Finite Group Databasebeta

← #13177221

Subgroups — #13177221

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88857C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×#930C211yesmaximal, characteristic, complemented
4#11723637C211yesmaximal, characteristic, complemented
5#11723637C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11723518C211yesmaximal, characteristic, complemented
9#11723507C211yesmaximal, characteristic, complemented
10#11723474C211yesmaximal, characteristic, complemented
11#11723473C211yesmaximal, characteristic, complemented
12#11723459C211yesmaximal, characteristic, complemented
13#11723428C211yesmaximal, characteristic, complemented
14#11723407C211yesmaximal, characteristic, complemented
15#11723405C211yesmaximal, characteristic, complemented
16#10596072—31nomaximal
17#10594962—34nomaximal
18C22×C33×C4C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×D12C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30#88857C2211yescharacteristic
31#88857C2211yescharacteristic
32#88857C2211yescharacteristic
33#88857C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×C4×C3⋊Dic3C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic
41#88806C2211yescharacteristic
42#88806C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×#121—31no—
54#64148—31no—
55#64148—31no—
56#64148—31no—
57#64144—31no—
58D4×C3⋊Dic3—31no—
59D4×C3⋊Dic3—31no—
60C4×#638D311yescharacteristic, complemented
61C2×#3750—31no—
62C2×#3750—34no—
63C2×#3750—64no—
64#64107—31no—
65#64098—31no—
66#64092—31no—
67#64090—31no—
68#64088—31no—
69#64086—31no—
70C3×#930D314yescomplemented
71C3×C4×#67—34no—
72#63980—34no—
73#63980—34no—
74#67⋊Dic3—34no—
75#67⋊Dic3—34no—
76#63905—34no—
77#63885—34no—
78#63884—34no—
79#63879—34no—
80#63877—34no—
81#63859—34no—
82#63858—34no—
83#63847—34no—
84C23×C33C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×C33×C4—41no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)—22no—
92C2×C3⋊(C3⋊Dic3)—41no—
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C3×#638—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—41no—
102C32×#67—22no—
103C32×#67—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×D12—41no—
107#6290—22no—
108#6290—41no—
109D3×C3⋊Dic3—22no—
110D3×C3⋊Dic3—41no—
111#5601—94no—
112#5540—91no—
113C2×C32×D4—31no—
114C2×C32×D4—31no—
115C2×C32×D4—31no—
116C22×C32×C4—24no—
117C22×C32×C4C2×D314yes—
118C22×C32×C4C2×D311yescharacteristic
119C2×#638—31no—
120C2×#638—31no—
121C2×#638C2×D311yescharacteristic
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—34no—
124C22×C3⋊Dic3—31no—
125C22×C3⋊Dic3—34no—
126C22×C3⋊Dic3—31no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—64no—
129C22×C3⋊Dic3—64no—
130C2×C4×C3⋊D3C2×D311yescharacteristic
131C2×C3×#67—34no—
132C2×C3×#67C2×D314yes—
133C2×C3×#67C2×D314yes—
134C2×C3×D12C2×D314yes—
135C2×C3×C4×D3—34no—
136C2×#625—34no—
137C2×#625—34no—
138C2×D3×Dic3—34no—
139C2×D3×Dic3—34no—
140C32×C4⋊C4—31no—
141C32×C22⋊C4—31no—
142C32×C22⋊C4—31no—
143#3757—31no—
144#3757—31no—
145#3757—31no—
146#3757—31no—
147#3757C2×D311yescharacteristic
148#3752—31no—
149#3752—31no—
150#3752C2×D311yescharacteristic
151C4⋊(C3⋊Dic3)—31no—
152C4⋊(C3⋊Dic3)—31no—
153#3750—31no—
154#3750—31no—
