Finite Group Databasebeta

← C2×#76087 #10965477

Subgroups — C2×#76087 #10965477

Order 768.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic, complemented
2C2×#4994C211yesmaximal, characteristic
3C2×#4994C211yesmaximal, characteristic
4C2×#4986C211yesmaximal, characteristic, complemented
5C2×#4982C211yesmaximal, characteristic, complemented
6C2×#4984C211yesmaximal, characteristic, complemented
7C2×#4990C211yesmaximal, characteristic
8C2×#4990C211yesmaximal, characteristic
9C2×#4980C211yesmaximal, characteristic, complemented
10C2×#4928C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
12#76087C2116yesmaximal, direct product factor
13C2×#4668C211yesmaximal, characteristic
14C2×#4668C211yesmaximal, characteristic
15C2×#4652C211yesmaximal, characteristic, complemented
16C2×#4649C211yesmaximal, characteristic, complemented
17C2×#2587—31nomaximal, Sylow
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C3×#389C2218yescomplemented
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
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#4994C2218yes—
55#4994C2218yes—
56#4990C2218yes—
57#4990C2218yes—
58#4986C2218yescomplemented
59#4984C2218yescomplemented
60#4982C2218yescomplemented
61#4980C2218yescomplemented
62C4×(C2×D3)⋊C4C2218yes—
63#4928C2218yescomplemented
64#4668C2218yes—
65#4668C2218yes—
66#4652C2218yescomplemented
67#4649C2218yescomplemented
68#2587—316no—
69C2×#400—31no—
70C2×#398—31no—
71C2×#396—31no—
72C2×#396—31no—
73C2×#389—31no—
74C2×#389—31no—
75C2×#389D311yescharacteristic, complemented
76C2×#388—31no—
77C2×#388—31no—
78C2×#387—31no—
79C2×#387—31no—
80C2×#385—31no—
81C2×#385—31no—
82C2×C4×C4⋊C4—31no—
83C2×C4×C22⋊C4—31no—
84C24×D3C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C22×C4×D3—24no—
100C22×C4×D3—42no—
101C22×C4×D3—42no—
102C22×C4×D3C2314yes—
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4—24no—
105C2×C3×C4⋊C4—24no—
106C2×C3×C4⋊C4—42no—
107C2×C3×C4⋊C4C2314yes—
108C2×C3×C4⋊C4C2314yes—
109C2×C3×C4⋊C4C2314yes—
110C2×C3×C4⋊C4C2314yes—
111C2×C3×C42—42no—
112C2×C3×C42C2314yes—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—42no—
117C2×(C2×D3)⋊C4—42no—
118C2×(C2×D3)⋊C4Q818yes—
119C2×(C2×D3)⋊C4C2314yes—
120C2×(C2×D3)⋊C4C2314yes—
121C2×(C2×D3)⋊C4C2314yes—
122C2×(C2×D3)⋊C4C2314yes—
123C2×(C2×D3)⋊C4C2314yes—
124C2×(C2×D3)⋊C4C2314yes—
125C2×C4⋊Dic3—24no—
126C2×C4⋊Dic3—42no—
127C2×C4⋊Dic3—42no—
128C2×C4⋊Dic3—42no—
129C2×C4⋊Dic3C2314yes—
130C2×C4⋊Dic3C2314yes—
131C2×C4⋊Dic3C2314yes—
132C2×C4⋊Dic3C2314yes—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—24no—
135C2×Dic3⋊C4—24no—
136C2×Dic3⋊C4—42no—
137C2×Dic3⋊C4C2314yes—
138C2×Dic3⋊C4C2314yes—
139C2×Dic3⋊C4C2314yes—
140C2×Dic3⋊C4C2314yes—
141C2×C4×Dic3—24no—
142C2×C4×Dic3—42no—
143C2×C4×Dic3—42no—
144C2×C4×Dic3C2314yes—
145C2×C4×Dic3C2314yes—
146C2×C4×Dic3C2314yes—
147C3×#95C2314yes—
148C3×#95C2314yes—
149C3⋊#95C2314yes—
150C3⋊#95C2314yes—
151C3⋊#95C2314yes—
152C3⋊#95C2314yes—
