Finite Group Databasebeta

← #11801991

Subgroups — #11801991

Order 1152.

2661 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×#64090C211yesmaximal, characteristic, complemented
3C2×#63977C211yesmaximal, characteristic
4C2×#63881C212yesmaximal, complemented
5C3×#4955C211yesmaximal, characteristic, complemented
6C3×#4946C211yesmaximal, characteristic, complemented
7#10591711C211yesmaximal, characteristic, complemented
8#10591705C211yesmaximal, characteristic, complemented
9#10591372C212yesmaximal, complemented
10#10591368C212yesmaximal, complemented
11#10591364C212yesmaximal, complemented
12#74379—31nomaximal
13#73818—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C23×C3×Dic3C2211yescharacteristic
19C22×#626C2212yes—
20C22×D3×Dic3—24no—
21C22×D3×Dic3—28no—
22C22×D3×Dic3C2212yes—
23C22×D3×Dic3C2212yes—
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3752C2211yescharacteristic, complemented
26C2×#3750C2211yescharacteristic, complemented
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28#64090—24no—
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×Dic3⋊C4C2212yescomplemented
34#63977C418yescomplemented
35C2×#3722C2212yescomplemented
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×Dic32C2212yescomplemented
38#63881—28no—
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C24×Dic3—31no—
43C23×C4×D3—31no—
44C2×#953—31no—
45C2×#893—32no—
46C2×#882—31no—
47C2×#67⋊C4—31no—
48C2×#67⋊C4—31no—
49C2×#67⋊C4—32no—
50C2×#67⋊C4—61no—
51C3×#385—31no—
52C3×#379—31no—
53#5213—31no—
54#4989—32no—
55#4958—31no—
56#4958—32no—
57#4955D311yescharacteristic, complemented
58#4946—32no—
59#4946D311yescharacteristic, complemented
60Dic3×C22⋊C4—31no—
61Dic3×C22⋊C4—31no—
62Dic3×C22⋊C4—32no—
63#4666—32no—
64#4665—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3—22no—
68C23×C3×D3—22no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3C2×C414yescomplemented
72C23×C3×D3C2312yes—
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C2×#638—22no—
76C2×#638—22no—
77C2×#638C2×C414yescomplemented
78C22×C3⋊Dic3—24no—
79C22×C3⋊Dic3D414yescomplemented
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3—24no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3—24no—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C2×#626—24no—
91C2×#626—24no—
92C2×#626C2×C418yescomplemented
93C2×D3×Dic3—232no—
94C2×D3×Dic3—24no—
95C2×D3×Dic3—24no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3—24no—
98C2×D3×Dic3—24no—
99C2×D3×Dic3D418yescomplemented
100C32×C22⋊C4—22no—
101#3752—22no—
102#3750—22no—
103C4×C3⋊Dic3—22no—
104C3×#217—22no—
105C3×#217C2×C414yescomplemented
106C3×(C2×D3)⋊C4—24no—
107C3×(C2×D3)⋊C4—24no—
108C3×Dic3⋊C4—24no—
109#3722—24no—
110(C2×D3)⋊Dic3C2×C418yescomplemented
111Dic32—24no—
112C4×#120—91noSylow
113C25×C3—31no—
114C24×D3C2×D311yescharacteristic
115C23×C3×C4—31no—
116C22×#67—31no—
117C22×#67—31no—
118C22×#67—32no—
119C22×#67—61no—
120C23×Dic3—31no—
121C23×Dic3—31no—
122C23×Dic3—32no—
123C23×Dic3—32no—
124C23×Dic3—61no—
125C23×Dic3—64no—
126C23×Dic3—68no—
127C23×Dic3C2×D311yescharacteristic
128C22×D12—32no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×C4×D3—61no—
134C22×C4×D3—68no—
135C22×C4×D3—64no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4C2×D311yescharacteristic
143C2×C3×C22⋊C4C2×D311yescharacteristic
144#953—38no—
145C2×#217—32no—
146C2×#217C2×D311yescharacteristic
147C2×#217C2×D311yescharacteristic
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—61no—
154C2×(C2×D3)⋊C4C2×D312yes—
155C2×(C2×D3)⋊C4C2×D312yes—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—61no—
159C2×Dic3⋊C4C2×D312yescomplemented
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—32no—
163C2×C4×Dic3—32no—
164C2×C4×Dic3—61no—
165#893—68no—
166#882—38no—
167#67⋊C4—68no—
168#67⋊C4—64no—
169#67⋊C4—64no—
170#67⋊C4—68no—
171C3×#95—32no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C3⋊#95—32no—
