Finite Group Databasebeta

← C2×#10594082 #11900440

Subgroups — C2×#10594082 #11900440

Order 1152.

3925 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C23×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#64086C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×#63902C212yesmaximal, complemented
9C2×#63899C212yesmaximal, complemented
10C2×#63898C212yesmaximal, complemented
11C2×#63885C212yesmaximal, complemented
12#10594082C2116yesmaximal, direct product factor
13C2×#5656—31nomaximal
14C2×#5586—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×D12C2212yes—
21C22×#627C2211yescharacteristic, complemented
22C22×#625C2212yes—
23C22×#625C2211yescharacteristic, complemented
24C2×#3805—28no—
25C2×#3805C2218yescomplemented
26C22×D3×Dic3—28no—
27C22×D3×Dic3C2212yes—
28C22×D3×Dic3C2212yes—
29C22×D3×Dic3C2218yescomplemented
30C22×D3×Dic3C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3750C2212yescomplemented
35C2×C4×C3⋊Dic3C2212yescomplemented
36#64086C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×C4⋊Dic3C2212yescomplemented
40C3×#886C2218yescomplemented
41C3×#882C2218yescomplemented
42#63976C2218yescomplemented
43C2×#3724C2212yescomplemented
44#63961C2218yescomplemented
45C2×(C2×D3)⋊Dic3C2212yes—
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47#63902C22116yescomplemented
48#63899C22116yescomplemented
49#63898C22116yescomplemented
50#63885C22116yescomplemented
51C24×Dic3—31no—
52C22×#237—31no—
53C22×#237—31no—
54C23×C4×D3—31no—
55C2×C3×#123—31no—
56C2×C3×#120—31no—
57C2×#953—31no—
58C2×#939—32no—
59C2×#937—31no—
60C2×#935—31no—
61C2×D4×Dic3—32no—
62C2×#929—31no—
63#5656—316no—
64#5586—316no—
65C2×#896—32no—
66C2×#893—32no—
67C2×#886D311yescharacteristic, complemented
68C2×#884—32no—
69C2×#882D311yescharacteristic, complemented
70C2×#67⋊C4—32no—
71C2×#67⋊C4—32no—
72C2×#878—32no—
73C2×#877—31no—
74C2×#877—31no—
75C2×#877—61no—
76C24×C32C2311yescharacteristic
77C23×C3×D3—24no—
78C23×C3×D3—28no—
79C23×C3×D3C2314yes—
80C23×C3×D3C2311yescharacteristic
81C23×C3×D3C2311yescharacteristic
82C23×C3×D3C2312yes—
83C22×C32×C4C2312yes—
84C22×C3⋊Dic3D418yescomplemented
85C22×C3⋊Dic3C2312yes—
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2314yes—
89C2×C3×#67—24no—
90C2×C3×#67—24no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2314yes—
93C22×C3×Dic3—24no—
94C22×C3×Dic3C2314yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2311yescharacteristic
98C2×C3×D12—28no—
99C2×C3×D12C2318yes—
100C2×#627—24no—
101C2×#627C2314yescomplemented
102C2×#625—28no—
103C2×#625—24no—
104C2×#625C2318yes—
105C2×#625C2314yescomplemented
106#3805—232no—
107C2×D3×Dic3—28no—
108C2×D3×Dic3—28no—
109C2×D3×Dic3—24no—
110C2×D3×Dic3—24no—
111C2×D3×Dic3—232no—
112C2×D3×Dic3C2318yes—
113C2×D3×Dic3C2318yes—
114C2×D3×Dic3C2314yescomplemented
115C2×D3×Dic3C2314yescomplemented
116C32×C22⋊C4C2314yes—
117#3757C2314yes—
118#3750C2318yescomplemented
119C4×C3⋊Dic3C2318yescomplemented
120C3×(C2×D3)⋊C4C2318yes—
121C3×(C2×D3)⋊C4C2318yescomplemented
122C3×C4⋊Dic3C2318yescomplemented
123#3724C2318yescomplemented
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#525—91noSylow
127C25×C3—31no—
128C24×D3C2×D311yescharacteristic
129C22×C3×D4—31no—
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C23×C3×C4—31no—
