Finite Group Databasebeta

← #13175320

Subgroups — #13175320

Order 1728.

1668 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723917C211yesmaximal, characteristic, complemented
2C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×#872C211yesmaximal, characteristic, complemented
4#11723520C211yesmaximal, characteristic, complemented
5#11723519C211yesmaximal, characteristic, complemented
6#11723518C211yesmaximal, characteristic, complemented
7#11723514C211yesmaximal, characteristic, complemented
8#11723512C211yesmaximal, characteristic, complemented
9#11723506C211yesmaximal, characteristic, complemented
10#11723482C211yesmaximal, characteristic, complemented
11#11723471C211yesmaximal, characteristic, complemented
12C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#11723438C211yesmaximal, characteristic, complemented
14#11723422C211yesmaximal, characteristic, complemented
15#11723401C211yesmaximal, characteristic, complemented
16#10596001—31nomaximal
17#10593922—34nomaximal
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C33×C42C2211yescharacteristic
31#88859C2211yescharacteristic
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34#88857C2211yescharacteristic
35#88857C2211yescharacteristic
36#88857C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
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#88803C2211yescharacteristic
50#88803C2211yescharacteristic
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#64085—31no—
66#64085—34no—
67#64085—64no—
68C4×C4⋊(C3⋊D3)—31no—
69C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
70C3×C4×D12—34no—
71C3×#872D314yescomplemented
72#63906—34no—
73#63906—34no—
74#63905—34no—
75#63904—34no—
76#63886—34no—
77#63885—34no—
78#63880—34no—
79#63879—34no—
80D3×Dic3⋊C4—34no—
81#63859—34no—
82#63854—34no—
83#63846—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
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
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C3×C4⋊(C3⋊D3)—22no—
97C3×C4×C3⋊D3—41no—
98C3×C4×C3⋊D3—41no—
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C32×C4×D3—22no—
103#6292—22no—
104#6292—22no—
105#6291—41no—
106#6290—22no—
107#6290—41no—
108#6289—41no—
109Dic3×C3⋊D3—22no—
110Dic3×C3⋊D3—41no—
111#5540—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)C2×D311yescharacteristic
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3C2×D311yescharacteristic
124C2×C4×C3⋊D3C2×D311yescharacteristic
125C2×C3×D12—34no—
126C2×C3×C4×D3—34no—
127C2×C3×C4×D3—34no—
128C2×C3×C4×D3C2×D314yes—
129C2×#626—34no—
130C2×#626—34no—
131C2×#626—34no—
132C2×#625—34no—
133C2×#625—34no—
134C2×#624—34no—
135C2×D3×Dic3—34no—
136C2×D3×Dic3—34no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C42—24no—
142C32×C42—31no—
143C32×C42C2×D314yes—
144C32×C42C2×D311yescharacteristic
145#3757—31no—
146#3752—31no—
147#3752—31no—
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3752—34no—
152#3752—34no—
153#3752—34no—
154#3752—64no—
155#3752—64no—
156#3752—64no—
157#3752C2×D311yescharacteristic
158#3752C2×D311yescharacteristic
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—34no—
166#3750—34no—
167#3750—34no—
168#3750—31no—
169#3750—31no—
170#3750—64no—
171#3750—64no—
172#3750—64no—
173C4×C3⋊Dic3—31no—
174C3×(C2×D3)⋊C4—34no—
175C3×(C2×D3)⋊C4—34no—
176C3×(C2×D3)⋊C4C2×D314yes—
177C3×(C2×D3)⋊C4C2×D314yes—
