Finite Group Databasebeta

← #13175202

Subgroups — #13175202

Order 1728.

1708 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723913C211yesmaximal, characteristic, complemented
2C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×C4×Dic6C211yesmaximal, characteristic, complemented
4C4×#6292C211yesmaximal, characteristic, complemented
5C4×#6292C211yesmaximal, characteristic, complemented
6#11723493C211yesmaximal, characteristic, complemented
7#11723488C211yesmaximal, characteristic, complemented
8#11723482C211yesmaximal, characteristic
9#11723476C211yesmaximal, characteristic, complemented
10C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
11#11723437C211yesmaximal, characteristic, complemented
12#11723407C211yesmaximal, characteristic, complemented
13#11723403C211yesmaximal, characteristic, complemented
14#11723401C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596051—31nomaximal
17#10593911—34nomaximal
18C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C33×C42C2211yescharacteristic
28#88859C2211yescharacteristic
29#88859C2211yescharacteristic
30#88857C2211yescharacteristic
31#88857C2211yescharacteristic
32C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41#88807C2211yescharacteristic
42#88807C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×C4×Q8—31no—
54#64156—31no—
55#64155—31no—
56#64107—31no—
57#64107—31no—
58#64104—31no—
59#64103—31no—
60#64103—31no—
61#64099—31no—
62C4×C4⋊(C3⋊D3)—31no—
63C4×C4⋊(C3⋊D3)—31no—
64C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
65#64081—31no—
66#64081—31no—
67#64081—34no—
68#64081—64no—
69C42×C3⋊D3—31no—
70C3×C4×D12—34no—
71C3×C4×Dic6D314yescomplemented
72#63907—34no—
73C4×#626—34no—
74C4×#626—34no—
75#63890—34no—
76#63887—34no—
77#63886—34no—
78#63884—34no—
79C4×D3×Dic3—34no—
80#63858—34no—
81#63855—34no—
82#63848—34no—
83#63846—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C3×C3⋊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—
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C3×C4⋊(C3⋊D3)—22no—
97C3×C4×C3⋊D3—22no—
98C3×C4×C3⋊D3—22no—
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C32×Dic6—22no—
104#6292—22no—
105#6292—22no—
106Dic3×C3⋊D3—22no—
107Dic3×C3⋊D3—22no—
108#5580—94no—
109#5538—91no—
110C2×C32×Q8—31no—
111C2×C4⋊(C3⋊D3)—31no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—34no—
118C2×C4×C3⋊D3—64no—
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×C4×C3⋊D3C2×D311yescharacteristic
121C2×C3×D12—34no—
122C2×C3×C4×D3—34no—
123C2×C3×C4×D3—34no—
124C2×C3×Dic6C2×D314yes—
125C2×#626—34no—
126C2×#626—34no—
127C2×D3×Dic3—34no—
128C2×D3×Dic3—34no—
129C32×C4⋊C4—31no—
130C32×C4⋊C4—31no—
131C32×C4⋊C4—31no—
132C32×C42—24no—
133C32×C42—31no—
134C32×C42—31no—
135C32×C42C2×D314yes—
