Finite Group Databasebeta

← #11801062

Subgroups — #11801062

Order 1152.

2305 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×#63855C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#10591399C212yesmaximal
7#10591367C212yesmaximal, complemented
8#10591366C212yesmaximal, complemented
9#10591362C212yesmaximal, complemented
10C4×#3722C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
12#82267—31nomaximal
13#73561—31nomaximal
14C23×D32C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C4×D32—24no—
22C2×C4×D32—24no—
23C2×C4×D32C418yescomplemented
24C2×C32×C42C2211yescharacteristic, complemented
25C2×#3752C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yescomplemented
30C2×C3×C4×Dic3C2211yescharacteristic, complemented
31C2×C3×C4×Dic3C2211yescharacteristic, complemented
32C3×#872—24no—
33C2×Dic3⋊Dic3C2212yescomplemented
34C2×#3722C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37#63855—24no—
38#63658C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—31no—
43C23×C4×D3—31no—
44C2×C3×#117—31no—
45C2×#926—31no—
46C2×#872—31no—
47C2×#872D311yescharacteristic, complemented
48C3×C4×C22⋊C4—31no—
49C4×#217—31no—
50#4987—32no—
51#4987—32no—
52#4955—32no—
53#4955—32no—
54#4943—32no—
55#4942—32no—
56C4×(C2×D3)⋊C4—31no—
57C4×(C2×D3)⋊C4—31no—
58C4×(C2×D3)⋊C4—31no—
59C4×(C2×D3)⋊C4—31no—
60C4×(C2×D3)⋊C4—31no—
61C4×(C2×D3)⋊C4—61no—
62C4×(C2×D3)⋊C4D311yescharacteristic, complemented
63#4667—32no—
64#4664—32no—
65C23×C3⋊D3C2311yescharacteristic
66C23×C3×D3C2311yescharacteristic
67C23×C3×D3C2311yescharacteristic
68C22×D32—24no—
69C22×D32—22no—
70C22×D32—22no—
71C22×D32—24no—
72C22×D32C2×C414yes—
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3C2×C414yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3C2×C414yes—
87C2×C3×C4×D3C2×C414yes—
88C2×C3×C4×D3D414yes—
89C2×C3×C4×D3D414yes—
90C2×#624—22no—
91C2×#624—22no—
92C2×#624C2×C414yes—
93C2×D3×Dic3—22no—
94C2×D3×Dic3—22no—
95C2×D3×Dic3—22no—
96C2×D3×Dic3—22no—
97C2×D3×Dic3C2×C414yes—
98C2×D3×Dic3C2×C414yes—
99C4×D32—232no—
100C32×C42—22no—
101#3752—24no—
102C4×C3⋊Dic3—22no—
103C3×(C2×D3)⋊C4—24no—
104C3×(C2×D3)⋊C4—24no—
105C3×Dic3⋊C4—24no—
106C3×C4×Dic3—22no—
107C3×C4×Dic3—22no—
108Dic3⋊Dic3—24no—
109#3722—24no—
110(C2×D3)⋊Dic3—24no—
111(C2×D3)⋊Dic3—24no—
112#2280—91noSylow
113C24×D3—31no—
114C24×D3—31no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×Dic3—31no—
118C23×Dic3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—38no—
126C22×C4×D3—38no—
127C22×C4×D3—61no—
128C22×C4×D3—64no—
129C22×C4×D3—64no—
130C22×C4×D3—64no—
131C22×C4×D3—64no—
132C22×C4×D3C2×D311yescharacteristic
133C22×C4×D3C2×D311yescharacteristic
134C3×#117—64no—
135C2×C3×C4⋊C4—32no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C42—21no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×C3×C42C2×D311yescharacteristic, complemented
142C2×C3×C42C2×D311yescharacteristic, complemented
143C2×#217—32no—
144C2×#217—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—62no—
