Finite Group Databasebeta

← C2×#77663 #11001418

Subgroups — C2×#77663 #11001418

Order 768.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic, complemented
2C2×#4994C211yesmaximal, characteristic, complemented
3C2×#4981C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic
5C2×#4949C211yesmaximal, characteristic, complemented
6C2×#4949C211yesmaximal, characteristic, complemented
7C2×#4961C211yesmaximal, characteristic
8C2×#4961C211yesmaximal, characteristic
9C2×#4945C211yesmaximal, characteristic, complemented
10#77663C2116yesmaximal, direct product factor
11C2×#4675C211yesmaximal, characteristic, complemented
12C2×#4676C211yesmaximal, characteristic, complemented
13C2×#4660C211yesmaximal, characteristic, complemented
14C2×#4661C211yesmaximal, characteristic, complemented
15C2×#4647C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2837—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C3×#397C2218yescomplemented
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54#4994C2218yescomplemented
55#4981C2218yescomplemented
56#4961C2218yes—
57#4961C2218yes—
58#4959C2218yes—
59#4949C2218yescomplemented
60#4949C2218yescomplemented
61#4945C2218yescomplemented
62#4676C2218yescomplemented
63#4675C2218yescomplemented
64#4670C2218yescomplemented
65#4661C2218yescomplemented
66#4660C2218yescomplemented
67#4647C2218yescomplemented
68#2837—316no—
69C2×#400—31no—
70C2×#399—31no—
71C2×#399—31no—
72C2×#398—31no—
73C2×#398—31no—
74C2×#397—31no—
75C2×#397D311yescharacteristic, complemented
76C2×#396—31no—
77C2×#396—31no—
78C2×#394—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#389—31no—
82C2×#388—31no—
83C2×#388—31no—
84C25×C3C2311yescharacteristic
85C24×D3C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C22×#67—42no—
93C22×#67—42no—
94C22×#67—42no—
95C22×#67C2314yes—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C2×C3×C4⋊C4—42no—
104C2×C3×C4⋊C4C2314yes—
105C2×C3×C22⋊C4—42no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4C2314yes—
109C2×C3×C22⋊C4C2314yes—
110C2×C3×C22⋊C4C2314yes—
111C2×#217—24no—
112C2×#217—42no—
113C2×#217—42no—
114C2×#217C2314yes—
115C2×#217C2314yes—
116C2×#217C2314yes—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—42no—
119C2×(C2×D3)⋊C4—42no—
120C2×(C2×D3)⋊C4—42no—
121C2×(C2×D3)⋊C4—42no—
122C2×(C2×D3)⋊C4—42no—
123C2×(C2×D3)⋊C4C2314yes—
124C2×(C2×D3)⋊C4C2314yes—
125C2×(C2×D3)⋊C4C2314yes—
126C2×(C2×D3)⋊C4C2314yes—
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×C4⋊Dic3—42no—
130C2×C4⋊Dic3—42no—
131C2×C4⋊Dic3—42no—
132C2×C4⋊Dic3—42no—
133C2×C4⋊Dic3C2314yes—
134C2×C4⋊Dic3C2314yes—
135C2×C4⋊Dic3C2314yes—
136C2×C4⋊Dic3C2314yes—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—42no—
139C2×Dic3⋊C4—42no—
140C2×Dic3⋊C4—42no—
141C2×Dic3⋊C4—42no—
142C2×Dic3⋊C4—42no—
143C2×Dic3⋊C4C2314yes—
144C2×Dic3⋊C4C2314yes—
145C2×Dic3⋊C4C2314yes—
146C2×Dic3⋊C4C2314yes—
147C2×Dic3⋊C4C2314yes—
148C2×Dic3⋊C4C2314yes—
149C2×C4×Dic3—42no—
150C2×C4×Dic3C2314yes—
151C3×#95C2314yes—
152C3×#95C2314yes—
153C3×#95C2314yes—
154C3⋊#95C2314yes—
155C3⋊#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C23×D4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4C2×D311yescharacteristic
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C22⋊C4C2×D311yescharacteristic
184C22×C22⋊C4C2×D311yescharacteristic
185C22×C42—31no—
186#400—38no—
187#399—38no—
188#399—38no—
189#398—38no—
190#398—38no—
191#397—38no—
192#397C2×D318yescomplemented
193#396—38no—
194#396—38no—
195#394—38no—
196#394—38no—
197#394—38no—
198#389—38no—
199#388—38no—
200#388—38no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3C2412yes—
219C24×C3C2411yescharacteristic
220C23×D3—22no—
221C23×D3—22no—
222C23×D3—22no—
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3—22no—