136C32×C42C2×D311yescharacteristic
137#3752—31no—
138#3752—31no—
139#3752—31no—
140#3752—31no—
141#3752—31no—
142#3752—31no—
143#3752—34no—
144#3752—34no—
145#3752—31no—
146#3752—31no—
147#3752—64no—
148#3752—64no—
149#3752C2×D311yescharacteristic
150#3752C2×D311yescharacteristic
151C4⋊(C3⋊Dic3)—31no—
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)C2×D311yescharacteristic
154#3750—31no—
155#3750—31no—
156#3750—34no—
157#3750—34no—
158#3750—31no—
159#3750—31no—
160#3750—64no—
161#3750—64no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—34no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—64no—
167C3×(C2×D3)⋊C4—34no—
168C3×(C2×D3)⋊C4—34no—
169C3×C4⋊Dic3—34no—
170C3×C4⋊Dic3C2×D314yes—
171C3×Dic3⋊C4C2×D314yes—
172C3×Dic3⋊C4C2×D314yes—
173C3×C4×Dic3C2×D314yes—
174C3×C4×Dic3C2×D314yes—
175Dic3⋊Dic3—34no—
176Dic3⋊Dic3—34no—
177Dic3⋊Dic3—34no—
178Dic3⋊Dic3—34no—
179#3722—34no—
180#3722—34no—
181(C2×D3)⋊Dic3—34no—
182(C2×D3)⋊Dic3—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185Dic32—34no—
186Dic32—34no—
187C22×C33C2411yescharacteristic
188C2×C3⋊(C3⋊D3)—21no—
189C2×C3⋊(C3⋊D3)—21no—
190C2×C3⋊(C3⋊D3)—21no—
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—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4#4112yes—
200C3⋊(C3⋊Dic3)—21no—
201C3⋊(C3⋊Dic3)—21no—
202C3⋊(C3⋊Dic3)—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3#4112yes—
209C3×C4×Q8—34no—
210C3×C4×D4—91no—
211#947—94no—
212#946—94no—
213#939—91no—
214#935—91no—
215C4×#67—91no—
216C4×#67—91no—
217#926—91no—
218C2×C4×Dic3—91no—
219#898—94no—
220#898—94no—
221#898—91no—
222#895—94no—
223#894—94no—
224#894—94no—
225#890—94no—
226#889—91no—
227#886—91no—
228#885—91no—
229#879—91no—
230#878—91no—
231C4×D12—34no—
232C4×D12—94no—
233C4×D12—94no—
234#872—94no—
235#872—94no—
236#872—91no—
237#872—184no—
238C42×D3—94no—
239C4×Dic6C3⋊D311yescharacteristic, complemented
240C22×C3⋊D3—31no—
241C22×C3⋊D3—34no—
242C22×C3⋊D3—64no—
243C22×C3⋊D3C22×D311yescharacteristic
244C22×C3⋊D3C22×D311yescharacteristic
245C22×C3×D3—34no—
246C22×C3×D3—34no—
247C32×Q8—62no—
248C2×C32×C4—24no—
249C2×C32×C4—24no—
250C2×C32×C4—24no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—31no—
255C2×C32×C4C22×D314yes—
256C2×C32×C4C22×D314yes—
257C2×C32×C4C22×D314yes—
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—34no—
265C2×C3⋊Dic3—34no—
266C2×C3⋊Dic3—34no—
267C2×C3⋊Dic3—64no—
268C2×C3⋊Dic3—64no—
269C2×C3⋊Dic3—64no—
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D311yescharacteristic
272C4⋊(C3⋊D3)—22no—
273C4⋊(C3⋊D3)—62no—
274C4⋊(C3⋊D3)—62no—
275C4×C3⋊D3—22no—
276C4×C3⋊D3—22no—
277C4×C3⋊D3—616no—
278C4×C3⋊D3—62no—
279C4×C3⋊D3—62no—
280C4×C3⋊D3—62no—
281C4×C3⋊D3—68no—
282C2×C3×Dic3—34no—
283C2×C3×Dic3—34no—
284C2×C3×Dic3C22×D314yes—
