Finite Group Databasebeta

← #13155850

Subgroups — #13155850

Order 1728.

1160 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×#88811C211yesmaximal, characteristic, complemented
3C2×#88797C211yesmaximal, characteristic, complemented
4C3×#63857C211yesmaximal, characteristic, complemented
5#11722035C211yesmaximal, characteristic, complemented
6C3×#63564C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10591183—31nomaximal
9#10590946—31nomaximal
10#10590596—31nomaximal
11C22×D3×C3⋊D3—21no—
12C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic, complemented
15C2×C32×C4×D3C2211yescharacteristic
16C2×#6292—21no—
17D3×C4⋊(C3⋊D3)—22no—
18D3×C4⋊(C3⋊D3)—22no—
19C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C32×C4⋊Dic3C2211yescharacteristic, complemented
21C2×C32×C3⋊C8C2211yescharacteristic, complemented
22#88811—22no—
23#88797—22no—
24C3×Dic3⋊Dic3—21no—
25C3×(C2×D3)⋊Dic3—21no—
26C22×C4⋊(C3⋊D3)—31no—
27C2×D3×D12—31no—
28C2×D3×D12—31no—
29C2×D3×D12—61no—
30C2×#3744—31no—
31C3×#924—31no—
32C3×#897—31no—
33#63857D311yescharacteristic, complemented
34C2×#3717—31no—
35C2×#3717—31no—
36C2×#3717—31no—
37C2×#3717—61no—
38C2×#3716—31no—
39C2×#3715—31no—
40#63636—31no—
41C3×#830—31no—
42C3×#821—31no—
43C3×(C2×D3)⋊C8—31no—
44C3×#809—31no—
45#63564—31no—
46#63564—31no—
47#63564—61no—
48#63564D311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)D311yescharacteristic, complemented
50C22×C3⋊(C3⋊D3)—21no—
51C22×C3×C3⋊D3—21no—
52C22×C32×D3D411yescharacteristic
53C2×D3×C3⋊D3—24no—
54C2×D3×C3⋊D3—42no—
55C2×D3×C3⋊D3—42no—
56C2×C33×C4C2311yescharacteristic
57C4⋊(C3⋊(C3⋊D3))—21no—
58C4⋊(C3⋊(C3⋊D3))D412yes—
59C2×C3×C3⋊Dic3—21no—
60C3×C4⋊(C3⋊D3)—21no—
61C3×C4⋊(C3⋊D3)D412yes—
62C3×#634—21no—
63C3×#634—21no—
64C2×C32×Dic3—21no—
65C2×C32×Dic3D411yescharacteristic
66C32×C4×D3—21no—
67C32×C4×D3—21no—
68#6292—24no—
69C3×C3⋊(C3⋊C8)—21no—
70C32×C3⋊C8—21no—
71#5046—91no—
72#4776—91no—
73#4731—91no—
74C23×C3⋊D3—61no—
75C22×D32—62no—
76C22×D32—61no—
77C22×D32—61no—
78C22×C32×C4—31no—
79C2×C4⋊(C3⋊D3)—31no—
80C2×C4⋊(C3⋊D3)—31no—
81C2×C4⋊(C3⋊D3)—31no—
82C2×C4⋊(C3⋊D3)—62no—
83C2×C4⋊(C3⋊D3)—61no—
84C2×C4⋊(C3⋊D3)—61no—
85C2×C4⋊(C3⋊D3)—62no—
86C2×C4⋊(C3⋊D3)—61no—
87C2×C4⋊(C3⋊D3)—61no—
88C2×C4⋊(C3⋊D3)—121no—
89C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
90C2×#634C2×D311yescharacteristic, complemented
91C2×C3×D12—31no—
92C2×C3×D12—31no—
93C2×C3×D12—61no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2×D311yescharacteristic
96C2×C3×C4×D3C2×D311yescharacteristic
97C2×C3×Dic6—31no—
98C2×C3×Dic6—31no—
99C2×C3×Dic6—61no—
100C2×#626—62no—
101C2×#626—61no—
102C2×#626—61no—
103D3×D12—62no—
104D3×D12—62no—
105D3×D12—62no—
106D3×D12—62no—
107D3×D12—64no—
108D3×D12—64no—
109C2×C32×C8—31no—
110C32×C4⋊C4—31no—
111C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
112#3744—62no—
113C3×#217—61no—
114C3×(C2×D3)⋊C4—61no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—61no—
117C3×C4⋊Dic3C2×D311yescharacteristic, complemented
118C3×C4⋊Dic3C2×D311yescharacteristic, complemented
119C3×Dic3⋊C4—61no—
120C2×C3×C3⋊C8—21no—
121C2×C3×C3⋊C8—31no—
122C2×C3×C3⋊C8—31no—
