Finite Group Databasebeta

← C2×#10591709 #11808157

Subgroups — C2×#10591709 #11808157

Order 1152.

2841 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×#3757C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7#10591709C218yesmaximal, direct product factor
8C2×#63579C211yesmaximal, characteristic, complemented
9C2×#5222—31nomaximal
10C2×#4961—31nomaximal
11C25×C32C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67—24no—
16C22×C3×#67—24no—
17C22×C3×#67—24no—
18C22×C3×#67C2214yes—
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C2×#3757—24no—
23C2×#3757C2214yescomplemented
24C2×C3×#217—24no—
25C2×C3×#217C2214yescomplemented
26C2×Dic3⋊Dic3—24no—
27C2×Dic3⋊Dic3C2214yescomplemented
28C2×(C2×D3)⋊Dic3—24no—
29C2×(C2×D3)⋊Dic3—24no—
30C2×(C2×D3)⋊Dic3C2214yescomplemented
31C2×(C2×D3)⋊Dic3C2214yescomplemented
32#63579C2214yescomplemented
33C23×C3×D4—31no—
34C23×#67D311yescharacteristic
35C22×C3×C22⋊C4—31no—
36C22×#217—31no—
37C22×#217—31no—
38C22×#217—31no—
39C22×#217—31no—
40C22×#217—61no—
41C22×#217D311yescharacteristic, complemented
42C22×(C2×D3)⋊C4—31no—
43C22×(C2×D3)⋊C4—31no—
44C22×C4⋊Dic3—31no—
45C22×Dic3⋊C4—31no—
46#5222—38no—
47C2×C3⋊#95—31no—
48C2×C3⋊#95—31no—
49#4961—38no—
50C24×C32—22no—
51C24×C32—22no—
52C24×C32—22no—
53C24×C32—22no—
54C24×C32—22no—
55C24×C32—22no—
56C24×C32D414yes—
57C24×C32C2312yes—
58C24×C32C2311yescharacteristic
59C23×C3×D3—22no—
60C23×C3×D3—22no—
61C23×C3×D3—22no—
62C23×C3×D3—22no—
63C23×C3×D3—22no—
64C23×C3×D3—22no—
65C23×C3×D3D414yes—
66C23×C3×D3C2312yes—
67C22×C3⋊Dic3—22no—
68C22×C3⋊Dic3—22no—
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—22no—
71C22×C3⋊Dic3—22no—
72C22×C3⋊Dic3—22no—
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2312yes—
75C2×C3×#67—232no—
76C2×C3×#67—28no—
77C2×C3×#67—28no—
78C2×C3×#67—28no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—22no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3D414yes—
87C22×C3×Dic3D414yescomplemented
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91#3757—28no—
92C3×#217—28no—
93Dic3⋊Dic3—28no—
94(C2×D3)⋊Dic3—28no—
95(C2×D3)⋊Dic3—28no—
96C2×#394—91noSylow
97C25×C3—21no—
98C25×C3—31no—
99C25×C3C2×D311yescharacteristic
100C25×C3C2×D311yescharacteristic
101C24×D3C2×D311yescharacteristic
102C22×C3×D4—34no—
103C22×C3×D4—64no—
104C22×C3×D4—64no—
105C22×C3×D4—64no—
106C23×C3×C4—31no—
107C23×C3×C4—31no—
108C23×C3×C4—31no—
109C22×#67—24no—
110C22×#67—24no—
111C22×#67—24no—
112C22×#67C2×D314yes—
113C23×Dic3—31no—
114C23×Dic3—31no—
115C23×Dic3—31no—
116C23×Dic3—31no—
117C23×Dic3—61no—
118C23×Dic3—61no—
119C23×Dic3C2×D311yescharacteristic
120C23×Dic3C2×D311yescharacteristic
121C23×Dic3C2×D311yescharacteristic
122C2×C3×C22⋊C4—34no—
123C2×C3×C22⋊C4—64no—
124C2×#217—24no—
125C2×#217—34no—
126C2×#217—34no—
127C2×#217—34no—
128C2×#217—34no—
129C2×#217—64no—
130C2×#217—64no—
131C2×#217—68no—
132C2×#217—64no—
133C2×#217—64no—
134C2×#217—64no—
135C2×#217C2×D314yescomplemented
136C2×(C2×D3)⋊C4—34no—
137C2×(C2×D3)⋊C4—34no—
138C2×(C2×D3)⋊C4—64no—
139C2×(C2×D3)⋊C4—64no—
140C2×C4⋊Dic3—34no—
141C2×C4⋊Dic3—64no—
142C2×Dic3⋊C4—34no—
143C2×Dic3⋊C4—64no—
144C3⋊#95—34no—
145C3⋊#95—34no—
146C23×C32—28no—
147C23×C32—22no—
148C23×C32—22no—
149C23×C32—28no—
150C23×C32—28no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—44no—
156C23×C32—44no—
157C23×C32—44no—
158C23×C32—44no—
159C23×C32C2×D414yes—
160C23×C32C2×D412yes—
161C23×C32C2×D412yes—
162C23×C32C2×D412yes—
163C23×C32C2×D412yes—
164C23×C32#4112yes—
165C23×C32#4112yes—
166C23×C32#4112yes—
167C23×C32C2411yescharacteristic
168C22×C3×D3—28no—
169C22×C3×D3—28no—
170C22×C3×D3—28no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—44no—