285C2×C3×Dic3C22×D314yes—
286C2×C3×Dic3C22×D314yes—
287C2×C3×Dic3C22×D314yes—
288C3×D12—68no—
289C3×C4×D3—68no—
290C3×C4×D3—68no—
291C3×Dic6—28no—
292#626—68no—
293#626—68no—
294D3×Dic3—68no—
295D3×Dic3—68no—
296#529—271noSylow
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C2×C33C2×#4111yescharacteristic
300C3⋊(C3⋊D3)—41no—
301C3×C3⋊D3—22no—
302C3×C3⋊D3—41no—
303C2×C3×Q8—34no—
304C2×C3×D4—91no—
305C22×C3×C4—91no—
306C22×C3×C4—91no—
307C2×#67—91no—
308C2×#67—91no—
309C22×Dic3—91no—
310C22×Dic3—91no—
311C2×D12—34no—
312C2×D12—94no—
313C2×D12—94no—
314C2×C4×D3—34no—
315C2×C4×D3—34no—
316C2×C4×D3—94no—
317C2×C4×D3—94no—
318C2×C4×D3—94no—
319C2×C4×D3—91no—
320C2×C4×D3—184no—
321C2×Dic6C2×C3⋊D311yescharacteristic
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—91no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4—91no—
328C3×C42—24no—
329C3×C42—34no—
330C3×C42—34no—
331C3×C42D3214yes—
332C3×C42C2×C3⋊D311yescharacteristic
333#217—91no—
334#217—91no—
335#217—91no—
336#217—91no—
337(C2×D3)⋊C4—34no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—94no—
340(C2×D3)⋊C4—94no—
341(C2×D3)⋊C4—94no—
342(C2×D3)⋊C4—94no—
343(C2×D3)⋊C4—94no—
344(C2×D3)⋊C4—94no—
345(C2×D3)⋊C4—94no—
346(C2×D3)⋊C4—94no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—91no—
351(C2×D3)⋊C4—184no—
352(C2×D3)⋊C4—184no—
353C4⋊Dic3—34no—
354C4⋊Dic3—94no—
355C4⋊Dic3—94no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3C2×C3⋊D311yescharacteristic
359Dic3⋊C4—94no—
360Dic3⋊C4—94no—
361Dic3⋊C4—94no—
362Dic3⋊C4—94no—
363Dic3⋊C4—91no—
364Dic3⋊C4—91no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—184no—
368Dic3⋊C4—184no—
369Dic3⋊C4C2×C3⋊D311yescharacteristic
370Dic3⋊C4C2×C3⋊D311yescharacteristic
371C4×Dic3—94no—
372C4×Dic3—94no—
373C4×Dic3—94no—
374C4×Dic3—91no—
375C4×Dic3—91no—
376C4×Dic3—91no—
377C4×Dic3—184no—
378C4×Dic3C2×C3⋊D311yescharacteristic
379C4×Dic3C2×C3⋊D311yescharacteristic
380C22×C32—24no—
381C22×C32C23×D314yes—
382C22×C32C23×D311yescharacteristic
383C2×C3⋊D3—21no—
384C2×C3⋊D3—21no—
385C2×C3⋊D3—21no—
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3—68no—
389C2×C3⋊D3—61no—
390C2×C3⋊D3—61no—
391C2×C3⋊D3—64no—
392C2×C3⋊D3—61no—
393C2×C3⋊D3—64no—
394C2×C3⋊D3—64no—
395C2×C3⋊D3—124no—
396C2×C3⋊D3—124no—
397C2×C3⋊D3#23512yes—
398C2×C3×D3—38no—
399C2×C3×D3—64no—
400C2×C3×D3—64no—
401C2×C3×D3—64no—
402C2×C3×D3—64no—
403C2×C3×D3—64no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—28no—
407C32×C4—24no—
408C32×C4—24no—
409C32×C4—32no—
410C32×C4—44no—
411C32×C4—44no—
412C32×C4—61no—
413C32×C4—61no—
414C32×C4—61no—
415C32×C4#23712yes—
416C32×C4#23918yes—
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—68no—
420C3⋊Dic3—61no—
421C3⋊Dic3—61no—
422C3⋊Dic3—64no—
423C3⋊Dic3—61no—
