Finite Group Databasebeta

← C2×#10595498 #11900445

Subgroups — C2×#10595498 #11900445

Order 1152.

4091 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×Dic3C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64162C211yesmaximal, characteristic, complemented
4C2×C3×#953C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6#10595498C2116yesmaximal, direct product factor
7C2×Dic3×#67C212yesmaximal, complemented
8C2×#63966C211yesmaximal, characteristic, complemented
9C2×#63964C212yesmaximal, complemented
10C2×#63961C211yesmaximal, characteristic, complemented
11C2×#63955C211yesmaximal, characteristic, complemented
12C2×#63952C212yesmaximal, complemented
13C2×#5791—31nomaximal
14C2×#5586—31nomaximal
15C25×C32C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×#638C2212yes—
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2212yes—
20C23×C3×Dic3—28no—
21C23×C3×Dic3C2212yes—
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2212yes—
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2218yescomplemented
26C22×#627C2211yescharacteristic, complemented
27C22×#626C2211yescharacteristic, complemented
28C22×#624C2211yescharacteristic, complemented
29C2×#3804—28no—
30C2×#3804C2218yescomplemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32#64162C2218yescomplemented
33C2×#3757C2211yescharacteristic
34C2×#3757C2212yes—
35C3×#953C2218yescomplemented
36C2×C3×#217C2212yes—
37C2×C3×#217C2211yescharacteristic
38#63978C22116yescomplemented
39Dic3×#67C22116yescomplemented
40C2×#3724C2212yescomplemented
41#63966C2218yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×Dic3⋊Dic3C2212yescomplemented
44#63964C22116yescomplemented
45C2×#3722C2212yescomplemented
46#63961C2218yescomplemented
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48#63955C2218yescomplemented
49C2×Dic32C2212yescomplemented
50#63952C22116yescomplemented
51C24×C3×C4—31no—
52C24×Dic3D311yescharacteristic, complemented
53C22×#237—31no—
54C22×#235—31no—
55C2×C3×#120—31no—
56C2×#953—31no—
57C2×#953—31no—
58C2×#953—61no—
59C2×#953D311yescharacteristic, complemented
60C2×#939—32no—
61C2×#935—31no—
62C2×D4×Dic3—32no—
63#5791—316no—
64C2×#930—32no—
65C2×#929—31no—
66C2×#929—31no—
67C2×C4×#67—32no—
68C2×C4×#67—32no—
69C2×#926—31no—
70C2×#924—32no—
71#5586—316no—
72C2×#886—31no—
73C2×#67⋊C4—32no—
74C2×#878—32no—
75C2×#877—31no—
76C24×C32—24no—
77C24×C32—28no—
78C24×C32C2314yes—
79C24×C32C2311yescharacteristic
80C24×C32C2312yes—
81C23×C3⋊D3C2311yescharacteristic
82C23×C3×D3C2311yescharacteristic
83C2×#638—24no—
84C2×#638—28no—
85C2×#638C2314yes—
86C2×#638C2318yes—
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2312yes—
89C2×C3×#67—24no—
90C2×C3×#67—28no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2318yes—
93C22×C3×Dic3—24no—
94C22×C3×Dic3—28no—
95C22×C3×Dic3—28no—
96C22×C3×Dic3—232no—
97C22×C3×Dic3D418yescomplemented
