Finite Group Databasebeta

← #11810278

Subgroups — #11810278

Order 1152.

2400 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic
3C2×#64138C211yesmaximal, characteristic, complemented
4C22×#3752C211yesmaximal, characteristic, complemented
5#10592919C211yesmaximal, characteristic, complemented
6#10592912C211yesmaximal, characteristic, complemented
7#10592909C211yesmaximal, characteristic, complemented
8#10592692C211yesmaximal, characteristic, complemented
9#10592691C211yesmaximal, characteristic, complemented
10#10592658C211yesmaximal, characteristic, complemented
11#10592658C211yesmaximal, characteristic, complemented
12#10592654C211yesmaximal, characteristic, complemented
13#10592641C211yesmaximal, characteristic, complemented
14#10592639C211yesmaximal, characteristic, complemented
15#10592639C211yesmaximal, characteristic, complemented
16#82404—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic
24C32×C4×D4—24no—
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic, complemented
28C2×C32×C42C2211yescharacteristic, complemented
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic, complemented
32C2×#3757C2211yescharacteristic, complemented
33#64146—24no—
34#64138—24no—
35C2×#3752—24no—
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic
46C2×#3750C2211yescharacteristic, complemented
47C2×#3750C2211yescharacteristic, complemented
48C2×#3750C2211yescharacteristic, complemented
49C2×#3750C2211yescharacteristic, complemented
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C2×C3×C4×D4D314yescomplemented
57C2×#937—34no—
58C2×#929—34no—
59C22×(C2×D3)⋊C4—34no—
60#5220—34no—
61#5213—34no—
62#5210—34no—
63#4993—34no—
64#4992—34no—
65#4959—34no—
66#4959—34no—
67#4955—34no—
68#4942—34no—
69#4940—34no—
70#4940—34no—
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C23×C3⋊D3—22no—
74C23×C3⋊D3—22no—
75C23×C3⋊D3—22no—
76C23×C3⋊D3—22no—
77C23×C3⋊D3—22no—
78C23×C3⋊D3—41no—
79C23×C3⋊D3—41no—
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C2×C32×D4—22no—
83C2×C32×D4—22no—
84C2×C32×D4D414yes—
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—22no—
88C22×C32×C4—22no—
89C22×C32×C4—41no—
90C22×C32×C4—41no—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—22no—
99C2×#638—22no—
100C2×#638—41no—
101C2×#638—41no—
102C22×C3⋊Dic3—22no—
103C22×C3⋊Dic3—22no—
104C22×C3⋊Dic3—41no—
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C32×C4⋊C4—22no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C42—22no—
115#3757—22no—
116#3757—22no—
117#3757—22no—
118#3757—41no—
119#3752—22no—
120#3752—22no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125#3752—22no—
126#3752—41no—
127#3752—41no—
128#3752D414yescomplemented
129#3750—22no—
130#3750—22no—
131#3750—41no—
132#3750—41no—
133#2418—91noSylow
134C24×D3—34no—
135C22×C3×D4C2×D314yes—
136C23×C3×C4C2×D314yes—
137C23×C3×C4C2×D314yescomplemented
138C22×#67—34no—
139C22×#67—34no—
140C23×Dic3—34no—
141C3×C4×D4—216no—
142C2×C3×C4⋊C4C2×D314yescomplemented
143C2×C3×C22⋊C4C2×D314yes—
144C2×C3×C22⋊C4C2×D314yescomplemented
145C2×C3×C42C2×D314yescomplemented
146C2×#217—34no—
147C2×#217—34no—
148C2×#217—34no—
149C2×#217—34no—
150#937—616no—
151#929—616no—
152C2×(C2×D3)⋊C4—34no—
153C2×(C2×D3)⋊C4—34no—
154C2×(C2×D3)⋊C4—34no—
155C2×(C2×D3)⋊C4—34no—
