Finite Group Databasebeta

← C2×#10594083 #11902528

Subgroups — C2×#10594083 #11902528

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C212yesmaximal, complemented
2C2×#64090C211yesmaximal, characteristic, complemented
3C2×C3×#886C212yesmaximal, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C22×#3724C211yesmaximal, characteristic, complemented
6C2×#63919C211yesmaximal, characteristic, complemented
7C2×#63912C211yesmaximal, characteristic, complemented
8C2×#63902C211yesmaximal, characteristic, complemented
9C2×#63900C211yesmaximal, characteristic, complemented
10C2×#63899C212yesmaximal, complemented
11C2×#63854C212yesmaximal, complemented
12#10594083C2116yesmaximal, direct product factor
13C2×#5655—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2212yes—
19C22×#627C2212yes—
20C22×#626C2212yes—
21C22×#625C2211yescharacteristic
22C22×#624C2212yes—
23C2×#3804—216no—
24C2×#3804C22116yescomplemented
25C22×D3×Dic3C2212yes—
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64090C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×C4⋊Dic3C2212yes—
34C2×C3×C4⋊Dic3C2212yes—
35C3×#886C22116yescomplemented
36#63980C2218yescomplemented
37C2×#3724C2212yes—
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×#3724C2218yescomplemented
42C2×(C2×D3)⋊Dic3C2212yes—
43#63919C2218yescomplemented
44#63912C2218yescomplemented
45#63902C2218yescomplemented
46#63900C2218yescomplemented
47#63899C22116yescomplemented
48#63854C22116yescomplemented
49C22×#237—32no—
50C22×#235—32no—
51C2×C3×#123—32no—
52C2×#939—32no—
53C22×Dic3⋊C4—32no—
54#5655—332no—
55C2×#896—32no—
56C2×#894—32no—
57C2×D3×C4⋊C4—32no—
58C2×#888—32no—
59C2×#886D312yescomplemented
60C2×#884—32no—
61C2×#883—32no—
62C2×#67⋊C4—32no—
63C2×#67⋊C4—32no—
64C2×#67⋊C4—61no—
65C2×#878—32no—
66C24×C32C2311yescharacteristic
67C23×C3⋊D3C2311yescharacteristic
68C23×C3×D3C2312yes—
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638D418yescomplemented
72C2×#638C2314yes—
73C22×C3⋊Dic3—24no—
74C22×C3⋊Dic3C2314yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3C2314yes—
80C2×C3×#67—28no—
81C2×C3×#67C2318yes—
82C22×C3×Dic3—28no—
83C22×C3×Dic3C2318yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×#627—28no—
88C2×#627C2318yes—
89C2×#626—28no—
90C2×#626C2318yes—
91C2×#625—24no—
92C2×#625C2314yes—
93C2×#624—28no—
94C2×#624C2318yes—
95#3804—264no—
96C2×D3×Dic3—28no—
97C2×D3×Dic3C2318yes—
98C32×C22⋊C4C2314yes—
99#3752C2314yes—
100#3750C2314yes—
101C4×C3⋊Dic3C2314yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2318yes—
105C3×C4⋊Dic3C2318yes—
106#3724C2318yes—
107#3724C2314yes—
108#3724C2314yes—
109#3724C2314yes—
110(C2×D3)⋊Dic3C2318yes—
111C2×#547—91noSylow
112C22×C3×D4—32no—
113C23×C3×C4—32no—
114C22×#67—32no—
115C22×#67—32no—
116C22×#67—32no—
117C22×#67—61no—
118C22×#67C2×D312yes—
119C23×Dic3—32no—
120C23×Dic3—32no—
121C23×Dic3—61no—
122C23×Dic3C2×D312yes—
123C2×#237—316no—
124C2×#237—616no—
125C2×#235—316no—
126C2×#235—616no—
127C22×D12—32no—
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—32no—
132C22×C4×D3—61no—
133C22×Dic6—32no—
134C22×Dic6—32no—
135C3×#123—316no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C4⋊C4—32no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4C2×D312yes—
