Finite Group Databasebeta

← C2×#10594521 #11902633

Subgroups — C2×#10594521 #11902633

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×#3798C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×#64102C211yesmaximal, characteristic, complemented
4C2×C3×#896C212yesmaximal, complemented
5C2×#63915C211yesmaximal, characteristic, complemented
6C2×#63912C211yesmaximal, characteristic, complemented
7C2×#63910C212yesmaximal, complemented
8C2×#63907C212yesmaximal, complemented
9C2×#63904C212yesmaximal, complemented
10C2×#63865C211yesmaximal, characteristic, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594521C2116yesmaximal, direct product factor
13C2×#5633—32nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×Dic6C2212yes—
19C22×#627C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2212yes—
22C22×#626C2212yes—
23C22×#625C2211yescharacteristic
24C22×#624C2212yes—
25C2×#3798—28no—
26C2×#3798C2218yescomplemented
27C2×#3797—28no—
28C2×#3797C2218yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64102C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2212yes—
38C3×#896C22116yescomplemented
39C2×#3724C2211yescharacteristic
40C2×#3722C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×Dic32C2212yes—
43#63915C2218yescomplemented
44#63912C2218yescomplemented
45#63910C22116yescomplemented
46#63907C22116yescomplemented
47#63904C22116yescomplemented
48#63865C2218yescomplemented
49#63838C2218yescomplemented
50C22×D3×Q8—32no—
51C22×#235—32no—
52C2×C3×C22⋊Q8—32no—
53C2×#947—32no—
54C2×C4×#67—32no—
55#5633—332no—
56C2×#896—32no—
57C2×#896D312yescomplemented
58C2×#895—32no—
59C2×#893—32no—
60C2×#893—32no—
61C2×#893—61no—
62C2×#887—32no—
63C2×#885—32no—
64C2×#885—32no—
65C2×#884—32no—
66C2×#884—32no—
67C23×C3⋊D3C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C2×C4⋊(C3⋊D3)—24no—
76C2×C4⋊(C3⋊D3)C2314yes—
77C2×C4×C3⋊D3—24no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3C2314yes—
80C2×C4×C3⋊D3C2314yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C2×C3×C4×D3—28no—
85C2×C3×C4×D3C2318yes—
86C2×C3×Dic6—28no—
87C2×C3×Dic6C2318yes—
88C2×#627—24no—
89C2×#627D418yescomplemented
90C2×#627C2314yes—
91C2×#627C2314yes—
92C2×#626—28no—
93C2×#626—28no—
94C2×#626C2318yes—
95C2×#626C2318yes—
96C2×#625—24no—
97C2×#625C2314yes—
98C2×#624—28no—
99C2×#624C2318yes—
100#3798—232no—
101#3797—232no—
102C32×C4⋊C4C2314yes—
103#3752C2314yes—
104#3752C2314yes—
105C4×C3⋊Dic3C2314yes—
106C3×(C2×D3)⋊C4C2318yes—
107C3×(C2×D3)⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2318yes—
110#3724C2314yes—
111#3722C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2318yes—
114C2×#548—91noSylow
115C22×C3×Q8—32no—
116C23×C3×C4—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67—32no—
120C2×D3×Q8—316no—
121C2×D3×Q8—616no—
122C2×#235—316no—
123C2×#235—616no—
124C22×D12—32no—
125C22×D12—32no—
126C22×D12—32no—
127C22×D12—61no—
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—32no—
132C22×C4×D3—61no—
133C22×C4×D3—61no—
134C22×C4×D3C2×D312yes—
135C22×Dic6—32no—
136C22×Dic6—32no—
137C22×Dic6C2×D312yes—
