Finite Group Databasebeta

← #11801990

Subgroups — #11801990

Order 1152.

2701 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×#63981C211yesmaximal, characteristic
4C2×#63904C212yesmaximal, complemented
5#10592654C211yesmaximal, characteristic, complemented
6C3×#4946C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591374C212yesmaximal, complemented
10#10591275C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12C4×#937—31nomaximal
13#74379—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic, complemented
19C22×#626C2212yes—
20C22×#624—24no—
21C22×#624—28no—
22C22×#624C2212yes—
23C22×#624C2212yes—
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2212yes—
27C2×#3752C2212yes—
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C2×C3×Dic3⋊C4C2212yescomplemented
31C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×C4×Dic3C2211yescharacteristic, complemented
33C3×#67⋊C4—24no—
34#63981C418yescomplemented
35C2×#3722C2212yes—
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37C2×Dic32C2212yescomplemented
38#63904—28no—
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—31no—
43C23×C4×D3—31no—
44C2×C3×C4×D4—31no—
45C2×#937—31no—
46C2×C4×#67—32no—
47C2×#893—32no—
48C2×#882—31no—
49C2×#67⋊C4D311yescharacteristic, complemented
50C3×#385—31no—
51#5220—31no—
52#5213—31no—
53C4×#217—31no—
54#4989—32no—
55#4989—32no—
56#4956—32no—
57#4955—31no—
58#4955—31no—
59#4955—61no—
60#4946D311yescharacteristic, complemented
61Dic3×C22⋊C4—31no—
62C4×(C2×D3)⋊C4—32no—
63#4666—32no—
64#4665—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3—22no—
67C23×C3⋊D3—22no—
68C23×C3⋊D3—24no—
69C23×C3⋊D3—24no—
70C23×C3⋊D3C2×C414yescomplemented
71C23×C3⋊D3C2312yes—
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3C2312yes—
76C2×C3×#67—22no—
77C2×C3×#67—22no—
78C2×C3×#67C2×C414yescomplemented
79C22×C3×Dic3—22no—
80C22×C3×Dic3—24no—
81C22×C3×Dic3—24no—
82C22×C3×Dic3D414yescomplemented
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C2×C3×C4×D3—22no—
89C2×C3×C4×D3—24no—
90C2×#626—24no—
91C2×#626—24no—
92C2×#626C2×C418yescomplemented
93C2×#624—232no—
94C2×#624—24no—
95C2×#624—24no—
96C2×#624—24no—
97C2×#624—24no—
98C2×#624—24no—
99C2×#624D418yescomplemented
100C32×C22⋊C4—22no—
101#3757—22no—
102#3752—24no—
103#3752—24no—
104C3×#217C2×C414yescomplemented
105C3×(C2×D3)⋊C4—22no—
106C3×Dic3⋊C4—22no—
107C3×Dic3⋊C4—24no—
108C3×C4×Dic3—22no—
109#3722C2×C418yescomplemented
110(C2×D3)⋊Dic3—24no—
111Dic32—24no—
112C4×#120—91noSylow
113C24×D3—31no—
114C24×D3—31no—
115C24×D3—61no—
116C22×C3×D4—31no—
117C23×C3×C4—31no—
118C23×C3×C4—31no—
119C23×C3×C4—31no—
120C22×#67—32no—
121C22×#67C2×D311yescharacteristic
122C23×Dic3C2×D311yescharacteristic
123C23×Dic3C2×D311yescharacteristic
124C22×D12—32no—
125C22×C4×D3—32no—
126C22×C4×D3—32no—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—68no—
130C22×C4×D3—68no—
131C22×C4×D3—64no—
132C22×C4×D3—64no—
133C22×C4×D3C2×D311yescharacteristic, complemented
134C3×C4×D4—64no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C22⋊C4C2×D311yescharacteristic
142C2×C3×C42—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—32no—
146C2×#217—61no—
147C2×#217C2×D311yescharacteristic
148#937—38no—