178C22×C3×D3—44no—
179C22×C3×D3—44no—
180C22×C3×D3—44no—
181C22×C3×D3C2×D414yes—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—44no—
189C2×C3⋊Dic3—44no—
190C3×#67—232no—
191C2×C3×Dic3—28no—
192C2×C3×Dic3—28no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—44no—
201C2×C3×Dic3C2×D414yes—
202C2×C3×Dic3C2×D414yescomplemented
203C23×D4—31no—
204C22×C4⋊C4—91no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—91no—
207C22×C22⋊C4—91no—
208C22×C22⋊C4—91no—
209#394—98no—
210C2×#95—91no—
211C24×C3—24no—
212C24×C3—24no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—24no—
226C24×C3—22no—
227C24×C3—21no—
228C24×C3—34no—
229C24×C3—32no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—42no—
233C24×C3—42no—
234C24×C3—62no—
235C24×C3—62no—
236C24×C3—62no—
237C24×C3—62no—
238C24×C3—62no—
239C24×C3—62no—
240C24×C3D1214yes—
241C24×C3#6714yes—
242C24×C3C22×D312yes—
243C24×C3C22×D312yes—
244C24×C3C22×D311yescharacteristic
245C24×C3C22×D311yescharacteristic
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3#6714yes—
253C23×D3C22×D312yes—
254C2×C3×D4—68no—
255C2×C3×D4—68no—
256C2×C3×D4—632no—
257C2×C3×D4—68no—
258C22×C3×C4—34no—
259C22×C3×C4—34no—
260C22×C3×C4—32no—
261C22×C3×C4—32no—
262C22×C3×C4—32no—
263C22×C3×C4—62no—
264C22×C3×C4—62no—
265C22×C3×C4—62no—
266C22×C3×C4—62no—
267C22×C3×C4—62no—
268C22×C3×C4—62no—
269C22×C3×C4—62no—
270C2×#67—232no—
271C2×#67—28no—
272C2×#67—28no—
273C2×#67—28no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—32no—
282C22×Dic3—32no—
283C22×Dic3—32no—
284C22×Dic3—32no—
285C22×Dic3—62no—
286C22×Dic3—62no—
287C22×Dic3—64no—
288C22×Dic3—64no—
289C22×Dic3—62no—
290C22×Dic3—62no—
291C22×Dic3—62no—
292C22×Dic3—62no—
293C22×Dic3—62no—
294C22×Dic3—62no—
295C22×Dic3—62no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—62no—
299C22×Dic3—62no—
300C22×Dic3—62no—
301C22×Dic3—122no—
302C22×Dic3—122no—
303C22×Dic3—122no—
304C22×Dic3—122no—
305C22×Dic3#6714yes—
306C22×Dic3#6714yescomplemented
307C22×Dic3C22×D312yes—
308C22×Dic3C22×D312yes—
309C22×Dic3C22×D312yes—
310C3×C22⋊C4—68no—
311#217—28no—
312#217—68no—
313#217—616no—
314#217—68no—
315#217—68no—
316#217—68no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4—68no—
319C4⋊Dic3—68no—
320Dic3⋊C4—68no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—24no—
324C22×C32—42no—
325C22×C32—42no—
326C22×C32—42no—
327C22×C32—42no—
328C22×C32—416no—
329C22×C32#12014yes—
330C22×C32#12114yes—
331C22×C32#12114yes—
332C22×C32#12114yes—
333C22×C32#12314yes—
334C22×C32#12314yes—
335C22×C32#12414yes—
336C22×C32C22×D411yescharacteristic
337C22×C32C22×D411yescharacteristic
338C22×C32C22×D411yescharacteristic
339C22×C32C22×D411yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—24no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3—42no—
349C2×C3×D3—42no—
350C2×C3×D3—416no—
351C3⋊Dic3—42no—
352C3⋊Dic3—42no—
353C3×Dic3—24no—
354C3×Dic3—24no—
355C3×Dic3—42no—
356C25—31no—
357C25D3211yescharacteristic
358C22×D4—34no—
359C22×D4—64no—
360C22×D4—64no—
361C22×D4—64no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—91no—
366C23×C4—91no—
367C2×C4⋊C4—94no—
368C2×C4⋊C4—184no—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—64no—
371C2×C22⋊C4—94no—
372C2×C22⋊C4—94no—
373C2×C22⋊C4—94no—
374C2×C22⋊C4—184no—
375C2×C22⋊C4—184no—
376C2×C22⋊C4—184no—
377#95—94no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—216no—
381C23×C3—28no—
382C23×C3—28no—
383C23×C3—28no—
384C23×C3—28no—
385C23×C3—28no—
386C23×C3—28no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—24no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—34no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—48no—
