Finite Group Databasebeta

← C2×#10594191 #11902636

Subgroups — C2×#10594191 #11902636

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×#64090C211yesmaximal, characteristic, complemented
4C2×C3×#885C212yesmaximal, complemented
5C2×#63982C211yesmaximal, characteristic, complemented
6C2×#63958C212yesmaximal, complemented
7C2×C4×#627C211yesmaximal, characteristic, complemented
8C2×#63915C211yesmaximal, characteristic, complemented
9C2×#63912C211yesmaximal, characteristic, complemented
10C2×#63887C212yesmaximal, complemented
11C2×#63880C212yesmaximal, complemented
12#10594191C2116yesmaximal, direct product factor
13C2×#5677—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×Dic6C2212yes—
19C22×#627C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2212yes—
22C22×#625C2211yescharacteristic
23C22×#624C2212yes—
24C2×#3805—28no—
25C2×#3805C2218yescomplemented
26C22×D3×Dic3C2212yes—
27C2×#3797—28no—
28C2×#3797C2218yescomplemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64090C2218yescomplemented
34C2×C3×#217C2212yes—
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4×Dic3C2212yes—
38C3×#885C22116yescomplemented
39#63982C2218yescomplemented
40C2×#3724C2211yescharacteristic
41C2×Dic3⋊Dic3C2212yes—
42C2×Dic3⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63958C22116yescomplemented
45C4×#627C2218yescomplemented
46#63915C2218yescomplemented
47#63912C2218yescomplemented
48#63887C22116yescomplemented
49#63880C22116yescomplemented
50C22×D3×Q8—32no—
51C22×#237—32no—
52C2×C3×#124—32no—
53C2×#946—32no—
54C2×#938—32no—
55#5677—332no—
56C2×#885—32no—
57C2×#885D312yescomplemented
58C2×#884—32no—
59C2×#884—32no—
60C2×#67⋊C4—32no—
61C2×#67⋊C4—32no—
62C2×#67⋊C4—61no—
63C2×#878—32no—
64C2×#878—32no—
65C2×C4×D12—32no—
66C2×C4×Dic6—32no—
67C24×C32C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×#638—24no—
73C2×#638C2314yes—
74C22×C3⋊Dic3—24no—
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2314yes—
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3C2314yes—
81C2×C3×#67—28no—
82C2×C3×#67C2318yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C2×C3×Dic6—28no—
87C2×C3×Dic6C2318yes—
88C2×#627—24no—
89C2×#627D418yescomplemented
90C2×#627C2314yes—
91C2×#627C2314yes—
92C2×#626—28no—
93C2×#626C2318yes—
94C2×#625—24no—
95C2×#625C2314yes—
96C2×#624—28no—
97C2×#624C2318yes—
98#3805—232no—
99C2×D3×Dic3—28no—
100C2×D3×Dic3C2318yes—
101#3797—232no—
102C32×C22⋊C4C2314yes—
103#3752C2314yes—
104#3750C2314yes—
105C4×C3⋊Dic3C2314yes—
106C3×#217C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×(C2×D3)⋊C4C2318yes—
109C3×C4×Dic3C2318yes—
110#3724C2314yes—
111Dic3⋊Dic3C2318yes—
112Dic3⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#548—91noSylow
115C22×C3×Q8—32no—
116C22×C3×D4—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67—32no—
120C22×#67—61no—
121C22×#67C2×D312yes—
122C23×Dic3—32no—
123C23×Dic3—32no—
124C23×Dic3—61no—
125C2×D3×Q8—316no—
126C2×D3×Q8—616no—
127C2×#237—316no—
128C2×#237—616no—
129C22×D12—32no—
130C22×C4×D3—32no—
131C22×C4×D3—32no—
132C22×C4×D3—32no—
133C22×C4×D3—32no—
134C22×C4×D3—61no—
135C22×Dic6—32no—
136C22×Dic6—32no—
137C22×Dic6C2×D312yes—
138C3×#124—316no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—32no—