142C2×#217—32no—
143#939—316no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—61no—
147C2×(C2×D3)⋊C4C2×D312yes—
148C2×(C2×D3)⋊C4C2×D312yes—
149C2×C4⋊Dic3C2×D312yes—
150C2×C4⋊Dic3C2×D312yes—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—316no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—61no—
159C2×C4×Dic3—32no—
160C2×C4×Dic3—61no—
161#896—316no—
162#894—316no—
163D3×C4⋊C4—316no—
164#888—316no—
165#886C2×D3116yescomplemented
166#884—316no—
167#883—316no—
168#67⋊C4—316no—
169#67⋊C4—316no—
170#67⋊C4—68no—
171#878—316no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32C2×D414yes—
175C23×C32C2412yes—
176C23×C32C2411yescharacteristic
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3C2×D414yes—
180C22×C3⋊D3C2412yes—
181C22×C3×D3—24no—
182C22×C3×D3—24no—
183C22×C3×D3—24no—
184C22×C3×D3C2414yes—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4C2412yes—
188C2×C32×C4C2412yes—
189#638C2×D4116yescomplemented
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—28no—
192C2×C3⋊Dic3C2×D414yes—
193C2×C3⋊Dic3#4114yescomplemented
194C2×C3⋊Dic3C2412yes—
195C2×C3⋊Dic3C2412yes—
196C2×C3⋊Dic3C2412yes—
197C4×C3⋊D3—28no—
198C3×#67—216no—
199C2×C3×Dic3—24no—
200C2×C3×Dic3—216no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3C2414yes—
204C2×C3×Dic3C2414yes—
205C2×C3×Dic3C2414yes—
206#627—216no—
207#626—216no—
208#625—28no—
209#624—216no—
210D3×Dic3—216no—
211C22×#41—92no—
212#547—916no—
213C2×C4⋊Q8—91no—
214C2×#123—32no—
215C2×#123—92no—
216C2×C22⋊Q8—92no—
217C2×#121—91no—
218C2×#121—91no—
219C2×C4×D4—91no—
220C2×C4×D4—91no—
221C22×C4⋊C4—91no—
222C22×C4⋊C4—91no—
223C24×C3—21no—
224C24×C3—32no—
225C24×C3C22×D312yes—
226C23×D3—32no—
227C23×D3—61no—
228C23×D3C22×D312yes—
229C2×C3×D4—38no—
230C2×C3×D4—68no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—38no—
236C22×C3×C4—32no—
237C22×C3×C4—68no—
238C22×C3×C4C22×D312yes—
239C22×C3×C4C22×D312yes—
240C2×#67—28no—
241C2×#67—316no—
242C2×#67—38no—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67—64no—
246C2×#67—68no—
247C2×#67—68no—
248C2×#67—68no—
249C2×#67C22×D318yes—
250C22×Dic3—28no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—38no—
254C22×Dic3—32no—
255C22×Dic3—38no—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—64no—
259C22×Dic3—61no—
260C22×Dic3—68no—
261C22×Dic3—68no—
262C22×Dic3—124no—
263C22×Dic3C22×D318yes—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D312yes—
267#237—664no—
268#235—664no—
269C2×D12—38no—
270C2×D12—68no—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—38no—
274C2×C4×D3—38no—
275C2×C4×D3—64no—
276C2×C4×D3—68no—
277C2×C4×D3—68no—
278C2×C4×D3—68no—
279C2×C4×D3—68no—
280C2×C4×D3—124no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—68no—
284C2×Dic6—68no—
285C3×C4⋊C4—38no—
286C3×C4⋊C4—38no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—38no—
289C3×C22⋊C4—38no—
290C3×C22⋊C4C22×D318yes—
291#217—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4C22×D318yes—
296(C2×D3)⋊C4C22×D318yes—
297C4⋊Dic3C22×D318yes—
298C4⋊Dic3C22×D318yes—
299Dic3⋊C4—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—64no—
306C4×Dic3—38no—
307C4×Dic3—64no—
308C22×C32—28no—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32C22×D414yes—
312C22×C32C22×D412yes—