414C23×C3—48no—
415C23×C3—48no—
416C23×C3—48no—
417C23×C3—48no—
418C23×C3—48no—
419C23×C3—44no—
420C23×C3—44no—
421C23×C3—44no—
422C23×C3—44no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—68no—
428C23×C3—68no—
429C23×C3—68no—
430C23×C3—62no—
431C23×C3—62no—
432C23×C3—62no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—62no—
436C23×C3—124no—
437C23×C3—124no—
438C23×C3—124no—
439C23×C3—124no—
440C23×C3C2×D1214yes—
441C23×C3C2×D1212yes—
442C23×C3#23512yes—
443C23×C3D3×D412yes—
444C23×C3D3×D412yes—
445C23×C3D3×D412yes—
446C23×C3#23712yes—
447C23×C3#23712yes—
448C23×C3#23712yes—
449C23×C3#23712yes—
450C23×C3#23712yes—
451C23×C3C2×#6714yes—
452C23×C3C2×#6712yes—
453C23×C3C2×#6712yes—
454C23×C3C2×#6712yes—
455C23×C3C2×#6712yes—
456C23×C3C23×D311yescharacteristic
457C23×C3C23×D311yescharacteristic
458C22×D3—28no—
459C22×D3—28no—
460C22×D3—28no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—44no—
468C22×D3—44no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3C2×#6714yes—
472C3×D4—632no—
473C2×C3×C4—34no—
474C2×C3×C4—34no—
475C2×C3×C4—68no—
476C2×C3×C4—68no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—124no—
485#67—232no—
486C2×Dic3—28no—
487C2×Dic3—28no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—44no—
496C2×Dic3—64no—
497C2×Dic3—64no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—122no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3—122no—
514C2×Dic3—128no—
515C2×Dic3—128no—
516C2×Dic3—124no—
517C2×Dic3—124no—
518C2×Dic3—124no—
519C2×Dic3—124no—
520C2×Dic3C2×#6714yes—
521C2×Dic3C2×#6714yescomplemented
522C2×C32—44no—
523C2×C32#39418yescomplemented
524C2×C32C2×#12011yescharacteristic
525C2×C32C2×#12111yescharacteristic
526C2×C32C2×#12111yescharacteristic
527C2×C32C2×#12111yescharacteristic
528C2×C32C2×#12311yescharacteristic
529C2×C32C2×#12311yescharacteristic
530C2×C32C2×#12411yescharacteristic
531C3×D3—44no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—32no—
539C24—34no—
540C24—62no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
546C24#62614yes—
547C24C2×D3212yes—
548C24C2×D3211yescharacteristic
549C2×D4—68no—
550C2×D4—68no—
551C2×D4—632no—
552C2×D4—68no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—34no—
556C22×C4—34no—
557C22×C4—32no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—92no—
566C22×C4—92no—
567C22×C4—182no—
568C22×C4—182no—
569C22×C4—182no—
570C22×C4—182no—
571C22×C4—182no—
572C22×C4—182no—
573C4⋊C4—188no—
574C22⋊C4—68no—
575C22⋊C4—188no—
576C22⋊C4—188no—
577C22⋊C4—188no—
578C22×C3—28no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—24no—
584C22×C3—24no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—432no—
606C22×C3—416no—
607C22×C3—416no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—1216no—
620C22×C3—122no—
621C22×C3—122no—
622C22×C3—122no—
623C22×C3—122no—
624C22×C3#88214yes—
625C22×C3#88314yes—
626C22×C3#88514yes—
627C22×C3#88614yes—
628C22×C3#93014yes—
629C22×C3#93514yes—
630C22×C3#93514yes—
631C22×C3#93614yes—
632C22×C3#93814yes—
633C22×C3#93814yes—
634C22×C3#93914yes—
635C22×C3#93914yes—
636C22×C3#93914yes—
637C22×C3#95314yes—
638C22×C3C22×D1211yescharacteristic
639C22×C3C2×#23511yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×#23711yescharacteristic
644C22×C3C2×#23711yescharacteristic
645C22×C3C2×#23711yescharacteristic
646C22×C3C2×#23711yescharacteristic
647C22×C3C2×#23711yescharacteristic
648C22×C3C22×#6711yescharacteristic
649C22×C3C22×#6711yescharacteristic
650C22×C3C22×#6711yescharacteristic
651C22×C3C22×#6711yescharacteristic
652C2×D3—24no—
653C2×D3—24no—
654C2×D3—24no—
655C2×D3—416no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—42no—
