Finite Group Databasebeta

← #13155854

Subgroups — #13155854

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×C3⋊D3×D12C211yesmaximal, characteristic
2#11723674C211yesmaximal, characteristic, complemented
3C2×#88797C211yesmaximal, characteristic, complemented
4C2×C3×#3716C211yesmaximal, characteristic, complemented
5#11722036C211yesmaximal, characteristic, complemented
6C3×#63563C211yesmaximal, characteristic, complemented
7C3×#63557C211yesmaximal, characteristic, complemented
8#10591467—31nomaximal
9#10590946—31nomaximal
10#10590942—31nomaximal
11C22×D3×C3⋊D3—21no—
12C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
13C2×C3×C4×C3⋊D3C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic, complemented
15C2×C32×D12C2211yescharacteristic
16C2×#6291—21no—
17C3⋊D3×D12—22no—
18C3⋊D3×D12—22no—
19C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
20C2×C32×C3⋊C8C2211yescharacteristic, complemented
21C2×C32×C3⋊C8C2211yescharacteristic, complemented
22#88815—21no—
23#88814—21no—
24#88797—22no—
25C3×#3716—22no—
26C2×D4×C3⋊D3—31no—
27C2×D3×D12—31no—
28C2×D3×D12—31no—
29C2×D3×D12—61no—
30C2×#3744—31no—
31C2×C3×#214—31no—
32C2×C3×#204—31no—
33#63871—31no—
34#63857—31no—
35#63856—31no—
36C2×#3717—31no—
37C2×#3717—31no—
38C2×#3717—61no—
39C2×#3716D311yescharacteristic, complemented
40#63648—31no—
41C3×#832—31no—
42C3×#821—31no—
43C3×(C2×D3)⋊C8—31no—
44C3×(C2×D3)⋊C8—31no—
45#63564—31no—
46#63564—31no—
47#63564—61no—
48#63563D311yescharacteristic, complemented
49#63557D311yescharacteristic, complemented
50C22×C3⋊(C3⋊D3)—21no—
51C22×C3×C3⋊D3D411yescharacteristic
52C22×C32×D3—21no—
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—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3D411yescharacteristic
62C3×C4×C3⋊D3—21no—
63C3×C4×C3⋊D3—21no—
64C3×#634—21no—
65C3×#634—21no—
66C32×D12—21no—
67C32×D12D412yes—
68#6291—24no—
69C32×C3⋊C8—21no—
70C32×C3⋊C8—21no—
71#5169—91no—
72#4776—91no—
73#4731—91no—
74C23×C3⋊D3—61no—
75C22×D32—61no—
76C22×D32—61no—
77C22×D32—62no—
78C2×C32×D4—31no—
79C2×#638—61no—
80D4×C3⋊D3—62no—
81D4×C3⋊D3—62no—
82C2×C4⋊(C3⋊D3)—31no—
83C2×C4⋊(C3⋊D3)—31no—
84C2×C4⋊(C3⋊D3)—31no—
85C2×C4⋊(C3⋊D3)—61no—
86C2×C4⋊(C3⋊D3)—61no—
87C2×C4⋊(C3⋊D3)—61no—
88C2×C4⋊(C3⋊D3)—121no—
89C2×C4×C3⋊D3C2×D311yescharacteristic
90C2×#634C2×D311yescharacteristic, complemented
91C2×C3×D12—21no—
92C2×C3×D12C2×D311yescharacteristic
93C2×C3×D12C2×D311yescharacteristic
94C2×C3×C4×D3—31no—
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—61no—
97C2×C3×Dic6—31no—
98C2×C3×Dic6—31no—
99C2×C3×Dic6—61no—
100C2×#626—61no—
101C2×#626—61no—
102C2×#626—62no—
103D3×D12—62no—
104D3×D12—62no—
105D3×D12—64no—
106D3×D12—64no—
107D3×D12—62no—
108D3×D12—62no—
109C2×C32×C8—31no—
110C2×C32×C8—31no—
111C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
112#3744—62no—
113C3×#214—62no—
114C3×C4⋊Dic3—31no—
115C3×C4⋊Dic3—31no—
116C3×C4⋊Dic3—61no—
117C2×C3×C3⋊C8—21no—
118C2×C3×C3⋊C8—21no—
119C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