155#3750—31no—
156#3750—31no—
157#3750—34no—
158#3750—34no—
159#3750—34no—
160#3750—34no—
161#3750—31no—
162#3750—31no—
163#3750—64no—
164#3750—64no—
165#3750—64no—
166#3750—64no—
167#3750C2×D311yescharacteristic
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3C2×D311yescharacteristic
171C3×#217—34no—
172C3×(C2×D3)⋊C4—34no—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×C4⋊Dic3C2×D314yes—
176C3×Dic3⋊C4—34no—
177C3×C4×Dic3—34no—
178#3724—34no—
179#3724—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182(C2×D3)⋊Dic3—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33#4112yes—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
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)#4112yes—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#121—34no—
215C3×C4×D4—91no—
216#939—94no—
217#939—94no—
218#939—94no—
219#939—91no—
220#939—91no—
221#935—94no—
222D4×Dic3—94no—
223D4×Dic3—94no—
224#930C3⋊D311yescharacteristic, complemented
225#929—91no—
226C4×#67—34no—
227C4×#67—91no—
228C2×Dic3⋊C4—94no—
229C2×Dic3⋊C4—91no—
230C2×Dic3⋊C4—184no—
231#898—94no—
232#894—91no—
233#889—94no—
234#889—91no—
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×C32—31no—
248C23×C32C22×D314yes—
249C23×C32C22×D311yescharacteristic
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—34no—
252C22×C3×D3C22×D314yes—
253C22×C3×D3C22×D314yes—
254C32×D4—62no—
255C32×D4—62no—
256C32×D4—121no—
257C2×C32×C4—24no—
258C2×C32×C4—24no—
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—121no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—62no—
284C2×C3⋊Dic3—62no—
285C2×C3⋊Dic3—68no—
286C2×C3⋊Dic3—616no—
287C2×C3⋊Dic3—121no—
288C2×C3⋊Dic3—121no—
289C2×C3⋊Dic3—124no—
290C2×C3⋊Dic3—128no—
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C4×C3⋊D3—41no—
295C3×#67—28no—
296C3×#67—28no—
297C3×#67—68no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3C22×D314yes—
302C2×C3×Dic3C22×D314yes—
303C3×D12—44no—
304C3×C4×D3—124no—
305#625—68no—
306#625—124no—
307D3×Dic3—68no—
308D3×Dic3—124no—
309#553—271noSylow
310C2×C33—22no—
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C2×C33H(5,𝔽2)11yescharacteristic
314C3×C3⋊D3—41no—
315C32×D3—41no—
316C32×D3—41no—
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C2×C3×D4—34no—
320C2×C3×D4—91no—
321C22×C3×C4—24no—
322C22×C3×C4—91no—
323C22×C3×C4D3214yes—
324C22×C3×C4C2×C3⋊D311yescharacteristic
325C2×#67—34no—
326C2×#67—94no—
327C2×#67—91no—
328C2×#67—94no—
329C2×#67—91no—
330C2×#67C2×C3⋊D311yescharacteristic
331C2×#67C2×C3⋊D311yescharacteristic
332C22×Dic3—94no—
333C22×Dic3—94no—
334C22×Dic3—94no—
335C22×Dic3—91no—
336C22×Dic3—94no—
337C22×Dic3—91no—
338C22×Dic3—184no—
339C22×Dic3—184no—
340C2×D12C2×C3⋊D311yescharacteristic
341C2×C4×D3—34no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350C3×C42—91no—
351#217—34no—
352#217—94no—
353#217—94no—
354#217—94no—
355#217—94no—
356#217—91no—
357#217—91no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
366(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
367C4⋊Dic3—94no—
368C4⋊Dic3—94no—
369C4⋊Dic3C2×C3⋊D311yescharacteristic
370Dic3⋊C4—34no—
371Dic3⋊C4—94no—
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—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—184no—
