Finite Group Databasebeta

← C2×#77096 #11001503

Subgroups — C2×#77096 #11001503

Order 768.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#4993C211yesmaximal, characteristic, complemented
5C2×#4978C211yesmaximal, characteristic, complemented
6C2×#4959C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4953C211yesmaximal, characteristic, complemented
9C2×#4948C211yesmaximal, characteristic, complemented
10C2×#4948C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4945C211yesmaximal, characteristic, complemented
14#77096C2116yesmaximal, direct product factor
15C2×#4657C211yesmaximal, characteristic, complemented
16C2×#4674C211yesmaximal, characteristic, complemented
17C2×#2829—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C3×#394C2218yescomplemented
46C2×C3×#95C2211yescharacteristic
47#5223C2218yes—
48#5222C2218yescomplemented
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4993C2218yescomplemented
57#4978C2218yescomplemented
58#4961C2218yescomplemented
59#4959C2218yescomplemented
60#4959C2218yescomplemented
61#4957C2218yescomplemented
62#4953C2218yescomplemented
63#4948C2218yescomplemented
64#4948C2218yescomplemented
65#4945C2218yescomplemented
66#4674C2218yescomplemented
67#4657C2218yescomplemented
68#2829—316no—
69C2×#399—31no—
70C2×#398—31no—
71C2×#397—31no—
72C2×#397—31no—
73C2×#396—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#394D311yescharacteristic, complemented
80C2×#392—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#387—31no—
84C25×C3C2311yescharacteristic
85C25×C3C2311yescharacteristic
86C24×D3C2311yescharacteristic
87C22×C3×D4—42no—
88C22×C3×D4—42no—
89C22×C3×D4—42no—
90C22×C3×D4C2314yes—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—24no—
97C22×#67—42no—
98C22×#67—42no—
99C22×#67—42no—
100C22×#67—42no—
101C22×#67—42no—
102C22×#67C2314yes—
103C22×#67C2314yes—
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C2×C3×C4⋊C4—42no—
112C2×C3×C4⋊C4C2314yes—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4—42no—
115C2×C3×C22⋊C4—42no—
116C2×C3×C22⋊C4—42no—
117C2×C3×C22⋊C4C2314yes—
118C2×C3×C22⋊C4C2314yes—
119C2×C3×C22⋊C4C2314yes—
120C2×C3×C22⋊C4C2314yes—
121C2×#217—24no—
122C2×#217—42no—
123C2×#217—42no—
124C2×#217—42no—
125C2×#217—42no—
126C2×#217—42no—
127C2×#217C2314yes—
128C2×#217C2314yes—
129C2×#217C2314yes—
130C2×#217C2314yes—
131C2×#217C2314yes—
132C2×#217C2314yes—
133C2×(C2×D3)⋊C4—42no—
134C2×(C2×D3)⋊C4—42no—
135C2×(C2×D3)⋊C4—42no—
136C2×(C2×D3)⋊C4—42no—
137C2×(C2×D3)⋊C4—42no—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×C4⋊Dic3—42no—
144C2×C4⋊Dic3—42no—
145C2×C4⋊Dic3C2314yes—
146C2×C4⋊Dic3C2314yes—
147C2×Dic3⋊C4—24no—
148C2×Dic3⋊C4—42no—
149C2×Dic3⋊C4—42no—
150C2×Dic3⋊C4—42no—
151C2×Dic3⋊C4—42no—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2314yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2314yes—
157C2×C4×Dic3—42no—
158C2×C4×Dic3C2314yes—
159C3×#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C23×D4—31no—
168C23×D4—31no—
169C23×D4C2×D311yescharacteristic
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4C2×D311yescharacteristic
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4C2×D311yescharacteristic
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C42—31no—
194#399—38no—
195#398—38no—
196#397—38no—
197#397—38no—
198#396—38no—
199#396—38no—
200#394—38no—
201#394—38no—
202#394—38no—
203#394—38no—
204#394C2×D318yescomplemented
205#392—38no—
206#390—38no—
207#388—38no—
208#387—38no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95C2×D311yescharacteristic
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3C2412yes—
232C24×C3C2412yes—
233C24×C3C2411yescharacteristic
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—22no—
241C23×D3C2412yes—
242C2×C3×D4—44no—
243C2×C3×D4—44no—
244C2×C3×D4—44no—
