
119C22×C3⋊Dic3—31no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—34no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—64no—
125C2×C4×C3⋊D3C2×D311yescharacteristic
126C2×C3×D12C2×D314yes—
127C2×C3×C4×D3—34no—
128C2×C3×Dic6C2×D314yescomplemented
129C2×#626—34no—
130C2×#625—34no—
131C2×#624—34no—
132C2×D3×Dic3—34no—
133C2×D3×Dic3—34no—
134C32×C22⋊C4—31no—
135C32×C22⋊C4—31no—
136C32×C22⋊C4—31no—
137C32×C22⋊C4—31no—
138C32×C42—24no—
139C32×C42C2×D314yescomplemented
140C32×C42C2×D311yescharacteristic, complemented
141#3757—31no—
142#3757—31no—
143#3757—31no—
144#3757—31no—
145#3752—31no—
146#3752—31no—
147#3752—31no—
148#3752—34no—
149#3752—34no—
150#3752—31no—
151#3752—64no—
152#3752—64no—
153#3752C2×D311yescharacteristic
154#3752C2×D311yescharacteristic
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157#3750—31no—
158#3750—31no—
159#3750—34no—
160#3750—34no—
161#3750—31no—
162#3750—31no—
163#3750—64no—
164#3750—64no—
165#3750C2×D311yescharacteristic, complemented
166#3750C2×D311yescharacteristic, complemented
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—34no—
169C4×C3⋊Dic3—64no—
170C4×C3⋊Dic3C2×D311yescharacteristic, complemented
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yescomplemented
176C3×(C2×D3)⋊C4C2×D314yescomplemented
177C3×Dic3⋊C4—34no—
178C3×Dic3⋊C4—34no—
179C3×C4×Dic3—34no—
180#3724—34no—
181Dic3⋊Dic3—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184#3722—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)#4112yes—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3#4112yes—
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203D3×C3⋊D3—44no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3⋊(C3⋊Dic3)—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#124—34no—
216C3×#117—91no—
217#946—94no—
218#946—94no—
219#937—94no—
220#935—94no—
221#929—91no—
222C2×(C2×D3)⋊C4—91no—
223#898—91no—
224#896—91no—
225#894—91no—
226#894—91no—
227#883—94no—
228#883—94no—
229#882—91no—
230#67⋊C4—94no—
231#67⋊C4—94no—
232#67⋊C4—91no—
233D3×C22⋊C4—94no—
234D3×C22⋊C4—94no—
235D3×C22⋊C4—91no—
236#879—94no—
237#879—94no—
238#878—91no—
239#876—91no—
240#875C3⋊D311yescharacteristic, complemented
241C4×D12—91no—
242#872—34no—
243#872—94no—
244#872—91no—
245#872—184no—
246C23×C32—31no—
247C23×C32—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—34no—
250C22×C3⋊D3—64no—
251C22×C3⋊D3—62no—
252C22×C3⋊D3—62no—
253C22×C3⋊D3—121no—
254C22×C3⋊D3C22×D311yescharacteristic
255C22×C3×D3—34no—
256C22×C3×D3C22×D314yes—
257C22×C3×D3C22×D314yes—
258C2×D32—68no—
259C2×D32—68no—
260C2×D32—124no—
261C32×Q8—121no—
262C32×D4—121no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—24no—
266C2×C32×C4—31no—
267C2×C32×C4—31no—
268C2×C32×C4C22×D314yes—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274#638—62no—
275#638—62no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—34no—
281C2×C3⋊Dic3—34no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—121no—
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C4×C3⋊D3—22no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—68no—
292C4×C3⋊D3—616no—
293C4×C3⋊D3—121no—
294C4×C3⋊D3—121no—
295C2×C3×Dic3—34no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3C22×D314yes—
299C2×C3×Dic3C22×D314yes—
300C3×D12—44no—
301C3×C4×D3—68no—
302C3×Dic6—44no—
303#626—68no—
304#625—68no—
305#624—124no—
306D3×Dic3—124no—
307D3×Dic3—124no—
308#551—271noSylow
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C3⋊(C3⋊D3)—22no—
313C3×C3⋊D3—22no—
314C32×D3—41no—
315C32×D3—41no—
316C23×D3—94no—
317C23×D3—91no—
318C2×C3×Q8—34no—
319C2×C3×D4—34no—
320C22×C3×C4—91no—
321C2×#67—94no—
322C2×#67—94no—
323C2×#67—91no—
324C22×Dic3—94no—
325C22×Dic3—91no—
326C2×D12—91no—
327C2×D12C2×C3⋊D311yescharacteristic
328C2×C4×D3—34no—
329C2×C4×D3—94no—
330C2×C4×D3—91no—
331C2×C4×D3—94no—
332C2×C4×D3—94no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—184no—
336C2×Dic6C2×C3⋊D311yescharacteristic, complemented
337C3×C4⋊C4—91no—
338C3×C4⋊C4—91no—
339C3×C22⋊C4—34no—