133C22×#67—31no—
134C22×#67—31no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67C2×D311yescharacteristic
138C22×#67C2×D311yescharacteristic
139C23×Dic3—31no—
140C23×Dic3—31no—
141C23×Dic3—32no—
142C23×Dic3—32no—
143C23×Dic3—31no—
144C23×Dic3—31no—
145C23×Dic3—38no—
146C23×Dic3—61no—
147C23×Dic3—68no—
148C23×Dic3C2×D311yescharacteristic
149C2×#237—38no—
150C2×#237—38no—
151C2×#237—68no—
152C2×#237—68no—
153C22×D12C2×D312yes—
154C22×C4×D3—38no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—68no—
160C22×Dic6—31no—
161C22×Dic6—31no—
162C3×#123—38no—
163C3×#120—38no—
164C2×C3×C4⋊C4—32no—
165C2×C3×C22⋊C4—21no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—32no—
168C2×C3×C22⋊C4C2×D311yescharacteristic
169C2×C3×C22⋊C4C2×D311yescharacteristic
170#953—38no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—32no—
174C2×#217—32no—
175C2×#217—61no—
176#939—316no—
177#937—38no—
178#935—38no—
179D4×Dic3—316no—
180#929—38no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4C2×D312yes—
184C2×(C2×D3)⋊C4C2×D312yescomplemented
185C2×C4⋊Dic3C2×D312yescomplemented
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—62no—
191C2×C4×Dic3—32no—
192C2×C4×Dic3—32no—
193C2×C4×Dic3—62no—
194#896—316no—
195#893—316no—
196#886C2×D318yescomplemented
197#884—316no—
198#882C2×D318yescomplemented
199#67⋊C4—316no—
200#67⋊C4—316no—
201#878—316no—
202#877—38no—
203#877—38no—
204#877—68no—
205C23×C32—24no—
206C23×C32C2×D414yes—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3×D3—232no—
210C22×C3×D3—28no—
211C22×C3×D3—24no—
212C22×C3×D3—24no—
213C22×C3×D3—216no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3#4118yescomplemented
219C22×C3×D3C2412yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2414yes—
222C2×C32×C4—24no—
223C2×C32×C4C2414yes—
224C2×C3⋊Dic3—24no—
225C2×C3⋊Dic3C2×D414yes—
226C2×C3⋊Dic3C2×D414yes—
227C2×C3⋊Dic3C2×D4116yescomplemented
228C2×C3⋊Dic3C2414yes—
229C2×C3⋊Dic3C2412yes—
230C2×C3⋊Dic3C2412yes—
231C3×#67—28no—
232C3×#67—28no—
233C2×C3×Dic3—28no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3C2412yes—
238C2×C3×Dic3C2414yes—
239C2×C3×Dic3C2412yes—
240C3×D12—216no—
241#627—28no—
242#625—216no—
243#625—28no—
244D3×Dic3—216no—
245D3×Dic3—216no—
246D3×Dic3—28no—
247D3×Dic3—28no—
248C22×#41—91no—
249C24×C4—91no—
250#525—916no—
251C2×#123—31no—
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—21no—
261C24×C3—32no—
262C24×C3—34no—
263C24×C3—31no—
264C24×C3—31no—
265C24×C3—68no—
266C24×C3—64no—
267C24×C3C22×D311yescharacteristic
268C24×C3C22×D311yescharacteristic
269C23×D3—24no—
270C23×D3—28no—
271C23×D3C22×D314yes—
272C23×D3C22×D311yescharacteristic
273C23×D3C22×D311yescharacteristic
274C23×D3C22×D312yes—
275C2×C3×D4—34no—
276C2×C3×D4—34no—
277C2×C3×D4—38no—
278C2×C3×D4—68no—
279C2×C3×D4—64no—
280C2×C3×D4—64no—
281C22×C3×C4—22no—
282C22×C3×C4—31no—
283C22×C3×C4—32no—
284C22×C3×C4—31no—
285C22×C3×C4—34no—
286C22×C3×C4—64no—
287C22×C3×C4C22×D312yes—
288C22×C3×C4C22×D312yes—
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—38no—
292C2×#67—38no—
293C2×#67—34no—
294C2×#67—34no—
295C2×#67—64no—
296C2×#67—64no—
297C2×#67—68no—
298C2×#67—68no—
299C2×#67C22×D314yes—
300C2×#67C22×D314yes—
301C22×Dic3—24no—
302C22×Dic3—38no—
303C22×Dic3—38no—
304C22×Dic3—34no—