153C3⋊#95C2314yes—
154C3⋊#95C2314yes—
155C3⋊#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C24×C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—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⋊C4C2×D311yescharacteristic
169C22×C4⋊C4C2×D311yescharacteristic
170C22×C4⋊C4C2×D311yescharacteristic
171C22×C4⋊C4C2×D311yescharacteristic
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C42—31no—
179C22×C42—31no—
180C22×C42—31no—
181C22×C42C2×D311yescharacteristic
182#400—38no—
183#398—38no—
184#396—38no—
185#396—38no—
186#389—38no—
187#389—38no—
188#389C2×D318yescomplemented
189#388—38no—
190#388—38no—
191#387—38no—
192#387—38no—
193#385—38no—
194#385—38no—
195C4×C4⋊C4—38no—
196C4×C22⋊C4—38no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C24×C3C2411yescharacteristic
210C23×D3—22no—
211C23×D3—22no—
212C23×D3—22no—
213C23×D3—22no—
214C23×D3—22no—
215C23×D3—22no—
216C23×D3C2×Q814yes—
217C23×D3C2412yes—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
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×C4C2×Q814yes—
236C22×C3×C4#4114yes—
237C22×C3×C4#4114yes—
238C22×C3×C4#4114yes—
239C22×C3×C4C2412yes—
240C22×C3×C4C2412yes—
241C22×C3×C4C2412yes—
242C22×C3×C4C2412yes—
243C22×C3×C4C2412yes—
244C22×C3×C4C2412yes—
245C22×C3×C4C2412yes—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
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×Dic3C2×Q814yes—
266C22×Dic3#4114yes—
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C22×Dic3C2412yes—
270C22×Dic3C2412yes—
271C22×Dic3C2412yes—
272C22×Dic3C2412yes—
273C22×Dic3C2412yes—
274C2×C4×D3—28no—
275C2×C4×D3—44no—
276C2×C4×D3—44no—
277C2×C4×D3—416no—
278C3×C4⋊C4—28no—
279C3×C4⋊C4—28no—
280C3×C4⋊C4—28no—
281C3×C4⋊C4—44no—
282C3×C42—44no—
283(C2×D3)⋊C4—28no—
284(C2×D3)⋊C4—28no—
285(C2×D3)⋊C4—28no—
286(C2×D3)⋊C4—44no—
287(C2×D3)⋊C4—44no—
288(C2×D3)⋊C4C2×Q8116yes—
289C4⋊Dic3—28no—
290C4⋊Dic3—44no—
291C4⋊Dic3—44no—
292C4⋊Dic3—44no—
293Dic3⋊C4—28no—
294Dic3⋊C4—28no—
295Dic3⋊C4—28no—
296Dic3⋊C4—44no—
297C4×Dic3—28no—
298C4×Dic3—44no—
299C4×Dic3—44no—
300C25—31no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—34no—
309C23×C4—64no—
310C23×C4—122no—
311C23×C4—122no—
312C23×C4C22×D311yescharacteristic
313C23×C4C22×D311yescharacteristic
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—34no—
323C2×C4⋊C4—34no—
324C2×C4⋊C4—34no—
325C2×C4⋊C4—34no—
326C2×C4⋊C4—34no—
327C2×C4⋊C4—34no—
328C2×C4⋊C4—34no—
329C2×C4⋊C4—34no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—64no—
332C2×C4⋊C4—64no—
333C2×C4⋊C4—64no—
334C2×C4⋊C4—64no—
335C2×C4⋊C4—122no—
336C2×C4⋊C4—122no—
337C2×C4⋊C4—122no—
338C2×C4⋊C4—122no—
339C2×C4⋊C4C22×D314yes—
340C2×C4⋊C4C22×D314yes—
341C2×C4⋊C4C22×D314yes—
342C2×C4⋊C4C22×D314yes—
343C2×C22⋊C4—38no—
344C2×C22⋊C4—34no—
345C2×C22⋊C4—34no—
346C2×C22⋊C4—34no—
347C2×C22⋊C4—34no—
348C2×C22⋊C4—34no—
349C2×C22⋊C4—34no—
350C2×C22⋊C4—64no—
351C2×C22⋊C4—64no—
352C2×C22⋊C4—64no—
353C2×C22⋊C4—122no—