340C3×C22⋊C4—34no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C42—24no—
346C3×C42—91no—
347C3×C42D3214yescomplemented
348C3×C42C2×C3⋊D311yescharacteristic, complemented
349#217—94no—
350#217—94no—
351#217—94no—
352#217—94no—
353#217—91no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—94no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—184no—
368(C2×D3)⋊C4—184no—
369(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
370(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
371(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
372(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
373C4⋊Dic3—94no—
374C4⋊Dic3—94no—
375C4⋊Dic3—91no—
376Dic3⋊C4—34no—
377Dic3⋊C4—34no—
378Dic3⋊C4—94no—
379Dic3⋊C4—94no—
380Dic3⋊C4—94no—
381Dic3⋊C4—94no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—184no—
388Dic3⋊C4—184no—
389C4×Dic3—34no—
390C4×Dic3—94no—
391C4×Dic3—91no—
392C4×Dic3—184no—
393C22×C32—24no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32—61no—
399C22×C32—61no—
400C22×C32C23×D314yes—
401C22×C32C23×D311yescharacteristic
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—32no—
405C2×C3⋊D3—38no—
406C2×C3⋊D3—68no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—64no—
410C2×C3⋊D3—64no—
411C2×C3⋊D3—124no—
412C2×C3⋊D3—124no—
413C2×C3⋊D3—124no—
414C2×C3⋊D3#23512yes—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—24no—
419C2×C3×D3—24no—
420C2×C3×D3—24no—
421C2×C3×D3—38no—
422C2×C3×D3—64no—
423C2×C3×D3—64no—
424D32—1216no—
425C32×C4—28no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—24no—
431C32×C4—24no—
432C32×C4—44no—
433C32×C4—44no—
434C32×C4—61no—
435C32×C4—61no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—68no—
440C3⋊Dic3—61no—
441C3⋊Dic3—64no—
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—
453#126—271no—
454#126—271no—
455#124—31no—
456#123—271no—
457#123—271no—
458#123—271no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461#120—271no—
462C4×D4—271no—
463C4×D4—271no—
464#117—91no—
465#117—271no—
466C2×C22⋊C4—271no—
467C2×C22⋊C4—271no—
468C33#55111yescharacteristic, complemented, Sylow
469C23×C3—34no—
470C23×C3—34no—
471C23×C3—91no—
472C22×D3—34no—
473C22×D3—94no—
474C22×D3—91no—
475C22×D3—184no—
476C22×D3—182no—
477C22×D3—182no—
478C22×D3—188no—
479C22×D3—188no—
480C22×D3—361no—
481C22×D3—364no—
482C22×D3C22×C3⋊D311yescharacteristic
483C22×D3C22×C3⋊D311yescharacteristic
484C3×Q8—124no—
485C3×D4—124no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—182no—
495C2×C3×C4C2×D3214yes—
496C2×C3×C4C2×D3214yes—
497C2×C3×C4C2×D3214yes—
498C2×C3×C4C22×C3⋊D311yescharacteristic
499C2×C3×C4C22×C3⋊D311yescharacteristic
500C2×C3×C4C22×C3⋊D311yescharacteristic
501#67—188no—
502#67—182no—
503#67—188no—
504C2×Dic3—34no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—94no—
508C2×Dic3—94no—
509C2×Dic3—94no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—184no—
514C2×Dic3—184no—
515C2×Dic3—184no—
516C2×Dic3—361no—
517C2×Dic3—364no—
518C2×Dic3C22×C3⋊D311yescharacteristic
519C2×Dic3C22×C3⋊D311yescharacteristic
520D12—41no—
521D12—182no—
522C4×D3—68no—
523C4×D3—188no—
524C4×D3—182no—
525C4×D3—1816no—
526C4×D3—361no—
527C4×D3—364no—
528C4×D3—364no—
529C4×D3—361no—
530Dic6—41no—
531C2×C32—24no—
532C2×C32—24no—
533C2×C32—24no—
534C2×C32—121no—
535C2×C32—121no—
536C2×C32C2×#23511yescharacteristic
537C2×C32#100414yes—
538C2×C32D3×#4114yes—
539C2×C32D3×#4114yes—
540C2×C32D3×#4111yescharacteristic
541C2×C32#100911yescharacteristic
542C3⋊D3—22no—
543C3⋊D3—62no—
544C3⋊D3—68no—
545C3⋊D3—128no—
546C3×D3—44no—
547C3×D3—44no—
548C3×D3—68no—
549C24—271no—
550C2×Q8—31no—
551C2×D4—31no—
552C2×D4—271no—
553C2×D4—271no—
554C22×C4—91no—
555C22×C4—271no—
556C22×C4—271no—
557C22×C4—271no—
558C22×C4—271no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—271no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C42—91no—
582C42—271no—
583C42D3×C3⋊D311yescharacteristic, complemented
584C22×C3—24no—
585C22×C3—64no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—64no—