143C2×C3×C22⋊C4C2×D312yes—
144C2×C3×C42—32no—
145C2×#217—32no—
146C2×#217C2×D312yes—
147#946—316no—
148#938—316no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—61no—
152C2×(C2×D3)⋊C4C2×D312yes—
153C2×(C2×D3)⋊C4C2×D312yes—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—61no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3—61no—
163C2×C4×Dic3C2×D312yes—
164#885—316no—
165#885C2×D3116yescomplemented
166#884—316no—
167#884—316no—
168#67⋊C4—316no—
169#67⋊C4—316no—
170#67⋊C4—68no—
171#878—316no—
172#878—316no—
173C4×D12—316no—
174C4×Dic6—316no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32C2412yes—
179C23×C32C2411yescharacteristic
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3#4114yescomplemented
183C22×C3⋊D3C2412yes—
184C22×C3×D3—24no—
185C22×C3×D3—24no—
186C22×C3×D3—24no—
187C22×C3×D3C2414yes—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4C2412yes—
191C2×C32×C4C2412yes—
192#638—28no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—28no—
196C2×C3⋊Dic3C2×D414yes—
197C2×C3⋊Dic3C2412yes—
198C2×C3⋊Dic3C2412yes—
199C2×C3⋊Dic3C2412yes—
200C4×C3⋊D3—28no—
201C3×#67—216no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3C2×D418yes—
205C2×C3×Dic3C2414yes—
206C2×C3×Dic3C2414yes—
207C2×C3×Dic3C2414yes—
208C3×Dic6—216no—
209#627—28no—
210#627C2×D4116yescomplemented
211#626—216no—
212#625—28no—
213#624—216no—
214D3×Dic3—216no—
215C22×#41—91no—
216C23×Q8—91no—
217#548—916no—
218C2×#124—32no—
219C2×#124—91no—
220C2×C22⋊Q8—91no—
221C2×C22⋊Q8—92no—
222C2×#121—91no—
223C2×#121—92no—
224C2×C4×Q8—91no—
225C2×C4×D4—92no—
226C2×C4×D4—91no—
227C24×C3—21no—
228C24×C3—32no—
229C24×C3C22×D312yes—
230C23×D3—32no—
231C23×D3—61no—
232C23×D3C22×D312yes—
233C2×C3×Q8—38no—
234C2×C3×Q8—68no—
235C2×C3×D4—38no—
236C2×C3×D4—68no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D312yes—
244C2×#67—28no—
245C2×#67—38no—
246C2×#67—38no—
247C2×#67—38no—
248C2×#67—64no—
249C2×#67—68no—
250C2×#67—68no—
251C2×#67—68no—
252C2×#67—68no—
253C2×#67C22×D318yes—
254C22×Dic3—32no—
255C22×Dic3—38no—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—38no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261C22×Dic3—64no—
262C22×Dic3—61no—
263C22×Dic3—68no—
264C22×Dic3—68no—
265C22×Dic3—124no—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D312yes—
269D3×Q8—664no—
270#237—664no—
271C2×D12—38no—
272C2×D12—68no—
273C2×C4×D3—38no—
274C2×C4×D3—38no—
275C2×C4×D3—38no—
276C2×C4×D3—38no—
277C2×C4×D3—64no—
278C2×C4×D3—68no—
279C2×C4×D3—68no—
280C2×C4×D3—68no—
281C2×C4×D3—68no—
282C2×C4×D3—124no—
283C2×Dic6—28no—
284C2×Dic6—316no—
285C2×Dic6—38no—
286C2×Dic6—38no—
287C2×Dic6—68no—
288C2×Dic6C22×D318yes—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C22⋊C4C22×D318yes—
294C3×C42—38no—
295#217—38no—
296#217C22×D318yes—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—64no—
300(C2×D3)⋊C4C22×D318yes—
301(C2×D3)⋊C4C22×D318yes—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—64no—
309C4×Dic3—38no—
310C4×Dic3—64no—
311C4×Dic3C22×D318yes—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—44no—
316C22×C32C22×D412yes—
317C22×C32C2×#4112yes—
318C22×C322−1+412yes—
319C22×C32C2511yescharacteristic
