Finite Group Databasebeta

← #11824451

Subgroups — #11824451

Order 1152.

2109 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×#63979C212yesmaximal, complemented
5C2×#63916C211yesmaximal, characteristic, complemented
6C2×#63908C211yesmaximal, characteristic, complemented
7C2×C4×#626C211yesmaximal, characteristic, complemented
8#10591724C212yesmaximal, complemented
9#10591723C212yesmaximal, complemented
10#10591707C212yesmaximal, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#83188—31nomaximal
13#82669—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2212yes—
23C22×#626C2211yescharacteristic
24C22×#625C2212yes—
25C2×#3757C2212yes—
26#64147—24no—
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C3×#217C2212yes—
29C3×#940—24no—
30C3×#938—24no—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#63979—28no—
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×Dic32C2212yes—
40#63916—24no—
41#63908—24no—
42C4×#626—24no—
43#63579C2212yes—
44C2×C3×#127—31no—
45C2×C3×#121—31no—
46C2×#940—32no—
47C2×#940—32no—
48C2×#940D311yescharacteristic, complemented
49C2×#938—31no—
50C2×#938—31no—
51C2×#938—31no—
52C2×#938—31no—
53C2×#938—61no—
54C2×#938D311yescharacteristic, complemented
55C2×#930—31no—
56C2×C4×#67—31no—
57C2×#895—31no—
58C2×C4×D12—31no—
59#5223—32no—
60#5223—32no—
61#5223—32no—
62#5221—32no—
63Dic3×C4⋊C4—31no—
64#4960—32no—
65#4957—32no—
66C4×C4⋊Dic3—31no—
67C24×C32C2312yes—
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C23×C3×D3C2311yescharacteristic
71C2×C32×D4—22no—
72C2×C32×D4—22no—
73C2×C32×D4—22no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—24no—
76C2×#638—24no—
77C2×#638—42no—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—22no—
83C2×C3×#67—24no—
84C2×C3×#67—24no—
85C2×C3×#67—24no—
86C2×C3×#67—24no—
87C2×C3×#67—24no—
88C2×C3×#67—24no—
89C2×C3×#67—42no—
90C2×C3×#67—42no—
91C2×C3×#67—42no—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C2×C3×D12—22no—
97C2×C3×D12—22no—
98C2×C3×D12—22no—
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C2×#626—22no—
103C2×#626—22no—
104C2×#626—24no—
105C2×#626—24no—
106C2×#626—42no—
107C2×#626D414yescomplemented
108C2×#625—24no—
109C2×#625—24no—
110C2×#625—42no—
111#3757—24no—
112C4⋊(C3⋊Dic3)D414yescomplemented
113C3×#217—24no—
114C3×C4⋊Dic3D414yescomplemented
115C3×C4×Dic3D414yescomplemented
116Dic3⋊Dic3—22no—
117#3722—22no—
118(C2×D3)⋊Dic3—24no—
119(C2×D3)⋊Dic3—22no—
120(C2×D3)⋊Dic3—24no—
121Dic32—24no—
122#2541—91noSylow
123C22×C3×D4—21no—
124C22×C3×D4—32no—
125C22×C3×D4—32no—
126C22×C3×D4—32no—
127C22×C3×D4—31no—
128C22×C3×D4C2×D311yescharacteristic
129C22×C3×D4C2×D311yescharacteristic
130C23×C3×C4—31no—
131C22×#67—32no—
132C22×#67—32no—
133C22×#67—32no—
134C22×#67—32no—
135C22×#67—31no—
136C22×#67—32no—
137C22×#67—62no—
138C22×#67C2×D312yes—
139C22×#67C2×D312yes—
140C22×#67C2×D312yes—
141C22×D12—31no—
142C22×D12—32no—
143C22×D12C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C22×C4×D3C2×D311yescharacteristic
148C3×#127—64no—
149C3×#121—64no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C42—31no—
153C2×#217—32no—
154C2×#217—32no—
155C2×#217—32no—
156C2×#217—32no—
157C2×#217—31no—
158C2×#217—62no—
159C2×#217C2×D312yes—
160#940—24no—
161#940—68no—
162#940—68no—
163#938—24no—
164#938—64no—
165#938—64no—
166#938—64no—
167#938—68no—
168#938—64no—
169#930—64no—
170C4×#67—64no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180C2×C4⋊Dic3C2×D311yescharacteristic
181C2×Dic3⋊C4—31no—
182C2×C4×Dic3—32no—
183C2×C4×Dic3—32no—
184C2×C4×Dic3C2×D311yescharacteristic
185#895—64no—
186C4×D12—64no—
187C3⋊#95—32no—
188C3⋊#95—32no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32C2411yescharacteristic
197C22×C3⋊D3—21no—
198C22×C3⋊D3—21no—
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3C2×D412yes—
