Finite Group Databasebeta

← #13175345

Subgroups — #13175345

Order 1728.

1836 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#64081C211yesmaximal, characteristic, complemented
3C32×#872C211yesmaximal, characteristic, complemented
4C4×#6293C211yesmaximal, characteristic, complemented
5#11723530C211yesmaximal, characteristic, complemented
6#11723527C211yesmaximal, characteristic
7C4×#6292C211yesmaximal, characteristic, complemented
8C4×#6291C211yesmaximal, characteristic, complemented
9C4×#6290C211yesmaximal, characteristic, complemented
10#11723448C211yesmaximal, characteristic, complemented
11#11723442C211yesmaximal, characteristic, complemented
12#11723433C211yesmaximal, characteristic, complemented
13#11723432C211yesmaximal, characteristic, complemented
14#11723421C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16#10595999—31nomaximal
17#10593980—34nomaximal
18C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×#6293C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C33×C42C2211yescharacteristic
28C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
29C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
30C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×C4×C3⋊Dic3C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41#88807C2211yescharacteristic
42#88807C2211yescharacteristic
43#88806C2211yescharacteristic
44#88806C2211yescharacteristic
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×#117—31no—
54C4×#638—31no—
55C4×#638—31no—
56#64107—31no—
57#64105—31no—
58#64103—31no—
59#64098—31no—
60#64094—31no—
61#64093—31no—
62#64092—31no—
63#64088—31no—
64C4×C4⋊(C3⋊D3)—31no—
65#64081D311yescharacteristic, complemented
66C42×C3⋊D3—31no—
67C42×C3⋊D3—34no—
68C42×C3⋊D3—64no—
69C4×#634—31no—
70C3×#872—34no—
71C3×#872D314yescomplemented
72C4×#627—34no—
73#63915—34no—
74#63912—34no—
75C4×#626—34no—
76C4×#626—34no—
77C4×#625—34no—
78#63870—34no—
79#63865—34no—
80#63862—34no—
81#63862—34no—
82#63853—34no—
83#63853—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C4×C3⋊(C3⋊D3)—22no—
94C4×C3⋊(C3⋊D3)—22no—
95C4×C3⋊(C3⋊D3)—22no—
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×C4×C3⋊D3—22no—
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C32×C4×D3—22no—
104#6293—22no—
105#6292—22no—
106#6291—22no—
107#6290—22no—
108#5528—94no—
109#5528—91no—
110C22×C32×C4—31no—
111C2×#638—31no—
112C2×#638—31no—
113C2×C4⋊(C3⋊D3)—31no—
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—34no—
118C2×C4×C3⋊D3—34no—
119C2×C4×C3⋊D3—34no—
120C2×C4×C3⋊D3—64no—
121C2×C4×C3⋊D3—64no—
122C2×C4×C3⋊D3—64no—
123C2×C4×C3⋊D3C2×D311yescharacteristic
124C2×#634—31no—
125C2×C3×C4×D3—34no—
126C2×C3×C4×D3C2×D314yes—
127C2×#627—34no—
128C2×#626—34no—
129C2×#626—34no—
130C2×#625—34no—
131C32×C4⋊C4—31no—
132C32×C4⋊C4—31no—
133C32×C22⋊C4—31no—
134C32×C22⋊C4—31no—