660C3×C4—64no—
661C3×C4—64no—
662C3×C4—122no—
663Dic3—24no—
664Dic3—24no—
665Dic3—42no—
666Dic3—124no—
667Dic3—124no—
668Dic3—122no—
669Dic3—122no—
670Dic3—122no—
671Dic3—122no—
672C32C2×#39411yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—28no—
680C23—28no—
681C23—28no—
682C23—34no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—68no—
694C23—68no—
695C23—68no—
696C23—124no—
697C23—124no—
698C23—124no—
699C23—124no—
700C23#380412yes—
701C23#380512yes—
702C23#380512yes—
703C23C2×#62614yes—
704C23C2×#62612yes—
705C23D3×#6712yes—
706C23D3×#6712yes—
707C23D3×#6712yes—
708C23C22×D3211yescharacteristic
709D4—632no—
710C2×C4—34no—
711C2×C4—34no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—68no—
717C2×C4—68no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—124no—
722C2×C4—182no—
723C2×C4—182no—
724C2×C4—182no—
725C2×C4—182no—
726C2×C4—182no—
727C2×C4—182no—
728C2×C4—364no—
729C2×C4—364no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—28no—
738C2×C3—48no—
739C2×C3—44no—
740C2×C3—44no—
741C2×C3—124no—
742C2×C3#496118yescomplemented
743C2×C3#522218yescomplemented
744C2×C3C2×#88211yescharacteristic
745C2×C3C2×#88311yescharacteristic
746C2×C3C2×#88511yescharacteristic
747C2×C3C2×#88611yescharacteristic
748C2×C3C2×#93011yescharacteristic
749C2×C3C2×#93511yescharacteristic
750C2×C3C2×#93511yescharacteristic
751C2×C3C2×#93611yescharacteristic
752C2×C3C2×#93811yescharacteristic
753C2×C3C2×#93811yescharacteristic
754C2×C3C2×#93911yescharacteristic
755C2×C3C2×#93911yescharacteristic
756C2×C3C2×#93911yescharacteristic
757C2×C3C2×#95311yescharacteristic
758D3—44no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—416no—
767C22—64no—
768C22—64no—
769C22—64no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—1216no—
775C22#6395914yes—
776C22#6396214yes—
777C22#6396914yes—
778C22#6397014yes—
779C22#6397014yes—
780C22#6397714yes—
781C22#6397814yes—
782C22C2×#380411yescharacteristic
783C22C2×#380511yescharacteristic
784C22C2×#380511yescharacteristic
785C22C22×#62611yescharacteristic
786C22C2×D3×#6711yescharacteristic
787C22C2×D3×#6711yescharacteristic
788C22C2×D3×#6711yescharacteristic
789C4—64no—
790C4—64no—
791C4—122no—
792C4—362no—
793C4—362no—
794C3—21no—
795C3C2×#496111yescharacteristic, complemented
796C3C2×#522211yescharacteristic, complemented
797C2—44no—
798C2—124no—
799C2#1059170918yesdirect product factor
800C2C2×#6395911yescharacteristic
801C2C2×#6396211yescharacteristic
802C2C2×#6396911yescharacteristic
803C2C2×#6397011yescharacteristic
804C2C2×#6397011yescharacteristic
805C2C2×#6397711yescharacteristic
806C2C2×#6397811yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC25×C32C22
socleC24×C32C23
prime radicalC23×C3×#67C2
hypercenterC25D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×#3757C2semidirect
3. C22×C3×#217C2semidirect
4. C22×Dic3⋊Dic3C2semidirect
5. C22×(C2×D3)⋊Dic3C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. #10591709C2direct (N × H)
8. C2×#63579C2semidirect
23. C2×#3757C22semidirect
25. C2×C3×#217C22semidirect
27. C2×Dic3⋊Dic3C22semidirect
30. C2×(C2×D3)⋊Dic3C22semidirect
31. C2×(C2×D3)⋊Dic3C22semidirect
32. #63579C22semidirect
41. C22×#217D3semidirect
87. C22×C3×Dic3D4semidirect
135. C2×#217C2×D3semidirect
202. C2×C3×Dic3C2×D4semidirect
306. C22×Dic3#67semidirect
521. C2×Dic3C2×#67semidirect
523. C2×C32#394semidirect
672. C32C2×#394semidirect
742. C2×C3#4961semidirect
743. C2×C3#5222semidirect
795. C3C2×#4961semidirect
796. C3C2×#5222semidirect
799. C2#10591709direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×#37572
C22×C3×#2172
C22×Dic3⋊Dic32
C22×(C2×D3)⋊Dic32
#105917092
C2×#635792
C2×#52223
C2×#49613