Finite Group Databasebeta

← #13177197

Subgroups — #13177197

Order 1728.

1740 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723970C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4#11723631C211yesmaximal, characteristic, complemented
5#11723624C211yesmaximal, characteristic, complemented
6#11723599C211yesmaximal, characteristic, complemented
7#11723597C211yesmaximal, characteristic, complemented
8#11723520C211yesmaximal, characteristic, complemented
9#11723506C211yesmaximal, characteristic, complemented
10#11723471C211yesmaximal, characteristic, complemented
11#11723469C211yesmaximal, characteristic, complemented
12C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#11723444C211yesmaximal, characteristic, complemented
14#11723428C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10596029—31nomaximal
17#10594943—34nomaximal
18C22×C33×C4C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30#88864C2211yescharacteristic
31#88859C2211yescharacteristic
32#88859C2211yescharacteristic
33#88857C2211yescharacteristic
34#88857C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×C4×C3⋊Dic3C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43#88807C2211yescharacteristic
44#88806C2211yescharacteristic
45#88806C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88804C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×C4×D4—31no—
54#64147—31no—
55#64147—31no—
56#64138—31no—
57#64138—31no—
58#64138—34no—
59#64138—64no—
60C4×#638—31no—
61C4×#638D311yescharacteristic, complemented
62#64101—31no—
63C4⋊C4×C3⋊D3—31no—
64#64093—31no—
65#64093—31no—
66#64088—31no—
67#64088—31no—
68C4×C4⋊(C3⋊D3)—31no—
69#64079—31no—
70C3×C4×#67—34no—
71C3×C4×#67D314yescomplemented
72#63971—34no—
73#63970—34no—
74#63958—34no—
75#63956—34no—
76#63906—34no—
77#63880—34no—
78#63879—34no—
79D3×Dic3⋊C4—34no—
80#63867—34no—
81#63859—34no—
82#63850—34no—
83#63836—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×C33×C4—41no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91#6312—41no—
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C3×#638—22no—
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×C4×C3⋊D3—41no—
100C32×#67—22no—
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×C4×D3—41no—
105#6292—22no—
106#6291—41no—
107#6290—22no—
108#6289—22no—
109Dic3×C3⋊D3—22no—
110Dic3×C3⋊D3—41no—
111#5558—94no—
112#5540—91no—
113C2×C32×D4—31no—
114C22×C32×C4—24no—
115C22×C32×C4—31no—
116C22×C32×C4C2×D314yes—
117C22×C32×C4C2×D311yescharacteristic
118C2×#638—31no—
119C2×#638—31no—
120C2×#638—34no—
121C2×#638—31no—
122C2×#638—64no—
123C2×#638C2×D311yescharacteristic
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3C2×D311yescharacteristic
129C2×C3×#67—34no—
130C2×C3×#67C2×D314yes—
131C2×C3×C4×D3—34no—
132C2×C3×C4×D3C2×D314yes—
133C2×#626—34no—
134C2×#626—34no—
135C2×#625—34no—
136C2×#624—34no—
137C2×D3×Dic3—34no—
138C2×D3×Dic3—34no—
139C32×C4⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C22⋊C4—31no—
142C32×C42—31no—
143#3757—31no—
144#3757—34no—
145#3757—31no—
146#3757—31no—
147#3757—64no—
148#3757C2×D311yescharacteristic
149#3752—31no—
150#3752—31no—
151#3752—34no—
152#3752—34no—
153#3752—31no—
154#3752—64no—
155#3752—64no—
156#3752C2×D311yescharacteristic
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—31no—
160#3750—31no—
161#3750—31no—
162#3750—34no—
163#3750—34no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—64no—
168#3750—64no—
169#3750C2×D311yescharacteristic
170C4×C3⋊Dic3—31no—
171C4×C3⋊Dic3C2×D311yescharacteristic
172C3×#217—34no—
173C3×#217C2×D314yes—
174C3×(C2×D3)⋊C4—34no—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×Dic3⋊C4—34no—
177C3×Dic3⋊C4C2×D314yes—
178C3×C4×Dic3—34no—
179C3×C4×Dic3C2×D314yes—
180#3724—34no—
181#3724—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185Dic3⋊Dic3—34no—
186#3722—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33C2411yescharacteristic
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—
205C3⋊(C3⋊Dic3)—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—34no—
215C3×C4×D4—91no—
216#939—91no—
217#939—91no—
218#938—94no—
219#938—94no—
220#930—91no—
221#929—94no—
222#929—94no—
223#929—91no—
224#929—184no—
225C4×#67—34no—
226C4×#67—94no—
227C4×#67C3⋊D311yescharacteristic, complemented
228C2×Dic3⋊C4—91no—
229#894—91no—
230#892—94no—
231D3×C4⋊C4—94no—
232#889—91no—
233#884—94no—
234#884—94no—
235#884—91no—
236#67⋊C4—91no—
237#67⋊C4—91no—
238#879—94no—