149C4×#67—68no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—62no—
158C2×(C2×D3)⋊C4—62no—
159C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
160C2×Dic3⋊C4C2×D312yescomplemented
161C2×Dic3⋊C4C2×D311yescharacteristic, complemented
162C2×C4×Dic3—32no—
163C2×C4×Dic3—32no—
164C2×C4×Dic3C2×D311yescharacteristic, complemented
165#893—68no—
166#882—38no—
167#67⋊C4—24no—
168C3×#95—32no—
169C3⋊#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—32no—
173C3⋊#95C2×D312yescomplemented
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C22×C412yes—
177C23×C32C2×D412yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3⋊D3—216no—
181C22×C3⋊D3—28no—
182C22×C3⋊D3—28no—
183C22×C3⋊D3—28no—
184C22×C3⋊D3—22no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—22no—
188C22×C3⋊D3—216no—
189C22×C3⋊D3C22×C414yes—
190C22×C3⋊D3C2×D414yes—
191C22×C3⋊D3#4114yes—
192C22×C3×D3—22no—
193C22×C3×D3—21no—
194C22×C3×D3—22no—
195C22×C3×D3—21no—
196C22×C3×D3C22×C412yescomplemented
197C2×C32×C4—21no—
198C2×C32×C4—22no—
199C2×C32×C4—21no—
200C2×C32×C4—22no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C3×#67—28no—
205C2×C3×Dic3—28no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—28no—
214C2×C3×Dic3C22×C412yescomplemented
215C2×C3×Dic3C22×C414yescomplemented
216C2×C3×Dic3C2×D414yes—
217C2×C3×Dic3C2×D414yes—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D412yes—
220C3×C4×D3—44no—
221#626—216no—
222#624—216no—
223#624—216no—
224C24×C4—91no—
225C2×#120—91no—
226C2×C4×D4—31no—
227C2×C4×D4—92no—
228#386—92no—
229#386—91no—
230#385—31no—
231#385—92no—
232#379—91no—
233C4×C22⋊C4—92no—
234C4×C22⋊C4—91no—
235C24×C3—21no—
236C24×C3—31no—
237C24×C3C22×D311yescharacteristic
238C24×C3C22×D311yescharacteristic
239C23×D3—32no—
240C23×D3—32no—
241C23×D3—34no—
242C23×D3—34no—
243C23×D3—62no—
244C23×D3—64no—
245C23×D3—64no—
246C23×D3—64no—
247C23×D3—64no—
248C23×D3—64no—
249C23×D3—62no—
250C23×D3—62no—
251C23×D3—62no—
252C23×D3—62no—
253C23×D3—124no—
254C23×D3—124no—
255C23×D3—122no—
256C23×D3—122no—
257C23×D3C22×D311yescharacteristic
258C2×C3×D4—34no—
259C2×C3×D4—62no—
260C2×C3×D4—62no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—31no—
264C22×C3×C4—34no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—32no—
268C22×C3×C4—32no—
269C22×C3×C4—64no—
270C22×C3×C4—62no—
271C22×C3×C4—64no—
272C22×C3×C4—64no—
273C22×C3×C4—62no—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—38no—
281C2×#67—64no—
282C2×#67—64no—
283C2×#67C4×D314yescomplemented
284C22×Dic3—22no—
285C22×Dic3—24no—
286C22×Dic3—24no—
287C22×Dic3—32no—
288C22×Dic3—32no—
289C22×Dic3—62no—
290C22×Dic3#6714yescomplemented
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D312yes—
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C2×D12—38no—
297C2×D12—64no—
298C2×D12—64no—
299C2×C4×D3—24no—
300C2×C4×D3—22no—
301C2×C4×D3—38no—
302C2×C4×D3—38no—
303C2×C4×D3—64no—
304C2×C4×D3—64no—
305C2×C4×D3—64no—
306C2×C4×D3—64no—
307C2×C4×D3—64no—
308C2×C4×D3—64no—
309C2×C4×D3—632no—
310C2×C4×D3—632no—
311C2×C4×D3—64no—
312C2×C4×D3—64no—
313C2×C4×D3—64no—
314C2×C4×D3—64no—
315C3×C4⋊C4—64no—
316C3×C4⋊C4—62no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—34no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—62no—
322C3×C42—62no—