354C2×C22⋊C4—122no—
355C2×C42—34no—
356C2×C42—34no—
357C2×C42—34no—
358C2×C42—42no—
359C2×C42—64no—
360C2×C42—122no—
361C2×C42—122no—
362C2×C42C22×D314yes—
363#95—34no—
364#95—34no—
365#95—34no—
366#95—34no—
367#95—34no—
368#95—34no—
369#95—34no—
370#95—34no—
371#95—34no—
372#95—34no—
373#95C22×D314yes—
374#95C22×D314yes—
375C23×C3C22×Q812yes—
376C23×C3C2×#4112yes—
377C23×C3C2×#4112yes—
378C23×C3C2×#4112yes—
379C23×C3C2×#4112yes—
380C23×C3H(5,𝔽2)12yes—
381C23×C3H(5,𝔽2)12yes—
382C23×C3C2511yescharacteristic
383C22×D3—28no—
384C22×D3—28no—
385C22×D3—28no—
386C22×D3—22no—
387C22×D3—22no—
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—44no—
393C22×D3—44no—
394C22×D3—44no—
395C22×D3—44no—
396C22×D3C22×Q814yes—
397C2×C3×C4—28no—
398C2×C3×C4—28no—
399C2×C3×C4—28no—
400C2×C3×C4—28no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—44no—
419C2×C3×C4—44no—
420C2×C3×C4—44no—
421C2×C3×C4C22×Q814yes—
422C2×C3×C4C2×#4114yes—
423C2×C3×C4C2×#4114yes—
424C2×C3×C4C2×#4114yes—
425C2×Dic3—28no—
426C2×Dic3—28no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—44no—
447C2×Dic3—44no—
448C2×Dic3—44no—
449C2×Dic3—44no—
450C2×Dic3—44no—
451C2×Dic3C22×Q814yes—
452C2×Dic3C2×#4114yes—
453C4×D3—416no—
454C24—34no—
455C24—32no—
456C24—62no—
457C24—62no—
458C24—62no—
459C24—62no—
460C24—62no—
461C24—62no—
462C24C23×D311yescharacteristic
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—34no—
481C22×C4—34no—
482C22×C4—32no—
483C22×C4—32no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—68no—
509C22×C4—124no—
510C22×C4—124no—
511C22×C4—1216no—
512C22×C4#23514yes—
513C22×C4#23714yes—
514C22×C4D3×Q814yes—
515C22×C4#23914yes—
516C22×C4C23×D312yes—
517C22×C4C23×D312yes—
518C22×C4C23×D312yes—
519C22×C4C23×D312yes—
520C22×C4C23×D312yes—
521C22×C4C23×D312yes—
522C22×C4C23×D312yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—44no—
527C4⋊C4—68no—
528C4⋊C4—68no—
529C4⋊C4—68no—
530C4⋊C4—68no—
531C4⋊C4—124no—
532C4⋊C4—124no—
533C4⋊C4—124no—
534C4⋊C4—124no—
535C22⋊C4—316no—
536C22⋊C4—68no—
537C22⋊C4—68no—
538C22⋊C4—68no—
539C22⋊C4—124no—
540C22⋊C4—124no—
541C42—44no—
542C42—68no—
543C42—124no—
544C42—124no—
545C22×C3#52914yes—
546C22×C3#53314yes—
547C22×C3#53814yes—
548C22×C3#55314yes—
549C22×C3#55314yes—
550C22×C3#55414yes—
551C22×C3#55414yes—
552C22×C3C23×Q811yescharacteristic
553C22×C3C22×#4111yescharacteristic
554C22×C3C22×#4111yescharacteristic
555C22×C3C22×#4111yescharacteristic
556C22×C3C22×#4111yescharacteristic
557C22×C3C2×H(5,𝔽2)11yescharacteristic
558C22×C3C2×H(5,𝔽2)11yescharacteristic
559C2×D3—24no—
560C2×D3—24no—
561C2×D3—24no—
562C2×D3—416no—
563C2×D3—42no—
564C2×D3—42no—
565C2×D3—42no—
566C2×D3—42no—
567C3×C4—24no—
568C3×C4—24no—
569C3×C4—24no—
570C3×C4—24no—
571C3×C4—42no—
572C3×C4—42no—
573C3×C4—42no—
574Dic3—24no—
575Dic3—24no—
576Dic3—42no—
577Dic3—42no—
578Dic3—42no—
579Dic3—42no—
580Dic3—42no—
581C23—34no—
582C23—68no—
583C23—62no—
584C23—62no—
585C23—62no—
586C23—62no—