589C22×C3—64no—
590C22×C3—64no—
591C22×C3—92no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3C22×D3214yes—
595C22×C3C23×C3⋊D311yescharacteristic
596C2×D3—21no—
597C2×D3—21no—
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—38no—
603C2×D3—64no—
604C2×D3—64no—
605C2×D3—98no—
606C2×D3—92no—
607C2×D3—188no—
608C2×D3—184no—
609C2×D3—184no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—364no—
613C2×D3—364no—
614C2×D3—364no—
615C2×D3—3616no—
616C3×C4—28no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—24no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—44no—
624C3×C4—44no—
625C3×C4—64no—
626C3×C4—64no—
627C3×C4—181no—
628C3×C4—181no—
629C3×C4—181no—
630Dic3—21no—
631Dic3—21no—
632Dic3—64no—
633Dic3—64no—
634Dic3—64no—
635Dic3—188no—
636Dic3—184no—
637Dic3—184no—
638Dic3—184no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—364no—
643Dic3—364no—
644C32—24no—
645C32#552711yescharacteristic, complemented
646C32#567914yescomplemented
647C23—31no—
648C23—31no—
649C23—91no—
650C23—271no—
651C23—542no—
652C23—542no—
653C23—1081no—
654Q8—121no—
655D4—121no—
656D4—542no—
657D4—542no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—182no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—542no—
668C2×C4—1081no—
669C2×C4—1081no—
670C2×C4—1081no—
671C2×C4C2×D3×C3⋊D311yescharacteristic
672C2×C4C2×D3×C3⋊D311yescharacteristic
673C2×C4C2×D3×C3⋊D311yescharacteristic
674C2×C3—24no—
675C2×C3—24no—
676C2×C3—24no—
677C2×C3—124no—
678C2×C3—124no—
679C2×C3—182no—
680C2×C3D3×#23514yes—
681C2×C3#6430614yes—
682C2×C3#6430714yes—
683C2×C3#6436111yescharacteristic
684C2×C3#41×C3⋊D311yescharacteristic
685C2×C3#41×C3⋊D311yescharacteristic
686D3—41no—
687D3—41no—
688D3—68no—
689D3—182no—
690D3—188no—
691D3—368no—
692C22—61no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—61no—
697C22—61no—
698C22—92no—
699C22—181no—
700C22—181no—
701C22—272no—
702C22—541no—
703C22—541no—
704C22—1084no—
705C22C22×D3×C3⋊D311yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—61no—
710C4—61no—
711C4—181no—
712C4—181no—
713C4—181no—
714C4—541no—
715C4—541no—
716C4—541no—
717C3—24no—
718C3#1059401614yescomplemented
719C3#1059615011yescharacteristic, complemented
720C2—121no—
721C2—121no—
722C2—182no—
723C2—542no—
724C2C3⋊D3×#23511yescharacteristic
725C2#1172457811yescharacteristic
726C2#1172457911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radical#11723540C2
hypercenterC42D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11723913C2semidirect
2. C3×#64081C2semidirect
3. C32×#875C2semidirect
5. #11723539C2semidirect
6. C3⋊D3×(C2×D3)⋊C4C2semidirect
7. #11723518C2semidirect
8. #11723508C2semidirect
9. #11723477C2semidirect
10. #11723476C2semidirect
11. #11723473C2semidirect
12. #11723461C2semidirect
13. #11723432C2semidirect
14. #11723428C2semidirect
15. #11723420C2semidirect
22. C2×C32×Dic6C22semidirect
27. C2×D3×C3⋊Dic3C22semidirect
28. C33×C42C22semidirect
31. #88857C22semidirect
32. #88857C22semidirect
33. C4×C3⋊(C3⋊Dic3)C22semidirect
36. C3×#3750C22semidirect
37. C3×#3750C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
69. #64081D3semidirect
70. C3×#875D3semidirect
128. C2×C3×Dic6C2×D3semidirect
139. C32×C42C2×D3semidirect
140. C32×C42C2×D3semidirect
165. #3750C2×D3semidirect
166. #3750C2×D3semidirect
170. C4×C3⋊Dic3C2×D3semidirect
175. C3×(C2×D3)⋊C4C2×D3semidirect
176. C3×(C2×D3)⋊C4C2×D3semidirect
240. #875C3⋊D3semidirect
336. C2×Dic6C2×C3⋊D3semidirect
347. C3×C42D32semidirect
348. C3×C42C2×C3⋊D3semidirect
371. (C2×D3)⋊C4C2×C3⋊D3semidirect
372. (C2×D3)⋊C4C2×C3⋊D3semidirect
468. C33#551semidirect
583. C42D3×C3⋊D3semidirect
645. C32#5527semidirect
646. C32#5679semidirect
718. C3#10594016semidirect
719. C3#10596150semidirect

Maximal subgroups

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

subgroupindex
#117239132
C3×#640812
C32×#8752
#117235402
#117235392
C3⋊D3×(C2×D3)⋊C42
#117235182
#117235082
#117234772
#117234762
#117234732
#117234612
#117234322
#117234282
#117234202
#105961503
#105940163