204C22×C3×D3—21no—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3C2×D412yes—
218C32×D4—44no—
219C2×C32×C4C2×D412yes—
220C2×C32×C4C2×D412yes—
221C2×C32×C4C2×D412yes—
222#638—48no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3C2×D414yes—
229C4×C3⋊D3—44no—
230C3×#67—48no—
231C3×#67—48no—
232C3×#67—48no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3C2×D412yes—
241C2×C3×Dic3C2×D412yes—
242C2×C3×Dic3C2×D414yes—
243C2×C3×Dic3C2×D412yes—
244C2×C3×Dic3#4112yes—
245C3×D12—44no—
246C3×C4×D3—44no—
247#626—28no—
248#626—48no—
249#625—48no—
250C2×#127—31no—
251C2×#127—92no—
252C2×#121—31no—
253C2×#121—91no—
254C2×#121—91no—
255C2×#121—91no—
256C2×C4×D4—91no—
257#392—92no—
258#392—92no—
259#390—92no—
260C4×C4⋊C4—91no—
261C24×C3—22no—
262C24×C3—31no—
263C24×C3—32no—
264C24×C3C22×D312yes—
265C24×C3C22×D312yes—
266C23×D3—31no—
267C23×D3—31no—
268C23×D3—61no—
269C23×D3C22×D312yes—
270C23×D3C22×D311yescharacteristic
271C2×C3×D4—24no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C2×C3×D4—22no—
275C2×C3×D4—22no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—64no—
281C2×C3×D4—64no—
282C2×C3×D4—64no—
283C2×C3×D4—64no—
284C2×C3×D4—64no—
285C2×C3×D4—64no—
286C2×C3×D4—62no—
287C2×C3×D4—62no—
288C2×C3×D4—62no—
289C2×C3×D4—122no—
290C2×C3×D4—122no—
291C2×C3×D4—122no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—32no—
296C22×C3×C4—31no—
297C22×C3×C4—62no—
298C22×C3×C4—62no—
299C22×C3×C4—62no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—24no—
306C2×#67—24no—
307C2×#67—24no—
308C2×#67—34no—
309C2×#67—42no—
310C2×#67—42no—
311C2×#67—42no—
312C2×#67—64no—
313C2×#67—64no—
314C2×#67—64no—
315C2×#67—64no—
316C2×#67—64no—
317C2×#67—64no—
318C2×#67—64no—
319C2×#67—64no—
320C2×#67—68no—
321C2×#67—64no—
322C2×#67—62no—
323C2×#67—62no—
324C2×#67—64no—
325C2×#67—124no—
326C2×#67—122no—
327C2×#67—122no—
328C2×#67—122no—
329C2×#67—122no—
330C2×#67—122no—
331C2×#67—124no—
332C22×Dic3—32no—
333C22×Dic3—32no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—62no—
337C22×Dic3—61no—
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D312yes—
341C22×Dic3C22×D311yescharacteristic
342C2×D12—22no—
343C2×D12—22no—
344C2×D12—22no—
345C2×D12—34no—
346C2×D12—62no—
347C2×D12—62no—
348C2×D12—64no—
349C2×D12—64no—
350C2×D12—122no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—64no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—122no—
362C2×C4×D3—122no—
363C3×C4⋊C4—34no—
364C3×C22⋊C4—64no—
365C3×C42—34no—
366#217—24no—
367#217—64no—
368#217—64no—
369#217—64no—
370#217—68no—
371#217—62no—
372#217—64no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—64no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—64no—
377(C2×D3)⋊C4—62no—
378C4⋊Dic3—34no—
379C4⋊Dic3—34no—
380C4⋊Dic3—64no—
381C4⋊Dic3—62no—
382C4⋊Dic3#6714yescomplemented
383Dic3⋊C4—62no—
384C4×Dic3—64no—
385C4×Dic3—64no—
386C4×Dic3#6714yescomplemented
387C22×C32—42no—
388C22×C32—42no—
389C22×C32—42no—
390C22×C32—42no—
391C22×C32—42no—
392C22×C32—42no—
393C22×C32—42no—
394C22×C32C22×D411yescharacteristic
395C22×C32C22×D411yescharacteristic
396C22×C32C22×D411yescharacteristic
397C22×C32C22×D411yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C22×C32H(5,𝔽2)11yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—42no—
418C2×C3×D3—42no—
419C2×C3×D3—42no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C32×C4#12714yescomplemented
423C3⋊Dic3—24no—
424C3⋊Dic3—41no—
425C3×Dic3—22no—
426C3×Dic3—24no—
427C3×Dic3—41no—
428C3×Dic3#12114yescomplemented
429C22×D4—32no—
430C22×D4—32no—
431C22×D4—32no—
432C22×D4—31no—
433C22×D4—91no—
434C22×D4—92no—
435C22×D4—92no—
436C22×D4—92no—
437C22×D4D3211yescharacteristic
438C23×C4—31no—
439C23×C4—91no—
440#127—64no—
441#127—188no—
442#121—64no—
443#121—184no—
444#121—184no—
445#121—184no—