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2312yes—
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2318yes—
102C22×C3×Dic3C2314yes—
103C22×C3×Dic3C2318yes—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2314yes—
107C2×#627—24no—
108C2×#627C2314yescomplemented
109C2×#626—24no—
110C2×#626C2314yescomplemented
111C2×#624—24no—
112C2×#624C2314yescomplemented
113#3804—232no—
114C2×D3×Dic3—24no—
115C2×D3×Dic3C2314yescomplemented
116#3757C2314yes—
117#3757C2318yes—
118C3×#217C2318yes—
119C3×#217C2314yes—
120#3724C2318yescomplemented
121Dic3⋊Dic3C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123#3722C2318yescomplemented
124(C2×D3)⋊Dic3C2318yescomplemented
125Dic32C2318yescomplemented
126C2×#525—91noSylow
127C25×C3—21no—
128C25×C3C2×D311yescharacteristic
129C25×C3C2×D311yescharacteristic
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C23×C3×C4—31no—
133C23×C3×C4—32no—
134C23×C3×C4—32no—
135C23×C3×C4—31no—
136C23×C3×C4—38no—
137C23×C3×C4—68no—
138C22×#67—31no—
139C22×#67—31no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—31no—
143C22×#67—62no—
144C22×#67—61no—
145C22×#67C2×D311yescharacteristic
146C22×#67C2×D312yes—
147C23×Dic3—28no—
148C23×Dic3—31no—
149C23×Dic3C2×D312yes—
150C23×Dic3C2×D312yes—
151C23×Dic3C2×D311yescharacteristic
152C23×Dic3C2×D311yescharacteristic
153C23×Dic3C2×D318yescomplemented
154C2×#237—38no—
155C2×#237—68no—
156C2×#235—38no—
157C2×#235—68no—
158C22×D12—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×Dic6—31no—
163C22×Dic6—31no—
164C3×#120—38no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—32no—
167#953—38no—
168#953—38no—
169#953—68no—
170#953C2×D318yescomplemented
171C2×#217—31no—
172C2×#217—32no—
173C2×#217—32no—
174C2×#217—31no—
175C2×#217—32no—
176C2×#217—61no—
177C2×#217—62no—
178C2×#217C2×D312yes—
179C2×#217C2×D311yescharacteristic
180#939—316no—
181#935—38no—
182D4×Dic3—316no—
183#930—316no—
184#929—38no—
185#929—38no—
186C4×#67—316no—
187C4×#67—316no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191#926—38no—
192C2×C4⋊Dic3—32no—
193C2×C4⋊Dic3—32no—
194#924—316no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—32no—
198C2×Dic3⋊C4—32no—
199C2×C4×Dic3—32no—
200C2×C4×Dic3—32no—
201#886—38no—
202#67⋊C4—316no—
203#878—316no—
204#877—38no—
205C23×C32—232no—
206C23×C32—28no—
207C23×C32—24no—
208C23×C32—24no—
209C23×C32—24no—
210C23×C32—216no—
211C23×C32C2×D414yes—
212C23×C32#4118yescomplemented
213C23×C32C2412yes—
214C23×C32C2414yes—
215C23×C32C2411yescharacteristic
216C22×C3⋊D3—22no—
217C22×C3⋊D3—24no—
218C22×C3⋊D3C2412yes—
219C22×C3×D3—22no—
220C22×C3×D3—24no—
221C22×C3×D3C2412yes—
222#638—28no—
223#638—216no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—24no—
226C2×C3⋊Dic3C2414yes—
227C2×C3⋊Dic3C2412yes—
228C3×#67—28no—
229C3×#67—216no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—28no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—216no—