239#879—94no—
240#879—91no—
241#876—91no—
242C4×D12—94no—
243#872—91no—
244#870—94no—
245C23×C32—24no—
246C23×C32—31no—
247C23×C32C22×D314yes—
248C23×C32C22×D311yescharacteristic
249C22×C3⋊D3—31no—
250C22×C3⋊D3—34no—
251C22×C3⋊D3—64no—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3C22×D314yes—
255C32×D4—62no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—41no—
262C2×C32×C4—44no—
263C2×C32×C4—48no—
264C2×C32×C4—121no—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D314yes—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269#638—22no—
270#638—62no—
271#638—121no—
272#638—121no—
273#638—124no—
274#638—128no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—34no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C4⋊(C3⋊D3)—62no—
288C4×C3⋊D3—41no—
289C4×C3⋊D3—62no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—121no—
292C3×#67—28no—
293C3×#67—68no—
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—44no—
301C3×C4×D3—124no—
302#626—68no—
303#626—124no—
304#625—68no—
305#624—68no—
306D3×Dic3—68no—
307D3×Dic3—124no—
308#553—271noSylow
309C2×C33—41no—
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C3⋊(C3⋊D3)—41no—
314C3×C3⋊D3—22no—
315C32×D3—41no—
316C2×C3×D4—34no—
317C2×C3×D4—91no—
318C22×C3×C4—24no—
319C22×C3×C4—34no—
320C22×C3×C4—91no—
321C22×C3×C4D3214yes—
322C22×C3×C4C2×C3⋊D311yescharacteristic
323C2×#67—34no—
324C2×#67—94no—
325C2×#67—94no—
326C2×#67—91no—
327C2×#67—94no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—184no—
331C2×#67C2×C3⋊D311yescharacteristic
332C22×Dic3—91no—
333C22×Dic3—91no—
334C2×D12—94no—
335C2×D12—91no—
336C2×C4×D3—34no—
337C2×C4×D3—94no—
338C2×C4×D3—94no—
339C2×C4×D3—91no—
340C2×C4×D3—94no—
341C2×C4×D3C2×C3⋊D311yescharacteristic
342C3×C4⋊C4—34no—
343C3×C4⋊C4—91no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C42—34no—
349C3×C42—91no—
350#217—34no—
351#217—94no—
352#217—94no—
353#217—94no—
354#217—91no—
355#217—184no—
356#217C2×C3⋊D311yescharacteristic
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—184no—
367(C2×D3)⋊C4—184no—
368(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
369C4⋊Dic3—94no—
370C4⋊Dic3—94no—
371C4⋊Dic3—94no—
372C4⋊Dic3—91no—
373Dic3⋊C4—34no—
374Dic3⋊C4—94no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—94no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—184no—
387Dic3⋊C4—184no—
388Dic3⋊C4C2×C3⋊D311yescharacteristic
389C4×Dic3—34no—
390C4×Dic3—94no—
391C4×Dic3—91no—
392C4×Dic3C2×C3⋊D311yescharacteristic
393C22×C32—28no—
394C22×C32—21no—
395C22×C32—24no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—24no—
399C22×C32—24no—
400C22×C32—24no—
401C22×C32—44no—
402C22×C32—44no—
403C22×C32—61no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32C23×D314yes—
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
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—124no—
417C2×C3⋊D3—124no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3#23512yes—
420C2×C3×D3—24no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—38no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—24no—
429C32×C4—24no—
430C32×C4—32no—
431C32×C4—44no—
432C32×C4—44no—
433C32×C4—61no—
434C32×C4—61no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—64no—
442C3⋊Dic3—64no—
443C3⋊Dic3—64no—
444C3⋊Dic3—124no—
445C3⋊Dic3—124no—
446C3⋊Dic3—124no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—64no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452C3×Dic3#23518yes—
453#126—271no—
454#126—271no—
455#125—271no—
456#123—271no—
457#123—271no—
458#121—271no—
459#121—271no—
460#121—271no—
461#121—271no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—271no—
465C4×D4—271no—
466#117—271no—
467C2×C4⋊C4—271no—
468C33#55311yescharacteristic, complemented, Sylow
469C23×C3—24no—
470C23×C3—34no—
471C23×C3—91no—
472C23×C3C2×D3214yes—
473C23×C3C22×C3⋊D311yescharacteristic
474C22×D3—34no—
475C22×D3—94no—
476C22×D3—91no—
477C22×D3—184no—
478C22×D3C22×C3⋊D311yescharacteristic
479C3×D4—68no—
480C3×D4—182no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—44no—
487C2×C3×C4—41no—
488C2×C3×C4—48no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—124no—
493C2×C3×C4—361no—
494C2×C3×C4C2×D3214yes—
495C2×C3×C4C2×D3214yes—
496C2×C3×C4C22×C3⋊D311yescharacteristic
497C2×C3×C4C22×C3⋊D311yescharacteristic
498#67—22no—
499#67—68no—
500#67—182no—
501#67—182no—
502#67—188no—
503#67—364no—
504#67—364no—
505#67—361no—