123C2×C3×C3⋊C8—61no—
124C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
125C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
126Dic3⋊Dic3—21no—
127(C2×D3)⋊Dic3—21no—
128#3717—62no—
129#3717—62no—
130#3717—64no—
131#3717—62no—
132#3716—62no—
133#3715—62no—
134C22×C33C2×D411yescharacteristic
135C2×C3⋊(C3⋊D3)—22no—
136C2×C3⋊(C3⋊D3)—41no—
137C2×C3⋊(C3⋊D3)—41no—
138C2×C3×C3⋊D3—22no—
139C2×C3×C3⋊D3—41no—
140C2×C3×C3⋊D3—41no—
141C2×C32×D3—21no—
142C2×C32×D3—21no—
143C2×C32×D3SD1612yescomplemented
144D3×C3⋊D3—48no—
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C3×C3⋊Dic3—41no—
148C32×Dic3—21no—
149C32×Dic3—41no—
150C2×D3×D4—91no—
151C22×D12—91no—
152C22×D12—91no—
153C22×D12—181no—
154C3×C22⋊Q8—91no—
155C2×#215—91no—
156C2×#215—91no—
157C2×#214—91no—
158#924—31no—
159C2×#204—91no—
160C2×#204—91no—
161C2×#204—91no—
162C2×#204—181no—
163#897—31no—
164C3×#102—91no—
165C3×C22⋊C8—91no—
166#830—31no—
167#821—31no—
168#821—91no—
169(C2×D3)⋊C8—31no—
170#809—31no—
171#809—91no—
172#809—91no—
173#809—181no—
174C23×C32—31no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—64no—
177C22×C3⋊D3—61no—
178C22×C3⋊D3—62no—
179C22×C3⋊D3—61no—
180C22×C3⋊D3—61no—
181C22×C3⋊D3—121no—
182C22×C3⋊D3—121no—
183C22×C3⋊D3—122no—
184C22×C3⋊D3—122no—
185C22×C3⋊D3—122no—
186C22×C3×D3—21no—
187C22×C3×D3—62no—
188C22×C3×D3—61no—
189C22×C3×D3—61no—
190C22×C3×D3D1211yescharacteristic
191C22×C3×D3#6711yescharacteristic
192C2×D32—68no—
193C2×D32—64no—
194C2×D32—64no—
195C2×D32—124no—
196C2×D32—122no—
197C2×D32—122no—
198C2×D32—124no—
199C2×D32—122no—
200C2×D32—122no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—31no—
205C2×C32×C4—41no—
206C2×C32×C4—61no—
207C2×C32×C4—61no—
208C2×C32×C4—61no—
209C2×C32×C4C22×D311yescharacteristic
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C22×D311yescharacteristic
212C2×C3⋊Dic3—21no—
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—32no—
215C4⋊(C3⋊D3)—32no—
216C4⋊(C3⋊D3)—32no—
217C4⋊(C3⋊D3)—62no—
218C4⋊(C3⋊D3)—62no—
219C4⋊(C3⋊D3)—62no—
220C4⋊(C3⋊D3)—64no—
221C4⋊(C3⋊D3)—61no—
222C4⋊(C3⋊D3)—62no—
223C4⋊(C3⋊D3)—61no—
224C4⋊(C3⋊D3)—61no—
225C4⋊(C3⋊D3)—122no—
226C4⋊(C3⋊D3)—121no—
227C4⋊(C3⋊D3)—121no—
228C4⋊(C3⋊D3)—122no—
229C4⋊(C3⋊D3)D1212yes—
230#634—21no—
231#634—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—121no—
239C2×C3×Dic3D1211yescharacteristic
240C2×C3×Dic3#6711yescharacteristic
241C3×D12—32no—
242C3×D12—32no—
243C3×D12—62no—
244C3×D12—62no—
245C3×D12—61no—
246C3×D12—61no—
247C3×C4×D3—22no—
248C3×C4×D3—22no—
249C3×C4×D3—21no—
250C3×C4×D3—21no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×Dic6—62no—
254C3×Dic6—61no—
255C3×Dic6—61no—
256C3×Dic6—61no—
257C3×Dic6—61no—
258C3×Dic6—121no—
259#626—68no—
260#626—64no—
261#626—64no—
262C32×C8—61no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—22no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—61no—
268C3×C3⋊C8—61no—
269C3×C3⋊C8—121no—
270#450—271noSylow
271C2×C33#12011yescharacteristic
272C2×C33C2×SD1611yescharacteristic
273C2×C33AGL(1,ℤ/8)11yescharacteristic
274C3⋊(C3⋊D3)—42no—
275C3×C3⋊D3—42no—
276C32×D3—22no—
277C23×D3—181no—
278C23×D3—181no—