135C32×C42—24no—
136C32×C42—31no—
137C32×C42C2×D314yes—
138C32×C42C2×D311yescharacteristic
139#3757—31no—
140#3757—31no—
141#3752—31no—
142#3752—31no—
143#3752—31no—
144#3752—31no—
145#3752C2×D311yescharacteristic
146#3752C2×D311yescharacteristic
147C4⋊(C3⋊Dic3)—31no—
148C4⋊(C3⋊Dic3)—31no—
149#3750—31no—
150#3750—31no—
151#3750—31no—
152#3750—31no—
153#3750C2×D311yescharacteristic
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3—31no—
156C4×C3⋊Dic3—31no—
157C4×C3⋊Dic3—31no—
158C4×C3⋊Dic3—34no—
159C4×C3⋊Dic3—34no—
160C4×C3⋊Dic3—34no—
161C4×C3⋊Dic3—64no—
162C4×C3⋊Dic3—64no—
163C4×C3⋊Dic3—64no—
164C4×C3⋊Dic3C2×D311yescharacteristic
165C3×(C2×D3)⋊C4—34no—
166C3×(C2×D3)⋊C4—34no—
167C3×(C2×D3)⋊C4C2×D314yes—
168C3×(C2×D3)⋊C4C2×D314yes—
169C3×Dic3⋊C4—34no—
170C3×Dic3⋊C4—34no—
171C3×Dic3⋊C4C2×D314yes—
172C3×Dic3⋊C4C2×D314yes—
173C3×C4×Dic3—34no—
174C3×C4×Dic3C2×D314yes—
175#3724—34no—
176#3724—34no—
177Dic3⋊Dic3—34no—
178Dic3⋊Dic3—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181#3722—34no—
182#3722—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187C22×C33C2411yescharacteristic
188C2×C3⋊(C3⋊D3)—21no—
189C2×C3⋊(C3⋊D3)—21no—
190C2×C3⋊(C3⋊D3)#4112yes—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—21no—
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3—21no—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4#4112yes—
200C3⋊(C3⋊Dic3)—21no—
201C3⋊(C3⋊Dic3)—21no—
202C3⋊(C3⋊Dic3)#4112yes—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—21no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C3×#117—34no—
210C3×#117—91no—
211C4×#67—94no—
212C4×#67—94no—
213C4×#67—91no—
214C4×#67—91no—
215#898—94no—
216#898—91no—
217#896—94no—
218#896—91no—
219#894—94no—
220#894—91no—
221#889—94no—
222#889—91no—
223#885—94no—
224#885—91no—
225#884—94no—
226#884—91no—
227#883—94no—
228#883—91no—
229#879—94no—
230#879—91no—
231C4×D12—94no—
232C4×D12—91no—
233#872—34no—
234#872C3⋊D311yescharacteristic, complemented
235C42×D3—94no—
236C42×D3—91no—
237C42×D3—184no—
238C4×Dic6—94no—
239C4×Dic6—91no—
240C23×C32—31no—
241C22×C3⋊D3—31no—
242C22×C3⋊D3—34no—
243C22×C3⋊D3—64no—
244C22×C3⋊D3C22×D311yescharacteristic
245C22×C3×D3—34no—
246C22×C3×D3C22×D314yes—
247C2×C32×C4—24no—
248C2×C32×C4—24no—
249C2×C32×C4—24no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—62no—
254C2×C32×C4C22×D314yes—
255C2×C32×C4C22×D314yes—
256C2×C32×C4C22×D314yes—
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260#638—62no—
261#638—62no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—34no—
266C2×C3⋊Dic3—34no—
267C2×C3⋊Dic3—34no—
268C2×C3⋊Dic3—64no—
269C2×C3⋊Dic3—64no—
270C2×C3⋊Dic3—64no—
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C4⋊(C3⋊D3)—62no—
275C4×C3⋊D3—22no—
276C4×C3⋊D3—62no—
277C4×C3⋊D3—68no—
278C4×C3⋊D3—62no—
279C4×C3⋊D3—68no—
280C4×C3⋊D3—616no—
281C4×C3⋊D3—616no—