587C23—62no—
588C23—62no—
589C23—68no—
590C23—68no—
591C23—124no—
592C23—124no—
593C23—124no—
594C23—124no—
595C23C2×#23512yes—
596C23C2×#23712yes—
597C23#100412yes—
598C23C2×D3×Q812yes—
599C23C2×#23912yes—
600C23D3×#4112yes—
601C23#100912yes—
602C23C24×D311yescharacteristic
603C2×C4—28no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—28no—
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—34no—
625C2×C4—34no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—68no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—68no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—1216no—
651C2×C4—124no—
652C2×C4—124no—
653C2×C4—124no—
654C2×C4—124no—
655C2×C4—124no—
656C2×C4C2×#23514yes—
657C2×C4C2×#23714yes—
658C2×C4C2×D3×Q814yes—
659C2×C4C2×#23914yes—
660C2×C3#258718yescomplemented
661C2×C3C2×#52911yescharacteristic
662C2×C3C2×#53311yescharacteristic
663C2×C3C2×#53811yescharacteristic
664C2×C3C2×#55311yescharacteristic
665C2×C3C2×#55311yescharacteristic
666C2×C3C2×#55411yescharacteristic
667C2×C3C2×#55411yescharacteristic
668D3—44no—
669C22—64no—
670C22—64no—
671C22—64no—
672C22—122no—
673C22—1216no—
674C22—122no—
675C22—122no—
676C22—122no—
677C22#551114yes—
678C22#556514yes—
679C22#558014yes—
680C22#560114yes—
681C22#564414yes—
682C22#569014yes—
683C22#572814yes—
684C22C22×#23511yescharacteristic
685C22C22×#23711yescharacteristic
686C22C2×#100411yescharacteristic
687C22C22×D3×Q811yescharacteristic
688C22C22×#23911yescharacteristic
689C22C2×D3×#4111yescharacteristic
690C22C2×#100911yescharacteristic
691C4—24no—
692C4—24no—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—64no—
699C4—64no—
700C4—122no—
701C4—122no—
702C4—122no—
703C4—122no—
704C4—122no—
705C3C2×#258711yescharacteristic, complemented, Sylow
706C2—124no—
707C2#7608718yesdirect product factor
708C2C2×#551111yescharacteristic
709C2C2×#556511yescharacteristic
710C2C2×#558011yescharacteristic
711C2C2×#560111yescharacteristic
712C2C2×#564411yescharacteristic
713C2C2×#569011yescharacteristic
714C2C2×#572811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#389C2
socleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#389D3
hypocenterC3C2×#2587
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C3×#389C2semidirect
4. C2×#4986C2semidirect
5. C2×#4982C2semidirect
6. C2×#4984C2semidirect
9. C2×#4980C2semidirect
10. C2×#4928C2semidirect
12. #76087C2direct (N × H)
15. C2×#4652C2semidirect
16. C2×#4649C2semidirect
41. C3×#389C22semidirect
58. #4986C22semidirect
59. #4984C22semidirect
60. #4982C22semidirect
61. #4980C22semidirect
63. #4928C22semidirect
66. #4652C22semidirect
67. #4649C22semidirect
75. C2×#389D3semidirect
188. #389C2×D3semidirect
660. C2×C3#2587semidirect
705. C3C2×#2587semidirect
707. C2#76087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C2×#49942
C2×#49862
C2×#49822
C2×#49842
C2×#49902
C2×#49802
C2×#49282
C2×C4×(C2×D3)⋊C42
#760872
C2×#46682
C2×#46522
C2×#46492
C2×#25873