279C23×D3—182no—
280C23×D3—181no—
281C2×C3×Q8—91no—
282C2×C3×D4—91no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—61no—
286C2×#67—181no—
287D3×D4—182no—
288D3×D4—182no—
289C2×D12—31no—
290C2×D12—31no—
291C2×D12—61no—
292C2×D12—91no—
293C2×D12—91no—
294C2×D12—91no—
295C2×D12—181no—
296C2×D12—181no—
297C2×D12—181no—
298C2×D12—182no—
299C2×D12—182no—
300C2×D12—182no—
301C2×D12—182no—
302C2×D12—184no—
303C2×D12—184no—
304C2×D12—181no—
305C2×D12—181no—
306C2×D12—182no—
307C2×D12—361no—
308C2×C4×D3D3211yescharacteristic
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—61no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8—61no—
315C2×C3×C8—91no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—181no—
320C3×C22⋊C4—181no—
321#217—61no—
322#215—182no—
323#215—182no—
324#214—182no—
325(C2×D3)⋊C4—61no—
326C4⋊Dic3—61no—
327C4⋊Dic3D3211yescharacteristic, complemented
328Dic3⋊C4—61no—
329C2×C3⋊C8—31no—
330C2×C3⋊C8—31no—
331C2×C3⋊C8—61no—
332C2×C3⋊C8D3211yescharacteristic, complemented
333#204—182no—
334#204—182no—
335#204—184no—
336#204—182no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—32no—
341C22×C32—41no—
342C22×C32—61no—
343C22×C32—61no—
344C22×C32C2×D1211yescharacteristic
345C22×C32D3×D411yescharacteristic
346C22×C32C2×#6711yescharacteristic
347C2×C3⋊D3—22no—
348C2×C3⋊D3—41no—
349C2×C3⋊D3—41no—
350C2×C3⋊D3—62no—
351C2×C3⋊D3—64no—
352C2×C3⋊D3—62no—
353C2×C3⋊D3—62no—
354C2×C3⋊D3—122no—
355C2×C3⋊D3—122no—
356C2×C3⋊D3—124no—
357C2×C3⋊D3—128no—
358C2×C3⋊D3—121no—
359C2×C3⋊D3—121no—
360C2×C3⋊D3—122no—
361C2×C3⋊D3—122no—
362C2×C3⋊D3—121no—
363C2×C3⋊D3—121no—
364C2×C3⋊D3—121no—
365C2×C3⋊D3—121no—
366C2×C3⋊D3—241no—
367C2×C3⋊D3—241no—
368C2×C3⋊D3—241no—
369C2×C3⋊D3—241no—
370C2×C3⋊D3—242no—
371C2×C3⋊D3—242no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—21no—
375C2×C3×D3—21no—
376C2×C3×D3—21no—
377C2×C3×D3—21no—
378C2×C3×D3—22no—
379C2×C3×D3—64no—
380C2×C3×D3—62no—
381C2×C3×D3—62no—
382C2×C3×D3—122no—
383C2×C3×D3—122no—
384C2×C3×D3—121no—
385C2×C3×D3—121no—
386C2×C3×D3—121no—
387C2×C3×D3—121no—
388C2×C3×D3#20412yescomplemented
389C2×C3×D3#21512yescomplemented
390D32—1216no—
391D32—128no—
392D32—128no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—61no—
402C32×C4—121no—
403C32×C4C2×D1211yescharacteristic
404C32×C4D3×D411yescharacteristic
405C32×C4D3×D411yescharacteristic
406C32×C4D3×D411yescharacteristic
407C32×C4D3×D411yescharacteristic
408C32×C4D3×D411yescharacteristic
409C3⋊Dic3—41no—
410C3×Dic3—22no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—81no—
416C3×Dic3—122no—
417C3×Dic3—121no—
418C3×Dic3—121no—
419C22×D4—271no—
420C2×SD16—271no—
421C2×SD16—271no—
422C22⋊Q8—91no—
423#102—91no—
424#102—271no—
425C22⋊C8—91no—
426C33#45011yescharacteristic, complemented, Sylow
427C23×C3—31no—
428C23×C3—31no—
429C23×C3—61no—
430C23×C3—181no—
431C22×D3—62no—
432C22×D3—61no—
433C22×D3—61no—
434C22×D3—184no—
435C22×D3—188no—
436C22×D3—184no—
437C22×D3—184no—
438C22×D3—182no—
439C22×D3—181no—
440C22×D3—181no—
441C22×D3—181no—
442C22×D3—361no—
443C22×D3—361no—
444C22×D3—362no—
445C22×D3—362no—
446C22×D3—362no—
447C22×D3—362no—
448C22×D3—364no—