323#217—62no—
324#217—62no—
325#217—64no—
326#217—122no—
327#217C4×D314yescomplemented
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4—38no—
330(C2×D3)⋊C4—38no—
331(C2×D3)⋊C4—64no—
332(C2×D3)⋊C4—64no—
333(C2×D3)⋊C4—64no—
334(C2×D3)⋊C4—64no—
335(C2×D3)⋊C4—64no—
336(C2×D3)⋊C4—124no—
337(C2×D3)⋊C4—124no—
338Dic3⋊C4—24no—
339Dic3⋊C4—22no—
340C4×Dic3—22no—
341C4×Dic3—64no—
342C4×Dic3—64no—
343C22×C32—24no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—24no—
347C22×C32C4×D414yescomplemented
348C22×C32C23×C411yescharacteristic
349C22×C32C22×D412yes—
350C22×C32C22×D411yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4112yes—
353C2×C3⋊D3—232no—
354C2×C3⋊D3—24no—
355C2×C3⋊D3—24no—
356C2×C3⋊D3—24no—
357C2×C3⋊D3—24no—
358C2×C3⋊D3—24no—
359C2×C3⋊D3—24no—
360C2×C3⋊D3C4×D418yescomplemented
361C2×C3×D3—24no—
362C2×C3×D3—22no—
363C2×C3×D3—41no—
364C2×C3×D3—42no—
365C2×C3×D3—41no—
366C32×C4—41no—
367C32×C4—41no—
368C3⋊Dic3—42no—
369C3×Dic3—24no—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—24no—
373C3×Dic3#12014yescomplemented
374C25—91no—
375C22×D4—31no—
376C22×D4—92no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—92no—
381C23×C4—92no—
382C23×C4—184no—
383C23×C4—188no—
384#120—98no—
385C4×D4—64no—
386C4×D4—188no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—31no—
391C2×C22⋊C4—92no—
392C2×C22⋊C4—92no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—92no—
395C2×C22⋊C4—92no—
396C2×C22⋊C4D3211yescharacteristic
397C2×C42—31no—
398C2×C42—92no—
399#95—32no—
400#95—92no—
401#95—92no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—32no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—62no—
417C23×C3C2×C4×D312yes—
418C23×C3C2×C4×D312yes—
419C23×C3#23512yes—
420C23×C3D3×D412yes—
421C23×C3#23912yes—
422C23×C3C2×#6712yes—
423C23×C3C23×D311yescharacteristic
424C23×C3C23×D311yescharacteristic
425C22×D3—21no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—21no—
429C22×D3—34no—
430C22×D3—34no—
431C22×D3—34no—
432C22×D3—34no—
433C22×D3—34no—
434C22×D3—34no—
435C22×D3—64no—
436C22×D3—64no—
437C22×D3—64no—
438C22×D3—616no—
439C22×D3—616no—
440C22×D3—68no—
441C22×D3—68no—
442C22×D3—68no—
443C22×D3—616no—
444C22×D3—68no—
445C22×D3—616no—
446C22×D3—68no—
447C22×D3—68no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—1216no—
457C22×D3—122no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3—128no—
462C22×D3—128no—
463C22×D3—1216no—
464C22×D3—128no—
465C22×D3C2×C4×D312yescomplemented
466C3×D4—68no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—34no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—34no—
479C2×C3×C4—34no—
480C2×C3×C4—32no—
481C2×C3×C4—42no—
482C2×C3×C4—42no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—68no—
486C2×C3×C4—68no—
487C2×C3×C4—62no—
488C2×C3×C4—61no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—61no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—124no—
495#67—28no—
496#67—616no—
497C2×Dic3—28no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—28no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—122no—
513C2×Dic3—122no—
514C2×Dic3—122no—
515C2×Dic3C2×C4×D312yescomplemented
516C2×Dic3C2×C4×D314yescomplemented
517C2×Dic3D3×D414yes—
518C2×Dic3D3×D414yes—
519C2×Dic3C2×#6712yes—