320C2×C3⋊D3—28no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3C2×#4114yescomplemented
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—24no—
327C2×C3×D3—48no—
328C32×C4—22no—
329C32×C4—22no—
330C3⋊Dic3—22no—
331C3⋊Dic3—22no—
332C3⋊Dic3C22×D414yes—
333C3×Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3C22×D418yes—
336C2×#41—98no—
337C2×#41—188no—
338C22×Q8—32no—
339C22×Q8—91no—
340C22×Q8—91no—
341C22×Q8—98no—
342C22×Q8—188no—
343C22×D4—32no—
344C22×D4—92no—
345C22×D4—91no—
346C22×D4—91no—
347C23×C4—92no—
348C23×C4—92no—
349C23×C4—91no—
350C23×C4—91no—
351#124—316no—
352#124—98no—
353C22⋊Q8—98no—
354C22⋊Q8—916no—
355#121—98no—
356#121—916no—
357C4×Q8—98no—
358C4×D4—916no—
359C4×D4—98no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—91no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4—32no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4D3211yescharacteristic
370C2×C42—32no—
371C2×C42—91no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—34no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—64no—
382C23×C3—64no—
383C23×C3—64no—
384C23×C3C23×D314yes—
385C23×C3C23×D312yes—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—38no—
390C22×D3—34no—
391C22×D3—64no—
392C22×D3—62no—
393C22×D3—64no—
394C22×D3—64no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3C23×D314yes—
398C3×Q8—616no—
399C3×D4—616no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—38no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—34no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—64no—
411C2×C3×C4—64no—
412C2×C3×C4C23×D314yes—
413C2×C3×C4C23×D314yes—
414#67—216no—
415#67—616no—
416#67—616no—
417#67—616no—
418#67—616no—
419C2×Dic3—24no—
420C2×Dic3—24no—
421C2×Dic3—38no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—616no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—64no—
433C2×Dic3—616no—
434C2×Dic3—128no—
435C2×Dic3—122no—
436C2×Dic3D3×D418yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D314yes—
439C2×Dic3C23×D314yes—
440D12—616no—
441C4×D3—616no—
442C4×D3—616no—
443C4×D3—616no—
444C4×D3—616no—
445C4×D3—128no—
446Dic6—216no—
447Dic6—332no—
448Dic6—616no—
449C2×C32—42no—
450C2×C32#54814yescomplemented
451C2×C32C23×D411yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C2×C32C2×2−1+411yescharacteristic
454C3⋊D3—24no—
455C3×D3—44no—
456C24—32no—
457C24—91no—
458C24C2×D3211yescharacteristic
459#41—1832no—
460C2×Q8—38no—
461C2×Q8—68no—
462C2×Q8—94no—
463C2×Q8—98no—
464C2×Q8—94no—
465C2×Q8—184no—
466C2×Q8—1832no—
467C2×D4—38no—
468C2×D4—68no—
469C2×D4—98no—
470C2×D4—94no—
471C2×D4—94no—
472C2×D4—188no—
473C2×D4—184no—
474C2×D4—184no—
475C22×C4—32no—
476C22×C4—32no—
477C22×C4—32no—
478C22×C4—98no—
479C22×C4—98no—
480C22×C4—91no—
481C22×C4—94no—
482C22×C4—91no—
483C22×C4—91no—
484C22×C4—94no—
485C22×C4—184no—
486C22×C4—188no—
487C22×C4—188no—
488C22×C4—184no—
489C22×C4C2×D3211yescharacteristic
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—98no—
492C4⋊C4—94no—
493C4⋊C4—98no—
494C4⋊C4—94no—
495C22⋊C4—38no—
496C22⋊C4—38no—
497C22⋊C4—38no—
498C22⋊C4—98no—
499C22⋊C4—94no—
500C22⋊C4C2×D3214yes—
501C42—38no—
502C42—94no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—48no—
514C22×C3—48no—
515C22×C3—64no—