178C3×C4⋊Dic3—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(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—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—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3#4112yes—
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×C4×D4—91no—
215C3×#117—34no—
216#939—91no—
217#939—91no—
218#930—94no—
219#930—91no—
220#929—91no—
221C4×#67—94no—
222C4×#67—91no—
223C2×Dic3⋊C4—91no—
224#895—94no—
225#894—91no—
226#893—94no—
227D3×C4⋊C4—94no—
228#890—94no—
229#889—91no—
230#884—94no—
231#884—94no—
232#884—91no—
233#883—94no—
234#883—94no—
235#67⋊C4—91no—
236#67⋊C4—91no—
237#879—91no—
238#876—94no—
239#876—94no—
240#876—91no—
241#876—184no—
242C4×D12—34no—
243C4×D12—94no—
244#872C3⋊D311yescharacteristic, complemented
245C23×C32—31no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—34no—
248C22×C3⋊D3—64no—
249C22×C3⋊D3C22×D311yescharacteristic
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—34no—
252C22×C3×D3—34no—
253C22×C3×D3C22×D314yes—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—62no—
261C2×C32×C4C22×D314yes—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267#638—62no—
268#638—121no—
269#638—121no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—34no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—64no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3C22×D311yescharacteristic
280C2×C3⋊Dic3C22×D311yescharacteristic
281C4⋊(C3⋊D3)—22no—
282C4⋊(C3⋊D3)—62no—
283C4⋊(C3⋊D3)—62no—
284C4×C3⋊D3—41no—
285C4×C3⋊D3—41no—
286C4×C3⋊D3—62no—
287C4×C3⋊D3—121no—
288C4×C3⋊D3—121no—
289C2×C3×Dic3—34no—
290C2×C3×Dic3—34no—
291C2×C3×Dic3C22×D314yes—
292C2×C3×Dic3C22×D314yes—
293C2×C3×Dic3C22×D314yes—
294C3×D12—68no—
295C3×C4×D3—28no—
296C3×C4×D3—124no—
297C3×C4×D3—124no—
298#626—68no—
299#626—68no—
300#626—124no—
301#625—68no—
302#625—124no—
303#624—124no—
304D3×Dic3—68no—
305D3×Dic3—124no—
306#553—271noSylow
307C2×C33C2×#4111yescharacteristic
308C2×C33C2×#4111yescharacteristic
309C2×C33H(5,𝔽2)11yescharacteristic
310C3⋊(C3⋊D3)—41no—
311C3×C3⋊D3—22no—
312C3×C3⋊D3—41no—
313C32×D3—41no—
314C2×C3×D4—91no—
315C22×C3×C4—34no—
316C22×C3×C4—91no—
317C22×C3×C4—91no—
318C2×#67—94no—
319C2×#67—94no—
320C2×#67—91no—
321C2×#67—94no—
322C2×#67—91no—
323C2×#67—91no—
324C2×#67—91no—
325C22×Dic3—91no—
326C22×Dic3—91no—
327C2×D12—34no—
328C2×D12—94no—
329C2×D12—94no—
330C2×D12—91no—
331C2×C4×D3—34no—
332C2×C4×D3—34no—
333C2×C4×D3—94no—
334C2×C4×D3—94no—
335C2×C4×D3—94no—
336C2×C4×D3—91no—
337C2×C4×D3C2×C3⋊D311yescharacteristic
338C3×C4⋊C4—34no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—91no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C42—24no—
346C3×C42—34no—
347C3×C42D3214yes—
348C3×C42C2×C3⋊D311yescharacteristic
349#217—94no—
350#217—91no—
351#217—91no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—94no—
355(C2×D3)⋊C4—94no—
356(C2×D3)⋊C4—91no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—184no—
364(C2×D3)⋊C4—184no—
365(C2×D3)⋊C4—184no—
366(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
367(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
368C4⋊Dic3—34no—
369C4⋊Dic3—94no—
370C4⋊Dic3—94no—
371C4⋊Dic3—91no—
372Dic3⋊C4—94no—
373Dic3⋊C4—94no—
374Dic3⋊C4—94no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—184no—
384Dic3⋊C4—184no—
385Dic3⋊C4—184no—
386Dic3⋊C4C2×C3⋊D311yescharacteristic
387Dic3⋊C4C2×C3⋊D311yescharacteristic