305C22×Dic3—34no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—32no—
311C22×Dic3—32no—
312C22×Dic3—38no—
313C22×Dic3—34no—
314C22×Dic3—38no—
315C22×Dic3—34no—
316C22×Dic3—64no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—68no—
320C22×Dic3—62no—
321C22×Dic3—64no—
322C22×Dic3—64no—
323C22×Dic3—68no—
324C22×Dic3—68no—
325C22×Dic3—632no—
326C22×Dic3C22×D314yes—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D312yes—
329C22×Dic3C22×D311yescharacteristic
330#237—632no—
331#237—632no—
332C2×D12—28no—
333C2×D12C22×D318yes—
334C2×C4×D3—34no—
335C2×C4×D3—38no—
336C2×C4×D3—38no—
337C2×C4×D3—34no—
338C2×C4×D3—68no—
339C2×C4×D3—68no—
340C2×C4×D3—632no—
341C2×C4×D3—64no—
342C2×C4×D3—64no—
343C2×Dic6—34no—
344C2×Dic6—34no—
345C2×Dic6—64no—
346C2×Dic6—64no—
347C3×C4⋊C4—38no—
348C3×C22⋊C4—24no—
349C3×C22⋊C4—38no—
350C3×C22⋊C4—38no—
351C3×C22⋊C4C22×D314yes—
352C3×C22⋊C4C22×D314yes—
353#217—34no—
354#217—34no—
355#217—38no—
356#217—38no—
357#217—64no—
358(C2×D3)⋊C4—38no—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4C22×D318yes—
361(C2×D3)⋊C4C22×D318yescomplemented
362C4⋊Dic3C22×D318yescomplemented
363Dic3⋊C4—38no—
364Dic3⋊C4—38no—
365Dic3⋊C4—38no—
366Dic3⋊C4—38no—
367Dic3⋊C4—68no—
368C4×Dic3—38no—
369C4×Dic3—38no—
370C4×Dic3—68no—
371C22×C32—28no—
372C22×C32—24no—
373C22×C32C22×D414yes—
374C22×C32C22×D412yes—
375C22×C32C2×#4114yes—
376C22×C32C2511yescharacteristic
377C2×C3×D3—232no—
378C2×C3×D3—216no—
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3—22no—
382C2×C3×D3—22no—
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C2×C3×D3—44no—
386C2×C3×D3—44no—
387C2×C3×D3C2×#4118yescomplemented
388C32×C4—24no—
389C3⋊Dic3—24no—
390C3⋊Dic3C22×D414yes—
391C3⋊Dic3C22×D414yes—
392C3×Dic3—24no—
393C3×Dic3—22no—
394C3×Dic3—22no—
395C25—31no—
396C2×#41—98no—
397C2×#41—188no—
398C22×Q8—91no—
399C22×D4—31no—
400C22×D4—31no—
401C22×D4—32no—
402C22×D4—92no—
403C22×D4—91no—
404C23×C4—31no—
405C23×C4—92no—
406C23×C4—91no—
407C23×C4—91no—
408C23×C4—92no—
409C23×C4—98no—
410C23×C4—91no—
411C23×C4—188no—
412#123—38no—
413#123—98no—
414C22⋊Q8—916no—
415#121—916no—
416#120—38no—
417#120—98no—
418C4×D4—916no—
419C4×D4—916no—
420#117—98no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—92no—
423C2×C4⋊C4—92no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—92no—
427C2×C22⋊C4—92no—
428C2×C22⋊C4—91no—
429C2×C22⋊C4D3211yescharacteristic
430C2×C42—92no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—22no—
434C23×C3—21no—
435C23×C3—24no—
436C23×C3—38no—
437C23×C3—34no—
438C23×C3—32no—
439C23×C3—32no—
440C23×C3—44no—
441C23×C3—616no—
442C23×C3—632no—
443C23×C3—68no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—62no—
447C23×C3—62no—
448C23×C3—64no—
449C23×C3—64no—
450C23×C3D3×D414yes—
451C23×C3D3×D414yes—
452C23×C3C23×D312yes—
453C23×C3C23×D312yes—
454C23×C3C23×D311yescharacteristic
455C23×C3C23×D311yescharacteristic
456C22×D3—232no—
457C22×D3—28no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—216no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3#23718yescomplemented
466C22×D3C23×D312yes—
467C22×D3C23×D312yes—
468C22×D3C23×D314yes—
469C3×D4—616no—
470C3×D4—68no—
471C3×D4—68no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—32no—
476C2×C3×C4—34no—
477C2×C3×C4—32no—