138C3×C22⋊Q8—316no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—32no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4C2×D312yes—
143C2×C3×C22⋊C4—32no—
144C2×C3×C22⋊C4—32no—
145C2×#217—32no—
146#947—316no—
147C4×#67—316no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—61no—
154C2×(C2×D3)⋊C4—61no—
155C2×(C2×D3)⋊C4C2×D312yes—
156C2×(C2×D3)⋊C4C2×D312yes—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4C2×D312yes—
159C2×Dic3⋊C4C2×D312yes—
160C2×C4×Dic3—32no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3—32no—
163C2×C4×Dic3—61no—
164#896—316no—
165#896C2×D3116yescomplemented
166#895—316no—
167#893—316no—
168#893—316no—
169#893—68no—
170#887—316no—
171#885—316no—
172#885—316no—
173#884—316no—
174#884—316no—
175C23×C32C2411yescharacteristic
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3#4114yescomplemented
182C22×C3⋊D3C2412yes—
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×C4—22no—
191C2×C32×C4C2412yes—
192C2×C32×C4C2412yes—
193C2×C32×C4C2412yes—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3C2×D414yes—
196C2×C3⋊Dic3C2412yes—
197C2×C3⋊Dic3C2412yes—
198C4⋊(C3⋊D3)—28no—
199C4×C3⋊D3—28no—
200C4×C3⋊D3—28no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3C2×D418yes—
204C2×C3×Dic3C2414yes—
205C2×C3×Dic3C2414yes—
206C2×C3×Dic3C2414yes—
207C3×C4×D3—216no—
208C3×Dic6—216no—
209#627—28no—
210#627C2×D4116yescomplemented
211#626—216no—
212#626—216no—
213#625—28no—
214#624—216no—
215C22×#41—91no—
216C23×Q8—91no—
217#548—916no—
218C2×#124—91no—
219C2×#124—92no—
220C2×C22⋊Q8—32no—
221C2×C22⋊Q8—91no—
222C2×#121—91no—
223C2×#121—92no—
224C2×C4×Q8—91no—
225C2×C4×D4—92no—
226C2×C4×D4—91no—
227C24×C3—32no—
228C23×D3—32no—
229C23×D3—32no—
230C23×D3—61no—
231C23×D3—61no—
232C23×D3C22×D312yes—
233C2×C3×Q8—38no—
234C2×C3×Q8—68no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—38no—
242C22×C3×C4—68no—
243C22×C3×C4C22×D312yes—
244C22×C3×C4C22×D312yes—
245C22×C3×C4C22×D312yes—
246C2×#67—38no—
247C2×#67—38no—
248C2×#67—38no—
249C2×#67—68no—
250C2×#67—68no—
251C2×#67—68no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D312yes—
259D3×Q8—664no—
260#235—664no—
261C2×D12—38no—
262C2×D12—38no—
263C2×D12—38no—
264C2×D12—64no—
265C2×D12—68no—
266C2×D12—68no—
267C2×D12—68no—
268C2×D12—68no—
269C2×C4×D3—28no—
270C2×C4×D3—38no—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—38no—
274C2×C4×D3—64no—
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×C4×D3—124no—
282C2×C4×D3C22×D318yes—
283C2×Dic6—28no—
284C2×Dic6—316no—
285C2×Dic6—38no—
286C2×Dic6—38no—
287C2×Dic6—68no—
288C2×Dic6C22×D318yes—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—38no—
292C3×C4⋊C4C22×D318yes—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—38no—
295#217—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303(C2×D3)⋊C4C22×D318yes—
304(C2×D3)⋊C4C22×D318yes—
305Dic3⋊C4—38no—
306Dic3⋊C4C22×D318yes—
307Dic3⋊C4C22×D318yes—
308C4×Dic3—38no—
309C4×Dic3—38no—
310C4×Dic3—38no—
311C4×Dic3—64no—
312C22×C32C22×D412yes—
313C22×C32C2×#4112yes—
314C22×C322−1+412yes—
315C22×C32C2511yescharacteristic
316C2×C3⋊D3—22no—