282C4×C3⋊D3—616no—
283C4×C3⋊D3—68no—
284C4×C3⋊D3—62no—
285#634—62no—
286C2×C3×Dic3—34no—
287C2×C3×Dic3—34no—
288C2×C3×Dic3—34no—
289C2×C3×Dic3C22×D314yes—
290C2×C3×Dic3C22×D314yes—
291C2×C3×Dic3C22×D314yes—
292C3×C4×D3—28no—
293C3×C4×D3—68no—
294#627—68no—
295#626—68no—
296#626—68no—
297#625—68no—
298#529—271noSylow
299C2×C33C2×#4111yescharacteristic
300C2×C33C2×#4111yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C3⋊(C3⋊D3)—22no—
303C3×C3⋊D3—41no—
304C32×D3—41no—
305C22×C3×C4—34no—
306C22×C3×C4—91no—
307C2×#67—94no—
308C2×#67—94no—
309C2×#67—91no—
310C2×#67—91no—
311C2×D12—94no—
312C2×D12—91no—
313C2×C4×D3—34no—
314C2×C4×D3—94no—
315C2×C4×D3—94no—
316C2×C4×D3—94no—
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—184no—
321C2×C4×D3—184no—
322C2×C4×D3—184no—
323C2×C4×D3C2×C3⋊D311yescharacteristic
324C2×Dic6—94no—
325C2×Dic6—91no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—91no—
333C3×C22⋊C4—91no—
334C3×C42—24no—
335C3×C42—34no—
336C3×C42—91no—
337C3×C42D3214yes—
338C3×C42C2×C3⋊D311yescharacteristic
339#217—94no—
340#217—94no—
341#217—91no—
342#217—91no—
343(C2×D3)⋊C4—34no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—94no—
346(C2×D3)⋊C4—94no—
347(C2×D3)⋊C4—94no—
348(C2×D3)⋊C4—94no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—91no—
351(C2×D3)⋊C4—91no—
352(C2×D3)⋊C4—91no—
353(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
354(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
355C4⋊Dic3—94no—
356C4⋊Dic3—94no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359Dic3⋊C4—34no—
360Dic3⋊C4—34no—
361Dic3⋊C4—94no—
362Dic3⋊C4—94no—
363Dic3⋊C4—94no—
364Dic3⋊C4—94no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4C2×C3⋊D311yescharacteristic
370Dic3⋊C4C2×C3⋊D311yescharacteristic
371C4×Dic3—34no—
372C4×Dic3—94no—
373C4×Dic3—94no—
374C4×Dic3—94no—
375C4×Dic3—91no—
376C4×Dic3—91no—
377C4×Dic3—91no—
378C4×Dic3—184no—
379C4×Dic3—184no—
380C4×Dic3—184no—
381C4×Dic3C2×C3⋊D311yescharacteristic
382C22×C32—24no—
383C22×C32—61no—
384C22×C32—61no—
385C22×C32—61no—
386C22×C32C23×D314yes—
387C22×C32C23×D311yescharacteristic
388C2×C3⋊D3—21no—
389C2×C3⋊D3—21no—
390C2×C3⋊D3—21no—
391C2×C3⋊D3—32no—
392C2×C3⋊D3—38no—
393C2×C3⋊D3—68no—
394C2×C3⋊D3—68no—
395C2×C3⋊D3—68no—
396C2×C3⋊D3—64no—
397C2×C3⋊D3—61no—
398C2×C3⋊D3—64no—
399C2×C3⋊D3—61no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3—24no—
403C2×C3×D3—64no—
404C2×C3×D3—64no—
405C2×C3×D3—64no—
406C32×C4—28no—
407C32×C4—28no—
408C32×C4—24no—
409C32×C4—24no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—28no—
413C32×C4—61no—
414C32×C4—61no—
415C32×C4—61no—
416C32×C4#23518yes—
417C32×C4#23512yes—
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—21no—
421C3⋊Dic3—32no—
422C3⋊Dic3—38no—
423C3⋊Dic3—68no—
424C3⋊Dic3—68no—
425C3⋊Dic3—68no—
426C3⋊Dic3—64no—
427C3⋊Dic3—61no—
428C3⋊Dic3—64no—