313C22×C32C2×#4112yes—
314C22×C322−1+412yes—
315C22×C32C2511yescharacteristic
316C2×C3⋊D3—28no—
317C2×C3⋊D3—22no—
318C2×C3⋊D3—22no—
319C2×C3⋊D3C22×D414yes—
320C2×C3×D3—24no—
321C2×C3×D3—24no—
322C2×C3×D3—24no—
323C2×C3×D3—48no—
324C32×C4—22no—
325C32×C4—22no—
326C3⋊Dic3—22no—
327C3⋊Dic3C22×D414yes—
328C3⋊Dic3C2×#4114yescomplemented
329C3×Dic3—24no—
330C3×Dic3—24no—
331C3×Dic3—24no—
332C2×#41—916no—
333C2×#41—1816no—
334C22×Q8—92no—
335C22×D4—32no—
336C22×D4—92no—
337C22×D4—91no—
338C22×D4—91no—
339C23×C4—32no—
340C23×C4—92no—
341C23×C4—92no—
342C23×C4—91no—
343C23×C4—91no—
344C4⋊Q8—98no—
345#123—316no—
346#123—916no—
347C22⋊Q8—916no—
348#121—98no—
349#121—98no—
350C4×D4—98no—
351C4×D4—98no—
352C2×C4⋊C4—32no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—98no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—98no—
360C2×C4⋊C4—91no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4D3211yescharacteristic
366C2×C42—91no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—24no—
372C23×C3—34no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—64no—
376C23×C3—64no—
377C23×C3—64no—
378C23×C3D3×D418yes—
379C23×C3C23×D314yes—
380C23×C3C23×D312yes—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—38no—
385C22×D3—34no—
386C22×D3—64no—
387C22×D3—62no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—122no—
391C22×D3—122no—
392C22×D3C23×D314yes—
393C3×D4—616no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—64no—
404C2×C3×C4—64no—
405C2×C3×C4—64no—
406C2×C3×C4—616no—
407C2×C3×C4C23×D314yes—
408C2×C3×C4C23×D314yes—
409#67—216no—
410#67—332no—
411#67—616no—
412#67—616no—
413#67—616no—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—216no—
418C2×Dic3—38no—
419C2×Dic3—38no—
420C2×Dic3—34no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—616no—
429C2×Dic3—616no—
430C2×Dic3—64no—
431C2×Dic3—128no—
432C2×Dic3—122no—
433C2×Dic3C23×D314yes—
434C2×Dic3C23×D314yes—
435C2×Dic3C23×D314yes—
436D12—616no—
437C4×D3—616no—
438C4×D3—616no—
439C4×D3—616no—
440C4×D3—616no—
441C4×D3—128no—
442Dic6—616no—
443Dic6—616no—
444C2×C32—24no—
445C2×C32#54714yescomplemented
446C2×C32C23×D411yescharacteristic
447C2×C32C22×#4111yescharacteristic
448C2×C32C2×2−1+411yescharacteristic
449C3⋊D3—24no—
450C3×D3—44no—
451C24—32no—
452C24—91no—
453C24C2×D3211yescharacteristic
454#41—1864no—
455C2×Q8—98no—
456C2×Q8—188no—
457C2×D4—38no—
458C2×D4—68no—
459C2×D4—98no—
460C2×D4—94no—
461C2×D4—98no—
462C2×D4—94no—
463C2×D4—188no—
464C2×D4—184no—
465C22×C4—38no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—68no—
470C22×C4—98no—
471C22×C4—98no—
472C22×C4—91no—
473C22×C4—91no—
474C22×C4—94no—
475C22×C4—91no—
476C22×C4—94no—
477C22×C4—184no—
478C22×C4—188no—
479C22×C4—188no—
480C22×C4—184no—
481C22×C4C2×D3211yescharacteristic
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—38no—
484C4⋊C4—38no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C4⋊C4—94no—
488C4⋊C4—98no—
489C4⋊C4—94no—
490C22⋊C4—38no—
491C22⋊C4—38no—
492C22⋊C4—98no—
493C22⋊C4—94no—
494C22⋊C4C2×D3214yes—
495C42—94no—
496C22×C3—216no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—22no—
500C22×C3—24no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—42no—
505C22×C3—48no—
506C22×C3—42no—