235C2×C3×Dic3—216no—
236C2×C3×Dic3C2×D414yes—
237C2×C3×Dic3C2×D414yes—
238C2×C3×Dic3C2×D4116yescomplemented
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2412yes—
244#627—28no—
245#626—28no—
246#624—28no—
247D3×Dic3—28no—
248C22×#41—91no—
249C24×C4—31no—
250#525—916no—
251C2×#123—91no—
252C2×#123—91no—
253C2×C22⋊Q8—92no—
254C2×#121—92no—
255C2×#120—31no—
256C2×#120—91no—
257C2×C4×D4—92no—
258C2×C4×D4—92no—
259C2×#117—91no—
260C24×C3—28no—
261C24×C3—24no—
262C24×C3—28no—
263C24×C3—24no—
264C24×C3—22no—
265C24×C3—21no—
266C24×C3—24no—
267C24×C3—31no—
268C24×C3—48no—
269C24×C3—44no—
270C24×C3C22×D314yes—
271C24×C3C22×D314yes—
272C24×C3C22×D312yes—
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D312yes—
275C24×C3C22×D311yescharacteristic
276C23×D3—31no—
277C23×D3—31no—
278C23×D3—61no—
279C23×D3C22×D311yescharacteristic
280C2×C3×D4—38no—
281C2×C3×D4—34no—
282C2×C3×D4—68no—
283C2×C3×D4—64no—
284C22×C3×C4—38no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—34no—
288C22×C3×C4—32no—
289C22×C3×C4—32no—
290C22×C3×C4—31no—
291C22×C3×C4—38no—
292C22×C3×C4—38no—
293C22×C3×C4—34no—
294C22×C3×C4—68no—
295C22×C3×C4—68no—
296C22×C3×C4—632no—
297C22×C3×C4—64no—
298C2×#67—24no—
299C2×#67—28no—
300C2×#67—38no—
301C2×#67—34no—
302C2×#67—38no—
303C2×#67—34no—
304C2×#67—34no—
305C2×#67—68no—
306C2×#67—64no—
307C2×#67—68no—
308C2×#67—64no—
309C2×#67—68no—
310C2×#67—64no—
311C2×#67—64no—
312C2×#67—128no—
313C2×#67—124no—
314C2×#67C22×D318yes—
315C2×#67C22×D314yes—
316C22×Dic3—24no—
317C22×Dic3—28no—
318C22×Dic3—28no—
319C22×Dic3—232no—
320C22×Dic3—32no—
321C22×Dic3—32no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—34no—
325C22×Dic3—62no—
326C22×Dic3—61no—
327C22×Dic3—64no—
328C22×Dic3#6718yescomplemented
329C22×Dic3C22×D318yes—
330C22×Dic3C22×D318yes—
331C22×Dic3C22×D314yes—
332C22×Dic3C22×D312yes—
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D312yes—
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D314yes—
338#237—632no—
339#235—632no—
340C2×D12—34no—
341C2×D12—64no—
342C2×C4×D3—34no—
343C2×C4×D3—34no—
344C2×C4×D3—34no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—64no—
348C2×Dic6—34no—
349C2×Dic6—34no—
350C2×Dic6—64no—
351C2×Dic6—64no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—38no—
354#217—34no—
355#217—38no—
356#217—38no—
357#217—34no—
358#217—38no—
359#217—64no—
360#217—68no—
361#217C22×D318yes—
362#217C22×D314yes—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366C4⋊Dic3—38no—
367C4⋊Dic3—38no—
368Dic3⋊C4—38no—
369Dic3⋊C4—38no—
370Dic3⋊C4—38no—
371Dic3⋊C4—38no—
372C4×Dic3—38no—
373C4×Dic3—38no—
374C22×C32—232no—
375C22×C32—28no—
376C22×C32—216no—
377C22×C32—24no—
378C22×C32—24no—
379C22×C32—24no—
380C22×C32C22×D414yes—
381C22×C32C22×D412yes—
382C22×C32C2×#4114yes—
383C22×C32C2×#4118yescomplemented
384C22×C32C2511yescharacteristic
