Finite Group Databasebeta

← #11810287

Subgroups — #11810287

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×#123C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5#10592921C211yesmaximal, characteristic, complemented
6#10592912C211yesmaximal, characteristic, complemented
7#10592692C211yesmaximal, characteristic, complemented
8#10592689C211yesmaximal, characteristic, complemented
9#10592688C211yesmaximal, characteristic, complemented
10#10592686C211yesmaximal, characteristic, complemented
11#10592660C211yesmaximal, characteristic, complemented
12#10592655C211yesmaximal, characteristic, complemented
13#10592654C211yesmaximal, characteristic, complemented
14#10592651C211yesmaximal, characteristic, complemented
15#10592650C211yesmaximal, characteristic, complemented
16#82896—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic, complemented
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C32×#123—24no—
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic, complemented
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic, complemented
34C2×#3757C2211yescharacteristic, complemented
35#64146—24no—
36C4×#638—24no—
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47C2×#3750C2211yescharacteristic, complemented
48C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
49C22⋊C4×C3⋊D3—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C2×C3×#123D314yescomplemented
57C2×#937—34no—
58C2×C4×#67—34no—
59C2×D3×C22⋊C4—34no—
60#5222—34no—
61#5213—34no—
62#4993—34no—
63#4990—34no—
64#4989—34no—
65#4987—34no—
66#4961—34no—
67#4956—34no—
68#4955—34no—
69#4952—34no—
70#4951—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×D4—41no—
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—41no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—41no—
98C2×#638D414yes—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—41no—
110C2×C4×C3⋊D3—41no—
111C32×C4⋊C4—22no—
112C32×C4⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—22no—
115C32×C22⋊C4D414yescomplemented
116#3757—22no—
117#3757—22no—
118#3757—22no—
119#3757—41no—
120#3757—41no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125#3752—22no—
126#3752—22no—
127#3752—22no—
128#3752—41no—
129C4⋊(C3⋊Dic3)—41no—
130#3750—22no—
131#3750—41no—
132C4×C3⋊Dic3—22no—
133#2418—91noSylow
134C24×D3—34no—
135C22×C3×D4C2×D314yes—
136C23×C3×C4C2×D314yescomplemented
137C22×#67—34no—
138C22×#67—34no—
139C22×C4×D3—34no—
140C22×C4×D3—34no—
141C3×#123—216no—
142C2×C3×C4⋊C4C2×D314yescomplemented
143C2×C3×C4⋊C4C2×D314yescomplemented
144C2×C3×C22⋊C4C2×D314yes—
145C2×C3×C22⋊C4C2×D314yes—
146C2×C3×C22⋊C4C2×D314yescomplemented
147C2×#217—34no—
148C2×#217—34no—
149C2×#217—34no—
150C2×#217—34no—
151C2×#217—34no—
152#937—616no—
153C4×#67—616no—
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×C4⋊Dic3—34no—
163C2×Dic3⋊C4—34no—
164C2×Dic3⋊C4—34no—
165C2×C4×Dic3—34no—
166D3×C22⋊C4—616no—
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×C32—21no—
184C23×C32—21no—
185C23×C32C2×D412yes—
186C23×C32C2×D412yes—
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—21no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—28no—
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—44no—
200C22×C3⋊D3—44no—
201C22×C3⋊D3—44no—
202C22×C3⋊D3—44no—
203C22×C3⋊D3—44no—
204C22×C3⋊D3—44no—
205C22×C3⋊D3C2×D412yes—
206C22×C3⋊D3#4112yes—
207C22×C3⋊D3#4112yes—
208C22×C3⋊D3#4112yes—
209C32×D4—44no—
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×C4C2×D412yes—
225C2×C32×C4C2×D412yes—
226#638—28no—
227#638—44no—
228C2×C3⋊Dic3—21no—
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⋊Dic3C2×D412yes—
246C4×C3⋊D3—44no—
247C4×C3⋊D3—44no—
248C2×#123C3⋊D311yescharacteristic, complemented
249C2×#120—91no—
250C2×C4×D4—91no—
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—44no—
277C22×C3×C4—28no—
278C22×C3×C4—28no—
279C22×C3×C4—44no—
280C22×C3×C4C22×D314yes—
281C22×C3×C4C22×D314yes—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D314yes—
284C22×C3×C4C22×D314yes—
285C2×#67—316no—
286C2×#67—68no—
287C2×#67—68no—
288C2×#67—68no—
289C2×#67—68no—
290C2×#67—124no—
291C22×Dic3—34no—
292C22×Dic3—34no—
293C22×Dic3—34no—
294C22×Dic3—34no—
295C22×Dic3—34no—
296C22×Dic3—34no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×C4×D3—68no—
300C2×C4×D3—68no—
301C2×C4×D3—124no—
302C2×C4×D3—124no—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—28no—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—28no—
307C3×C22⋊C4#67116yescomplemented
308#217—68no—
309#217—68no—
310#217—68no—
311#217—124no—
312#217—124no—
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—68no—
320(C2×D3)⋊C4—124no—
321C4⋊Dic3—124no—
322Dic3⋊C4—68no—
323Dic3⋊C4—124no—
324C4×Dic3—68no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
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—22no—
353C2×C3⋊D3—22no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—416no—