507C22×C3—64no—
508C22×C3—64no—
509C22×C3—64no—
510C22×C3—128no—
511C22×C3C2×D3×D418yes—
512C22×C3C2×D3×D414yes—
513C22×C3D3×#4114yes—
514C22×C3#101014yes—
515C22×C3C24×D312yes—
516C2×D3—24no—
517C2×D3—24no—
518C2×D3—24no—
519C2×D3—38no—
520C2×D3—48no—
521C2×D3—64no—
522C2×D3—616no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—122no—
526C2×D3—128no—
527C2×D3—122no—
528C3×C4—24no—
529C3×C4—24no—
530C3×C4—42no—
531C3×C4—42no—
532C3×C4—64no—
533C3×C4—64no—
534C3×C4—64no—
535Dic3—24no—
536Dic3—24no—
537Dic3—24no—
538Dic3—38no—
539Dic3—38no—
540Dic3—64no—
541Dic3—64no—
542Dic3—64no—
543Dic3—122no—
544C32C2×#54711yescharacteristic, complemented, Sylow
545C23—22no—
546C23—22no—
547C23—34no—
548C23—64no—
549C23—64no—
550C23—64no—
551C23—94no—
552C23—92no—
553C23—182no—
554C23—182no—
555C23#380214yes—
556C23C22×D3212yes—
557C23C22×D3211yescharacteristic
558Q8—1816no—
559D4—616no—
560D4—916no—
561D4—1816no—
562D4—188no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—34no—
566C2×C4—34no—
567C2×C4—34no—
568C2×C4—64no—
569C2×C4—64no—
570C2×C4—616no—
571C2×C4—64no—
572C2×C4—94no—
573C2×C4—94no—
574C2×C4—92no—
575C2×C4—92no—
576C2×C4—92no—
577C2×C4—188no—
578C2×C4—1816no—
579C2×C4—1816no—
580C2×C4—188no—
581C2×C4—182no—
582C2×C4C22×D3212yes—
583C2×C4C22×D3212yes—
584C2×C3—28no—
585C2×C3—24no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—44no—
590C2×C3—124no—
591C2×C3#565518yescomplemented
592C2×C3C22×D3×D412yes—
593C2×C3C2×D3×#4112yes—
594C2×C3C2×#101012yes—
595D3—44no—
596D3—68no—
597D3—124no—
598C22—28no—
599C22—22no—
600C22—22no—
601C22—64no—
602C22—64no—
603C22—64no—
604C22—94no—
605C22—128no—
606C22—188no—
607C22—182no—
608C22—182no—
609C22C2×#380214yes—
610C22C2×#380212yes—
611C22#6430912yes—
612C22#6431212yes—
613C22C23×D3211yescharacteristic
614C4—22no—
615C4—22no—
616C4—64no—
617C4—64no—
618C4—64no—
619C4—94no—
620C4—94no—
621C4—182no—
622C3—21no—
623C3C2×#565512yescomplemented
624C2—24no—
625C2—124no—
626C2—184no—
627C2#1059408314yesdirect product factor
628C2C22×#380211yescharacteristic
629C2C2×#6430911yescharacteristic
630C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#547
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×#3804C2semidirect
2. C2×#64090C2semidirect
3. C2×C3×#886C2semidirect
4. C2×#63980C2semidirect
5. C22×#3724C2semidirect
6. C2×#63919C2semidirect
7. C2×#63912C2semidirect
8. C2×#63902C2semidirect
9. C2×#63900C2semidirect
10. C2×#63899C2semidirect
11. C2×#63854C2semidirect
12. #10594083C2direct (N × H)
24. C2×#3804C22semidirect
30. #64090C22semidirect
35. C3×#886C22semidirect
36. #63980C22semidirect
41. C2×#3724C22semidirect
43. #63919C22semidirect
44. #63912C22semidirect
45. #63902C22semidirect
46. #63900C22semidirect
47. #63899C22semidirect
48. #63854C22semidirect
59. C2×#886D3semidirect
71. C2×#638D4semidirect
165. #886C2×D3semidirect
189. #638C2×D4semidirect
193. C2×C3⋊Dic3#41semidirect
328. C3⋊Dic3C2×#41semidirect
445. C2×C32#547semidirect
544. C32C2×#547semidirect
591. C2×C3#5655semidirect
623. C3C2×#5655semidirect
627. C2#10594083direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C2×#640902
C2×C3×#8862
C2×#639802
C22×#37242
C2×#639192
C2×#639122
C2×#639022
C2×#639002
C2×#638992
C2×#638542
#105940832
C2×#56553