385C2×C3⋊D3—22no—
386C2×C3⋊D3—24no—
387C2×C3⋊D3—44no—
388C2×C3×D3—22no—
389C2×C3×D3—24no—
390C2×C3×D3—44no—
391C3⋊Dic3—22no—
392C3⋊Dic3—24no—
393C3×Dic3—22no—
394C3×Dic3—24no—
395C3×Dic3—24no—
396C3×Dic3C22×D414yes—
397C3×Dic3C22×D414yes—
398C25D3211yescharacteristic
399C2×#41—98no—
400C2×#41—188no—
401C22×Q8—91no—
402C22×D4—32no—
403C22×D4—31no—
404C22×D4—91no—
405C22×D4—92no—
406C22×D4—91no—
407C23×C4—31no—
408C23×C4—32no—
409C23×C4—32no—
410C23×C4—31no—
411C23×C4—38no—
412C23×C4—68no—
413C23×C4—91no—
414C23×C4—91no—
415#123—98no—
416#123—98no—
417C22⋊Q8—916no—
418#121—916no—
419#120—38no—
420#120—98no—
421C4×D4—916no—
422C4×D4—916no—
423#117—98no—
424C2×C4⋊C4—92no—
425C2×C4⋊C4—92no—
426C2×C4⋊C4—92no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—92no—
430C2×C22⋊C4—92no—
431C2×C22⋊C4—91no—
432C2×C22⋊C4—92no—
433C2×C42—92no—
434C23×C3—232no—
435C23×C3—232no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—216no—
439C23×C3—28no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—216no—
444C23×C3—28no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—22no—
448C23×C3—21no—
449C23×C3—28no—
450C23×C3—24no—
451C23×C3—32no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3—416no—
455C23×C3—44no—
456C23×C3—48no—
457C23×C3—432no—
458C23×C3—64no—
459C23×C3—62no—
460C23×C3#23518yescomplemented
461C23×C3D3×D414yes—
462C23×C3#23718yescomplemented
463C23×C3C2×#6714yes—
464C23×C3C23×D314yes—
465C23×C3C23×D312yes—
466C23×C3C23×D314yes—
467C23×C3C23×D312yes—
468C23×C3C23×D311yescharacteristic
469C23×C3C23×D311yescharacteristic
470C22×D3—22no—
471C22×D3—24no—
472C22×D3—32no—
473C22×D3—32no—
474C22×D3—62no—
475C22×D3—64no—
476C22×D3—62no—
477C22×D3—64no—
478C22×D3—62no—
479C22×D3—124no—
480C22×D3—122no—
481C22×D3C23×D312yes—
482C3×D4—616no—
483C3×D4—68no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—316no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—34no—
490C2×C3×C4—34no—
491C2×C3×C4—32no—
492C2×C3×C4—616no—
493C2×C3×C4—616no—
494C2×C3×C4—64no—
495C2×C3×C4—68no—
496C2×C3×C4—64no—
497C2×C3×C4—62no—
498#67—28no—
499#67—216no—
500#67—616no—
501#67—68no—
502#67—616no—
503#67—68no—
504#67—68no—
505#67—1216no—
506#67—128no—
507C2×Dic3—22no—
508C2×Dic3—24no—
509C2×Dic3—28no—
510C2×Dic3—24no—
511C2×Dic3—216no—
512C2×Dic3—216no—
513C2×Dic3—34no—
514C2×Dic3—34no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—64no—
518C2×Dic3—62no—
519C2×Dic3—64no—
520C2×Dic3—62no—
521C2×Dic3—64no—
522C2×Dic3—62no—
523C2×Dic3—68no—
524C2×Dic3—124no—
525C2×Dic3—122no—
526C2×Dic3C2×#6714yes—
527C2×Dic3C2×#6714yes—
528C2×Dic3C2×#67116yescomplemented
529C2×Dic3C23×D314yes—
530C2×Dic3C23×D312yes—
531C2×Dic3C23×D314yes—
532C2×Dic3C23×D312yes—
533C2×Dic3C23×D312yes—
534D12—68no—
535C4×D3—68no—
536C4×D3—68no—
537C4×D3—68no—
538Dic6—68no—
539Dic6—68no—
540C2×C32—24no—
541C2×C32—28no—
542C2×C32#52514yescomplemented