317C2×C3⋊D3—28no—
318C2×C3⋊D3—22no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—22no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—44no—
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—
330C32×C4—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—92no—
344C22×D4—92no—
345C22×D4—91no—
346C22×D4—91no—
347C23×C4—32no—
348C23×C4—92no—
349C23×C4—91no—
350C23×C4—91no—
351#124—98no—
352#124—916no—
353C22⋊Q8—316no—
354C22⋊Q8—98no—
355#121—98no—
356#121—916no—
357C4×Q8—98no—
358C4×D4—916no—
359C4×D4—98no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4D3211yescharacteristic
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—91no—
370C2×C42—92no—
371C2×C42—91no—
372C23×C3—21no—
373C23×C3—34no—
374C23×C3—64no—
375C23×C3—64no—
376C23×C3—64no—
377C23×C3C23×D312yes—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—38no—
382C22×D3—34no—
383C22×D3—34no—
384C22×D3—64no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—64no—
391C22×D3—64no—
392C22×D3—64no—
393C22×D3—122no—
394C22×D3—122no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3C23×D314yes—
398C3×Q8—616no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—38no—
407C2×C3×C4—34no—
408C2×C3×C4—34no—
409C2×C3×C4—34no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—616no—
413C2×C3×C4—64no—
414C2×C3×C4—64no—
415C2×C3×C4C23×D314yes—
416C2×C3×C4C23×D314yes—
417C2×C3×C4C23×D314yes—
418#67—616no—
419#67—616no—
420#67—616no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—38no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—64no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—64no—
430C2×Dic3—122no—
431C2×Dic3D3×D418yes—
432C2×Dic3C23×D314yes—
433C2×Dic3C23×D314yes—
434C2×Dic3C23×D314yes—
435D12—616no—
436D12—616no—
437D12—616no—
438D12—616no—
439C4×D3—216no—
440C4×D3—616no—
441C4×D3—616no—
442C4×D3—616no—
443C4×D3—616no—
444C4×D3—128no—
445C4×D3—128no—
446Dic6—216no—
447Dic6—332no—
448Dic6—616no—
449C2×C32#54814yescomplemented
450C2×C32C23×D411yescharacteristic
451C2×C32C22×#4111yescharacteristic
452C2×C32C2×2−1+411yescharacteristic
453C3⋊D3—24no—
454C3⋊D3—42no—
455C3×D3—44no—
456C24—32no—
457C24—91no—
458C24—91no—
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—98no—
468C2×D4—98no—
469C2×D4—94no—
470C2×D4—94no—
471C2×D4—184no—
472C2×D4—188no—
473C2×D4—188no—
474C2×D4—184no—
475C22×C4—32no—
476C22×C4—32no—
477C22×C4—32no—
478C22×C4—38no—
479C22×C4—68no—
480C22×C4—98no—
481C22×C4—91no—
482C22×C4—91no—
483C22×C4—94no—
484C22×C4—94no—
485C22×C4—184no—
486C22×C4—184no—
487C22×C4—188no—
488C22×C4C2×D3211yescharacteristic
489C22×C4C2×D3211yescharacteristic
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—38no—
492C4⋊C4—38no—
493C4⋊C4—94no—
494C4⋊C4C2×D3214yes—
495C22⋊C4—38no—
496C22⋊C4—38no—
497C22⋊C4—98no—
498C22⋊C4—98no—
499C22⋊C4—94no—
500C22⋊C4—94no—
501C42—98no—
502C42—94no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—21no—
507C22×C3—64no—
508C22×C3—64no—
509C22×C3—64no—
510C22×C3—128no—
511C22×C3C2×D3×D414yes—
512C22×C3#100714yes—
513C22×C3D3×#4114yes—
514C22×C3C24×D312yes—
515C2×D3—24no—
