Finite Group Databasebeta

← C2×#76801 #10965429

Subgroups — C2×#76801 #10965429

Order 768.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#393C211yesmaximal, characteristic
2C2×#5230C211yesmaximal, characteristic, complemented
3C2×#5229C211yesmaximal, characteristic, complemented
4C2×#4948C211yesmaximal, characteristic
5C2×#4945C211yesmaximal, characteristic
6C2×#4944C211yesmaximal, characteristic
7C2×#4946C211yesmaximal, characteristic
8C2×#4942C211yesmaximal, characteristic
9C2×Dic3×C22⋊C4C211yesmaximal, characteristic
10#76801C2116yesmaximal, direct product factor
11C2×#4657C211yesmaximal, characteristic, complemented
12C2×#4652C211yesmaximal, characteristic, complemented
13C2×#4652C211yesmaximal, characteristic, complemented
14C2×#4652C211yesmaximal, characteristic, complemented
15C2×#4650C211yesmaximal, characteristic, complemented
16C2×#4649C211yesmaximal, characteristic, complemented
17C2×#2574—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C3×#393C2218yes—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43#5230C2218yescomplemented
44#5229C2218yescomplemented
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
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4948C2218yes—
57#4946C2218yes—
58#4945C2218yes—
59#4944C2218yes—
60#4942C2218yes—
61Dic3×C22⋊C4C2218yes—
62#4657C2218yescomplemented
63#4652C2218yescomplemented
64#4652C2218yescomplemented
65#4652C2218yescomplemented
66#4650C2218yescomplemented
67#4649C2218yescomplemented
68#2574—316no—
69C2×#398—31no—
70C2×#396—31no—
71C2×#395—31no—
72C2×#393D311yescharacteristic
73C2×#391—31no—
74C2×#388—31no—
75C2×#388—31no—
76C2×#387—31no—
77C2×#387—31no—
78C2×#387—31no—
79C2×#385—31no—
80C2×#382—31no—
81C2×#380—31no—
82C2×C4×C4⋊C4—31no—
83C2×C4×C22⋊C4—31no—
84C25×C3C2311yescharacteristic
85C22×C3×Q8—24no—
86C22×C3×Q8—42no—
87C22×C3×Q8—42no—
88C22×C3×Q8C2314yes—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×Dic3—24no—
96C23×Dic3—24no—
97C23×Dic3—42no—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2314yes—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—42no—
109C2×C3×C22⋊C4—42no—
110C2×C3×C22⋊C4C2314yes—
111C2×C3×C22⋊C4C2314yes—
112C2×C3×C22⋊C4C2314yes—
113C2×#217—24no—
114C2×#217—42no—
115C2×#217Q818yescomplemented
116C2×#217C2314yes—
117C2×#217C2314yes—
118C2×#217C2314yes—
119C2×C4⋊Dic3—42no—
120C2×C4⋊Dic3C2314yes—
121C2×Dic3⋊C4—24no—
122C2×Dic3⋊C4—24no—
123C2×Dic3⋊C4—24no—
124C2×Dic3⋊C4—24no—
125C2×Dic3⋊C4—24no—
126C2×Dic3⋊C4—42no—
127C2×Dic3⋊C4—42no—
128C2×Dic3⋊C4—42no—
129C2×Dic3⋊C4C2314yes—
130C2×Dic3⋊C4C2314yes—
131C2×Dic3⋊C4C2314yes—
132C2×Dic3⋊C4C2314yes—
133C2×Dic3⋊C4C2314yes—
134C2×Dic3⋊C4C2314yes—
135C2×Dic3⋊C4C2314yes—
136C2×Dic3⋊C4C2314yes—
137C2×C4×Dic3—24no—
138C2×C4×Dic3—24no—
139C2×C4×Dic3—42no—
140C2×C4×Dic3—42no—
141C2×C4×Dic3C2314yes—
142C2×C4×Dic3C2314yes—
143C2×C4×Dic3C2314yes—
144C2×C4×Dic3C2314yes—
145C3×#95C2314yes—
146C3×#95C2314yes—
147C3×#95C2314yes—
148C3⋊#95C2314yes—
149C3⋊#95C2314yes—
150C3⋊#95C2314yes—
151C3⋊#95C2314yes—
152C3⋊#95C2314yes—
153C3⋊#95C2314yes—
154C3⋊#95C2314yes—
155C3⋊#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C23×Q8C2×D311yescharacteristic
160C24×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⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4C2×D311yescharacteristic
174C22×C22⋊C4C2×D311yescharacteristic
175C22×C22⋊C4C2×D311yescharacteristic
176C22×C42—31no—
177C22×C42—31no—
178C22×C42—31no—
179C22×C42—31no—
180#398—38no—
181#396—38no—
182#395—38no—
183#393C2×D318yes—
184#391—38no—
185#388—38no—
186#388—38no—
187#387—38no—
188#387—38no—
189#387—38no—
190#385—38no—
191#382—38no—
192#380—38no—
193C4×C4⋊C4—38no—
194C4×C22⋊C4—38no—
195C2×#95—31no—
196C2×#95—31no—
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×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3C2×Q814yes—