388C4×Dic3—94no—
389C4×Dic3—91no—
390C4×Dic3C2×C3⋊D311yescharacteristic
391C22×C32—24no—
392C22×C32—61no—
393C22×C32—61no—
394C22×C32—61no—
395C22×C32C23×D314yes—
396C22×C32C23×D311yescharacteristic
397C2×C3⋊D3—21no—
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—61no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—64no—
406C2×C3⋊D3—64no—
407C2×C3⋊D3—64no—
408C2×C3⋊D3—124no—
409C2×C3⋊D3—124no—
410C2×C3⋊D3—124no—
411C2×C3⋊D3#23512yes—
412C2×C3×D3—24no—
413C2×C3×D3—24no—
414C2×C3×D3—24no—
415C2×C3×D3—38no—
416C2×C3×D3—64no—
417C2×C3×D3—64no—
418C2×C3×D3—64no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—24no—
425C32×C4—24no—
426C32×C4—24no—
427C32×C4—32no—
428C32×C4—44no—
429C32×C4—44no—
430C32×C4—44no—
431C32×C4—61no—
432C32×C4—61no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—61no—
436C3⋊Dic3—61no—
437C3⋊Dic3—61no—
438C3⋊Dic3—64no—
439C3⋊Dic3—64no—
440C3⋊Dic3—64no—
441C3⋊Dic3—124no—
442C3⋊Dic3—124no—
443C3⋊Dic3—124no—
444C3×Dic3—24no—
445C3×Dic3—24no—
446C3×Dic3—64no—
447C3×Dic3—64no—
448C3×Dic3#23518yes—
449#126—271no—
450#126—271no—
451#125—271no—
452#123—271no—
453#123—271no—
454#121—271no—
455#121—271no—
456#121—271no—
457#121—271no—
458C4×D4—91no—
459C4×D4—271no—
460C4×D4—271no—
461C4×D4—271no—
462#117—31no—
463C2×C4⋊C4—271no—
464C33#55311yescharacteristic, complemented, Sylow
465C23×C3—34no—
466C23×C3—91no—
467C23×C3—91no—
468C22×D3—34no—
469C22×D3—34no—
470C22×D3—94no—
471C22×D3—91no—
472C22×D3—184no—
473C22×D3C22×C3⋊D311yescharacteristic
474C3×D4—182no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—34no—
479C2×C3×C4—34no—
480C2×C3×C4—34no—
481C2×C3×C4—68no—
482C2×C3×C4—91no—
483C2×C3×C4—91no—
484C2×C3×C4—361no—
485C2×C3×C4—361no—
486C2×C3×C4C2×D3214yes—
487C2×C3×C4C2×D3214yes—
488C2×C3×C4C2×D3214yes—
489C2×C3×C4C22×C3⋊D311yescharacteristic
490C2×C3×C4C22×C3⋊D311yescharacteristic
491C2×C3×C4C22×C3⋊D311yescharacteristic
492#67—182no—
493#67—182no—
494#67—188no—
495#67—182no—
496#67—364no—
497#67—361no—
498#67—364no—
499C2×Dic3—34no—
500C2×Dic3—34no—
501C2×Dic3—94no—
502C2×Dic3—94no—
503C2×Dic3—94no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—184no—
508C2×Dic3—184no—
509C2×Dic3—184no—
510C2×Dic3—182no—
511C2×Dic3—361no—
512C2×Dic3C22×C3⋊D311yescharacteristic
513C2×Dic3C22×C3⋊D311yescharacteristic
514C2×Dic3C22×C3⋊D311yescharacteristic
515D12—68no—
516D12—188no—
517D12—188no—
518D12—361no—
519C4×D3—22no—
520C4×D3—124no—
521C4×D3—124no—
522C4×D3—188no—
523C4×D3—361no—
524C4×D3—364no—
525C4×D3—364no—
526C2×C32—24no—
527C2×C32—24no—
528C2×C32—24no—
529C2×C32—121no—
530C2×C32C2×#23514yes—
531C2×C32C2×#23511yescharacteristic
532C2×C32#100411yescharacteristic
533C2×C32D3×#4114yes—
534C2×C32D3×#4111yescharacteristic
535C2×C32#100914yes—
536C3⋊D3—22no—
537C3⋊D3—41no—
538C3⋊D3—121no—
539C3⋊D3—124no—
540C3⋊D3—244no—
541C3×D3—44no—
542C3×D3—68no—
543C3×D3—124no—
544C2×D4—91no—
545C2×D4—271no—
546C2×D4—271no—
547C2×D4—271no—
548C2×D4—271no—
549C2×D4—271no—
550C22×C4—31no—
551C22×C4—91no—
552C22×C4—91no—
553C22×C4—271no—
554C22×C4—271no—
555C22×C4—271no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—91no—
559C4⋊C4—271no—
560C4⋊C4—271no—
561C4⋊C4—271no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C22⋊C4—31no—
567C22⋊C4—31no—
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—271no—
571C22⋊C4—271no—
572C22⋊C4—271no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C42—31no—