424C3⋊Dic3—64no—
425C3⋊Dic3—64no—
426C3⋊Dic3—124no—
427C3⋊Dic3—124no—
428C3×Dic3—24no—
429C3×Dic3—24no—
430C3×Dic3—24no—
431C3×Dic3—64no—
432C3×Dic3—64no—
433C3×Dic3#23518yes—
434#126—271no—
435#126—271no—
436#125—271no—
437#124—271no—
438#123—271no—
439#123—271no—
440C22⋊Q8—271no—
441#121—271no—
442C4×Q8—31no—
443C4×D4—91no—
444C4×D4—271no—
445C4×D4—271no—
446#117—271no—
447#117—271no—
448C2×C42—271no—
449C33#52911yescharacteristic, complemented, Sylow
450C23×C3—91no—
451C23×C3—91no—
452C22×D3—34no—
453C22×D3—34no—
454C22×D3—94no—
455C22×D3—91no—
456C22×D3—184no—
457C3×Q8—68no—
458C3×D4—182no—
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—34no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—182no—
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—182no—
478C2×Dic3—34no—
479C2×Dic3—34no—
480C2×Dic3—94no—
481C2×Dic3—94no—
482C2×Dic3—94no—
483C2×Dic3—91no—
484C2×Dic3—91no—
485C2×Dic3—91no—
486C2×Dic3—184no—
487C2×Dic3—184no—
488C2×Dic3—184no—
489C2×Dic3—182no—
490C2×Dic3—182no—
491C2×Dic3C22×C3⋊D311yescharacteristic
492C2×Dic3C22×C3⋊D311yescharacteristic
493C2×Dic3C22×C3⋊D311yescharacteristic
494C2×Dic3C22×C3⋊D311yescharacteristic
495D12—68no—
496D12—188no—
497D12—188no—
498C4×D3—68no—
499C4×D3—68no—
500C4×D3—1816no—
501C4×D3—188no—
502C4×D3—188no—
503C4×D3—188no—
504C4×D3—182no—
505Dic6—22no—
506C2×C32—24no—
507C2×C32—24no—
508C2×C32—24no—
509C2×C32C2×#23514yes—
510C2×C32C2×#23511yescharacteristic
511C2×C32C2×#23711yescharacteristic
512C2×C32C2×#23914yes—
513C2×C32D3×#4114yes—
514C2×C32D3×#4111yescharacteristic
515C3⋊D3—22no—
516C3⋊D3—41no—
517C3⋊D3—128no—
518C3⋊D3—121no—
519C3⋊D3—124no—
520C3×D3—68no—
521C3×D3—124no—
522C2×Q8—31no—
523C2×D4—91no—
524C2×D4—271no—
525C2×D4—271no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—271no—
529C22×C4—271no—
530C22×C4—271no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—91no—
535C4⋊C4—271no—
536C4⋊C4—271no—
537C4⋊C4—271no—
538C4⋊C4—271no—
539C4⋊C4—271no—
540C4⋊C4—271no—
541C22⋊C4—91no—
542C22⋊C4—91no—
543C22⋊C4—271no—
544C22⋊C4—271no—
545C22⋊C4—271no—
546C22⋊C4—271no—
547C22⋊C4—271no—
548C22⋊C4—271no—
549C22⋊C4—271no—
550C22⋊C4—271no—
551C42—31no—
552C42—31no—
553C42—271no—
554C42—271no—
555C42—271no—
556C42D3×C3⋊D311yescharacteristic
557C22×C3—24no—
558C22×C3—92no—
559C22×C3—181no—
560C22×C3—181no—
561C22×C3—181no—
562C22×C3—181no—
563C22×C3—181no—
564C22×C3C22×D3214yes—
565C22×C3C23×C3⋊D311yescharacteristic
566C2×D3—38no—
567C2×D3—64no—
568C2×D3—64no—
569C2×D3—64no—
570C2×D3—64no—
571C2×D3—64no—
572C2×D3—188no—
573C2×D3—184no—
574C2×D3—184no—
575C2×D3—184no—
576C2×D3—181no—
577C2×D3—181no—
578C2×D3—181no—
579C2×D3—364no—
580C2×D3—364no—
581C3×C4—24no—
582C3×C4—24no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—28no—