446C4×D4—184no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C22⋊C4—32no—
451C2×C22⋊C4—91no—
452C2×C22⋊C4—91no—
453C2×C22⋊C4—92no—
454C2×C22⋊C4—92no—
455C2×C22⋊C4—92no—
456C2×C42—31no—
457C2×C42—92no—
458#95—92no—
459C23×C3—24no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—21no—
475C23×C3—32no—
476C23×C3—42no—
477C23×C3—42no—
478C23×C3—42no—
479C23×C3—42no—
480C23×C3—42no—
481C23×C3—42no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—62no—
491C23×C3—62no—
492C23×C3—62no—
493C23×C3—62no—
494C23×C3—62no—
495C23×C3C23×D311yescharacteristic
496C23×C3C23×D311yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—121no—
528C22×D3—121no—
529C22×D3—121no—
530C22×D3—121no—
531C22×D3D3×D412yes—
532C3×D4—48no—
533C3×D4—44no—
534C3×D4—44no—
535C3×D4—128no—
536C3×D4—128no—
537C3×D4—128no—
538C3×D4—124no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—34no—
547C2×C3×C4—62no—
548C2×C3×C4—62no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—124no—
555C2×C3×C4D3×D412yes—
556C2×C3×C4D3×D412yes—
557C2×C3×C4D3×D412yes—
558C2×C3×C4D3×D412yes—
559C2×C3×C4C2×#6712yes—
560C2×C3×C4C2×#6712yes—
561#67—48no—
562#67—48no—
563#67—48no—
564#67—68no—
565#67—128no—
566#67—128no—
567#67—128no—
568#67—128no—
569#67—128no—
570#67—1216no—
571C2×Dic3—22no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—22no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—34no—
579C2×Dic3—34no—
580C2×Dic3—64no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—62no—
585C2×Dic3—62no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3—122no—
596C2×Dic3D3×D412yes—
597C2×Dic3#23712yes—
598C2×Dic3C2×#6712yes—
599C2×Dic3C2×#6714yes—
600C2×Dic3C2×#6712yes—
601D12—44no—
602D12—68no—
603D12—128no—
604C4×D3—44no—
605C4×D3—128no—
606C4×D3—124no—
607C4×D3—124no—
608C2×C32—82no—
609C2×C32C2×#12111yescharacteristic
610C2×C32C2×#12711yescharacteristic
611C2×C32#53511yescharacteristic
612C2×C32D4211yescharacteristic
613C2×C32D4211yescharacteristic
614C2×C32#55011yescharacteristic
615C2×C32#55011yescharacteristic
616C3⋊D3—42no—
617C3×D3—42no—
618C3×D3—82no—
619C24—31no—
620C24—32no—
621C24—91no—
622C24C2×D3212yes—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—64no—
627C2×D4—64no—
628C2×D4—64no—
629C2×D4—64no—
630C2×D4—64no—
631C2×D4—64no—
632C2×D4—62no—
633C2×D4—62no—
634C2×D4—62no—
635C2×D4—94no—
636C2×D4—122no—
637C2×D4—122no—
638C2×D4—122no—
639C2×D4—182no—
640C2×D4—182no—
641C2×D4—184no—
642C2×D4—184no—
643C2×D4—184no—
644C2×D4—184no—
645C2×D4—184no—
646C2×D4—184no—
647C2×D4—362no—
648C2×D4—362no—
649C2×D4—362no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—32no—
653C22×C4—31no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—92no—
658C22×C4—91no—
659C22×C4—182no—
660C22×C4—182no—
661C22×C4—182no—
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—94no—
665C4⋊C4—182no—
666C22⋊C4—64no—
667C22⋊C4—182no—
668C22⋊C4—182no—
669C22⋊C4—184no—
670C22⋊C4—184no—
671C22⋊C4—184no—
672C42—34no—
673C42—184no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—44no—
682C22×C3—44no—
683C22×C3—44no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—62no—
701C22×C3—82no—
702C22×C3—82no—
703C22×C3—82no—
704C22×C3—82no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—122no—
710C22×C3—122no—
711C22×C3—122no—
712C22×C3—122no—
713C22×C3—122no—
714C22×C3—122no—
715C22×C3—122no—
716C22×C3C2×D3×D411yescharacteristic
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C2×D3×D411yescharacteristic
720C22×C3C2×D3×D411yescharacteristic
721C22×C3C2×D3×D411yescharacteristic
722C22×C3C2×#23711yescharacteristic
723C22×C3#100411yescharacteristic
724C22×C3#100411yescharacteristic
725C22×C3#100411yescharacteristic
726C22×C3D3×#4111yescharacteristic
727C22×C3#100911yescharacteristic
728C22×C3C22×#6711yescharacteristic
729C22×C3C22×#6711yescharacteristic