152C2×(C2×D3)⋊C4C2×D312yes—
153C2×(C2×D3)⋊C4C2×D312yes—
154#926—64no—
155C2×C4⋊Dic3—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4C2×D312yescomplemented
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—61no—
161C2×C4×Dic3C2×D311yescharacteristic, complemented
162C2×C4×Dic3C2×D311yescharacteristic, complemented
163#872—24no—
164#872—64no—
165C3×#95—32no—
166C3⋊#95—32no—
167C3⋊#95—32no—
168C3⋊#95—32no—
169C3⋊#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—62no—
173C3⋊#95C2×D312yescomplemented
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3C22×C412yes—
179C22×C3⋊D3#4114yes—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3C22×C412yes—
186C22×C3×D3C22×C412yes—
187C22×C3×D3C2×D412yes—
188C22×C3×D3C2×D412yes—
189C22×C3×D3#4114yes—
190C2×D32—216no—
191C2×D32—216no—
192C2×D32—28no—
193C2×D32—28no—
194C2×D32—28no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4C22×C412yes—
199C2×C32×C4C2×D412yes—
200C2×C32×C4C2×D412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3C22×C412yes—
207C4×C3⋊D3—28no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3C22×C412yes—
217C2×C3×Dic3C22×C412yes—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D412yes—
220C3×C4×D3—28no—
221C3×C4×D3C22⋊C4116yescomplemented
222#624—28no—
223D3×Dic3—28no—
224D3×Dic3—28no—
225C24×C4—91no—
226C2×#117—31no—
227C2×#117—91no—
228#381—92no—
229#380—92no—
230#380—92no—
231#379—92no—
232C4×C22⋊C4—31no—
233C4×C22⋊C4—91no—
234C4×C22⋊C4—91no—
235C4×C22⋊C4—91no—
236C24×C3—31no—
237C24×C3—31no—
238C23×D3—31no—
239C23×D3—31no—
240C23×D3—34no—
241C23×D3—34no—
242C23×D3—61no—
243C23×D3—64no—
244C23×D3—64no—
245C23×D3—62no—
246C23×D3—62no—
247C23×D3—64no—
248C23×D3—62no—
249C23×D3—64no—
250C23×D3—62no—
251C23×D3C22×D311yescharacteristic
252C23×D3C22×D311yescharacteristic
253C22×C3×C4—22no—
254C22×C3×C4—21no—
255C22×C3×C4—31no—
256C22×C3×C4—34no—
257C22×C3×C4—34no—
258C22×C3×C4—34no—
259C22×C3×C4—31no—
260C22×C3×C4—34no—
261C22×C3×C4—32no—
262C22×C3×C4—32no—
263C22×C3×C4—62no—
264C22×C3×C4—62no—
265C22×C3×C4C22×D312yes—
266C22×C3×C4C22×D312yes—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C22×D311yescharacteristic
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—34no—
272C22×Dic3—34no—
273C22×Dic3—32no—
274C22×Dic3—32no—
275C22×Dic3—61no—
276C22×Dic3—62no—
277C22×Dic3—62no—
278C22×Dic3—62no—
279C22×Dic3—62no—
280C22×Dic3—62no—
281C22×Dic3C22×D312yes—
282C22×Dic3C22×D312yes—
283C22×Dic3C22×D311yescharacteristic
284C22×Dic3C22×D311yescharacteristic
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—34no—
288C2×C4×D3—34no—
289C2×C4×D3—34no—
290C2×C4×D3—34no—
291C2×C4×D3—34no—
292C2×C4×D3—34no—
293C2×C4×D3—64no—
294C2×C4×D3—632no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×C4×D3—62no—
300C2×C4×D3—62no—
301C2×C4×D3—62no—
302C2×C4×D3—62no—
303C2×C4×D3—62no—
304C2×C4×D3—62no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C2×C4×D3—632no—
308C2×C4×D3—122no—