120C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
121C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
122C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
123C3×#204—62no—
124#3724—61no—
125Dic3⋊Dic3—61no—
126Dic3⋊Dic3—61no—
127#3722—61no—
128(C2×D3)⋊Dic3—61no—
129(C2×D3)⋊Dic3—61no—
130#3717—62no—
131#3717—62no—
132#3717—64no—
133#3716—22no—
134C22×C33C2×D411yescharacteristic
135C2×C3⋊(C3⋊D3)—22no—
136C2×C3⋊(C3⋊D3)—41no—
137C2×C3⋊(C3⋊D3)—41no—
138C2×C3×C3⋊D3—21no—
139C2×C3×C3⋊D3—21no—
140C2×C3×C3⋊D3SD1612yescomplemented
141C2×C32×D3—22no—
142C2×C32×D3—41no—
143C2×C32×D3—41no—
144D3×C3⋊D3—48no—
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C3×C3⋊Dic3—21no—
148C3×C3⋊Dic3—41no—
149C3×C3⋊Dic3—41no—
150C2×D3×D4—91no—
151C2×D3×D4—91no—
152C2×D3×D4—181no—
153C22×D12—91no—
154C2×C3×SD16—91no—
155#946—91no—
156C2×#215—91no—
157C2×#214—31no—
158#924—91no—
159C2×#204—31no—
160C2×#204—91no—
161C2×#204—91no—
162C2×#204—181no—
163#897—91no—
164C3×#102—91no—
165C3×C22⋊C8—91no—
166#832—31no—
167#821—31no—
168#821—91no—
169#821—91no—
170#821—181no—
171(C2×D3)⋊C8—31no—
172(C2×D3)⋊C8—31no—
173#809—91no—
174C23×C32—61no—
175C22×C3⋊D3—64no—
176C22×C3⋊D3—61no—
177C22×C3⋊D3—62no—
178C22×C3⋊D3—61no—
179C22×C3⋊D3—61no—
180C22×C3⋊D3—121no—
181C22×C3⋊D3—121no—
182C22×C3⋊D3—122no—
183C22×C3⋊D3—122no—
184C22×C3⋊D3—122no—
185C22×C3⋊D3D1211yescharacteristic
186C22×C3×D3—22no—
187C22×C3×D3—21no—
188C22×C3×D3—21no—
189C22×C3×D3—31no—
190C22×C3×D3—31no—
191C22×C3×D3—61no—
192C2×D32—68no—
193C2×D32—64no—
194C2×D32—64no—
195C2×D32—122no—
196C2×D32—122no—
197C2×D32—124no—
198C2×D32—124no—
199C2×D32—122no—
200C2×D32—122no—
201C32×D4—32no—
202C32×D4—61no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—41no—
207C2×C32×C4C22×D311yescharacteristic
208C2×C32×C4C22×D311yescharacteristic
209C2×C32×C4C22×D311yescharacteristic
210#638—64no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3D1211yescharacteristic
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)—61no—
221C4⋊(C3⋊D3)—62no—
222C4⋊(C3⋊D3)—61no—
223C4⋊(C3⋊D3)—61no—
224C4⋊(C3⋊D3)—122no—
225C4⋊(C3⋊D3)—121no—
226C4⋊(C3⋊D3)—121no—
227C4⋊(C3⋊D3)—122no—
228C4×C3⋊D3—21no—
229C4×C3⋊D3—21no—
230#634—21no—
231#634—21no—
232C2×C3×Dic3—31no—
233C2×C3×Dic3—31no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—121no—
240C2×C3×Dic3—121no—
241C3×D12—22no—
242C3×D12—21no—
243C3×D12—21no—
244C3×D12—22no—
245C3×D12D1212yes—
246C3×D12#6712yes—
247C3×C4×D3—62no—
248C3×C4×D3—62no—
249C3×C4×D3—61no—
250C3×C4×D3—61no—
251C3×C4×D3—61no—
252C3×C4×D3—61no—
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—
263C32×C8—61no—
264C3×C3⋊C8—22no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—41no—
270#450—271noSylow
271C2×C33#12011yescharacteristic
272C2×C33C2×SD1611yescharacteristic
273C2×C33AGL(1,ℤ/8)11yescharacteristic
274C3⋊(C3⋊D3)—42no—
275C3×C3⋊D3—22no—
276C32×D3—42no—
277C23×D3—181no—
278C23×D3—181no—
279C23×D3—181no—
280C23×D3—182no—
281C2×C3×Q8—91no—
282C2×C3×D4—31no—
283C2×C3×D4—31no—
284C2×C3×D4—61no—