156C2×(C2×D3)⋊C4—34no—
157C2×(C2×D3)⋊C4—34no—
158C2×(C2×D3)⋊C4—34no—
159C2×(C2×D3)⋊C4—34no—
160C2×(C2×D3)⋊C4—34no—
161C2×(C2×D3)⋊C4—34no—
162C2×(C2×D3)⋊C4—616no—
163C2×Dic3⋊C4—34no—
164C2×Dic3⋊C4—34no—
165C2×Dic3⋊C4—34no—
166C2×Dic3⋊C4—34no—
167C3⋊#95—34no—
168C3⋊#95—34no—
169C3⋊#95—34no—
170C3⋊#95—34no—
171C3⋊#95—34no—
172C3⋊#95—34no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32C2×D412yes—
184C23×C32C2×D412yes—
185C23×C32#4112yes—
186C23×C32#4112yes—
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—28no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—21no—
193C22×C3⋊D3—21no—
194C22×C3⋊D3—21no—
195C22×C3⋊D3—21no—
196C22×C3⋊D3—21no—
197C22×C3⋊D3—21no—
198C22×C3⋊D3—21no—
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—44no—
202C22×C3⋊D3—44no—
203C22×C3⋊D3—44no—
204C22×C3⋊D3—44no—
205C22×C3⋊D3—44no—
206C22×C3⋊D3—44no—
207C22×C3⋊D3C2×D412yes—
208C22×C3⋊D3#4112yes—
209C32×D4—28no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—44no—
224C2×C32×C4—44no—
225C2×C32×C4C2×D412yes—
226C2×C32×C4C2×D412yes—
227#638—44no—
228#638—44no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—44no—
247C2×C3⋊Dic3C2×D412yes—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4C3⋊D311yescharacteristic, complemented
251C22×C22⋊C4—91no—
252#399—91no—
253#397—91no—
254#394—91no—
255#394—91no—
256#388—91no—
257#388—91no—
258#386—91no—
259#386—91no—
260#385—91no—
261#380—91no—
262#379—91no—
263C24×C3C22×D314yes—
264C24×C3C22×D314yes—
265C23×D3—34no—
266C23×D3—34no—
267C23×D3—68no—
268C23×D3—68no—
269C23×D3—68no—
270C23×D3—68no—
271C23×D3—68no—
272C23×D3—124no—
273C23×D3—124no—
274C2×C3×D4—28no—
275C2×C3×D4—28no—
276C2×C3×D4#67116yes—
277C22×C3×C4—28no—
278C22×C3×C4—28no—
279C22×C3×C4—28no—
280C22×C3×C4—28no—
281C22×C3×C4—44no—
282C22×C3×C4—44no—
283C22×C3×C4C22×D314yes—
284C22×C3×C4C22×D314yes—
285C22×C3×C4C22×D314yes—
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C2×#67—68no—
289C2×#67—68no—
290C2×#67—68no—
291C2×#67—68no—
292C2×#67—124no—
293C2×#67—124no—
294C22×Dic3—34no—
295C22×Dic3—34no—
296C22×Dic3—34no—
297C22×Dic3—34no—
298C22×Dic3—34no—
299C22×Dic3—34no—
300C22×Dic3—68no—
301C22×Dic3—68no—
302C22×Dic3—124no—
303C3×C4⋊C4—28no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—28no—
306C3×C42—28no—
307#217—68no—
308#217—68no—
309#217—68no—
310#217—124no—
311(C2×D3)⋊C4—316no—
312(C2×D3)⋊C4—68no—
313(C2×D3)⋊C4—68no—
314(C2×D3)⋊C4—68no—
315(C2×D3)⋊C4—68no—
316(C2×D3)⋊C4—68no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4—68no—
319(C2×D3)⋊C4—124no—
320(C2×D3)⋊C4—124no—
321Dic3⋊C4—68no—
322Dic3⋊C4—68no—
323Dic3⋊C4—124no—
324Dic3⋊C4—124no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32#12314yescomplemented
339C22×C32C22×D411yescharacteristic
340C22×C32C22×D411yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C22×C32C2×#4111yescharacteristic
344C22×C32H(5,𝔽2)11yescharacteristic
345C22×C32H(5,𝔽2)11yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3—22no—
349C2×C3⋊D3—22no—
350C2×C3⋊D3—22no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—416no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C2×C3⋊D3—41no—
356C2×C3⋊D3—41no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3—41no—