429C3⋊Dic3—61no—
430C3×Dic3—24no—
431C3×Dic3—24no—
432C3×Dic3—24no—
433C3×Dic3—64no—
434C3×Dic3—64no—
435C3×Dic3—64no—
436#126—271no—
437#126—271no—
438#125—271no—
439#124—271no—
440#123—271no—
441#123—271no—
442C22⋊Q8—271no—
443#121—271no—
444C4×Q8—271no—
445C4×D4—271no—
446C4×D4—271no—
447C4×D4—271no—
448#117—31no—
449#117—91no—
450C2×C42—271no—
451C33#52911yescharacteristic, complemented, Sylow
452C23×C3—34no—
453C23×C3—91no—
454C22×D3—34no—
455C22×D3—94no—
456C22×D3—91no—
457C22×D3—184no—
458C22×D3C22×C3⋊D311yescharacteristic
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—34no—
463C2×C3×C4—34no—
464C2×C3×C4—34no—
465C2×C3×C4—68no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—182no—
470C2×C3×C4C2×D3214yes—
471C2×C3×C4C2×D3214yes—
472C2×C3×C4C2×D3214yes—
473C2×C3×C4C22×C3⋊D311yescharacteristic
474C2×C3×C4C22×C3⋊D311yescharacteristic
475C2×C3×C4C22×C3⋊D311yescharacteristic
476#67—182no—
477#67—188no—
478#67—182no—
479#67—188no—
480C2×Dic3—34no—
481C2×Dic3—34no—
482C2×Dic3—34no—
483C2×Dic3—94no—
484C2×Dic3—91no—
485C2×Dic3—94no—
486C2×Dic3—94no—
487C2×Dic3—91no—
488C2×Dic3—91no—
489C2×Dic3—184no—
490C2×Dic3—184no—
491C2×Dic3—184no—
492C2×Dic3C22×C3⋊D311yescharacteristic
493C2×Dic3C22×C3⋊D311yescharacteristic
494C2×Dic3C22×C3⋊D311yescharacteristic
495D12—188no—
496D12—182no—
497C4×D3—22no—
498C4×D3—68no—
499C4×D3—188no—
500C4×D3—182no—
501C4×D3—188no—
502C4×D3—182no—
503C4×D3—1816no—
504C4×D3—1816no—
505C4×D3—1816no—
506C4×D3—188no—
507C4×D3—182no—
508Dic6—182no—
509Dic6—188no—
510C2×C32—24no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—121no—
514C2×C32C2×#23514yes—
515C2×C32C2×#23511yescharacteristic
516C2×C32D3×#4114yes—
517C2×C32D3×#4114yes—
518C2×C32D3×#4111yescharacteristic
519C2×C32D3×#4111yescharacteristic
520C3⋊D3—41no—
521C3⋊D3—616no—
522C3⋊D3—68no—
523C3⋊D3—62no—
524C3×D3—44no—
525C3×D3—124no—
526C2×Q8—271no—
527C2×D4—271no—
528C2×D4—271no—
529C2×D4—271no—
530C22×C4—31no—
531C22×C4—91no—
532C22×C4—271no—
533C22×C4—271no—
534C22×C4—271no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4—271no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C22⋊C4—31no—
546C22⋊C4—31no—
547C22⋊C4—91no—
548C22⋊C4—91no—
549C22⋊C4—271no—
550C22⋊C4—271no—
551C22⋊C4—271no—
552C22⋊C4—271no—
553C22⋊C4—271no—
554C22⋊C4—271no—
555C42—31no—
556C42—91no—
557C42—271no—
558C42—271no—
559C42—271no—
560C42D3×C3⋊D311yescharacteristic
561C22×C3—24no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—64no—
565C22×C3—181no—
566C22×C3—181no—
567C22×C3—181no—
568C22×C3C22×D3214yes—
569C22×C3C23×C3⋊D311yescharacteristic
570C2×D3—21no—
571C2×D3—21no—
572C2×D3—21no—
573C2×D3—64no—
574C2×D3—64no—
575C2×D3—64no—
576C2×D3—98no—
577C2×D3—92no—
578C2×D3—188no—
579C2×D3—188no—
580C2×D3—188no—
581C2×D3—184no—
582C2×D3—184no—
583C2×D3—181no—
584C2×D3—181no—
585C3×C4—28no—