216C24×C3C2412yes—
217C24×C3C2411yescharacteristic
218C2×C3×Q8—28no—
219C2×C3×Q8—44no—
220C2×C3×Q8—44no—
221C2×C3×Q8—416no—
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×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4#4114yes—
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×Dic3—28no—
266C22×Dic3—28no—
267C22×Dic3—44no—
268C22×Dic3—416no—
269C22×Dic3C2×Q814yes—
270C22×Dic3C2×Q814yes—
271C22×Dic3#4114yes—
272C22×Dic3#4114yes—
273C22×Dic3#4114yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2412yes—
282C3×C22⋊C4—28no—
283C3×C22⋊C4—44no—
284C3×C22⋊C4—44no—
285#217—28no—
286#217—44no—
287#217C2×Q8116yescomplemented
288C4⋊Dic3—44no—
289Dic3⋊C4—28no—
290Dic3⋊C4—28no—
291Dic3⋊C4—28no—
292Dic3⋊C4—28no—
293Dic3⋊C4—28no—
294Dic3⋊C4—44no—
295Dic3⋊C4—44no—
296Dic3⋊C4—44no—
297C4×Dic3—28no—
298C4×Dic3—28no—
299C4×Dic3—44no—
300C4×Dic3—44no—
301C25C22×D311yescharacteristic
302C22×Q8—24no—
303C22×Q8—42no—
304C22×Q8—42no—
305C22×Q8C22×D314yes—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—34no—
315C23×C4—64no—
316C23×C4—64no—
317C23×C4—122no—
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D311yescharacteristic
321C23×C4C22×D311yescharacteristic
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D311yescharacteristic
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—34no—
331C2×C4⋊C4—34no—
332C2×C4⋊C4—34no—
333C2×C4⋊C4—64no—
334C2×C4⋊C4—64no—
335C2×C4⋊C4—64no—
336C2×C4⋊C4—64no—
337C2×C4⋊C4—64no—
338C2×C4⋊C4—122no—
339C2×C4⋊C4—122no—
340C2×C4⋊C4—122no—
341C2×C4⋊C4—122no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—38no—
344C2×C22⋊C4—34no—
345C2×C22⋊C4—34no—
346C2×C22⋊C4—34no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4—122no—
351C2×C22⋊C4C22×D314yes—
352C2×C22⋊C4C22×D314yes—
353C2×C22⋊C4C22×D314yes—
354C2×C42—34no—
355C2×C42—34no—
356C2×C42—34no—
357C2×C42—34no—
358C2×C42—64no—
359C2×C42—64no—
360C2×C42—122no—
361C2×C42—122no—
362#95—34no—
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—
375#95C22×D314yes—
376C23×C3—28no—
377C23×C3—28no—
378C23×C3—28no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—44no—
386C23×C3—44no—
387C23×C3—44no—
388C23×C3—44no—
389C23×C3C22×Q814yes—
390C23×C3C22×Q812yes—
391C23×C3C2×#4112yes—
392C23×C3C2×#4112yes—
393C23×C3C2×#4112yes—
394C23×C3C2×#4112yes—
395C23×C3H(5,𝔽2)12yes—
396C23×C3H(5,𝔽2)12yes—
397C23×C3C2511yescharacteristic
398C3×Q8—416no—
399C2×C3×C4—28no—
400C2×C3×C4—22no—
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—44no—
418C2×C3×C4—44no—
419C2×C3×C4—44no—
420C2×C3×C4—44no—
421C2×C3×C4—44no—
422C2×C3×C4C2×#4114yes—
423C2×Dic3—28no—
424C2×Dic3—28no—
425C2×Dic3—28no—
426C2×Dic3—28no—
427C2×Dic3—28no—
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—22no—
447C2×Dic3—416no—
448C2×Dic3—44no—
449C2×Dic3—44no—
450C2×Dic3—44no—
451C2×Dic3C22×Q814yes—
452C2×Dic3C22×Q814yes—
453C2×Dic3C2×#4114yes—
454C2×Dic3C2×#4114yes—
455C2×Dic3C2×#4114yes—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24D3×Q814yes—
463C24C23×D312yes—
464C24C23×D311yescharacteristic
465C2×Q8—28no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—416no—
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—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—34no—
487C22×C4—34no—
488C22×C4—34no—
489C22×C4—34no—
490C22×C4—34no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—32no—
499C22×C4—68no—
500C22×C4—68no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—124no—
521C22×C4—1216no—
522C22×C4#23714yes—
523C22×C4C23×D312yes—
524C22×C4C23×D312yes—
525C22×C4C23×D312yes—
526C22×C4C23×D312yes—
527C22×C4C23×D312yes—
528C22×C4C23×D312yes—
529C4⋊C4—68no—
530C4⋊C4—68no—
531C4⋊C4—68no—
532C4⋊C4—68no—
533C4⋊C4—68no—
534C4⋊C4—124no—
535C4⋊C4—124no—
536C4⋊C4—124no—
537C4⋊C4—124no—
538C22⋊C4—28no—
539C22⋊C4—316no—
540C22⋊C4—44no—
541C22⋊C4—44no—
542C22⋊C4—68no—