386Dic3⋊C4—184no—
387Dic3⋊C4—184no—
388Dic3⋊C4—184no—
389C4×Dic3—34no—
390C4×Dic3—94no—
391C4×Dic3—94no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C22×C32—28no—
395C22×C32—28no—
396C22×C32—24no—
397C22×C32—21no—
398C22×C32—24no—
399C22×C32—21no—
400C22×C32—24no—
401C22×C32—28no—
402C22×C32—61no—
403C22×C32—61no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32#23512yes—
409C22×C32#23718yes—
410C22×C32C23×D314yes—
411C22×C32C23×D311yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—24no—
419C2×C3×D3—24no—
420C2×C3×D3—24no—
421C2×C3×D3—64no—
422C2×C3×D3—64no—
423C2×C3×D3—64no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—24no—
427C32×C4—24no—
428C32×C4—44no—
429C32×C4—44no—
430C32×C4—61no—
431C32×C4—61no—
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—32no—
436C3⋊Dic3—38no—
437C3⋊Dic3—68no—
438C3⋊Dic3—68no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—64no—
442C3⋊Dic3—61no—
443C3⋊Dic3—64no—
444C3⋊Dic3—64no—
445C3⋊Dic3—124no—
446C3⋊Dic3—124no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—64no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452#126—271no—
453#126—271no—
454#125—271no—
455#123—271no—
456#123—271no—
457#121—31no—
458#121—271no—
459#121—271no—
460#121—271no—
461C4×D4—91no—
462C4×D4—271no—
463C4×D4—271no—
464C4×D4—271no—
465#117—271no—
466C2×C4⋊C4—271no—
467C33#55311yescharacteristic, complemented, Sylow
468C23×C3—24no—
469C23×C3—34no—
470C23×C3—34no—
471C23×C3—91no—
472C23×C3C2×D3214yes—
473C23×C3C22×C3⋊D311yescharacteristic
474C22×D3—34no—
475C22×D3C22×C3⋊D311yescharacteristic
476C22×D3C22×C3⋊D311yescharacteristic
477C3×D4—68no—
478C3×D4—68no—
479C3×D4—124no—
480C3×D4—182no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—44no—
486C2×C3×C4—41no—
487C2×C3×C4—48no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—361no—
492C2×C3×C4C2×D3214yes—
493C2×C3×C4C2×D3214yes—
494C2×C3×C4C22×C3⋊D311yescharacteristic
495C2×C3×C4C22×C3⋊D311yescharacteristic
496#67—22no—
497#67—22no—
498#67—68no—
499#67—182no—
500#67—188no—
501#67—361no—
502#67—364no—
503C2×Dic3—34no—
504C2×Dic3—34no—
505C2×Dic3—34no—
506C2×Dic3—94no—
507C2×Dic3—91no—
508C2×Dic3—94no—
509C2×Dic3—94no—
510C2×Dic3—94no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—184no—
515C2×Dic3—184no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—188no—
519C2×Dic3—188no—
520C2×Dic3—182no—
521C2×Dic3—1816no—
522C2×Dic3—364no—
523C2×Dic3—364no—
524C2×Dic3—361no—
525C2×Dic3—368no—
526C2×Dic3C22×C3⋊D311yescharacteristic
527C2×Dic3C22×C3⋊D311yescharacteristic
528D12—41no—
529C4×D3—124no—
530C4×D3—182no—
531C4×D3—361no—
532C2×C32—216no—
533C2×C32—22no—
534C2×C32—28no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—121no—
539C2×C32—121no—
540C2×C32C2×#23511yescharacteristic
541C2×C32C2×#23714yes—
542C2×C32#100414yes—
543C2×C32#100411yescharacteristic
544C2×C32D3×#4114yes—
545C2×C32D3×#4111yescharacteristic
546C3⋊D3—41no—
547C3×D3—44no—
548C3×D3—44no—
549C3×D3—124no—
550C2×D4—31no—
551C2×D4—31no—
552C2×D4—31no—
553C2×D4—91no—
554C2×D4—271no—
555C2×D4—271no—
556C22×C4—91no—
557C22×C4—271no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4D3×C3⋊D311yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—91no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C42—91no—