586C3×C4—28no—
587C3×C4—24no—
588C3×C4—24no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—28no—
592C3×C4—64no—
593C3×C4—64no—
594C3×C4—64no—
595C3×C4—181no—
596C3×C4—181no—
597C3×C4—181no—
598C3×C4#379818yes—
599C3×C4#382812yes—
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3—64no—
604Dic3—64no—
605Dic3—64no—
606Dic3—98no—
607Dic3—92no—
608Dic3—188no—
609Dic3—188no—
610Dic3—188no—
611Dic3—184no—
612Dic3—184no—
613Dic3—181no—
614Dic3—181no—
615C32—24no—
616C32#552814yescomplemented
617C32#552811yescharacteristic, complemented
618C23—31no—
619C23—91no—
620C23—271no—
621Q8—542no—
622D4—542no—
623D4—542no—
624D4—542no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—62no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—91no—
632C2×C4—182no—
633C2×C4—271no—
634C2×C4—271no—
635C2×C4—271no—
636C2×C4—542no—
637C2×C4—542no—
638C2×C4—542no—
639C2×C4C2×D3×C3⋊D311yescharacteristic
640C2×C4C2×D3×C3⋊D311yescharacteristic
641C2×C4C2×D3×C3⋊D311yescharacteristic
642C2×C3—24no—
643C2×C3—24no—
644C2×C3—24no—
645C2×C3—124no—
646C2×C3—361no—
647C2×C3C2×#379814yes—
648C2×C3#6430614yes—
649C2×C3#6430614yes—
650C2×C3C2×#382811yescharacteristic
651C2×C3#41×C3⋊D311yescharacteristic
652C2×C3#41×C3⋊D311yescharacteristic
653D3—41no—
654D3—124no—
655D3—1816no—
656D3—182no—
657D3—188no—
658C22—61no—
659C22—61no—
660C22—61no—
661C22—181no—
662C22—181no—
663C22—181no—
664C22—272no—
665C22—541no—
666C22—541no—
667C22C22×D3×C3⋊D311yescharacteristic
668C4—21no—
669C4—21no—
670C4—61no—
671C4—61no—
672C4—61no—
673C4—181no—
674C4—181no—
675C4—181no—
676C4—272no—
677C4—541no—
678C4—541no—
679C4#8902012yes—
680C3—24no—
681C3#1059398014yescomplemented
682C3#1059599911yescharacteristic, complemented
683C2—121no—
684C2—361no—
685C2—542no—
686C2C2×#8902011yescharacteristic
687C2#1172457811yescharacteristic
688C2#1172457811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
prime radical#11723527C2
hypercenterC42D3×C3⋊D3
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C42×C3⋊(C3⋊D3)C2semidirect
2. C3×#64081C2semidirect
3. C32×#872C2semidirect
4. C4×#6293C2semidirect
5. #11723530C2semidirect
7. C4×#6292C2semidirect
8. C4×#6291C2semidirect
9. C4×#6290C2semidirect
10. #11723448C2semidirect
11. #11723442C2semidirect
12. #11723433C2semidirect
13. #11723432C2semidirect
14. #11723421C2semidirect
15. #11723420C2semidirect
65. #64081D3semidirect
71. C3×#872D3semidirect
234. #872C3⋊D3semidirect
451. C33#529semidirect
616. C32#5528semidirect
617. C32#5528semidirect
681. C3#10593980semidirect
682. C3#10595999semidirect

Maximal subgroups

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

subgroupindex
C42×C3⋊(C3⋊D3)2
C3×#640812
C32×#8722
C4×#62932
#117235302
#117235272
C4×#62922
C4×#62912
C4×#62902
#117234482
#117234422
#117234332
#117234322
#117234212
#117234202
#105959993
#105939803