516C22×C3—64no—
517C22×C3—64no—
518C22×C3—128no—
519C22×C3C2×D3×D414yes—
520C22×C3D3×#4114yes—
521C22×C3#101014yes—
522C22×C3C24×D312yes—
523C2×D3—24no—
524C2×D3—24no—
525C2×D3—24no—
526C2×D3—38no—
527C2×D3—48no—
528C2×D3—64no—
529C2×D3—616no—
530C2×D3—64no—
531C2×D3—64no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—128no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—38no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—64no—
541C3×C4—64no—
542Dic3—24no—
543Dic3—24no—
544Dic3—38no—
545Dic3—64no—
546Dic3—64no—
547Dic3—64no—
548Dic3—64no—
549Dic3—122no—
550Dic3C2×D3×D418yes—
551C32C2×#54811yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—22no—
555C23—34no—
556C23—64no—
557C23—64no—
558C23—64no—
559C23—94no—
560C23—92no—
561C23—182no—
562C23—182no—
563C23C22×D3212yes—
564C23C22×D3211yescharacteristic
565Q8—616no—
566Q8—916no—
567Q8—188no—
568D4—616no—
569D4—1816no—
570D4—188no—
571D4—188no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—38no—
575C2×C4—34no—
576C2×C4—34no—
577C2×C4—34no—
578C2×C4—64no—
579C2×C4—64no—
580C2×C4—94no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—188no—
585C2×C4—1816no—
586C2×C4—1816no—
587C2×C4—188no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4C22×D3212yes—
591C2×C4C22×D3212yes—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—24no—
596C2×C3—44no—
597C2×C3—44no—
598C2×C3—124no—
599C2×C3#567718yescomplemented
600C2×C3C22×D3×D412yes—
601C2×C3C2×D3×#4112yes—
602C2×C3C2×#101012yes—
603D3—44no—
604D3—68no—
605D3—124no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—44no—
610C22—64no—
611C22—64no—
612C22—64no—
613C22—94no—
614C22—128no—
615C22—182no—
616C22—182no—
617C22—188no—
618C22#6430612yes—
619C22#6430912yes—
620C22D32×D412yes—
621C22C23×D3211yescharacteristic
622C4—22no—
623C4—22no—
624C4—38no—
625C4—64no—
626C4—64no—
627C4—94no—
628C4—182no—
629C4—182no—
630C3—21no—
631C3C2×#567712yescomplemented
632C2—42no—
633C2—124no—
634C2—184no—
635C2#1059419114yesdirect product factor
636C2C2×#6430611yescharacteristic
637C2C2×#6430911yescharacteristic
638C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#548
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. C22×#3797C2semidirect
3. C2×#64090C2semidirect
4. C2×C3×#885C2semidirect
5. C2×#63982C2semidirect
6. C2×#63958C2semidirect
7. C2×C4×#627C2semidirect
8. C2×#63915C2semidirect
9. C2×#63912C2semidirect
10. C2×#63887C2semidirect
11. C2×#63880C2semidirect
12. #10594191C2direct (N × H)
25. C2×#3805C22semidirect
28. C2×#3797C22semidirect
33. #64090C22semidirect
38. C3×#885C22semidirect
39. #63982C22semidirect
44. #63958C22semidirect
45. C4×#627C22semidirect
46. #63915C22semidirect
47. #63912C22semidirect
48. #63887C22semidirect
49. #63880C22semidirect
57. C2×#885D3semidirect
89. C2×#627D4semidirect
165. #885C2×D3semidirect
182. C22×C3⋊D3#41semidirect
210. #627C2×D4semidirect
323. C2×C3⋊D3C2×#41semidirect
450. C2×C32#548semidirect
551. C32C2×#548semidirect
599. C2×C3#5677semidirect
631. C3C2×#5677semidirect
635. C2#10594191direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×#37972
C2×#640902
C2×C3×#8852
C2×#639822
C2×#639582
C2×C4×#6272
C2×#639152
C2×#639122
C2×#638872
C2×#638802
#105941912
C2×#56773