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C3⋊Dic3—22no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C25—91no—
373C22×D4—91no—
374C22×D4—91no—
375C22×D4C2×C3⋊D311yescharacteristic
376C23×C4—91no—
377C23×C4C2×C3⋊D311yescharacteristic
378C23×C4C2×C3⋊D311yescharacteristic, complemented
379#123—184no—
380#120—184no—
381C4×D4—24no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—91no—
392C2×C22⋊C4—91no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—91no—
395C2×C22⋊C4—91no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—91no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—91no—
400C2×C22⋊C4—91no—
401C2×C22⋊C4—184no—
402C2×C22⋊C4C2×C3⋊D311yescharacteristic
403C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
404C2×C42C2×C3⋊D311yescharacteristic, complemented
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3#23518yes—
422C23×C3#23518yes—
423C23×C3C2×#6718yes—
424C23×C3C2×#6718yes—
425C23×C3C23×D314yes—
426C22×D3—38no—
427C22×D3—38no—
428C22×D3—632no—
429C22×D3—64no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—64no—
435C22×D3—64no—
436C22×D3—64no—
437C22×D3—64no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—1216no—
442C22×D3—1216no—
443C22×D3—1216no—
444C22×D3—1216no—
445C22×D3—1216no—
446C22×D3—1216no—
447C3×D4—232no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—416no—
462C2×C3×C4—416no—
463C2×C3×C4D3×D418yes—
464C2×C3×C4C2×#6718yes—
465#67—1216no—
466#67—1216no—
467C2×Dic3—38no—
468C2×Dic3—64no—
469C2×Dic3—64no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—64no—
473C2×Dic3—64no—
474C2×Dic3—64no—
475C2×Dic3—64no—
476C2×Dic3—64no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—64no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—64no—
484C2×Dic3—64no—
485C2×Dic3—1216no—
486C2×C32—24no—
487C2×C32—42no—
488C2×C32C2×#12311yescharacteristic
489C2×C32#52511yescharacteristic
490C2×C32#53811yescharacteristic
491C2×C32D4211yescharacteristic
492C2×C32#54611yescharacteristic
493C2×C32#54611yescharacteristic
494C2×C32#55111yescharacteristic
495C3⋊D3—42no—
496C3⋊D3—42no—
497C24—91no—
498C24—91no—
499C24—182no—
500C24—182no—
501C24—182no—
502C24—182no—
503C24—182no—
504C24—361no—
505C24—361no—
506C24C22×C3⋊D311yescharacteristic
507C24C22×C3⋊D311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—361no—
515C2×D4—361no—
516C2×D4#63814yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—182no—
530C22×C4—182no—
531C22×C4—361no—
532C22×C4C22×C3⋊D311yescharacteristic
533C22×C4C22×C3⋊D311yescharacteristic
534C22×C4C22×C3⋊D311yescharacteristic
535C22×C4C22×C3⋊D311yescharacteristic
536C22×C4C22×C3⋊D311yescharacteristic
537C4⋊C4—22no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—94no—
545C22⋊C4—182no—
546C22⋊C4—182no—
547C22⋊C4—182no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—182no—
552C22⋊C4—182no—
553C22⋊C4—182no—
554C22⋊C4—182no—
555C22⋊C4—361no—
556C22⋊C4—361no—
557C22⋊C4—361no—
558C42—22no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3#929116yescomplemented
573C22×C3C2×#23514yes—
574C22×C3C2×#23514yes—
575C22×C3C2×D3×D414yes—
576C22×C3#100414yes—
577C22×C3D3×#4114yes—
578C22×C3#100914yes—
579C22×C3C22×#6714yes—
580C2×D3—68no—
581C2×D3—68no—
582C2×D3—68no—
583C2×D3—68no—
584C2×D3—68no—
585C2×D3—68no—
586C2×D3—1264no—
587C2×D3—124no—
588C2×D3—124no—
589C2×D3—124no—