309C2×C4×D3—122no—
310C2×C4×D3C4×D314yes—
311C2×C4×D3C4×D314yes—
312C2×C4×D3D1214yes—
313C2×C4×D3#6714yes—
314C3×C4⋊C4—64no—
315C3×C22⋊C4—64no—
316C3×C22⋊C4—64no—
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—42no—
320C3×C42—62no—
321C3×C42—62no—
322#217—64no—
323#217—64no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—64no—
327(C2×D3)⋊C4—64no—
328(C2×D3)⋊C4—64no—
329(C2×D3)⋊C4—64no—
330(C2×D3)⋊C4—68no—
331(C2×D3)⋊C4—64no—
332(C2×D3)⋊C4—64no—
333C4⋊Dic3—64no—
334Dic3⋊C4—24no—
335Dic3⋊C4—64no—
336C4×Dic3—22no—
337C4×Dic3—22no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—122no—
341C22×C32C23×C411yescharacteristic
342C22×C32C22×D411yescharacteristic
343C22×C32C22×D411yescharacteristic
344C22×C32C2×#4112yes—
345C22×C32C2×#4112yes—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3—24no—
349C2×C3⋊D3—24no—
350C2×C3⋊D3#11714yescomplemented
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3—24no—
359C2×C3×D3C2×C22⋊C414yes—
360C2×C3×D3#11714yescomplemented
361D32—232no—
362C32×C4—42no—
363C32×C4C2×C22⋊C414yes—
364C3⋊Dic3—22no—
365C3⋊Dic3—42no—
366C3×Dic3—22no—
367C3×Dic3—42no—
368C3×Dic3—42no—
369C3×Dic3C2×C22⋊C414yes—
370C25—91no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—91no—
374C23×C4—98no—
375C23×C4—91no—
376C23×C4—91no—
377C23×C4—91no—
378C23×C4—184no—
379C23×C4—184no—
380#117—64no—
381#117—184no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—92no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—92no—
387C2×C22⋊C4—92no—
388C2×C22⋊C4—92no—
389C2×C22⋊C4—92no—
390C2×C42—31no—
391C2×C42—31no—
392C2×C42—91no—
393C2×C42D3211yescharacteristic, complemented
394#95—32no—
395#95—92no—
396#95—92no—
397#95—92no—
398C23×C3—21no—
399C23×C3—32no—
400C23×C3—32no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—34no—
404C23×C3—61no—
405C23×C3—62no—
406C23×C3—62no—
407C23×C3—62no—
408C23×C3—61no—
409C23×C3C23×D311yescharacteristic
410C23×C3C23×D311yescharacteristic
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—34no—
419C22×D3—34no—
420C22×D3—62no—
421C22×D3—64no—
422C22×D3—68no—
423C22×D3—68no—
424C22×D3—68no—
425C22×D3—68no—
426C22×D3—616no—
427C22×D3—616no—
428C22×D3—616no—
429C22×D3—616no—
430C22×D3—61no—
431C22×D3—62no—
432C22×D3—61no—
433C22×D3—61no—
434C22×D3—62no—
435C22×D3—61no—
436C22×D3—68no—
437C22×D3—68no—
438C22×D3—121no—
439C22×D3—121no—
440C22×D3—122no—
441C22×D3C2×C4×D312yes—
442C22×D3C2×C4×D312yes—
443C22×D3C2×D1212yes—
444C22×D3#23514yes—
445C22×D3C2×#6712yes—
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—316no—
460C2×C3×C4—32no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—68no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4C2×C4×D312yes—
473C2×C3×C4C2×C4×D312yes—
474C2×C3×C4C2×D1212yes—
475C2×C3×C4D3×D412yes—
476C2×C3×C4D3×D412yes—
477C2×C3×C4C2×#6712yes—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—32no—
487C2×Dic3—32no—
488C2×Dic3—62no—
489C2×Dic3—68no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—68no—