245C2×C3×D4—416no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4C2412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C2×#67—28no—
267C2×#67—44no—
268C2×#67—44no—
269C2×#67—44no—
270C2×#67—44no—
271C2×#67—44no—
272C2×#67—416no—
273C2×#67—416no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3#4114yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C3×C4⋊C4—44no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306C3×C22⋊C4—44no—
307#217—28no—
308#217—44no—
309#217—44no—
310#217—44no—
311#217—44no—
312#217—44no—
313(C2×D3)⋊C4—44no—
314(C2×D3)⋊C4—44no—
315(C2×D3)⋊C4—44no—
316(C2×D3)⋊C4—44no—
317(C2×D3)⋊C4—44no—
318C4⋊Dic3—44no—
319C4⋊Dic3—44no—
320Dic3⋊C4—28no—
321Dic3⋊C4—44no—
322Dic3⋊C4—44no—
323Dic3⋊C4—44no—
324Dic3⋊C4—44no—
325C4×Dic3—44no—
326C25—31no—
327C25C22×D311yescharacteristic
328C25C22×D311yescharacteristic
329C22×D4—34no—
330C22×D4—34no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—64no—
335C22×D4—122no—
336C22×D4—122no—
337C22×D4—122no—
338C22×D4—122no—
339C22×D4—122no—
340C22×D4C22×D314yes—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C2×C4⋊C4—34no—
354C2×C4⋊C4—34no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—34no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—122no—
363C2×C4⋊C4—122no—
364C2×C4⋊C4—122no—
365C2×C4⋊C4—122no—
366C2×C4⋊C4—122no—
367C2×C4⋊C4—122no—
368C2×C4⋊C4C22×D314yes—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—34no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—34no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—122no—
386C2×C22⋊C4—122no—
387C2×C22⋊C4—122no—
388C2×C22⋊C4—122no—
389C2×C22⋊C4—122no—
390C2×C22⋊C4—122no—
391C2×C22⋊C4—122no—
392C2×C22⋊C4—122no—
393C2×C22⋊C4—122no—
394C2×C22⋊C4—122no—
395C2×C22⋊C4C22×D314yes—
396C2×C22⋊C4C22×D314yes—
397C2×C22⋊C4C22×D314yes—
398C2×C22⋊C4C22×D314yes—
399C2×C42—34no—
400C2×C42—122no—
401#95—34no—
402#95—34no—
403#95—34no—
404#95—34no—
405#95—34no—
406#95—34no—
407#95—34no—
408#95C22×D314yes—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3—44no—
436C23×C3—44no—
437C23×C3C2×#4112yes—
438C23×C3H(5,𝔽2)12yes—
439C23×C3H(5,𝔽2)12yes—
440C23×C3H(5,𝔽2)12yes—
441C23×C3H(5,𝔽2)12yes—
442C23×C3H(5,𝔽2)12yes—
443C23×C32−1+412yes—
444C23×C3C2511yescharacteristic
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—44no—
453C22×D3—44no—
454C22×D3—44no—
455C22×D3—44no—
456C22×D3—44no—
457C22×D3—44no—
458C22×D3—44no—
459C3×D4—416no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—44no—
476C2×C3×C4—44no—
477C2×C3×C4—44no—
478C2×C3×C4—44no—
479C2×C3×C4—44no—
480#67—416no—
481#67—416no—
482C2×Dic3—28no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—44no—
504C2×Dic3—44no—
505C2×Dic3—44no—
506C2×Dic3—44no—
507C2×Dic3—44no—
508C2×Dic3—44no—
509C2×Dic3C2×#4114yes—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—32no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—62no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24C23×D312yes—
533C24C23×D312yes—
534C24C23×D311yescharacteristic
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—416no—
539C2×D4—68no—
540C2×D4—124no—
541C2×D4—124no—
542C2×D4—124no—
543C2×D4—124no—
544C2×D4—124no—
545C2×D4—1216no—
546C2×D4—1216no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—34no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4C23×D312yes—
591C22×C4C23×D312yes—
592C22×C4C23×D312yes—
593C22×C4C23×D312yes—
594C22×C4C23×D312yes—
595C4⋊C4—44no—
596C4⋊C4—68no—
597C4⋊C4—124no—
598C4⋊C4—124no—
599C4⋊C4—124no—
600C4⋊C4—124no—
601C4⋊C4—124no—
602C4⋊C4—124no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—68no—
608C22⋊C4—124no—
609C22⋊C4—124no—
610C22⋊C4—124no—
611C22⋊C4—124no—
612C22⋊C4—124no—
613C22⋊C4—124no—
614C22⋊C4—124no—
615C22⋊C4—124no—
616C22⋊C4—124no—
617C22⋊C4—124no—
618C42—124no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—88no—