449C22×D3—364no—
450C22×D3—362no—
451C22×D3—362no—
452C22×D3—362no—
453C22×D3#62611yescharacteristic
454C3×Q8—181no—
455C3×Q8—181no—
456C3×D4—92no—
457C3×D4—181no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—41no—
464C2×C3×C4—61no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—121no—
474C2×C3×C4—181no—
475C2×C3×C4C2×D3211yescharacteristic
476C2×C3×C4C2×D3211yescharacteristic
477C2×C3×C4C2×D3211yescharacteristic
478#67—184no—
479C2×Dic3—21no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—121no—
483C2×Dic3#62611yescharacteristic
484D12—32no—
485D12—32no—
486D12—62no—
487D12—62no—
488D12—61no—
489D12—61no—
490D12—92no—
491D12—92no—
492D12—92no—
493D12—182no—
494D12—182no—
495D12—182no—
496D12—182no—
497D12—188no—
498D12—184no—
499D12—184no—
500D12—181no—
501D12—181no—
502D12—181no—
503D12—362no—
504D12—361no—
505D12—361no—
506D12—362no—
507C4×D3—21no—
508C4×D3—21no—
509Dic6—62no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—121no—
515C3×C8—62no—
516C3×C8—61no—
517C3×C8—61no—
518C3×C8—181no—
519C3⋊C8—21no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—121no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32—62no—
536C2×C32#88211yescharacteristic
537C2×C32#88211yescharacteristic
538C2×C32C2×#20411yescharacteristic
539C2×C32#90811yescharacteristic
540C2×C32#91111yescharacteristic
541C2×C32D3×SD1611yescharacteristic
542C2×C32#93711yescharacteristic
543C2×C32C2×#21511yescharacteristic
544C2×C32#94911yescharacteristic
545C3⋊D3—42no—
546C3⋊D3—122no—
547C3⋊D3—124no—
548C3⋊D3—122no—
549C3⋊D3—122no—
550C3⋊D3—242no—
551C3⋊D3—242no—
552C3⋊D3—244no—
553C3×D3—24no—
554C3×D3—22no—
555C3×D3—22no—
556C3×D3—124no—
557C3×D3—122no—
558C3×D3—122no—
559C24—541no—
560C2×Q8—91no—
561C2×D4—91no—
562C2×D4—271no—
563C2×D4—541no—
564C2×D4—542no—
565C2×D4—542no—
566C22×C4—31no—
567SD16—542no—
568SD16—542no—
569C2×C8—31no—
570C2×C8—91no—
571C4⋊C4—31no—
572C4⋊C4—181no—
573C22⋊C4—181no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—32no—
578C22×C3—32no—
579C22×C3—41no—
580C22×C3—62no—
581C22×C3—62no—
582C22×C3—62no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—182no—
588C22×C3—361no—
589C22×C3—361no—
590C22×C3D3×D1211yescharacteristic
591C22×C3C2×#62611yescharacteristic
592C22×C3D3×#6711yescharacteristic
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—64no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—122no—
599C2×D3—122no—
600C2×D3—121no—
601C2×D3—121no—
602C2×D3—121no—
603C2×D3—121no—
604C2×D3—184no—
605C2×D3—182no—
606C2×D3—182no—
607C2×D3—182no—
608C2×D3—362no—
609C2×D3—362no—
610C2×D3—364no—
611C2×D3—368no—
612C2×D3—3616no—
613C2×D3—368no—
614C2×D3—368no—
615C2×D3—362no—
616C2×D3—362no—
617C2×D3—361no—
618C2×D3—361no—
619C2×D3—361no—
620C2×D3—361no—
621C2×D3—361no—
622C2×D3—361no—
623C2×D3—721no—
624C2×D3—721no—
625C2×D3—721no—
626C2×D3—721no—
627C2×D3—722no—
628C2×D3—722no—
629C2×D3#371712yescomplemented
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—62no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—241no—
644C3×C4—361no—
645C3×C4D3×D1211yescharacteristic
646C3×C4D3×D1211yescharacteristic