495C2×Dic3—64no—
496C2×Dic3—62no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—122no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—122no—
506C2×Dic3C2×C4×D312yes—
507C2×Dic3C2×C4×D312yes—
508C2×Dic3C2×D1212yes—
509C2×Dic3C2×#6712yes—
510C4×D3—28no—
511C4×D3—68no—
512C4×D3—68no—
513C4×D3—68no—
514C4×D3—68no—
515C4×D3—68no—
516C4×D3—68no—
517C4×D3—128no—
518C4×D3(C2×D3)⋊C4116yescomplemented
519C2×C32C22×C22⋊C411yescharacteristic
520C2×C32C2×#11711yescharacteristic
521C2×C32C2×#11711yescharacteristic
522C2×C32#52512yes—
523C2×C32#52512yes—
524C3⋊D3—24no—
525C3×D3—24no—
526C3×D3—24no—
527C24—31no—
528C24—31no—
529C24—94no—
530C24—91no—
531C24—182no—
532C24—182no—
533C24—184no—
534C24—184no—
535C22×C4—31no—
536C22×C4—34no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—31no—
540C22×C4—34no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—94no—
546C22×C4—94no—
547C22×C4—94no—
548C22×C4—91no—
549C22×C4—94no—
550C22×C4—92no—
551C22×C4—182no—
552C22×C4—182no—
553C22×C4—1832no—
554C22×C4—182no—
555C22×C4—182no—
556C22×C4—182no—
557C22×C4—182no—
558C22×C4—182no—
559C22×C4—182no—
560C22×C4C2×D3212yes—
561C22×C4C2×D3211yescharacteristic
562C4⋊C4—64no—
563C4⋊C4—184no—
564C22⋊C4—64no—
565C22⋊C4—64no—
566C22⋊C4—184no—
567C22⋊C4—184no—
568C22⋊C4—184no—
569C22⋊C4—184no—
570C42—22no—
571C42—62no—
572C42—62no—
573C42—182no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—34no—
580C22×C3—34no—
581C22×C3—62no—
582C22×C3—62no—
583C22×C3—62no—
584C22×C3—64no—
585C22×C3—62no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—64no—
589C22×C3C22×C4×D311yescharacteristic
590C22×C3C22×C4×D311yescharacteristic
591C22×C3C22×D1211yescharacteristic
592C22×C3C2×#23512yes—
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C22×C3D3×#4112yes—
596C22×C3D3×#4112yes—
597C22×C3D3×#4112yes—
598C22×C3C22×#6711yescharacteristic
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—24no—
604C2×D3—24no—
605C2×D3—24no—
606C2×D3—24no—
607C2×D3—34no—
608C2×D3—34no—
609C2×D3—64no—
610C2×D3—632no—
611C2×D3—632no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—64no—
616C2×D3—62no—
617C2×D3—64no—
618C2×D3—64no—
619C2×D3—64no—
620C2×D3—122no—
621C2×D3—122no—
622C2×D3—124no—
623C2×D3—124no—
624C2×D3#87214yescomplemented
625C2×D3C2×(C2×D3)⋊C414yes—
626C3×C4—24no—
627C3×C4—34no—
628C3×C4—44no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—62no—
632C3×C4—122no—
633C3×C4—122no—
634C3×C4D3×C22⋊C414yes—
635C3×C4C2×(C2×D3)⋊C414yes—
636Dic3—22no—
637Dic3—42no—
638Dic3—42no—
639Dic3—62no—
640Dic3—62no—
641Dic3—122no—
642Dic3—124no—
643Dic3—122no—
644Dic3—122no—
645Dic3C2×(C2×D3)⋊C414yes—
646C32#228011yescharacteristic, complemented, Sylow
647C23—32no—
648C23—32no—
649C23—32no—
650C23—34no—
651C23—32no—
652C23—61no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—61no—
657C23—92no—
658C23—94no—
659C23—188no—
660C23—188no—
661C23—188no—
662C23—1816no—
663C23—1816no—
664C23—181no—