478C2×C3×C4—44no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—68no—
482C2×C3×C4—64no—
483C2×C3×C4C23×D314yes—
484C2×C3×C4C23×D314yes—
485#67—28no—
486#67—28no—
487#67—68no—
488#67—68no—
489#67—616no—
490#67—616no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—28no—
494C2×Dic3—24no—
495C2×Dic3—34no—
496C2×Dic3—34no—
497C2×Dic3—34no—
498C2×Dic3—34no—
499C2×Dic3—316no—
500C2×Dic3—316no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—64no—
508C2×Dic3—64no—
509C2×Dic3—616no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—64no—
513C2×Dic3—68no—
514C2×Dic3—68no—
515C2×Dic3—616no—
516C2×Dic3—616no—
517C2×Dic3—64no—
518C2×Dic3—64no—
519C2×Dic3—124no—
520C2×Dic3C23×D312yes—
521C2×Dic3C23×D314yes—
522C2×Dic3C23×D312yes—
523D12—216no—
524C4×D3—616no—
525C4×D3—616no—
526C4×D3—68no—
527C4×D3—68no—
528Dic6—68no—
529Dic6—68no—
530C2×C32—24no—
531C2×C32#52514yescomplemented
532C2×C32C23×D411yescharacteristic
533C2×C32C22×#4112yes—
534C3×D3—28no—
535C3×D3—42no—
536C3×D3—42no—
537C24—32no—
538C24—34no—
539C24—31no—
540C24—31no—
541C24—68no—
542C24—64no—
543C24C2×D3211yescharacteristic
544#41—1832no—
545C2×Q8—94no—
546C2×Q8—184no—
547C2×D4—34no—
548C2×D4—34no—
549C2×D4—38no—
550C2×D4—68no—
551C2×D4—64no—
552C2×D4—64no—
553C2×D4—98no—
554C2×D4—94no—
555C2×D4—184no—
556C2×D4—188no—
557C22×C4—34no—
558C22×C4—31no—
559C22×C4—32no—
560C22×C4—31no—
561C22×C4—64no—
562C22×C4—98no—
563C22×C4—94no—
564C22×C4—94no—
565C22×C4—98no—
566C22×C4—94no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—98no—
570C22×C4—92no—
571C22×C4—188no—
572C22×C4—188no—
573C22×C4—1832no—
574C22×C4—184no—
575C22×C4—184no—
576C22×C4C2×D3212yes—
577C4⋊C4—38no—
578C4⋊C4—98no—
579C4⋊C4—98no—
580C22⋊C4—38no—
581C22⋊C4—38no—
582C22⋊C4—98no—
583C22⋊C4—98no—
584C22⋊C4—94no—
585C22⋊C4C2×D3214yes—
586C42—98no—
587C22×C3—28no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—28no—
591C22×C3—22no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—21no—
595C22×C3—38no—
596C22×C3—48no—
597C22×C3—44no—
598C22×C3—632no—
599C22×C3—616no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—62no—
603C22×C3—62no—
604C22×C3—64no—
605C22×C3—64no—
606C22×C3—124no—
607C22×C3—124no—
608C22×C3C2×D3×D414yes—
609C22×C3C2×D3×D414yes—
610C22×C3C2×D3×D412yes—
611C22×C3C2×D3×D412yes—
612C22×C3C2×#23714yes—
613C22×C3D3×#4114yes—
614C22×C3C24×D311yescharacteristic
615C22×C3C24×D311yescharacteristic
616C2×D3—232no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—216no—
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—24no—
623C2×D3—24no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3C2×#23718yescomplemented
627C3×C4—24no—
628C3×C4—24no—
629C3×C4—44no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—64no—
633Dic3—22no—
634Dic3—22no—
635Dic3—24no—
636Dic3—34no—
637Dic3—34no—
638Dic3—34no—
639Dic3—34no—
640Dic3—64no—
641Dic3—64no—
642Dic3—64no—
643Dic3—64no—
644Dic3—124no—
645C32C2×#52511yescharacteristic, complemented, Sylow
646C23—24no—
647C23—38no—
648C23—34no—
649C23—32no—
650C23—32no—
651C23—616no—
652C23—632no—
653C23—68no—
654C23—64no—
655C23—64no—
656C23—62no—
657C23—62no—
658C23—64no—
659C23—64no—
660C23#380214yes—
661C23C22×D3212yes—
662C23C22×D3211yescharacteristic
663Q8—188no—
664D4—616no—
665D4—68no—
666D4—68no—
667D4—188no—