227C23×D3C2412yes—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4C2412yes—
247C22×C3×C4C2412yes—
248C22×C3×C4C2412yes—
249C22×C3×C4C2412yes—
250C22×C3×C4C2412yes—
251C22×C3×C4C2412yes—
252C2×#67—44no—
253C2×#67—44no—
254C2×#67—44no—
255C2×#67—416no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3#4114yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2412yes—
282C22×Dic3C2412yes—
283C22×Dic3C2412yes—
284C3×C4⋊C4—44no—
285C3×C22⋊C4—44no—
286C3×C22⋊C4—44no—
287C3×C22⋊C4—44no—
288#217—28no—
289#217—44no—
290#217—44no—
291(C2×D3)⋊C4—28no—
292(C2×D3)⋊C4—44no—
293(C2×D3)⋊C4—44no—
294(C2×D3)⋊C4—44no—
295(C2×D3)⋊C4—44no—
296(C2×D3)⋊C4—44no—
297C4⋊Dic3—44no—
298C4⋊Dic3—44no—
299C4⋊Dic3—44no—
300C4⋊Dic3—44no—
301Dic3⋊C4—28no—
302Dic3⋊C4—44no—
303Dic3⋊C4—44no—
304Dic3⋊C4—44no—
305Dic3⋊C4—44no—
306Dic3⋊C4—44no—
307C4×Dic3—44no—
308C25—31no—
309C25C22×D311yescharacteristic
310C22×D4—34no—
311C22×D4—122no—
312C22×D4—122no—
313C22×D4—122no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4C22×D311yescharacteristic
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D311yescharacteristic
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C23×C4C22×D311yescharacteristic
327C2×C4⋊C4—34no—
328C2×C4⋊C4—34no—
329C2×C4⋊C4—34no—
330C2×C4⋊C4—34no—
331C2×C4⋊C4—34no—
332C2×C4⋊C4—34no—
333C2×C4⋊C4—34no—
334C2×C4⋊C4—34no—
335C2×C4⋊C4—34no—
336C2×C4⋊C4—34no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—64no—
339C2×C4⋊C4—122no—
340C2×C4⋊C4—122no—
341C2×C4⋊C4—122no—
342C2×C4⋊C4—122no—
343C2×C4⋊C4—122no—
344C2×C4⋊C4—122no—
345C2×C4⋊C4—122no—
346C2×C4⋊C4—122no—
347C2×C4⋊C4—122no—
348C2×C4⋊C4C22×D314yes—
349C2×C22⋊C4—34no—
350C2×C22⋊C4—34no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—34no—
354C2×C22⋊C4—34no—
355C2×C22⋊C4—34no—
356C2×C22⋊C4—34no—
357C2×C22⋊C4—34no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—122no—
364C2×C22⋊C4—122no—
365C2×C22⋊C4—122no—
366C2×C22⋊C4—122no—
367C2×C22⋊C4—122no—
368C2×C22⋊C4—122no—
369C2×C22⋊C4—122no—
370C2×C22⋊C4C22×D314yes—
371C2×C22⋊C4C22×D314yes—
372C2×C22⋊C4C22×D314yes—
373C2×C42—34no—
374C2×C42—122no—
375#95—34no—
376#95—34no—
377#95—34no—
378#95—34no—
379#95—34no—
380#95—34no—
381#95—34no—
382#95C22×D314yes—
383#95C22×D314yes—
384#95C22×D314yes—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—44no—
399C23×C3C2×#4112yes—
400C23×C3H(5,𝔽2)12yes—
401C23×C3H(5,𝔽2)12yes—
402C23×C3H(5,𝔽2)12yes—
403C23×C3H(5,𝔽2)12yes—
404C23×C32−1+412yes—
405C23×C32−1+412yes—
406C23×C3C2511yescharacteristic
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—44no—
415C22×D3—44no—
416C22×D3—44no—
417C22×D3—44no—
418C22×D3—44no—
419C22×D3—44no—
420C22×D3—44no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—44no—
440C2×C3×C4—44no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445#67—416no—
446C2×Dic3—28no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—44no—
468C2×Dic3—44no—
469C2×Dic3—44no—
470C2×Dic3—44no—
471C2×Dic3—44no—
472C2×Dic3—44no—
473C2×Dic3C2×#4114yes—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—32no—
482C24—62no—
483C24—62no—
484C24—62no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24C23×D312yes—
490C24C23×D311yescharacteristic
491C2×D4—124no—
492C2×D4—124no—
493C2×D4—124no—
494C2×D4—1216no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—34no—
514C22×C4—32no—
515C22×C4—32no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4C23×D312yes—
542C22×C4C23×D312yes—
543C22×C4C23×D312yes—
544C22×C4C23×D312yes—
545C22×C4C23×D312yes—
546C22×C4C23×D312yes—
547C4⋊C4—44no—
548C4⋊C4—68no—
549C4⋊C4—124no—
550C4⋊C4—124no—
551C4⋊C4—124no—
552C4⋊C4—124no—
553C4⋊C4—124no—
554C4⋊C4—124no—
555C4⋊C4—124no—
556C4⋊C4—124no—
557C4⋊C4—124no—
558C22⋊C4—44no—
559C22⋊C4—44no—
560C22⋊C4—44no—
561C22⋊C4—68no—
562C22⋊C4—68no—
563C22⋊C4—124no—
564C22⋊C4—124no—