356C2×C3⋊D3—41no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3#12314yescomplemented
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×C4—91no—
378C23×C4C2×C3⋊D311yescharacteristic, complemented
379#123—24no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
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—184no—
401C2×C22⋊C4C2×C3⋊D311yescharacteristic
402C2×C22⋊C4C2×C3⋊D311yescharacteristic
403C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
404C2×C42—91no—
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—24no—
422C23×C3—24no—
423C23×C3D3×D418yes—
424C23×C3C2×#6718yes—
425C23×C3C23×D314yes—
426C22×D3—38no—
427C22×D3—38no—
428C22×D3—38no—
429C22×D3—38no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—632no—
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—416no—
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×C4C2×#6718yes—
463C2×C3×C4C2×#6718yes—
464#67—632no—
465#67—1216no—
466C2×Dic3—38no—
467C2×Dic3—64no—
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—
484C4×D3—1216no—
485C4×D3—1216no—
486C2×C32—42no—
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—24no—
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—41no—
511C2×D4—94no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—182no—
516C2×D4—361no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—182no—
530C22×C4—361no—
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—22no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—182no—
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—361no—
555C22⋊C4—361no—
556C22⋊C4—361no—
557C22⋊C4#63814yescomplemented
558C42—182no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3C2×D3×D414yes—
574C22×C3#100414yes—
575C22×C3D3×#4114yes—
576C22×C3D3×#4114yes—
577C22×C3D3×#4114yes—
578C22×C3#100914yes—
579C22×C3C22×#6714yes—
580C2×D3—316no—
581C2×D3—68no—
582C2×D3—68no—
583C2×D3—68no—
584C2×D3—68no—
585C2×D3—68no—
586C2×D3—68no—
587C2×D3—68no—
588C2×D3—68no—
589C2×D3—68no—
590C2×D3—1264no—
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—21no—
618C23—21no—
619C23—92no—
620C23—92no—
621C23—92no—
622C23—92no—
623C23—188no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23—364no—
639C23—364no—
640C23D4×C3⋊D312yes—
641C23C2×#63812yes—
642C23C23×C3⋊D311yescharacteristic
643D4—44no—
644D4—188no—
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—92no—
661C2×C4—181no—
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—364no—
679C2×C4—364no—
680C2×C4C2×#63812yes—
681C2×C4C2×#63812yes—
682C2×C3—48no—
683C2×C3—48no—
684C2×C3D3×#12314yes—
685C2×C3#565414yes—
686C2×C3#565714yes—
687C2×C3#565914yes—
688C2×C3D4×#6714yes—
689C2×C3#582814yes—
690C2×C3#582914yes—
691D3—616no—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—94no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22—182no—
714C22—182no—
715C22—182no—
716C22—182no—
717C22—3616no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22—361no—
722C22C2×D4×C3⋊D311yescharacteristic
723C22#6436111yescharacteristic
724C22#41×C3⋊D311yescharacteristic
725C22#41×C3⋊D311yescharacteristic
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#8289614yescomplemented
741C2—42no—
742C2—42no—
743C2—184no—
744C2—362no—
745C2C3⋊D3×#12311yescharacteristic
746C2#1059612511yescharacteristic
747C2#1059612811yescharacteristic
748C2#1059613011yescharacteristic
749C2D4×#63811yescharacteristic
750C2#1059629911yescharacteristic
751C2#1059630011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×#123C2
prime radicalC2×#64146C2
hypercenterC2×#123C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C22⋊C4×C3⋊D3C2semidirect
5. #10592921C2semidirect
6. #10592912C2semidirect
7. #10592692C2semidirect
8. #10592689C2semidirect
9. #10592688C2semidirect
10. #10592686C2semidirect
11. #10592660C2semidirect
12. #10592655C2semidirect
13. #10592654C2semidirect
14. #10592651C2semidirect
15. #10592650C2semidirect
19. C23×C32×C4C22semidirect
25. C2×C32×C4⋊C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
29. C2×C32×C22⋊C4C22semidirect
33. C2×#3757C22semidirect
34. C2×#3757C22semidirect
45. C2×C4⋊(C3⋊Dic3)C22semidirect
46. C2×#3750C22semidirect
47. C2×#3750C22semidirect
48. C2×C4×C3⋊Dic3C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. C2×C3×#123D3semidirect
115. C32×C22⋊C4D4semidirect
136. C23×C3×C4C2×D3semidirect
142. C2×C3×C4⋊C4C2×D3semidirect
143. C2×C3×C4⋊C4C2×D3semidirect
146. C2×C3×C22⋊C4C2×D3semidirect
248. C2×#123C3⋊D3semidirect
307. C3×C22⋊C4#67semidirect
360. C2×C3⋊D3#123semidirect
378. C23×C4C2×C3⋊D3semidirect
385. C2×C4⋊C4C2×C3⋊D3semidirect
386. C2×C4⋊C4C2×C3⋊D3semidirect
403. C2×C22⋊C4C2×C3⋊D3semidirect
557. C22⋊C4#638semidirect
606. C32#2418semidirect
740. C3#82896semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C2×#641462
C2×C4×#6382
C2×C22⋊C4×C3⋊D32
#105929212
#105929122
#105926922
#105926892
#105926882
#105926862
#105926602
#105926552
#105926542
#105926512
#105926502
#828963