577C42—271no—
578C42D3×C3⋊D311yescharacteristic
579C22×C3—24no—
580C22×C3—64no—
581C22×C3—64no—
582C22×C3—64no—
583C22×C3—92no—
584C22×C3—181no—
585C22×C3—181no—
586C22×C3—181no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3C22×D3214yes—
590C22×C3C23×C3⋊D311yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—21no—
594C2×D3—38no—
595C2×D3—64no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—184no—
601C2×D3—184no—
602C2×D3—184no—
603C2×D3—181no—
604C2×D3—181no—
605C2×D3—181no—
606C2×D3—364no—
607C2×D3—364no—
608C2×D3—364no—
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—38no—
616C3×C4—44no—
617C3×C4—44no—
618C3×C4—44no—
619C3×C4—64no—
620C3×C4—64no—
621C3×C4—181no—
622C3×C4—181no—
623Dic3—21no—
624Dic3—21no—
625Dic3—64no—
626Dic3—64no—
627Dic3—184no—
628Dic3—184no—
629Dic3—184no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—364no—
634Dic3—364no—
635Dic3—364no—
636Dic3#382812yes—
637C32—24no—
638C32#553014yescomplemented
639C32#554011yescharacteristic, complemented
640C23—31no—
641C23—91no—
642C23—91no—
643C23—271no—
644D4—182no—
645D4—542no—
646D4—542no—
647D4—542no—
648D4—1081no—
649D4—1081no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—62no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—271no—
657C2×C4—271no—
658C2×C4—271no—
659C2×C4—361no—
660C2×C4—361no—
661C2×C4—542no—
662C2×C4—1081no—
663C2×C4—1081no—
664C2×C4C2×D3×C3⋊D311yescharacteristic
665C2×C4C2×D3×C3⋊D311yescharacteristic
666C2×C4C2×D3×C3⋊D311yescharacteristic
667C2×C3—24no—
668C2×C3—24no—
669C2×C3—24no—
670C2×C3—124no—
671C2×C3—182no—
672C2×C3—361no—
673C2×C3D3×#23514yes—
674C2×C3D3×#23514yes—
675C2×C3#6430714yes—
676C2×C3C2×#382811yescharacteristic
677C2×C3#41×C3⋊D311yescharacteristic
678C2×C3#6436611yescharacteristic
679D3—41no—
680D3—68no—
681D3—124no—
682D3—364no—
683D3—361no—
684D3—724no—
685C22—61no—
686C22—61no—
687C22—61no—
688C22—92no—
689C22—181no—
690C22—181no—
691C22—181no—
692C22—181no—
693C22—181no—
694C22—541no—
695C22—541no—
696C22—541no—
697C22C22×D3×C3⋊D311yescharacteristic
698C4—21no—
699C4—21no—
700C4—21no—
701C4—32no—
702C4—61no—
703C4—61no—
704C4—181no—
705C4—181no—
706C4—541no—
707C4—541no—
708C4—541no—
709C3—24no—
710C3#1059392214yescomplemented
711C3#1059600111yescharacteristic, complemented
712C2—121no—
713C2—182no—
714C2—361no—
715C2—1081no—
716C2D3×#382811yescharacteristic
717C2C3⋊D3×#23511yescharacteristic
718C2#1172458011yescharacteristic
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. #11723917C2semidirect
2. C3×C4×C4⋊(C3⋊D3)C2semidirect
3. C32×#872C2semidirect
4. #11723520C2semidirect
5. #11723519C2semidirect
6. #11723518C2semidirect
7. #11723514C2semidirect
8. #11723512C2semidirect
9. #11723506C2semidirect
10. #11723482C2semidirect
11. #11723471C2semidirect
12. C3⋊D3×Dic3⋊C4C2semidirect
13. #11723438C2semidirect
14. #11723422C2semidirect
15. #11723401C2semidirect
69. C4×C4⋊(C3⋊D3)D3semidirect
71. C3×#872D3semidirect
244. #872C3⋊D3semidirect
464. C33#553semidirect
638. C32#5530semidirect
639. C32#5540semidirect
710. C3#10593922semidirect
711. C3#10596001semidirect

Maximal subgroups

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

subgroupindex
#117239172
C3×C4×C4⋊(C3⋊D3)2
C32×#8722
#117235202
#117235192
#117235182
#117235142
#117235122
#117235062
#117234822
#117234712
C3⋊D3×Dic3⋊C42
#117234382
#117234222
#117234012
#105960013
#105939223