175C3⋊#95—32no—
176C3⋊#95C2×D312yescomplemented
177C23×C32—22no—
178C23×C32—22no—
179C23×C32C22×C412yes—
180C23×C32C2×D412yes—
181C23×C32#4112yes—
182C23×C32C2411yescharacteristic
183C22×C3⋊D3—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3C22×C412yescomplemented
188C22×C3×D3—216no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3—28no—
192C22×C3×D3—22no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—216no—
197C22×C3×D3C22×C414yes—
198C22×C3×D3C2×D414yes—
199C22×C3×D3#4114yes—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204#638—28no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—28no—
209C2×C3⋊Dic3C22×C412yescomplemented
210C2×C3⋊Dic3C2×D412yes—
211C2×C3⋊Dic3C2×D414yes—
212C2×C3⋊Dic3C2×D412yes—
213C4×C3⋊D3—44no—
214C2×C3×Dic3—28no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3C22×C414yescomplemented
223C2×C3×Dic3C2×D414yes—
224#626—216no—
225D3×Dic3—216no—
226D3×Dic3—216no—
227C24×C4—91no—
228C2×#120—91no—
229C2×C4×D4—92no—
230C2×C4×D4—91no—
231#386—92no—
232#386—91no—
233#385—31no—
234#385—92no—
235#379—31no—
236C4×C22⋊C4—92no—
237C4×C22⋊C4—91no—
238C24×C3—21no—
239C24×C3—32no—
240C24×C3—34no—
241C24×C3—64no—
242C24×C3—64no—
243C24×C3—62no—
244C24×C3—62no—
245C24×C3C22×D311yescharacteristic
246C24×C3C22×D311yescharacteristic
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—24no—
250C23×D3—24no—
251C23×D3—31no—
252C23×D3—31no—
253C23×D3—61no—
254C23×D3C4×D314yescomplemented
255C23×D3C22×D312yes—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—32no—
259C22×C3×C4—32no—
260C22×C3×C4—32no—
261C22×C3×C4—64no—
262C22×C3×C4—62no—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C2×#67—34no—
268C2×#67—34no—
269C2×#67—38no—
270C2×#67—64no—
271C2×#67—64no—
272C2×#67—64no—
273C2×#67—64no—
274C2×#67—64no—
275C2×#67—62no—
276C2×#67—62no—
277C2×#67—62no—
278C2×#67—62no—
279C22×Dic3—22no—
280C22×Dic3—24no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—34no—
284C22×Dic3—34no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—38no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—64no—
293C22×Dic3—61no—
294C22×Dic3—64no—
295C22×Dic3—64no—
296C22×Dic3—64no—
297C22×Dic3—64no—
298C22×Dic3—632no—
299C22×Dic3—64no—
300C22×Dic3—64no—
301C22×Dic3—64no—
302C22×Dic3—124no—
303C22×Dic3C22×D312yes—
304C22×Dic3C22×D312yes—
305C22×Dic3C22×D312yes—
306C2×D12—38no—
307C2×D12—64no—
308C2×D12—64no—
309C2×C4×D3—38no—
310C2×C4×D3—64no—
311C2×C4×D3—64no—
312C2×C4×D3—64no—
313C2×C4×D3—64no—
314C2×C4×D3—632no—
315C2×C4×D3—64no—
316C2×C4×D3—62no—
317C2×C4×D3—62no—
318C2×C4×D3—64no—
319C2×C4×D3—64no—
320C2×C4×D3—64no—
321C2×C4×D3—124no—
322C3×C4⋊C4—64no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—22no—
325C3×C22⋊C4—22no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—64no—
328C3×C22⋊C4—64no—
329C3×C22⋊C4—62no—
330#217—22no—
331#217—38no—
332#217C4×D314yescomplemented
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—64no—
337(C2×D3)⋊C4—62no—
338(C2×D3)⋊C4—62no—
339(C2×D3)⋊C4—64no—
340(C2×D3)⋊C4—64no—
341Dic3⋊C4—24no—
342Dic3⋊C4—62no—
343Dic3⋊C4—62no—
344Dic3⋊C4—64no—
345C4×Dic3—64no—
346C4×Dic3—64no—
347C4×Dic3—62no—
348C4×Dic3—62no—
349C4×Dic3—64no—
350C22×C32—24no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—24no—
354C22×C32C4×D414yescomplemented
355C22×C32C23×C411yescharacteristic
356C22×C32C22×D412yes—
357C22×C32C22×D411yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32C2×#4112yes—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—24no—
362C2×C3⋊D3—41no—
363C2×C3⋊D3—41no—
364C2×C3⋊D3—42no—
365C2×C3×D3—232no—
366C2×C3×D3—24no—
367C2×C3×D3—24no—
368C2×C3×D3—24no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3C4×D418yescomplemented
373C32×C4—41no—
374C32×C4—41no—
375C3⋊Dic3—22no—
376C3⋊Dic3—22no—
377C3⋊Dic3#12014yescomplemented
378C3×Dic3—24no—
379C3×Dic3—24no—
380C3×Dic3—42no—
381C25—31no—
382C22×D4—92no—
383C22×D4—91no—
384C23×C4—31no—