634C22×C3—88no—
635C22×C3#53814yes—
636C22×C3#54014yes—
637C22×C3#54214yes—
638C22×C3#56014yes—
639C22×C3#56014yes—
640C22×C3#56214yes—
641C22×C3#56214yes—
642C22×C3C22×#4111yescharacteristic
643C22×C3C2×H(5,𝔽2)11yescharacteristic
644C22×C3C2×H(5,𝔽2)11yescharacteristic
645C22×C3C2×H(5,𝔽2)11yescharacteristic
646C22×C3C2×H(5,𝔽2)11yescharacteristic
647C22×C3C2×H(5,𝔽2)11yescharacteristic
648C22×C3C2×2−1+411yescharacteristic
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—88no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662Dic3—24no—
663Dic3—42no—
664Dic3—42no—
665Dic3—42no—
666Dic3—42no—
667Dic3—42no—
668Dic3—42no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23—62no—
701C23—62no—
702C23—62no—
703C23—62no—
704C23—124no—
705C23—124no—
706C23—124no—
707C23—124no—
708C23—124no—
709C23—124no—
710C23—124no—
711C23#100412yes—
712C23#100412yes—
713C23#100412yes—
714C23#100412yes—
715C23D3×#4112yes—
716C23#100912yes—
717C23#101012yes—
718C23C24×D311yescharacteristic
719D4—416no—
720D4—1216no—
721D4—1216no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—34no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—68no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—124no—
765C2×C4—124no—
766C2×C4—124no—
767C2×C4—124no—
768C2×C4—124no—
769C2×C4—124no—
770C2×C3—82no—
771C2×C3—82no—
772C2×C3#282918yescomplemented
773C2×C3C2×#53811yescharacteristic
774C2×C3C2×#54011yescharacteristic
775C2×C3C2×#54211yescharacteristic
776C2×C3C2×#56011yescharacteristic
777C2×C3C2×#56011yescharacteristic
778C2×C3C2×#56211yescharacteristic
779C2×C3C2×#56211yescharacteristic
780D3—82no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—88no—
796C22—88no—
797C22—122no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22—248no—
805C22#559514yes—
806C22#561314yes—
807C22#562014yes—
808C22#562114yes—
809C22#566214yes—
810C22#566314yes—
811C22#568414yes—
812C22C2×#100411yescharacteristic
813C22C2×#100411yescharacteristic
814C22C2×#100411yescharacteristic
815C22C2×#100411yescharacteristic
816C22C2×D3×#4111yescharacteristic
817C22C2×#100911yescharacteristic
818C22C2×#101011yescharacteristic
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—64no—
825C4—122no—
826C4—122no—
827C4—122no—
828C4—122no—
829C4—122no—
830C4—122no—
831C3C2×#282911yescharacteristic, complemented, Sylow
832C2—82no—
833C2—82no—
834C2—242no—
835C2#7709618yesdirect product factor
836C2C2×#559511yescharacteristic
837C2C2×#561311yescharacteristic
838C2C2×#562011yescharacteristic
839C2C2×#562111yescharacteristic
840C2C2×#566311yescharacteristic
841C2C2×#566211yescharacteristic
842C2C2×#568411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#394C2
socleC24×C3C24
prime radicalC2×#5223C2
hypercenterC2×#394D3
hypocenterC3C2×#2829
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×C3×#394C2semidirect
3. C2×#5222C2semidirect
4. C2×#4993C2semidirect
5. C2×#4978C2semidirect
6. C2×#4959C2semidirect
7. C2×#4959C2semidirect
8. C2×#4953C2semidirect
9. C2×#4948C2semidirect
10. C2×#4948C2semidirect
11. C2×#4961C2semidirect
12. C2×#4957C2semidirect
13. C2×#4945C2semidirect
14. #77096C2direct (N × H)
15. C2×#4657C2semidirect
16. C2×#4674C2semidirect
45. C3×#394C22semidirect
48. #5222C22semidirect
56. #4993C22semidirect
57. #4978C22semidirect
58. #4961C22semidirect
59. #4959C22semidirect
60. #4959C22semidirect
61. #4957C22semidirect
62. #4953C22semidirect
63. #4948C22semidirect
64. #4948C22semidirect
65. #4945C22semidirect
66. #4674C22semidirect
67. #4657C22semidirect
79. C2×#394D3semidirect
204. #394C2×D3semidirect
772. C2×C3#2829semidirect
831. C3C2×#2829semidirect
835. C2#77096direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×#52232
C2×#52222
C2×#49932
C2×#49782
C2×#49592
C2×#49532
C2×#49482
C2×#49612
C2×#49572
C2×#49452
#770962
C2×#46572
C2×#46742
C2×#28293