506#67—368no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—34no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—94no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—184no—
519C2×Dic3—182no—
520C2×Dic3—361no—
521C2×Dic3C22×C3⋊D311yescharacteristic
522C2×Dic3C22×C3⋊D311yescharacteristic
523C2×Dic3C22×C3⋊D311yescharacteristic
524D12—188no—
525D12—361no—
526C4×D3—41no—
527C4×D3—124no—
528C4×D3—188no—
529C4×D3—188no—
530C4×D3—182no—
531C4×D3—364no—
532C2×C32—24no—
533C2×C32—24no—
534C2×C32—24no—
535C2×C32—48no—
536C2×C32—41no—
537C2×C32—44no—
538C2×C32—121no—
539C2×C32C2×#23514yes—
540C2×C32C2×#23511yescharacteristic
541C2×C32#100414yes—
542C2×C32#100411yescharacteristic
543C2×C32D3×#4114yes—
544C2×C32D3×#4111yescharacteristic
545C3⋊D3—22no—
546C3⋊D3—121no—
547C3⋊D3—124no—
548C3⋊D3—244no—
549C3×D3—44no—
550C3×D3—68no—
551C2×D4—31no—
552C2×D4—91no—
553C2×D4—271no—
554C2×D4—271no—
555C2×D4—271no—
556C2×D4—271no—
557C22×C4—31no—
558C22×C4—91no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4D3×C3⋊D311yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—91no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C42—31no—
584C42—91no—
585C42—271no—
586C22×C3—28no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—24no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—92no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3C22×D3214yes—
603C22×C3C23×C3⋊D311yescharacteristic
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—38no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—184no—
611C2×D3—184no—
612C2×D3—184no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—364no—
617C2×D3—364no—
618C2×D3—364no—
619C3×C4—24no—
620C3×C4—24no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—38no—
624C3×C4—44no—
625C3×C4—44no—
626C3×C4—64no—
627C3×C4—64no—
628C3×C4—181no—
629C3×C4—181no—
630C3×C4—181no—
631Dic3—21no—
632Dic3—21no—
633Dic3—64no—
634Dic3—64no—
635Dic3—64no—
636Dic3—184no—
637Dic3—184no—
638Dic3—184no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—364no—
643Dic3—364no—
644Dic3—364no—
645Dic3#382812yes—
646C32—24no—
647C32#554011yescharacteristic, complemented
648C32#555814yescomplemented
649C23—31no—
650C23—91no—
651C23—271no—
652C23C2×D3×C3⋊D311yescharacteristic
653D4—62no—
654D4—182no—
655D4—542no—
656D4—542no—
657D4—1081no—
658D4—1081no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—41no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—121no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—361no—
671C2×C4—542no—
672C2×C4—542no—
673C2×C4—1081no—
674C2×C4C2×D3×C3⋊D311yescharacteristic
675C2×C4C2×D3×C3⋊D311yescharacteristic
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—48no—
680C2×C3—44no—
681C2×C3—41no—
682C2×C3—124no—
683C2×C3—182no—
684C2×C3D3×#23514yes—
685C2×C3D3×#23514yes—
686C2×C3#6433014yes—
687C2×C3C2×#382811yescharacteristic
688C2×C3#6436111yescharacteristic
689C2×C3#41×C3⋊D311yescharacteristic
690D3—41no—
691D3—68no—
692D3—364no—
693D3—361no—
694D3—724no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—61no—
699C22—61no—
700C22—61no—
701C22—92no—
702C22—181no—
703C22—181no—
704C22—541no—
705C22—541no—
706C22—541no—
707C22C22×D3×C3⋊D311yescharacteristic
708C4—21no—
709C4—21no—
710C4—32no—
711C4—61no—
712C4—61no—
713C4—181no—
714C4—181no—
715C4—181no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—24no—
720C3#1059494314yescomplemented
721C3#1059602911yescharacteristic, complemented
722C2—41no—
723C2—121no—
724C2—182no—
725C2—1081no—
726C2D3×#382811yescharacteristic
727C2C3⋊D3×#23511yescharacteristic
728C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11723970C2semidirect
2. C3×C4×#638C2semidirect
3. C32×C4×#67C2semidirect
4. #11723631C2semidirect
5. #11723624C2semidirect
6. #11723599C2semidirect
7. #11723597C2semidirect
8. #11723520C2semidirect
9. #11723506C2semidirect
10. #11723471C2semidirect
11. #11723469C2semidirect
12. C3⋊D3×Dic3⋊C4C2semidirect
13. #11723444C2semidirect
14. #11723428C2semidirect
15. #11723414C2semidirect
61. C4×#638D3semidirect
71. C3×C4×#67D3semidirect
227. C4×#67C3⋊D3semidirect
468. C33#553semidirect
647. C32#5540semidirect
648. C32#5558semidirect
720. C3#10594943semidirect
721. C3#10596029semidirect

Maximal subgroups

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

subgroupindex
#117239702
C3×C4×#6382
C32×C4×#672
#117236312
#117236242
#117235992
#117235972
#117235202
#117235062
#117234712
#117234692
C3⋊D3×Dic3⋊C42
#117234442
#117234282
#117234142
#105960293
#105949433