385C23×C4—92no—
386C23×C4—92no—
387C23×C4—91no—
388C23×C4—91no—
389C23×C4—188no—
390C23×C4—184no—
391#120—98no—
392C4×D4—184no—
393C4×D4—188no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—91no—
396C2×C22⋊C4—31no—
397C2×C22⋊C4—31no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—92no—
401C2×C22⋊C4—92no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4D3211yescharacteristic
404C2×C42—92no—
405C2×C42—91no—
406#95—32no—
407#95—92no—
408#95—92no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—21no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—34no—
418C23×C3—34no—
419C23×C3—34no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—616no—
423C23×C3—68no—
424C23×C3—68no—
425C23×C3—616no—
426C23×C3—68no—
427C23×C3—62no—
428C23×C3—62no—
429C23×C3—62no—
430C23×C3—62no—
431C23×C3C2×C4×D312yes—
432C23×C3C2×C4×D312yes—
433C23×C3D3×D412yes—
434C23×C3D3×D412yes—
435C23×C3#23712yes—
436C23×C3#23912yes—
437C23×C3C23×D311yescharacteristic
438C23×C3C23×D311yescharacteristic
439C22×D3—28no—
440C22×D3—216no—
441C22×D3—28no—
442C22×D3—28no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—216no—
448C22×D3—32no—
449C22×D3—32no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—62no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—62no—
461C22×D3—122no—
462C22×D3—122no—
463C22×D3C2×C4×D314yes—
464C22×D3D3×D414yes—
465C22×D3#23714yes—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480C2×C3×C4—68no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488#67—616no—
489#67—616no—
490#67—68no—
491#67—68no—
492C2×Dic3—28no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—34no—
501C2×Dic3—32no—
502C2×Dic3—34no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—64no—
511C2×Dic3—62no—
512C2×Dic3—616no—
513C2×Dic3—616no—
514C2×Dic3—68no—
515C2×Dic3—68no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—128no—
525C2×Dic3—122no—
526C2×Dic3C2×C4×D314yescomplemented
527C2×Dic3D3×D414yes—
528D12—616no—
529C4×D3—616no—
530C4×D3—616no—
531C4×D3—124no—
532C4×D3—124no—
533C4×D3—128no—
534C2×C32—24no—
535C2×C32C2×C4×D411yescharacteristic
536C2×C32C2×C4×D412yes—
537C2×C32C2×#12011yescharacteristic
538C2×C32#52511yescharacteristic
539C2×C32#52512yes—
540C3⋊D3—42no—
541C3×D3—28no—
542C24—32no—
543C24—34no—
544C24—64no—
545C24—64no—
546C24—62no—
547C24—62no—
548C24—91no—
549C24C2×D3211yescharacteristic
550C2×D4—98no—
551C2×D4—94no—
552C2×D4—184no—
553C2×D4—184no—
554C2×D4—182no—
555C2×D4—182no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—98no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—91no—
565C22×C4—94no—
566C22×C4—182no—
567C22×C4—184no—
568C22×C4—184no—
569C22×C4—184no—
570C22×C4—184no—
571C22×C4—184no—
572C22×C4—184no—
573C22×C4—1832no—
574C22×C4—184no—
575C22×C4C2×D3211yescharacteristic
576C22×C4C2×D3211yescharacteristic
577C4⋊C4—64no—
578C4⋊C4—182no—
579C22⋊C4—22no—
580C22⋊C4—34no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—62no—
584C22⋊C4—98no—
585C22⋊C4—182no—
586C22⋊C4—184no—
587C42—182no—
588C42—184no—
589C22×C3—22no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—24no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—24no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—21no—
602C22×C3—24no—
603C22×C3—38no—
604C22×C3—42no—
605C22×C3—44no—
606C22×C3—42no—
607C22×C3—44no—
608C22×C3—632no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—64no—
613C22×C3—64no—
614C22×C3—64no—
615C22×C3#67⋊C414yescomplemented
616C22×C3#89314yescomplemented
617C22×C3C22×C4×D311yescharacteristic
618C22×C3C22×C4×D311yescharacteristic
619C22×C3C2×D3×D412yes—
620C22×C3C2×D3×D412yes—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C2×#23711yescharacteristic
624C22×C3C2×#23712yes—
625C22×C3C2×#23911yescharacteristic
626C22×C3D3×#4112yes—
627C2×D3—232no—
628C2×D3—24no—
629C2×D3—24no—
630C2×D3—24no—
631C2×D3—24no—
632C2×D3—24no—
633C2×D3—24no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—64no—