543C22⋊C4—124no—
544C42—68no—
545C42—68no—
546C42—124no—
547C42—124no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—416no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3#52914yes—
557C22×C3#53314yes—
558C22×C3#53814yes—
559C22×C3#55114yes—
560C22×C3#55414yes—
561C22×C3#55414yes—
562C22×C3#55514yes—
563C22×C3C23×Q811yescharacteristic
564C22×C3C22×#4111yescharacteristic
565C22×C3C22×#4111yescharacteristic
566C22×C3C22×#4111yescharacteristic
567C22×C3C22×#4111yescharacteristic
568C22×C3C2×H(5,𝔽2)11yescharacteristic
569C22×C3C2×H(5,𝔽2)11yescharacteristic
570C3×C4—24no—
571C3×C4—42no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—42no—
576Dic3—24no—
577Dic3—24no—
578Dic3—24no—
579Dic3—24no—
580Dic3—24no—
581Dic3—42no—
582Dic3—42no—
583Dic3—42no—
584C23—28no—
585C23—28no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—28no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23C2×#23712yes—
598C23#100412yes—
599C23#100412yes—
600C23C2×D3×Q814yes—
601C23C2×D3×Q812yes—
602C23D3×#4112yes—
603C23D3×#4112yes—
604C23D3×#4112yes—
605C23C24×D311yescharacteristic
606Q8—416no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—28no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
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—22no—
625C2×C4—34no—
626C2×C4—34no—
627C2×C4—34no—
628C2×C4—34no—
629C2×C4—34no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—68no—
636C2×C4—68no—
637C2×C4—68no—
638C2×C4—68no—
639C2×C4—68no—
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—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—1216no—
660C2×C4—124no—
661C2×C4—124no—
662C2×C4—124no—
663C2×C4C2×#23714yes—
664C2×C3—44no—
665C2×C3#257418yescomplemented
666C2×C3C2×#52911yescharacteristic
667C2×C3C2×#53311yescharacteristic
668C2×C3C2×#53811yescharacteristic
669C2×C3C2×#55111yescharacteristic
670C2×C3C2×#55411yescharacteristic
671C2×C3C2×#55411yescharacteristic
672C2×C3C2×#55511yescharacteristic
673C22—24no—
674C22—24no—
675C22—24no—
676C22—416no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22#559314yes—
682C22#562214yes—
683C22#563614yes—
684C22#563614yes—
685C22#567014yes—
686C22#567914yes—
687C22#568014yes—
688C22C22×#23711yescharacteristic
689C22C2×#100411yescharacteristic
690C22C2×#100411yescharacteristic
691C22C22×D3×Q811yescharacteristic
692C22C2×D3×#4111yescharacteristic
693C22C2×D3×#4111yescharacteristic
694C22C2×D3×#4111yescharacteristic
695C4—24no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—64no—
702C4—64no—
703C4—64no—
704C4—64no—
705C4—64no—
706C4—122no—
707C4—122no—
708C4—122no—
709C3C2×#257411yescharacteristic, complemented, Sylow
710C2—44no—
711C2#7680118yesdirect product factor
712C2C2×#559311yescharacteristic
713C2C2×#562211yescharacteristic
714C2C2×#563611yescharacteristic
715C2C2×#563611yescharacteristic
716C2C2×#568011yescharacteristic
717C2C2×#567011yescharacteristic
718C2C2×#567911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#393C2
socleC24×C3C24
prime radicalC25×C3C23
hypercenterC2×#393D3
hypocenterC3C2×#2574
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
2. C2×#5230C2semidirect
3. C2×#5229C2semidirect
10. #76801C2direct (N × H)
11. C2×#4657C2semidirect
12. C2×#4652C2semidirect
13. C2×#4652C2semidirect
14. C2×#4652C2semidirect
15. C2×#4650C2semidirect
16. C2×#4649C2semidirect
43. #5230C22semidirect
44. #5229C22semidirect
62. #4657C22semidirect
63. #4652C22semidirect
64. #4652C22semidirect
65. #4652C22semidirect
66. #4650C22semidirect
67. #4649C22semidirect
115. C2×#217Q8semidirect
287. #217C2×Q8semidirect
665. C2×C3#2574semidirect
709. C3C2×#2574semidirect
711. C2#76801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3932
C2×#52302
C2×#52292
C2×#49482
C2×#49452
C2×#49442
C2×#49462
C2×#49422
C2×Dic3×C22⋊C42
#768012
C2×#46572
C2×#46522
C2×#46502
C2×#46492
C2×#25743