Finite Group Databasebeta

← #13177198

Subgroups — #13177198

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6312C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×#929C211yesmaximal, characteristic, complemented
4#11723631C211yesmaximal, characteristic, complemented
5#11723624C211yesmaximal, characteristic, complemented
6#11723616C211yesmaximal, characteristic, complemented
7#11723596C211yesmaximal, characteristic, complemented
8#11723520C211yesmaximal, characteristic, complemented
9#11723508C211yesmaximal, characteristic, complemented
10#11723472C211yesmaximal, characteristic, complemented
11C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#11723459C211yesmaximal, characteristic, complemented
13#11723448C211yesmaximal, characteristic, complemented
14#11723446C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16#10596132—31nomaximal
17#10594944—34nomaximal
18C22×C33×C4C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30#88864C2211yescharacteristic
31#88859C2211yescharacteristic
32#88857C2211yescharacteristic
33C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×C4×C3⋊Dic3C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43#88807C2211yescharacteristic
44#88806C2211yescharacteristic
45#88806C2211yescharacteristic
46#88806C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×#123—31no—
54#64148—31no—
55#64147—31no—
56C4×#638—31no—
57C4×#638—34no—
58C4×#638—64no—
59C4×#638D311yescharacteristic, complemented
60#64107—31no—
61#64102—31no—
62C4⋊C4×C3⋊D3—31no—
63#64098—31no—
64#64093—31no—
65#64093—31no—
66#64092—31no—
67#64090—31no—
68#64088—31no—
69#64086—31no—
70C3×#929D314yescomplemented
71C3×C4×#67—34no—
72#63971—34no—
73#63971—34no—
74#63970—34no—
75#63956—34no—
76#63906—34no—
77#63902—34no—
78#63881—34no—
79#63877—34no—
80D3×Dic3⋊C4—34no—
81#63870—34no—
82#63868—34no—
83#63853—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—22no—
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C4×C3⋊(C3⋊D3)—41no—
96C3×#638—22no—
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4×C3⋊D3—41no—
101C32×#67—41no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105#6292—22no—
106#6291—41no—
107#6290—22no—
108Dic3×C3⋊D3—22no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—22no—
111#5661—94no—
112#5540—91no—
113C2×C32×D4—31no—
114C22×C32×C4—24no—
115C22×C32×C4C2×D314yes—
116C22×C32×C4C2×D311yescharacteristic
117C2×#638—31no—
118C2×#638—34no—
119C2×#638—31no—
120C2×#638—31no—
121C2×#638—64no—
122C2×#638C2×D311yescharacteristic
123C22×C3⋊Dic3—31no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—34no—
129C2×C4×C3⋊D3—64no—
130C2×C4×C3⋊D3C2×D311yescharacteristic
131C2×C3×#67—34no—
132C2×C3×#67C2×D314yes—
133C2×C3×C4×D3—34no—
134C2×#626—34no—
135C2×#626—34no—
136C2×#625—34no—
137C2×D3×Dic3—34no—
138C2×D3×Dic3—34no—
139C2×D3×Dic3—34no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C22⋊C4—31no—
143C32×C22⋊C4—31no—
144C32×C22⋊C4—31no—
145#3757—31no—
146#3757—34no—
147#3757—31no—
148#3757—64no—
149#3757C2×D311yescharacteristic
150#3752—31no—
151#3752—34no—
152#3752—31no—
153#3752—31no—
154#3752—64no—
155#3752C2×D311yescharacteristic
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158#3750—31no—
159#3750—34no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—64no—
165#3750C2×D311yescharacteristic
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—34no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—64no—
170C4×C3⋊Dic3C2×D311yescharacteristic
171C3×#217—34no—
172C3×#217C2×D314yes—
173C3×(C2×D3)⋊C4—34no—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×(C2×D3)⋊C4C2×D314yes—
176C3×Dic3⋊C4—34no—
177C3×Dic3⋊C4C2×D314yes—
178C3×Dic3⋊C4C2×D314yes—
179C3×C4×Dic3—34no—
180#3724—34no—
181#3724—34no—
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185Dic3⋊Dic3—34no—
186#3722—34no—
187#3722—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)#4112yes—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#123—34no—
215C3×C4×D4—91no—
216#939—94no—
217#939—91no—
218#939—91no—
219#938—94no—
220#930—91no—
221#929C3⋊D311yescharacteristic, complemented
222C4×#67—34no—
223C4×#67—94no—
224C4×#67—91no—
225C4×#67—184no—
226C2×Dic3⋊C4—91no—
227#898—94no—
228#894—91no—
229#893—94no—
230D3×C4⋊C4—94no—
231#889—94no—
232#889—91no—
233#884—94no—
234#884—94no—