639C2×D3—124no—
640C2×D3—122no—
641C2×D3—124no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—122no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—122no—
649C2×D3#67⋊C418yescomplemented
650C3×C4—42no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—64no—
657C3×C4—64no—
658C3×C4—122no—
659Dic3—24no—
660Dic3—24no—
661Dic3—34no—
662Dic3—34no—
663Dic3—42no—
664Dic3—64no—
665Dic3—64no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—62no—
670Dic3—122no—
671C32C4×#12011yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—34no—
675C23—34no—
676C23—34no—
677C23—616no—
678C23—68no—
679C23—616no—
680C23—68no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—68no—
686C23—92no—
687C23—181no—
688C23—182no—
689C23—182no—
690C23—181no—
691C23#379612yes—
692C23C4×D3212yes—
693C23#381112yes—
694C23C22×D3211yescharacteristic
695D4—1816no—
696D4—188no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—34no—
702C2×C4—34no—
703C2×C4—68no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—94no—
712C2×C4—92no—
713C2×C4—92no—
714C2×C4—92no—
715C2×C4—1816no—
716C2×C4—1816no—
717C2×C4—188no—
718C2×C4—181no—
719C2×C4—182no—
720C2×C4—181no—
721C2×C4—364no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—22no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—22no—
728C2×C3—21no—
729C2×C3—44no—
730C2×C3—68no—
731C2×C3C2×#67⋊C411yescharacteristic
732C2×C3C2×#67⋊C412yes—
733C2×C3C2×#89311yescharacteristic
734C2×C3C4×D3×D412yes—
735C2×C3#558612yes—
736C2×C3#558611yescharacteristic
737C2×C3D3×#12011yescharacteristic
738C2×C3D3×#12011yescharacteristic
739C2×C3#562712yes—
740C2×C3#565611yescharacteristic
741D3—28no—
742D3—124no—
743D3—122no—
744D3—122no—
745C22—24no—
746C22—22no—
747C22—24no—
748C22—22no—
749C22—38no—
750C22—632no—
751C22—64no—
752C22—64no—
753C22—64no—
754C22—64no—
755C22—64no—
756C22—64no—
757C22—182no—
758C22—184no—
759C22—362no—
760C22—361no—
761C22—361no—
762C22#6388114yescomplemented
763C22C2×#379611yescharacteristic
764C22C2×C4×D3211yescharacteristic
765C22D32×D412yes—
766C22D3×#23712yes—
767C22C2×#381111yescharacteristic
768C4—41no—
769C4—41no—
770C4—64no—
771C4—64no—
772C4—94no—
773C4—122no—
774C4—182no—
775C4—182no—
776C3—21no—
777C3#7381811yescharacteristic, complemented
778C3#7437911yescharacteristic, complemented
779C2—24no—
780C2—68no—
781C2—362no—
782C2#1059405512yes—
783C2D3×#67⋊C412yes—
784C2C2×#6388111yescharacteristic
785C2#1059516011yescharacteristic
786C2#1059527811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
2. C2×#64090C2semidirect
4. C2×#63881C2semidirect
5. C3×#4955C2semidirect
6. C3×#4946C2semidirect
7. #10591711C2semidirect
8. #10591705C2semidirect
9. #10591372C2semidirect
10. #10591368C2semidirect
11. #10591364C2semidirect
17. C22×C4×C3⋊D3C22semidirect
25. C2×#3752C22semidirect
26. C2×#3750C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. #63977C4semidirect
35. C2×#3722C22semidirect
37. C2×Dic32C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
57. #4955D3semidirect
59. #4946D3semidirect
71. C23×C3×D3C2×C4semidirect
77. C2×#638C2×C4semidirect
79. C22×C3⋊Dic3D4semidirect
92. C2×#626C2×C4semidirect
99. C2×D3×Dic3D4semidirect
105. C3×#217C2×C4semidirect
110. (C2×D3)⋊Dic3C2×C4semidirect
159. C2×Dic3⋊C4C2×D3semidirect
176. C3⋊#95C2×D3semidirect
187. C22×C3⋊D3C22×C4semidirect
209. C2×C3⋊Dic3C22×C4semidirect
222. C2×C3×Dic3C22×C4semidirect
254. C23×D3C4×D3semidirect
332. #217C4×D3semidirect
354. C22×C32C4×D4semidirect
372. C2×C3×D3C4×D4semidirect
377. C3⋊Dic3#120semidirect
526. C2×Dic3C2×C4×D3semidirect
615. C22×C3#67⋊C4semidirect
616. C22×C3#893semidirect
649. C2×D3#67⋊C4semidirect
671. C32C4×#120semidirect
762. C22#63881semidirect
777. C3#73818semidirect
778. C3#74379semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×#640902
C2×#639772
C2×#638812
C3×#49552
C3×#49462
#105917112
#105917052
#105913722
#105913682
#105913642
#743793
#738183