520C2×Dic3C2×#6712yes—
521D12—616no—
522C4×D3—44no—
523C4×D3—616no—
524C4×D3—616no—
525C4×D3—616no—
526C4×D3—616no—
527C2×C32—24no—
528C2×C32C2×C4×D411yescharacteristic
529C2×C32C2×C4×D412yes—
530C2×C32C2×#12011yescharacteristic
531C2×C32#52511yescharacteristic
532C2×C32#52512yes—
533C3⋊D3—28no—
534C3×D3—42no—
535C24—31no—
536C24—92no—
537C24—94no—
538C24—184no—
539C24—184no—
540C24—182no—
541C24—182no—
542C24C2×D3211yescharacteristic
543C2×D4—34no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—98no—
547C2×D4—184no—
548C2×D4—184no—
549C22×C4—31no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—34no—
555C22×C4—62no—
556C22×C4—64no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—62no—
560C22×C4—98no—
561C22×C4—92no—
562C22×C4—184no—
563C22×C4—184no—
564C22×C4—184no—
565C22×C4—184no—
566C22×C4—184no—
567C22×C4—1832no—
568C22×C4C2×D3211yescharacteristic
569C22×C4C2×D3211yescharacteristic
570C4⋊C4—62no—
571C4⋊C4—64no—
572C22⋊C4—22no—
573C22⋊C4—34no—
574C22⋊C4—62no—
575C22⋊C4—98no—
576C22⋊C4—184no—
577C22⋊C4—184no—
578C22⋊C4—184no—
579C22⋊C4—182no—
580C42—62no—
581C42—184no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—24no—
585C22×C3—24no—
586C22×C3—24no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—24no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—24no—
596C22×C3—44no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—44no—
600C22×C3—62no—
601C22×C3—64no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—122no—
605C22×C3#89314yescomplemented
606C22×C3C4×#6714yescomplemented
607C22×C3C22×C4×D311yescharacteristic
608C22×C3C22×C4×D311yescharacteristic
609C22×C3C2×#23511yescharacteristic
610C22×C3C2×D3×D412yes—
611C22×C3C2×D3×D412yes—
612C22×C3C2×D3×D411yescharacteristic
613C22×C3C2×#23911yescharacteristic
614C22×C3D3×#4112yes—
615C22×C3D3×#4112yes—
616C22×C3C22×#6711yescharacteristic
617C2×D3—22no—
618C2×D3—24no—
619C2×D3—38no—
620C2×D3—38no—
621C2×D3—41no—
622C2×D3—42no—
623C2×D3—41no—
624C2×D3—68no—
625C2×D3—632no—
626C2×D3—632no—
627C2×D3—64no—
628C2×D3—64no—
629C2×D3—64no—
630C2×D3—64no—
631C2×D3—64no—
632C2×D3—64no—
633C2×D3—64no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—64no—
637C2×D3—64no—
638C2×D3—64no—
639C2×D3—124no—
640C2×D3—124no—
641C2×D3—124no—
642C2×D3—124no—
643C2×D3—124no—
644C2×D3—124no—
645C2×D3—1232no—
646C3×C4—34no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—62no—
652C3×C4—64no—
653C3×C4—64no—
654C3×C4—62no—
655C3×C4—81no—
656C3×C4—81no—
657Dic3—22no—
658Dic3—22no—
659Dic3—24no—
660Dic3—24no—
661Dic3—122no—
662Dic3—122no—
663Dic3—242no—
664Dic3#93714yescomplemented
665C32C4×#12011yescharacteristic, complemented, Sylow
666C23—22no—
667C23—22no—
668C23—32no—
669C23—61no—
670C23—62no—
671C23—62no—
672C23—61no—
673C23—94no—
674C23—94no—
675C23—94no—
676C23—1816no—
677C23—188no—
678C23—1816no—
679C23—188no—
680C23—182no—
681C23—182no—
682C23—182no—
683C23—182no—
684C23—188no—
685C23#379912yes—
686C23C4×D3212yes—
687C23D3×#6712yes—
688C23C22×D3211yescharacteristic
689D4—68no—
690D4—1816no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—34no—
696C2×C4—32no—
697C2×C4—34no—
698C2×C4—32no—
699C2×C4—34no—
700C2×C4—32no—
701C2×C4—68no—
702C2×C4—68no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—124no—