668D4—1816no—
669C2×C4—24no—
670C2×C4—32no—
671C2×C4—34no—
672C2×C4—32no—
673C2×C4—68no—
674C2×C4—64no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—94no—
678C2×C4—94no—
679C2×C4—916no—
680C2×C4—92no—
681C2×C4—92no—
682C2×C4—94no—
683C2×C4—1816no—
684C2×C4—1816no—
685C2×C4—188no—
686C2×C4—188no—
687C2×C4—184no—
688C2×C4C22×D3214yes—
689C2×C3—24no—
690C2×C3—24no—
691C2×C3—24no—
692C2×C3—21no—
693C2×C3—22no—
694C2×C3—44no—
695C2×C3—68no—
696C2×C3—122no—
697C2×C3—122no—
698C2×C3#558614yescomplemented
699C2×C3#565614yescomplemented
700C2×C3C22×D3×D411yescharacteristic
701C2×C3C22×D3×D411yescharacteristic
702C2×C3C22×#23712yes—
703C2×C3C2×D3×#4112yes—
704D3—28no—
705D3—42no—
706D3—42no—
707C22—28no—
708C22—24no—
709C22—38no—
710C22—632no—
711C22—616no—
712C22—64no—
713C22—64no—
714C22—62no—
715C22—62no—
716C22—64no—
717C22—64no—
718C22—124no—
719C22—124no—
720C22C2×#380214yes—
721C22C2×#380212yes—
722C22D3×#23714yes—
723C22C23×D3211yescharacteristic
724C4—24no—
725C4—64no—
726C4—62no—
727C4—62no—
728C4—94no—
729C4—94no—
730C4—184no—
731C3—21no—
732C3C2×#558611yescharacteristic, complemented
733C3C2×#565611yescharacteristic, complemented
734C2—24no—
735C2—68no—
736C2—122no—
737C2—122no—
738C2#1059408214yesdirect product factor
739C2C22×#380211yescharacteristic
740C2C2×D3×#23712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C23×D3×Dic3C2semidirect
3. C2×#64086C2semidirect
4. C2×C3×#886C2semidirect
5. C2×C3×#882C2semidirect
6. C2×#63976C2semidirect
7. C2×#63961C2semidirect
8. C2×#63902C2semidirect
9. C2×#63899C2semidirect
10. C2×#63898C2semidirect
11. C2×#63885C2semidirect
12. #10594082C2direct (N × H)
21. C22×#627C22semidirect
23. C22×#625C22semidirect
25. C2×#3805C22semidirect
29. C22×D3×Dic3C22semidirect
30. C22×D3×Dic3C22semidirect
31. C22×D3×Dic3C22semidirect
34. C2×#3750C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. #64086C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×#886C22semidirect
41. C3×#882C22semidirect
42. #63976C22semidirect
43. C2×#3724C22semidirect
44. #63961C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63902C22semidirect
48. #63899C22semidirect
49. #63898C22semidirect
50. #63885C22semidirect
67. C2×#886D3semidirect
69. C2×#882D3semidirect
84. C22×C3⋊Dic3D4semidirect
101. C2×#627C23semidirect
105. C2×#625C23semidirect
114. C2×D3×Dic3C23semidirect
115. C2×D3×Dic3C23semidirect
118. #3750C23semidirect
119. C4×C3⋊Dic3C23semidirect
121. C3×(C2×D3)⋊C4C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. #3724C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
184. C2×(C2×D3)⋊C4C2×D3semidirect
185. C2×C4⋊Dic3C2×D3semidirect
196. #886C2×D3semidirect
198. #882C2×D3semidirect
218. C22×C3×D3#41semidirect
227. C2×C3⋊Dic3C2×D4semidirect
361. (C2×D3)⋊C4C22×D3semidirect
362. C4⋊Dic3C22×D3semidirect
387. C2×C3×D3C2×#41semidirect
465. C22×D3#237semidirect
531. C2×C32#525semidirect
626. C2×D3C2×#237semidirect
645. C32C2×#525semidirect
698. C2×C3#5586semidirect
699. C2×C3#5656semidirect
732. C3C2×#5586semidirect
733. C3C2×#5656semidirect
738. C2#10594082direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C23×D3×Dic32
C2×#640862
C2×C3×#8862
C2×C3×#8822
C2×#639762
C2×#639612
C2×#639022
C2×#638992
C2×#638982
C2×#638852
#105940822
C2×#56563
C2×#55863