590C2×D3—124no—
591C2×D3—124no—
592C2×D3—124no—
593C2×D3—124no—
594C2×D3—124no—
595C3×C4—28no—
596C3×C4—28no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—44no—
600Dic3—68no—
601Dic3—124no—
602Dic3—124no—
603Dic3—124no—
604Dic3—124no—
605Dic3—124no—
606C32#241811yescharacteristic, complemented, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—92no—
618C23—92no—
619C23—188no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—364no—
633C23—364no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23#382812yes—
639C23#382812yes—
640C23C2×#63812yes—
641C23C2×#63812yes—
642C23C23×C3⋊D311yescharacteristic
643D4—28no—
644D4—364no—
645D4—364no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—92no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—364no—
680C2×C4D4×C3⋊D312yes—
681C2×C4C2×#63812yes—
682C2×C3—216no—
683C2×C3—48no—
684C2×C3#554714yes—
685C2×C3#555014yes—
686C2×C3#555614yes—
687C2×C3#556014yes—
688C2×C3C2×#92914yes—
689C2×C3D4×#6714yes—
690C2×C3#582914yes—
691D3—128no—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—3616no—
713C22—361no—
714C22—361no—
715C22—361no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22#6413814yescomplemented
722C22C2×#382811yescharacteristic
723C22C2×#382811yescharacteristic
724C22C2×D4×C3⋊D311yescharacteristic
725C22#6436111yescharacteristic
726C22#41×C3⋊D311yescharacteristic
727C22#6436611yescharacteristic
728C22C22×#63811yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—182no—
735C4—361no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#8240414yescomplemented
741C2—24no—
742C2—42no—
743C2—362no—
744C2—362no—
745C2#1059601811yescharacteristic
746C2#1059602111yescharacteristic
747C2#1059602711yescharacteristic
748C2#1059603111yescharacteristic
749C2C2×#6413811yescharacteristic
750C2D4×#63811yescharacteristic
751C2#1059630011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4×D4C2
prime radicalC2×#64146C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×#64138C2semidirect
4. C22×#3752C2semidirect
5. #10592919C2semidirect
6. #10592912C2semidirect
7. #10592909C2semidirect
8. #10592692C2semidirect
9. #10592691C2semidirect
10. #10592658C2semidirect
11. #10592658C2semidirect
12. #10592654C2semidirect
13. #10592641C2semidirect
14. #10592639C2semidirect
15. #10592639C2semidirect
20. C23×C32×C4C22semidirect
25. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C22⋊C4C22semidirect
28. C2×C32×C42C22semidirect
31. C2×#3757C22semidirect
32. C2×#3757C22semidirect
46. C2×#3750C22semidirect
47. C2×#3750C22semidirect
48. C2×#3750C22semidirect
49. C2×#3750C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. C2×C3×C4×D4D3semidirect
128. #3752D4semidirect
137. C23×C3×C4C2×D3semidirect
142. C2×C3×C4⋊C4C2×D3semidirect
144. C2×C3×C22⋊C4C2×D3semidirect
145. C2×C3×C42C2×D3semidirect
250. C2×C4×D4C3⋊D3semidirect
338. C22×C32#123semidirect
378. C23×C4C2×C3⋊D3semidirect
386. C2×C4⋊C4C2×C3⋊D3semidirect
403. C2×C22⋊C4C2×C3⋊D3semidirect
404. C2×C42C2×C3⋊D3semidirect
572. C22×C3#929semidirect
606. C32#2418semidirect
721. C22#64138semidirect
740. C3#82404semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641462
C2×#641382
C22×#37522
#105929192
#105929122
#105929092
#105926922
#105926912
#105926582
#105926542
#105926412
#105926392
#824043