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—64no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C3×C4—24no—
766C3×C4—34no—
767C3×C4—64no—
768C3×C4—62no—
769C3×C4—121no—
770C3×C4#94014yescomplemented
771C3×C4#94014yescomplemented
772Dic3—24no—
773Dic3—22no—
774Dic3—41no—
775Dic3—64no—
776Dic3—64no—
777Dic3—124no—
778Dic3—122no—
779Dic3—121no—
780Dic3—121no—
781Dic3#93814yescomplemented
782C32#254111yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—32no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—61no—
795C23—61no—
796C23—61no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—92no—
805C23—181no—
806C23—181no—
807C23—181no—
808C23—181no—
809C23—181no—
810C23—181no—
811C23C22×D3211yescharacteristic
812D4—44no—
813D4—128no—
814D4—128no—
815D4—128no—
816D4—124no—
817D4—188no—
818D4—368no—
819D4—368no—
820D4—368no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—34no—
826C2×C4—62no—
827C2×C4—61no—
828C2×C4—62no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—94no—
834C2×C4—124no—
835C2×C4—182no—
836C2×C4—182no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—364no—
841C2×C4D3×#6712yes—
842C2×C4D3×#6712yes—
843C2×C4#381112yes—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—84no—
852C2×C3—82no—
853C2×C3—82no—
854C2×C3—122no—
855C2×C3—242no—
856C2×C3#559911yescharacteristic
857C2×C3D3×#12111yescharacteristic
858C2×C3#560711yescharacteristic
859C2×C3#560911yescharacteristic
860C2×C3#571711yescharacteristic
861C2×C3#571711yescharacteristic
862C2×C3#571811yescharacteristic
863C2×C3#571811yescharacteristic
864C2×C3C2×#93811yescharacteristic
865C2×C3D4×#6711yescharacteristic
866C2×C3C2×#94011yescharacteristic
867C2×C3C2×#94011yescharacteristic
868C2×C3#580511yescharacteristic
869C2×C3#583411yescharacteristic
870D3—42no—
871D3—82no—
872D3—124no—
873D3—122no—
874D3—122no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—62no—
883C22—62no—
884C22—62no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—122no—
890C22—122no—
891C22—122no—
892C22—122no—
893C22—122no—
894C22—122no—
895C22—122no—
896C22—182no—
897C22—182no—
898C22—182no—
899C22—361no—
900C22—361no—
901C22—361no—
902C22—361no—
903C22D32×D411yescharacteristic
904C22D3×#23711yescharacteristic
905C22#6431311yescharacteristic
906C22#6431411yescharacteristic
907C22C2×D3×#6711yescharacteristic
908C22C2×D3×#6711yescharacteristic
909C22C2×#381111yescharacteristic
910C4—34no—
911C4—62no—
912C4—64no—
913C4—121no—
914C4—184no—
915C4—361no—
916C4#6397914yescomplemented
917C3—21no—
918C3#8266911yescharacteristic, complemented
919C3#8318811yescharacteristic, complemented
920C2—82no—
921C2—122no—
922C2—242no—
923C2—362no—
924C2#1059515811yescharacteristic
925C2#1059516411yescharacteristic
926C2#1059523111yescharacteristic
927C2D3×#93811yescharacteristic
928C2#1059529311yescharacteristic
929C2#1059529711yescharacteristic
930C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64147C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#938C2semidirect
4. C2×#63979C2semidirect
5. C2×#63916C2semidirect
6. C2×#63908C2semidirect
7. C2×C4×#626C2semidirect
8. #10591724C2semidirect
9. #10591723C2semidirect
10. #10591707C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
48. C2×#940D3semidirect
54. C2×#938D3semidirect
107. C2×#626D4semidirect
112. C4⋊(C3⋊Dic3)D4semidirect
114. C3×C4⋊Dic3D4semidirect
115. C3×C4×Dic3D4semidirect
382. C4⋊Dic3#67semidirect
386. C4×Dic3#67semidirect
422. C32×C4#127semidirect
428. C3×Dic3#121semidirect
770. C3×C4#940semidirect
771. C3×C4#940semidirect
781. Dic3#938semidirect
782. C32#2541semidirect
916. C4#63979semidirect
918. C3#82669semidirect
919. C3#83188semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#9402
C2×C3×#9382
C2×#639792
C2×#639162
C2×#639082
C2×C4×#6262
#105917242
#105917232
#105917072
Dic3×C4⋊Dic32
#831883
#826693