516C2×D3—24no—
517C2×D3—24no—
518C2×D3—38no—
519C2×D3—48no—
520C2×D3—64no—
521C2×D3—616no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—64no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—128no—
532C2×D3—122no—
533C2×D3—128no—
534C2×D3—128no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—24no—
538C3×C4—24no—
539C3×C4—38no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—64no—
543C3×C4—64no—
544Dic3—24no—
545Dic3—24no—
546Dic3—38no—
547Dic3—64no—
548Dic3—64no—
549Dic3—122no—
550Dic3C2×D3×D418yes—
551C32C2×#54811yescharacteristic, complemented, Sylow
552C23—34no—
553C23—64no—
554C23—64no—
555C23—64no—
556C23—94no—
557C23—92no—
558C23—92no—
559C23—182no—
560C23—182no—
561C23—182no—
562C23—182no—
563C23—182no—
564C23C22×D3211yescharacteristic
565Q8—616no—
566Q8—916no—
567Q8—188no—
568D4—188no—
569D4—1816no—
570D4—1816no—
571D4—188no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—38no—
576C2×C4—34no—
577C2×C4—34no—
578C2×C4—34no—
579C2×C4—616no—
580C2×C4—64no—
581C2×C4—64no—
582C2×C4—94no—
583C2×C4—92no—
584C2×C4—92no—
585C2×C4—188no—
586C2×C4—188no—
587C2×C4—1816no—
588C2×C4—182no—
589C2×C4C22×D3212yes—
590C2×C4C22×D3212yes—
591C2×C4C22×D3212yes—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—24no—
596C2×C3—124no—
597C2×C3#563318yescomplemented
598C2×C3C22×D3×D412yes—
599C2×C3C2×#100712yes—
600C2×C3C2×D3×#4112yes—
601D3—44no—
602D3—68no—
603D3—124no—
604D3—124no—
605D3—124no—
606C22—64no—
607C22—64no—
608C22—64no—
609C22—94no—
610C22—128no—
611C22—182no—
612C22—182no—
613C22—188no—
614C22—182no—
615C22—182no—
616C22—182no—
617C22—364no—
618C22#6430612yes—
619C22D32×D412yes—
620C22#6431612yes—
621C22C23×D3211yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—38no—
626C4—64no—
627C4—64no—
628C4—94no—
629C4—182no—
630C3—21no—
631C3C2×#563312yescomplemented
632C2—124no—
633C2—184no—
634C2—362no—
635C2#1059452114yesdirect product factor
636C2C2×#6430611yescharacteristic
637C2C2×D32×D411yescharacteristic
638C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3798C2semidirect
2. C22×#3797C2semidirect
3. C2×#64102C2semidirect
4. C2×C3×#896C2semidirect
5. C2×#63915C2semidirect
6. C2×#63912C2semidirect
7. C2×#63910C2semidirect
8. C2×#63907C2semidirect
9. C2×#63904C2semidirect
10. C2×#63865C2semidirect
11. C2×#63838C2semidirect
12. #10594521C2direct (N × H)
26. C2×#3798C22semidirect
28. C2×#3797C22semidirect
33. #64102C22semidirect
38. C3×#896C22semidirect
43. #63915C22semidirect
44. #63912C22semidirect
45. #63910C22semidirect
46. #63907C22semidirect
47. #63904C22semidirect
48. #63865C22semidirect
49. #63838C22semidirect
57. C2×#896D3semidirect
89. C2×#627D4semidirect
165. #896C2×D3semidirect
181. C22×C3⋊D3#41semidirect
210. #627C2×D4semidirect
323. C2×C3⋊D3C2×#41semidirect
449. C2×C32#548semidirect
551. C32C2×#548semidirect
597. C2×C3#5633semidirect
631. C3C2×#5633semidirect
635. C2#10594521direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C22×#37972
C2×#641022
C2×C3×#8962
C2×#639152
C2×#639122
C2×#639102
C2×#639072
C2×#639042
C2×#638652
C2×#638382
#105945212
C2×#56333