235#884—91no—
236#883—94no—
237#67⋊C4—94no—
238#67⋊C4—91no—
239#67⋊C4—91no—
240#879—94no—
241#879—91no—
242#877—94no—
243#876—91no—
244#872—91no—
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—121no—
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×C4C22×D314yes—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—22no—
269#638—62no—
270#638—68no—
271#638—616no—
272#638—62no—
273#638—121no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—62no—
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—121no—
291C4×C3⋊D3—124no—
292C4×C3⋊D3—121no—
293C4×C3⋊D3—128no—
294C3×#67—44no—
295C3×#67—68no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3C22×D314yes—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C3×C4×D3—124no—
303#626—68no—
304#626—124no—
305#625—68no—
306D3×Dic3—68no—
307D3×Dic3—68no—
308D3×Dic3—124no—
309#553—271noSylow
310C2×C33—41no—
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C2×C33H(5,𝔽2)11yescharacteristic
314C3⋊(C3⋊D3)—41no—
315C3×C3⋊D3—22no—
316C32×D3—41no—
317C2×C3×D4—34no—
318C2×C3×D4—91no—
319C22×C3×C4—24no—
320C22×C3×C4—91no—
321C22×C3×C4D3214yes—
322C22×C3×C4C2×C3⋊D311yescharacteristic
323C2×#67—34no—
324C2×#67—94no—
325C2×#67—94no—
326C2×#67—94no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—184no—
331C2×#67C2×C3⋊D311yescharacteristic
332C22×Dic3—94no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C2×D12—94no—
336C2×D12—91no—
337C2×C4×D3—34no—
338C2×C4×D3—94no—
339C2×C4×D3—91no—
340C2×C4×D3—94no—
341C2×C4×D3—94no—
342C2×C4×D3—91no—
343C2×C4×D3—184no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—91no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C42—91no—
353#217—34no—
354#217—94no—
355#217—94no—
356#217—91no—
357#217—184no—
358#217C2×C3⋊D311yescharacteristic
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—91no—
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)⋊C4C2×C3⋊D311yescharacteristic
369(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
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—184no—
386Dic3⋊C4C2×C3⋊D311yescharacteristic
387Dic3⋊C4C2×C3⋊D311yescharacteristic
388C4×Dic3—34no—
389C4×Dic3—94no—
390C4×Dic3—94no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—184no—
394C22×C32—28no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—24no—
398C22×C32—21no—
399C22×C32—24no—
400C22×C32—24no—
401C22×C32—24no—
402C22×C32—44no—
403C22×C32—44no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D314yes—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—68no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—61no—
414C2×C3⋊D3—64no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—64no—
417C2×C3⋊D3—64no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3#23512yes—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—38no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C32×C4—28no—
428C32×C4—21no—
429C32×C4—24no—
430C32×C4—21no—
431C32×C4—24no—
432C32×C4—44no—
433C32×C4—61no—
434C32×C4—61no—
435C32×C4—61no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—32no—
440C3⋊Dic3—38no—
441C3⋊Dic3—68no—
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—24no—
451C3×Dic3—64no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454#126—271no—
455#126—271no—
456#125—271no—
457#123—31no—
458#123—271no—
459#121—271no—
460#121—271no—
461#121—271no—
462#121—271no—
463C4×D4—91no—
464C4×D4—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—271no—
468C2×C4⋊C4—271no—
469C33#55311yescharacteristic, complemented, Sylow
470C23×C3—24no—
471C23×C3—34no—
472C23×C3—91no—
473C23×C3C2×D3214yes—
474C23×C3C22×C3⋊D311yescharacteristic
475C22×D3—34no—
476C22×D3—94no—
477C22×D3—91no—
478C22×D3—184no—
479C22×D3C22×C3⋊D311yescharacteristic
480C3×D4—124no—
481C3×D4—182no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—34no—
487C2×C3×C4—44no—
488C2×C3×C4—41no—
489C2×C3×C4—48no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—361no—
494C2×C3×C4C2×D3214yes—
495C2×C3×C4C2×D3214yes—
496C2×C3×C4C22×C3⋊D311yescharacteristic
497C2×C3×C4C22×C3⋊D311yescharacteristic
498#67—41no—
499#67—68no—
500#67—182no—
501#67—188no—
502#67—182no—
503#67—182no—
504#67—188no—
505#67—1816no—
506#67—364no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—34no—
510C2×Dic3—94no—
511C2×Dic3—91no—
512C2×Dic3—94no—