586C3×C4—38no—
587C3×C4—44no—
588C3×C4—44no—
589C3×C4—64no—
590C3×C4—64no—
591C3×C4—64no—
592C3×C4—181no—
593C3×C4—181no—
594C3×C4#379618yes—
595C3×C4#383212yes—
596Dic3—21no—
597Dic3—21no—
598Dic3—21no—
599Dic3—64no—
600Dic3—64no—
601Dic3—188no—
602Dic3—184no—
603Dic3—184no—
604Dic3—184no—
605Dic3—181no—
606Dic3—181no—
607Dic3—181no—
608Dic3—364no—
609Dic3—364no—
610Dic3#382812yes—
611C32—24no—
612C32#553811yescharacteristic, complemented
613C32#558014yescomplemented
614C23—91no—
615C23—91no—
616C23—271no—
617Q8—62no—
618D4—182no—
619D4—542no—
620D4—542no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—91no—
626C2×C4—91no—
627C2×C4—182no—
628C2×C4—182no—
629C2×C4—271no—
630C2×C4—271no—
631C2×C4—271no—
632C2×C4—542no—
633C2×C4—542no—
634C2×C4—542no—
635C2×C4C2×D3×C3⋊D311yescharacteristic
636C2×C4C2×D3×C3⋊D311yescharacteristic
637C2×C4C2×D3×C3⋊D311yescharacteristic
638C2×C3—24no—
639C2×C3—24no—
640C2×C3—24no—
641C2×C3—182no—
642C2×C3—361no—
643C2×C3C2×#379614yes—
644C2×C3D3×#23514yes—
645C2×C3D3×#23514yes—
646C2×C3C2×#382811yescharacteristic
647C2×C3C2×#383211yescharacteristic
648C2×C3#41×C3⋊D311yescharacteristic
649D3—68no—
650D3—124no—
651D3—368no—
652D3—364no—
653D3—361no—
654C22—92no—
655C22—181no—
656C22—181no—
657C22—181no—
658C22—181no—
659C22—181no—
660C22—541no—
661C22—541no—
662C22—541no—
663C22C22×D3×C3⋊D311yescharacteristic
664C4—21no—
665C4—21no—
666C4—32no—
667C4—61no—
668C4—61no—
669C4—61no—
670C4—181no—
671C4—181no—
672C4—541no—
673C4—541no—
674C4—541no—
675C4#8901712yes—
676C3—24no—
677C3#1059391114yescomplemented
678C3#1059605111yescharacteristic, complemented
679C2—182no—
680C2—361no—
681C2—1081no—
682C2C2×#8901711yescharacteristic
683C2D3×#382811yescharacteristic
684C2C3⋊D3×#23511yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
prime radical#11723482C2
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. #11723913C2semidirect
2. C3×C4×C4⋊(C3⋊D3)C2semidirect
3. C32×C4×Dic6C2semidirect
4. C4×#6292C2semidirect
5. C4×#6292C2semidirect
6. #11723493C2semidirect
7. #11723488C2semidirect
9. #11723476C2semidirect
10. C4×Dic3×C3⋊D3C2semidirect
11. #11723437C2semidirect
12. #11723407C2semidirect
13. #11723403C2semidirect
14. #11723401C2semidirect
15. #11723392C2semidirect
64. C4×C4⋊(C3⋊D3)D3semidirect
71. C3×C4×Dic6D3semidirect
239. C4×Dic6C3⋊D3semidirect
449. C33#529semidirect
612. C32#5538semidirect
613. C32#5580semidirect
677. C3#10593911semidirect
678. C3#10596051semidirect

Maximal subgroups

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

subgroupindex
#117239132
C3×C4×C4⋊(C3⋊D3)2
C32×C4×Dic62
C4×#62922
#117234932
#117234882
#117234822
#117234762
C4×Dic3×C3⋊D32
#117234372
#117234072
#117234032
#117234012
#117233922
#105960513
#105939113