285C22×C3×C4—91no—
286C2×#67—181no—
287C2×#67—181no—
288C2×#67—182no—
289D3×D4—182no—
290D3×D4—182no—
291D3×D4—182no—
292D3×D4—182no—
293D3×D4—184no—
294D3×D4—184no—
295C2×D12—91no—
296C2×D12—91no—
297C2×D12—91no—
298C2×D12—181no—
299C2×D12—181no—
300C2×D12—181no—
301C2×D12—182no—
302C2×D12—181no—
303C2×D12—182no—
304C2×D12—361no—
305C2×D12D3211yescharacteristic
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—61no—
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—61no—
312C3×SD16—182no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8—61no—
318C2×C3×C8—61no—
319C3×C4⋊C4—91no—
320#217—181no—
321#215—182no—
322#214—62no—
323(C2×D3)⋊C4—181no—
324(C2×D3)⋊C4—181no—
325C4⋊Dic3—31no—
326C4⋊Dic3—31no—
327C4⋊Dic3—61no—
328C4⋊Dic3—181no—
329Dic3⋊C4—181no—
330Dic3⋊C4—181no—
331C2×C3⋊C8D3211yescharacteristic, complemented
332C2×C3⋊C8D3211yescharacteristic, complemented
333#204—62no—
334#204—182no—
335#204—182no—
336#204—184no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—41no—
341C22×C32—62no—
342C22×C32—121no—
343C22×C32—121no—
344C22×C32C2×D1211yescharacteristic
345C22×C32D3×D411yescharacteristic
346C22×C32D3×D411yescharacteristic
347C2×C3⋊D3—21no—
348C2×C3⋊D3—21no—
349C2×C3⋊D3—62no—
350C2×C3⋊D3—64no—
351C2×C3⋊D3—62no—
352C2×C3⋊D3—62no—
353C2×C3⋊D3—122no—
354C2×C3⋊D3—122no—
355C2×C3⋊D3—124no—
356C2×C3⋊D3—128no—
357C2×C3⋊D3—121no—
358C2×C3⋊D3—121no—
359C2×C3⋊D3—122no—
360C2×C3⋊D3—122no—
361C2×C3⋊D3—121no—
362C2×C3⋊D3—121no—
363C2×C3⋊D3—121no—
364C2×C3⋊D3—121no—
365C2×C3⋊D3—241no—
366C2×C3⋊D3—241no—
367C2×C3⋊D3—241no—
368C2×C3⋊D3—241no—
369C2×C3⋊D3—242no—
370C2×C3⋊D3—242no—
371C2×C3⋊D3#20412yescomplemented
372C2×C3×D3—24no—
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—32no—
376C2×C3×D3—32no—
377C2×C3×D3—42no—
378C2×C3×D3—42no—
379C2×C3×D3—41no—
380C2×C3×D3—41no—
381C2×C3×D3—41no—
382C2×C3×D3—41no—
383C2×C3×D3—62no—
384C2×C3×D3—62no—
385C2×C3×D3—62no—
386C2×C3×D3—61no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C2×C3×D3—61no—
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×C4C2×D1211yescharacteristic
402C32×C4D3×D411yescharacteristic
403C32×C4D3×D411yescharacteristic
404C32×C4D3×D411yescharacteristic
405C32×C4D3×D411yescharacteristic
406C32×C4C2×#6711yescharacteristic
407C3⋊Dic3—21no—
408C3⋊Dic3—41no—
409C3⋊Dic3—41no—
410C3×Dic3—62no—
411C3×Dic3—61no—
412C3×Dic3—61no—
413C3×Dic3—122no—
414C3×Dic3—121no—
415C3×Dic3—121no—
416C3×Dic3—121no—
417C3×Dic3—121no—
418C3×Dic3—241no—
419C22×D4—271no—
420C2×SD16—91no—
421C2×SD16—271no—
422C22⋊Q8—271no—
423#102—91no—
424#102—271no—
425C22⋊C8—91no—
426C33#45011yescharacteristic, complemented, Sylow
427C23×C3—62no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—91no—
431C22×D3—21no—
432C22×D3—31no—
433C22×D3—31no—
434C22×D3—61no—
435C22×D3—184no—
436C22×D3—188no—
437C22×D3—184no—
438C22×D3—184no—
439C22×D3—182no—
440C22×D3—181no—
441C22×D3—181no—
442C22×D3—181no—
443C22×D3—361no—
444C22×D3—361no—
445C22×D3—362no—
446C22×D3—362no—
447C22×D3—362no—