665C23—182no—
666C23—181no—
667C23C22×D3211yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—316no—
675C2×C4—32no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—68no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—92no—
686C2×C4—188no—
687C2×C4—188no—
688C2×C4—188no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—188no—
692C2×C4—182no—
693C2×C4—182no—
694C2×C4—182no—
695C2×C4C4×D3212yes—
696C2×C4D3×D1212yes—
697C2×C4D3×#6712yes—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—22no—
701C2×C3—21no—
702C2×C3—22no—
703C2×C3—64no—
704C2×C3—64no—
705C2×C3C2×#87211yescharacteristic
706C2×C3C2×D3×C22⋊C411yescharacteristic
707C2×C3D3×#11711yescharacteristic
708C2×C3D3×#11711yescharacteristic
709C2×C3D3×#11711yescharacteristic
710C2×C3#552412yes—
711C2×C3#554712yes—
712C2×C3#554712yes—
713C2×C3C22×(C2×D3)⋊C411yescharacteristic
714C2×C3#582812yes—
715D3—24no—
716D3—24no—
717D3—64no—
718D3—64no—
719D3—124no—
720C22—34no—
721C22—34no—
722C22—62no—
723C22—62no—
724C22—62no—
725C22—64no—
726C22—64no—
727C22—62no—
728C22—64no—
729C22—64no—
730C22—94no—
731C22—1832no—
732C22—182no—
733C22—184no—
734C22—182no—
735C22—184no—
736C22C2×C4×D3211yescharacteristic
737C22C2×D3×D1211yescharacteristic
738C22D3×#23512yes—
739C22#6430612yes—
740C22C2×D3×#6711yescharacteristic
741C4—34no—
742C4—42no—
743C4—62no—
744C4—122no—
745C4—122no—
746C4—182no—
747C4—362no—
748C4D3×(C2×D3)⋊C414yes—
749C3—21no—
750C3#7356111yescharacteristic, complemented
751C3#8226711yescharacteristic, complemented
752C2—64no—
753C2—64no—
754C2—184no—
755C2D3×#87211yescharacteristic
756C2#1059399211yescharacteristic
757C2#1059399712yes—
758C2C2×D3×(C2×D3)⋊C411yescharacteristic
759C2#1059506012yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C42D32
hypocenterC32#2280
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#872C2semidirect
3. C2×#63855C2semidirect
4. C4×#3752C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
7. #10591367C2semidirect
8. #10591366C2semidirect
9. #10591362C2semidirect
10. C4×#3722C2semidirect
11. C4×(C2×D3)⋊Dic3C2semidirect
23. C2×C4×D32C4semidirect
24. C2×C32×C42C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. C2×C3×C4×Dic3C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
38. #63658C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
47. C2×#872D3semidirect
62. C4×(C2×D3)⋊C4D3semidirect
141. C2×C3×C42C2×D3semidirect
142. C2×C3×C42C2×D3semidirect
157. C2×Dic3⋊C4C2×D3semidirect
161. C2×C4×Dic3C2×D3semidirect
162. C2×C4×Dic3C2×D3semidirect
173. C3⋊#95C2×D3semidirect
221. C3×C4×D3C22⋊C4semidirect
350. C2×C3⋊D3#117semidirect
360. C2×C3×D3#117semidirect
393. C2×C42D32semidirect
518. C4×D3(C2×D3)⋊C4semidirect
624. C2×D3#872semidirect
646. C32#2280semidirect
750. C3#73561semidirect
751. C3#82267semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×C3×#8722
C2×#638552
C4×#37522
C3×C4×(C2×D3)⋊C42
#105913992
#105913672
#105913662
#105913622
C4×#37222
C4×(C2×D3)⋊Dic32
#822673
#735613