543C2×C32C23×D411yescharacteristic
544C2×C32C22×#4112yes—
545C3⋊D3—42no—
546C3×D3—42no—
547C24—28no—
548C24—24no—
549C24—31no—
550C24—91no—
551C24C2×D3214yes—
552C24C2×D3212yes—
553C24C2×D3211yescharacteristic
554#41—1832no—
555C2×Q8—94no—
556C2×Q8—184no—
557C2×D4—38no—
558C2×D4—34no—
559C2×D4—68no—
560C2×D4—64no—
561C2×D4—94no—
562C2×D4—98no—
563C2×D4—94no—
564C2×D4—184no—
565C2×D4—188no—
566C2×D4—184no—
567C22×C4—34no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—38no—
571C22×C4—38no—
572C22×C4—38no—
573C22×C4—34no—
574C22×C4—32no—
575C22×C4—31no—
576C22×C4—32no—
577C22×C4—68no—
578C22×C4—68no—
579C22×C4—632no—
580C22×C4—64no—
581C22×C4—94no—
582C22×C4—94no—
583C22×C4—92no—
584C22×C4—91no—
585C22×C4—184no—
586C22×C4—184no—
587C4⋊C4—98no—
588C4⋊C4—98no—
589C4⋊C4—98no—
590C22⋊C4—34no—
591C22⋊C4—38no—
592C22⋊C4—98no—
593C22⋊C4—98no—
594C22⋊C4—94no—
595C22⋊C4—98no—
596C42—98no—
597C22×C3—232no—
598C22×C3—232no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—216no—
606C22×C3—28no—
607C22×C3—28no—
608C22×C3—216no—
609C22×C3—24no—
610C22×C3—28no—
611C22×C3—22no—
612C22×C3—24no—
613C22×C3—21no—
614C22×C3—44no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—416no—
618C22×C3—48no—
619C22×C3—432no—
620C22×C3—64no—
621C22×C3—62no—
622C22×C3—124no—
623C22×C3C2×#23514yes—
624C22×C3C2×#23518yescomplemented
625C22×C3C2×D3×D414yes—
626C22×C3C2×D3×D412yes—
627C22×C3C2×#23714yes—
628C22×C3C2×#23718yescomplemented
629C22×C3C22×#6714yes—
630C22×C3C22×#6712yes—
631C22×C3C24×D311yescharacteristic
632C22×C3C24×D311yescharacteristic
633C2×D3—22no—
634C2×D3—24no—
635C2×D3—44no—
636C2×D3—64no—
637C2×D3—62no—
638C2×D3—64no—
639C2×D3—62no—
640C2×D3—124no—
641C2×D3—122no—
642C2×D3—124no—
643C2×D3—124no—
644C2×D3—244no—
645C3×C4—34no—
646C3×C4—34no—
647C3×C4—64no—
648C3×C4—64no—
649C3×C4—62no—
650Dic3—22no—
651Dic3—24no—
652Dic3—24no—
653Dic3—64no—
654Dic3—62no—
655Dic3—64no—
656Dic3—62no—
657Dic3—124no—
658Dic3—122no—
659Dic3C22×#6714yes—
660Dic3C22×#6714yes—
661C32C2×#52511yescharacteristic, complemented, Sylow
662C23—232no—
663C23—24no—
664C23—24no—
665C23—216no—
666C23—28no—
667C23—24no—
668C23—32no—
669C23—64no—
670C23—62no—
671C23—92no—
672C23—184no—
673C23—182no—
674C23#380418yescomplemented
675C23D3×#6714yes—
676C23C22×D3214yes—
677C23C22×D3212yes—
678C23C22×D3211yescharacteristic
679Q8—188no—
680D4—616no—
681D4—68no—
682D4—188no—
683D4—1816no—
684D4—188no—
685C2×C4—34no—
686C2×C4—34no—
687C2×C4—316no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—34no—
691C2×C4—32no—
692C2×C4—34no—
693C2×C4—616no—
694C2×C4—616no—
695C2×C4—64no—
696C2×C4—68no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—94no—
700C2×C4—92no—
701C2×C4—188no—
702C2×C4—188no—
703C2×C4—184no—
704C2×C4—182no—
705C2×C3—24no—
706C2×C3—28no—
707C2×C3—28no—
708C2×C3—24no—
709C2×C3—22no—
710C2×C3—21no—
711C2×C3—24no—
712C2×C3—48no—