513C2×Dic3—94no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—184no—
519C2×Dic3—182no—
520C2×Dic3—188no—
521C2×Dic3—361no—
522C2×Dic3C22×C3⋊D311yescharacteristic
523C2×Dic3C22×C3⋊D311yescharacteristic
524C2×Dic3C22×C3⋊D311yescharacteristic
525D12—188no—
526D12—361no—
527C4×D3—124no—
528C4×D3—188no—
529C4×D3—182no—
530C4×D3—364no—
531C4×D3—361no—
532C4×D3—364no—
533C4×D3—368no—
534C2×C32—24no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—48no—
538C2×C32—44no—
539C2×C32—41no—
540C2×C32—121no—
541C2×C32C2×#23511yescharacteristic
542C2×C32#100414yes—
543C2×C32#100411yescharacteristic
544C2×C32D3×#4114yes—
545C2×C32D3×#4114yes—
546C2×C32D3×#4111yescharacteristic
547C3⋊D3—22no—
548C3⋊D3—128no—
549C3⋊D3—124no—
550C3⋊D3—121no—
551C3×D3—44no—
552C3×D3—68no—
553C2×D4—31no—
554C2×D4—91no—
555C2×D4—271no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—91no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4D3×C3⋊D311yescharacteristic
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C42—91no—
586C42—271no—
587C42—271no—
588C22×C3—28no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—24no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—92no—
602C22×C3—181no—
603C22×C3—181no—
604C22×C3C22×D3214yes—
605C22×C3C23×C3⋊D311yescharacteristic
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—38no—
610C2×D3—64no—
611C2×D3—64no—
612C2×D3—188no—
613C2×D3—184no—
614C2×D3—184no—
615C2×D3—184no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—364no—
620C2×D3—364no—
621C3×C4—28no—
622C3×C4—24no—
623C3×C4—24no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—44no—
627C3×C4—64no—
628C3×C4—64no—
629C3×C4—64no—
630C3×C4—181no—
631C3×C4—181no—
632C3×C4—181no—
633Dic3—21no—
634Dic3—21no—
635Dic3—21no—
636Dic3—64no—
637Dic3—64no—
638Dic3—64no—
639Dic3—98no—
640Dic3—92no—
641Dic3—188no—
642Dic3—184no—
643Dic3—184no—
644Dic3—181no—
645Dic3—181no—
646Dic3—364no—
647Dic3—364no—
648C32—24no—
649C32#554011yescharacteristic, complemented
650C32#566114yescomplemented
651C23—31no—
652C23—91no—
653C23—271no—
654C23C2×D3×C3⋊D311yescharacteristic
655D4—121no—
656D4—182no—
657D4—542no—
658D4—542no—
659D4—542no—
660D4—1081no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—41no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—361no—
672C2×C4—542no—
673C2×C4—542no—
674C2×C4—1081no—
675C2×C4—1081no—
676C2×C4C2×D3×C3⋊D311yescharacteristic
677C2×C4C2×D3×C3⋊D311yescharacteristic
678C2×C3—24no—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—48no—
682C2×C3—41no—
683C2×C3—44no—
684C2×C3—124no—
685C2×C3—182no—
686C2×C3D3×#23514yes—
687C2×C3#6430614yes—
688C2×C3#6433014yes—
689C2×C3#6436111yescharacteristic
690C2×C3#41×C3⋊D311yescharacteristic
691C2×C3#41×C3⋊D311yescharacteristic
692D3—41no—
693D3—68no—
694D3—368no—
695D3—361no—
696D3—364no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—61no—
701C22—61no—
702C22—61no—
703C22—92no—
704C22—181no—
705C22—181no—
706C22—541no—
707C22—541no—
708C22—541no—
709C22C22×D3×C3⋊D311yescharacteristic
710C4—21no—
711C4—21no—
712C4—61no—
713C4—61no—
714C4—61no—
715C4—181no—
716C4—181no—
717C4—181no—
718C4—272no—
719C4—541no—
720C4—541no—
721C3—24no—
722C3#1059494414yescomplemented
723C3#1059613211yescharacteristic, complemented
724C2—41no—
725C2—121no—
726C2—182no—
727C2—1081no—
728C2C3⋊D3×#23511yescharacteristic
729C2#1172457811yescharacteristic
730C2#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. C4×#6312C2semidirect
2. C3×C4×#638C2semidirect
3. C32×#929C2semidirect
4. #11723631C2semidirect
5. #11723624C2semidirect
6. #11723616C2semidirect
7. #11723596C2semidirect
8. #11723520C2semidirect
9. #11723508C2semidirect
10. #11723472C2semidirect
11. C3⋊D3×Dic3⋊C4C2semidirect
12. #11723459C2semidirect
13. #11723448C2semidirect
14. #11723446C2semidirect
15. #11723420C2semidirect
59. C4×#638D3semidirect
70. C3×#929D3semidirect
221. #929C3⋊D3semidirect
469. C33#553semidirect
649. C32#5540semidirect
650. C32#5661semidirect
722. C3#10594944semidirect
723. C3#10596132semidirect

Maximal subgroups

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

subgroupindex
C4×#63122
C3×C4×#6382
C32×#9292
#117236312
#117236242
#117236162
#117235962
#117235202
#117235082
#117234722
C3⋊D3×Dic3⋊C42
#117234592
#117234482
#117234462
#117234202
#105961323
#105949443