647C3×C4#380211yescharacteristic
648C3×C4#381111yescharacteristic
649C3×C4#381111yescharacteristic
650C3×C4#381111yescharacteristic
651Dic3—21no—
652Dic3—41no—
653Dic3—122no—
654Dic3—121no—
655Dic3—121no—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32#473111yescharacteristic, complemented
661C32#477611yescharacteristic, complemented
662C32#504611yescharacteristic, complemented
663C23—31no—
664C23—181no—
665C23—544no—
666C23—541no—
667C23—1082no—
668C23—1082no—
669Q8—181no—
670Q8—181no—
671D4—92no—
672D4—181no—
673D4—272no—
674D4—544no—
675D4—541no—
676C2×C4—31no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—181no—
681C2×C4D3311yescharacteristic
682C8—61no—
683C8—181no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—64no—
697C2×C3—62no—
698C2×C3—62no—
699C2×C3—362no—
700C2×C3D3×#20411yescharacteristic
701C2×C3#6379511yescharacteristic
702C2×C3#6382511yescharacteristic
703C2×C3C2×#371711yescharacteristic
704C2×C3#6392211yescharacteristic
705C2×C3#6392311yescharacteristic
706C2×C3#6392511yescharacteristic
707C2×C3D3×#21511yescharacteristic
708C2×C3#6398111yescharacteristic
709D3—22no—
710D3—124no—
711D3—122no—
712D3—122no—
713D3—364no—
714D3—362no—
715D3—362no—
716D3—362no—
717D3—722no—
718D3—722no—
719D3—724no—
720C22—32no—
721C22—61no—
722C22—61no—
723C22—182no—
724C22—361no—
725C22—361no—
726C22—542no—
727C22—1088no—
728C22—1081no—
729C22—1081no—
730C22D3×#62611yescharacteristic
731C4—61no—
732C4—121no—
733C4—361no—
734C4#8895411yescharacteristic
735C4#8895511yescharacteristic
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059059611yescharacteristic, complemented
741C3#1059094611yescharacteristic, complemented
742C3#1059118311yescharacteristic, complemented
743C2—62no—
744C2—362no—
745C2—1082no—
746C2D3×#371711yescharacteristic
747C2#1172287011yescharacteristic
748C2#1172295011yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, Fitting, cosocleC2×C33×C4C23
Frattini, hypercenterC2×C4D33
socleC22×C33C2×D4
prime radicalC2×D3×C4⋊(C3⋊D3)C2
hypocenterC33#450
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88811C2semidirect
3. C2×#88797C2semidirect
4. C3×#63857C2semidirect
5. #11722035C2semidirect
6. C3×#63564C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
14. C2×C3×#634C22semidirect
19. C2×C3×C3⋊(C3⋊C8)C22semidirect
20. C32×C4⋊Dic3C22semidirect
21. C2×C32×C3⋊C8C22semidirect
33. #63857D3semidirect
48. #63564D3semidirect
49. (C2×D3)⋊(C3⋊C8)D3semidirect
90. C2×#634C2×D3semidirect
111. C2×C3⋊(C3⋊C8)C2×D3semidirect
117. C3×C4⋊Dic3C2×D3semidirect
118. C3×C4⋊Dic3C2×D3semidirect
124. C2×C3×C3⋊C8C2×D3semidirect
125. C2×C3×C3⋊C8C2×D3semidirect
143. C2×C32×D3SD16semidirect
327. C4⋊Dic3D32semidirect
332. C2×C3⋊C8D32semidirect
388. C2×C3×D3#204semidirect
389. C2×C3×D3#215semidirect
426. C33#450semidirect
629. C2×D3#3717semidirect
660. C32#4731semidirect
661. C32#4776semidirect
662. C32#5046semidirect
740. C3#10590596semidirect
741. C3#10590946semidirect
742. C3#10591183semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C2×#888112
C2×#887972
C3×#638572
#117220352
C3×#635642
C3×(C2×D3)⋊(C3⋊C8)2
#105911833
#105909463
#105905963