713C2×C3—44no—
714C2×C3—122no—
715C2×C3#558614yescomplemented
716C2×C3#579114yescomplemented
717C2×C3C22×#23512yes—
718C2×C3C22×D3×D411yescharacteristic
719C2×C3C22×#23712yes—
720C2×C3C23×#6711yescharacteristic
721D3—42no—
722D3—122no—
723D3—122no—
724D3—242no—
725C22—232no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—216no—
730C22—28no—
731C22—64no—
732C22—62no—
733C22—124no—
734C22—184no—
735C22—182no—
736C22—364no—
737C22C2×#380414yes—
738C22C2×#380418yescomplemented
739C22C2×D3×#6714yes—
740C22C2×D3×#6712yes—
741C22C23×D3211yescharacteristic
742C4—34no—
743C4—34no—
744C4—64no—
745C4—64no—
746C4—62no—
747C4—184no—
748C4—182no—
749C3—21no—
750C3C2×#558611yescharacteristic, complemented
751C3C2×#579111yescharacteristic, complemented
752C2—28no—
753C2—24no—
754C2—122no—
755C2—362no—
756C2#1059549814yesdirect product factor
757C2C22×#380412yes—
758C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C24×C3×Dic3C2semidirect
2. C22×#3804C2semidirect
3. C2×#64162C2semidirect
4. C2×C3×#953C2semidirect
5. C2×#63978C2semidirect
6. #10595498C2direct (N × H)
7. C2×Dic3×#67C2semidirect
8. C2×#63966C2semidirect
9. C2×#63964C2semidirect
10. C2×#63961C2semidirect
11. C2×#63955C2semidirect
12. C2×#63952C2semidirect
25. C23×C3×Dic3C22semidirect
26. C22×#627C22semidirect
27. C22×#626C22semidirect
28. C22×#624C22semidirect
30. C2×#3804C22semidirect
31. C22×D3×Dic3C22semidirect
32. #64162C22semidirect
35. C3×#953C22semidirect
38. #63978C22semidirect
39. Dic3×#67C22semidirect
40. C2×#3724C22semidirect
41. #63966C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. #63964C22semidirect
45. C2×#3722C22semidirect
46. #63961C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. #63955C22semidirect
49. C2×Dic32C22semidirect
50. #63952C22semidirect
52. C24×Dic3D3semidirect
59. C2×#953D3semidirect
97. C22×C3×Dic3D4semidirect
108. C2×#627C23semidirect
110. C2×#626C23semidirect
112. C2×#624C23semidirect
115. C2×D3×Dic3C23semidirect
120. #3724C23semidirect
121. Dic3⋊Dic3C23semidirect
122. Dic3⋊Dic3C23semidirect
123. #3722C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. Dic32C23semidirect
153. C23×Dic3C2×D3semidirect
170. #953C2×D3semidirect
212. C23×C32#41semidirect
238. C2×C3×Dic3C2×D4semidirect
328. C22×Dic3#67semidirect
383. C22×C32C2×#41semidirect
460. C23×C3#235semidirect
462. C23×C3#237semidirect
528. C2×Dic3C2×#67semidirect
542. C2×C32#525semidirect
624. C22×C3C2×#235semidirect
628. C22×C3C2×#237semidirect
661. C32C2×#525semidirect
674. C23#3804semidirect
715. C2×C3#5586semidirect
716. C2×C3#5791semidirect
738. C22C2×#3804semidirect
750. C3C2×#5586semidirect
751. C3C2×#5791semidirect
756. C2#10595498direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×Dic32
C22×#38042
C2×#641622
C2×C3×#9532
C2×#639782
#105954982
C2×Dic3×#672
C2×#639662
C2×#639642
C2×#639612
C2×#639552
C2×#639522
C2×#57913
C2×#55863