448C22×D3—362no—
449C22×D3—362no—
450C22×D3—364no—
451C22×D3—364no—
452C22×D3—362no—
453C22×D3—362no—
454C3×Q8—181no—
455C3×Q8—181no—
456C3×D4—32no—
457C3×D4—32no—
458C3×D4—62no—
459C3×D4—62no—
460C3×D4—61no—
461C3×D4—61no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—41no—
466C2×C3×C4—91no—
467C2×C3×C4—181no—
468C2×C3×C4—181no—
469C2×C3×C4—181no—
470C2×C3×C4—181no—
471C2×C3×C4C2×D3211yescharacteristic
472C2×C3×C4C2×D3211yescharacteristic
473C2×C3×C4C2×D3211yescharacteristic
474#67—188no—
475#67—184no—
476#67—184no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486D12—21no—
487D12—92no—
488D12—92no—
489D12—92no—
490D12—182no—
491D12—182no—
492D12—182no—
493D12—182no—
494D12—184no—
495D12—181no—
496D12—181no—
497D12—181no—
498D12—362no—
499D12—361no—
500D12—361no—
501D12—362no—
502D12#62612yes—
503C4×D3—62no—
504C4×D3—62no—
505C4×D3—61no—
506C4×D3—61no—
507C4×D3—61no—
508C4×D3—61no—
509Dic6—62no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—121no—
515C3×C8—62no—
516C3×C8—61no—
517C3×C8—61no—
518C3×C8—61no—
519C3×C8—61no—
520C3×C8—121no—
521C3⋊C8—21no—
522C3⋊C8—21no—
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—122no—
536C2×C32#88211yescharacteristic
537C2×C32#88211yescharacteristic
538C2×C32C2×#20411yescharacteristic
539C2×C32#90811yescharacteristic
540C2×C32#91111yescharacteristic
541C2×C32D3×SD1611yescharacteristic
542C2×C32D3×SD1611yescharacteristic
543C2×C32#91411yescharacteristic
544C2×C32#93711yescharacteristic
545C3⋊D3—22no—
546C3⋊D3—122no—
547C3⋊D3—124no—
548C3⋊D3—122no—
549C3⋊D3—122no—
550C3⋊D3—242no—
551C3⋊D3—242no—
552C3⋊D3—244no—
553C3×D3—44no—
554C3×D3—42no—
555C3×D3—42no—
556C3×D3—64no—
557C3×D3—62no—
558C3×D3—62no—
559C24—541no—
560C2×Q8—91no—
561C2×D4—31no—
562C2×D4—271no—
563C2×D4—541no—
564C2×D4—542no—
565C2×D4—542no—
566C22×C4—91no—
567SD16—182no—
568SD16—542no—
569C2×C8—31no—
570C2×C8—31no—
571C4⋊C4—91no—
572C4⋊C4—541no—
573C22⋊C4—541no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—41no—
578C22×C3—64no—
579C22×C3—62no—
580C22×C3—62no—
581C22×C3—92no—
582C22×C3—122no—
583C22×C3—122no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3—181no—
589C22×C3—181no—
590C22×C3D3×D1211yescharacteristic
591C22×C3D3×D1211yescharacteristic
592C22×C3#381111yescharacteristic
593C2×D3—22no—
594C2×D3—32no—
595C2×D3—32no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—184no—
606C2×D3—182no—
607C2×D3—182no—
608C2×D3—182no—
609C2×D3—362no—
610C2×D3—362no—
611C2×D3—364no—
612C2×D3—368no—
613C2×D3—3616no—
614C2×D3—368no—
615C2×D3—368no—
616C2×D3—362no—
617C2×D3—362no—
618C2×D3—361no—
619C2×D3—361no—
620C2×D3—361no—
621C2×D3—361no—
622C2×D3—361no—
623C2×D3—361no—
624C2×D3—721no—
625C2×D3—721no—
626C2×D3—721no—
627C2×D3—721no—
628C2×D3—722no—
629C2×D3—722no—
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—181no—
639C3×C4—361no—
640C3×C4—361no—
641C3×C4D3×D1211yescharacteristic
642C3×C4#380211yescharacteristic
643C3×C4C2×#62611yescharacteristic
644C3×C4D3×#6711yescharacteristic
645C3×C4#381111yescharacteristic