583C42—271no—
584C42—271no—
585C22×C3—28no—
586C22×C3—28no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—24no—
592C22×C3—28no—
593C22×C3—64no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3#379518yes—
603C22×C3#383012yes—
604C22×C3C22×D3214yes—
605C22×C3C23×C3⋊D311yescharacteristic
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—64no—
613C2×D3—64no—
614C2×D3—64no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—44no—
620C3×C4—44no—
621C3×C4—64no—
622C3×C4—64no—
623C3×C4—181no—
624C3×C4—181no—
625C3×C4—181no—
626Dic3—21no—
627Dic3—21no—
628Dic3—64no—
629Dic3—64no—
630Dic3—64no—
631Dic3—98no—
632Dic3—92no—
633Dic3—188no—
634Dic3—188no—
635Dic3—184no—
636Dic3—184no—
637Dic3—184no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—364no—
642Dic3—364no—
643C32—24no—
644C32#554011yescharacteristic, complemented
645C32#560114yescomplemented
646C23—31no—
647C23—31no—
648C23—91no—
649C23C2×D3×C3⋊D311yescharacteristic
650D4—62no—
651D4—62no—
652D4—121no—
653D4—182no—
654D4—542no—
655D4—1081no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—41no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—361no—
667C2×C4—542no—
668C2×C4—542no—
669C2×C4—1081no—
670C2×C4—1081no—
671C2×C4C2×D3×C3⋊D311yescharacteristic
672C2×C4C2×D3×C3⋊D311yescharacteristic
673C2×C3—216no—
674C2×C3—28no—
675C2×C3—22no—
676C2×C3—24no—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—124no—
680C2×C3—124no—
681C2×C3—361no—
682C2×C3C2×#379514yes—
683C2×C3#6430614yes—
684C2×C3#6433014yes—
685C2×C3C2×#383011yescharacteristic
686C2×C3#6436111yescharacteristic
687C2×C3#41×C3⋊D311yescharacteristic
688D3—41no—
689D3—41no—
690D3—124no—
691C22—21no—
692C22—21no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—61no—
697C22—61no—
698C22—61no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22#8901412yes—
703C22C22×D3×C3⋊D311yescharacteristic
704C4—21no—
705C4—21no—
706C4—61no—
707C4—61no—
708C4—181no—
709C4—181no—
710C4—181no—
711C4—272no—
712C4—541no—
713C4—541no—
714C4—541no—
715C3—24no—
716C3#1059496214yescomplemented
717C3#1059607211yescharacteristic, complemented
718C2—22no—
719C2—121no—
720C2—121no—
721C2—361no—
722C2C2×#8901411yescharacteristic
723C2#1172457811yescharacteristic
724C2#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. C2×#88857C2semidirect
2. C3×C4×#638C2semidirect
3. C32×#930C2semidirect
4. #11723637C2semidirect
5. #11723637C2semidirect
6. #67⋊(C3⋊Dic3)C2semidirect
7. #67⋊(C3⋊Dic3)C2semidirect
8. #11723518C2semidirect
9. #11723507C2semidirect
10. #11723474C2semidirect
11. #11723473C2semidirect
12. #11723459C2semidirect
13. #11723428C2semidirect
14. #11723407C2semidirect
15. #11723405C2semidirect
60. C4×#638D3semidirect
70. C3×#930D3semidirect
224. #930C3⋊D3semidirect
467. C33#553semidirect
644. C32#5540semidirect
645. C32#5601semidirect
716. C3#10594962semidirect
717. C3#10596072semidirect

Maximal subgroups

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

subgroupindex
C2×#888572
C3×C4×#6382
C32×#9302
#117236372
#67⋊(C3⋊Dic3)2
#117235182
#117235072
#117234742
#117234732
#117234592
#117234282
#117234072
#117234052
#105960723
#105949623