565C22⋊C4—124no—
566C22⋊C4—124no—
567C22⋊C4—124no—
568C22⋊C4—124no—
569C22⋊C4—124no—
570C42—124no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—88no—
579C22×C3#53914yes—
580C22×C3#54014yes—
581C22×C3#54214yes—
582C22×C3#56014yes—
583C22×C3#56214yes—
584C22×C3#56214yes—
585C22×C3#56314yes—
586C22×C3C22×#4111yescharacteristic
587C22×C3C2×H(5,𝔽2)11yescharacteristic
588C22×C3C2×H(5,𝔽2)11yescharacteristic
589C22×C3C2×H(5,𝔽2)11yescharacteristic
590C22×C3C2×H(5,𝔽2)11yescharacteristic
591C22×C3C2×2−1+411yescharacteristic
592C22×C3C2×2−1+411yescharacteristic
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—88no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—42no—
607Dic3—24no—
608Dic3—42no—
609Dic3—42no—
610Dic3—42no—
611Dic3—42no—
612Dic3—42no—
613Dic3—42no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—124no—
636C23—124no—
637C23—124no—
638C23—124no—
639C23—124no—
640C23—124no—
641C23—124no—
642C23#100412yes—
643C23#100412yes—
644C23D3×#4112yes—
645C23#100912yes—
646C23#100912yes—
647C23#101012yes—
648C23#101012yes—
649C23C24×D311yescharacteristic
650D4—1216no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—34no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—62no—
677C2×C4—68no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—124no—
698C2×C4—124no—
699C2×C4—124no—
700C2×C4—124no—
701C2×C4—124no—
702C2×C4—124no—
703C2×C3—82no—
704C2×C3#283718yescomplemented
705C2×C3C2×#53911yescharacteristic
706C2×C3C2×#54011yescharacteristic
707C2×C3C2×#54211yescharacteristic
708C2×C3C2×#56011yescharacteristic
709C2×C3C2×#56211yescharacteristic
710C2×C3C2×#56211yescharacteristic
711C2×C3C2×#56311yescharacteristic
712D3—82no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—88no—
721C22—122no—
722C22—122no—
723C22—122no—
724C22—122no—
725C22—122no—
726C22—122no—
727C22—122no—
728C22—248no—
729C22#562114yes—
730C22#566314yes—
731C22#566614yes—
732C22#566714yes—
733C22#566914yes—
734C22#570714yes—
735C22#571214yes—
736C22C2×#100411yescharacteristic
737C22C2×#100411yescharacteristic
738C22C2×D3×#4111yescharacteristic
739C22C2×#100911yescharacteristic
740C22C2×#100911yescharacteristic
741C22C2×#101011yescharacteristic
742C22C2×#101011yescharacteristic
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—64no—
750C4—122no—
751C4—122no—
752C4—122no—
753C4—122no—
754C4—122no—
755C4—122no—
756C3C2×#283711yescharacteristic, complemented, Sylow
757C2—82no—
758C2—242no—
759C2#7766318yesdirect product factor
760C2C2×#562111yescharacteristic
761C2C2×#566311yescharacteristic
762C2C2×#566611yescharacteristic
763C2C2×#566711yescharacteristic
764C2C2×#566911yescharacteristic
765C2C2×#571211yescharacteristic
766C2C2×#570711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#397C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#397D3
hypocenterC3C2×#2837
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C3×#397C2semidirect
2. C2×#4994C2semidirect
3. C2×#4981C2semidirect
5. C2×#4949C2semidirect
6. C2×#4949C2semidirect
9. C2×#4945C2semidirect
10. #77663C2direct (N × H)
11. C2×#4675C2semidirect
12. C2×#4676C2semidirect
13. C2×#4660C2semidirect
14. C2×#4661C2semidirect
15. C2×#4647C2semidirect
16. C2×#4670C2semidirect
43. C3×#397C22semidirect
54. #4994C22semidirect
55. #4981C22semidirect
59. #4949C22semidirect
60. #4949C22semidirect
61. #4945C22semidirect
62. #4676C22semidirect
63. #4675C22semidirect
64. #4670C22semidirect
65. #4661C22semidirect
66. #4660C22semidirect
67. #4647C22semidirect
75. C2×#397D3semidirect
192. #397C2×D3semidirect
704. C2×C3#2837semidirect
756. C3C2×#2837semidirect
759. C2#77663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×#49942
C2×#49812
C2×#49592
C2×#49492
C2×#49612
C2×#49452
#776632
C2×#46752
C2×#46762
C2×#46602
C2×#46612
C2×#46472
C2×#46702
C2×#28373