646C3×C4#381111yescharacteristic
647Dic3—62no—
648Dic3—61no—
649Dic3—61no—
650Dic3—122no—
651Dic3—121no—
652Dic3—121no—
653Dic3—121no—
654Dic3—121no—
655Dic3—241no—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32#473111yescharacteristic, complemented
661C32#477611yescharacteristic, complemented
662C32#516911yescharacteristic, complemented
663C23—61no—
664C23—91no—
665C23—544no—
666C23—541no—
667C23—1082no—
668C23—1082no—
669Q8—181no—
670Q8—181no—
671D4—32no—
672D4—61no—
673D4—272no—
674D4—544no—
675D4—541no—
676C2×C4—91no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4D3311yescharacteristic
682C8—61no—
683C8—61no—
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—124no—
697C2×C3—122no—
698C2×C3—122no—
699C2×C3—182no—
700C2×C3D3×#20411yescharacteristic
701C2×C3D3×#20411yescharacteristic
702C2×C3#6379411yescharacteristic
703C2×C3#6379511yescharacteristic
704C2×C3#6392211yescharacteristic
705C2×C3#6392311yescharacteristic
706C2×C3#6393011yescharacteristic
707C2×C3#6393711yescharacteristic
708C2×C3#6398111yescharacteristic
709D3—42no—
710D3—64no—
711D3—62no—
712D3—62no—
713D3—364no—
714D3—362no—
715D3—362no—
716D3—362no—
717D3—722no—
718D3—722no—
719D3—724no—
720C22—62no—
721C22—92no—
722C22—121no—
723C22—121no—
724C22—181no—
725C22—181no—
726C22—542no—
727C22—1088no—
728C22—1081no—
729C22—1081no—
730C22#8895511yescharacteristic
731C4—181no—
732C4—361no—
733C4—361no—
734C4D3×#62611yescharacteristic
735C4#8895411yescharacteristic
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059094211yescharacteristic, complemented
741C3#1059094611yescharacteristic, complemented
742C3#1059146711yescharacteristic, complemented
743C2—122no—
744C2—182no—
745C2—1082no—
746C2#1172284211yescharacteristic
747C2#1172287911yescharacteristic
748C2#1172295011yescharacteristic
subgroupG/H
centerC22#88955
commutator, Fitting, cosocleC2×C33×C4C23
Frattini, hypercenterC2×C4D33
socleC22×C33C2×D4
prime radicalC2×C3⋊D3×D12C2
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. #11723674C2semidirect
3. C2×#88797C2semidirect
4. C2×C3×#3716C2semidirect
5. #11722036C2semidirect
6. C3×#63563C2semidirect
7. C3×#63557C2semidirect
14. C2×C3×#634C22semidirect
19. C3×C4⋊(C3⋊Dic3)C22semidirect
20. C2×C32×C3⋊C8C22semidirect
21. C2×C32×C3⋊C8C22semidirect
39. C2×#3716D3semidirect
48. #63563D3semidirect
49. #63557D3semidirect
90. C2×#634C2×D3semidirect
111. C4⋊(C3⋊Dic3)C2×D3semidirect
119. C2×C3×C3⋊C8C2×D3semidirect
120. C2×C3×C3⋊C8C2×D3semidirect
121. C2×C3×C3⋊C8C2×D3semidirect
122. C2×C3×C3⋊C8C2×D3semidirect
140. C2×C3×C3⋊D3SD16semidirect
331. C2×C3⋊C8D32semidirect
332. C2×C3⋊C8D32semidirect
371. C2×C3⋊D3#204semidirect
426. C33#450semidirect
660. C32#4731semidirect
661. C32#4776semidirect
662. C32#5169semidirect
740. C3#10590942semidirect
741. C3#10590946semidirect
742. C3#10591467semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×D122
#117236742
C2×#887972
C2×C3×#37162
#117220362
C3×#635632
C3×#635572
#105914673
#105909463
#105909423