711C2×C4—1816no—
712C2×C4—1816no—
713C2×C4—182no—
714C2×C4—182no—
715C2×C4—182no—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—22no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—22no—
723C2×C3—44no—
724C2×C3—122no—
725C2×C3C2×#89311yescharacteristic
726C2×C3C4×D3×D412yes—
727C2×C3C4×D3×D412yes—
728C2×C3#554712yes—
729C2×C3D3×#12011yescharacteristic
730C2×C3#562712yes—
731C2×C3#565611yescharacteristic
732C2×C3C2×C4×#6711yescharacteristic
733C2×C3C2×#93711yescharacteristic
734C2×C3#582811yescharacteristic
735D3—42no—
736D3—68no—
737D3—68no—
738D3—128no—
739C22—24no—
740C22—22no—
741C22—22no—
742C22—24no—
743C22—62no—
744C22—64no—
745C22—98no—
746C22—122no—
747C22—121no—
748C22—121no—
749C22—1832no—
750C22—184no—
751C22—184no—
752C22—184no—
753C22—184no—
754C22—184no—
755C22—184no—
756C22#6390414yescomplemented
757C22C2×#379911yescharacteristic
758C22C2×C4×D3211yescharacteristic
759C22D32×D412yes—
760C22#6431212yes—
761C22C2×D3×#6711yescharacteristic
762C4—34no—
763C4—41no—
764C4—41no—
765C4—62no—
766C4—64no—
767C4—62no—
768C4—64no—
769C4—362no—
770C3—21no—
771C3#7437911yescharacteristic, complemented
772C3C4×#93711yescharacteristic, complemented
773C2—24no—
774C2—122no—
775C2—188no—
776C2#1059406612yes—
777C2#1059425512yes—
778C2C2×#6390411yescharacteristic
779C2#1059515911yescharacteristic
780C2D3×#93711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
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×#624C2semidirect
2. C2×C3×#67⋊C4C2semidirect
4. C2×#63904C2semidirect
5. #10592654C2semidirect
6. C3×#4946C2semidirect
7. #10591710C2semidirect
8. Dic3×#217C2semidirect
9. #10591374C2semidirect
10. #10591275C2semidirect
11. #10591233C2semidirect
18. C22×C3×C4×D3C22semidirect
29. C2×C3×(C2×D3)⋊C4C22semidirect
30. C2×C3×Dic3⋊C4C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
32. C2×C3×C4×Dic3C22semidirect
34. #63981C4semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
37. C2×Dic32C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
49. C2×#67⋊C4D3semidirect
60. #4946D3semidirect
70. C23×C3⋊D3C2×C4semidirect
78. C2×C3×#67C2×C4semidirect
82. C22×C3×Dic3D4semidirect
92. C2×#626C2×C4semidirect
99. C2×#624D4semidirect
104. C3×#217C2×C4semidirect
109. #3722C2×C4semidirect
133. C22×C4×D3C2×D3semidirect
159. C2×(C2×D3)⋊C4C2×D3semidirect
160. C2×Dic3⋊C4C2×D3semidirect
161. C2×Dic3⋊C4C2×D3semidirect
164. C2×C4×Dic3C2×D3semidirect
173. C3⋊#95C2×D3semidirect
196. C22×C3×D3C22×C4semidirect
214. C2×C3×Dic3C22×C4semidirect
215. C2×C3×Dic3C22×C4semidirect
283. C2×#67C4×D3semidirect
290. C22×Dic3#67semidirect
327. #217C4×D3semidirect
347. C22×C32C4×D4semidirect
360. C2×C3⋊D3C4×D4semidirect
373. C3×Dic3#120semidirect
465. C22×D3C2×C4×D3semidirect
515. C2×Dic3C2×C4×D3semidirect
516. C2×Dic3C2×C4×D3semidirect
605. C22×C3#893semidirect
606. C22×C3C4×#67semidirect
664. Dic3#937semidirect
665. C32C4×#120semidirect
756. C22#63904semidirect
771. C3#74379semidirect
772. C3C4×#937semidirect

Maximal subgroups

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

subgroupindex
C23×#6242
C2×C3×#67⋊C42
C2×#639812
C2×#639042
#105926542
C3×#49462
#105917102
Dic3×#2172
#105913742
#105912752
#105912332
C4×#9373
#743793