Finite Group Databasebeta

← C2×#10595367 #11900839

Subgroups — C2×#10595367 #11900839

Order 1152.

2481 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595367C2116yesmaximal, direct product factor
5C2×#63919C211yesmaximal, characteristic, complemented
6C2×#63899C212yesmaximal
7C2×#63877C212yesmaximal
8C2×C4×D3×Dic3C211yesmaximal, characteristic
9C2×#63857C211yesmaximal, characteristic
10C2×#63847C212yesmaximal, complemented
11C2×#63844C211yesmaximal, characteristic, complemented
12C2×#63837C212yesmaximal, complemented
13C2×#5622—31nomaximal
14C2×#5578—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#627C2212yes—
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21#64153C2218yescomplemented
22C2×#3750C2212yes—
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C3×#946C2218yes—
26C3×Q8×Dic3C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2212yes—
34C2×#3724C2212yes—
35C2×#3724C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63919C2218yescomplemented
42#63899C22116yes—
43#63877C22116yes—
44C4×D3×Dic3C2218yes—
45#63857C2218yes—
46#63847C22116yescomplemented
47#63844C2218yescomplemented
48#63837C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#946D311yescharacteristic
52C2×Q8×Dic3D311yescharacteristic, complemented
53C2×#944—31no—
54C2×#944—31no—
55C2×#944—61no—
56C2×#924—31no—
57C22×C4×Dic3—31no—
58#5622—316no—
59#5578—316no—
60C2×#897—31no—
61C2×#896—32no—
62C2×#889—32no—
63C2×#889—32no—
64C2×#888—31no—
65C2×#888—31no—
66C2×#887—31no—
67C2×#887—32no—
68C2×#878—32no—
69C2×#877—32no—
70C2×#872—32no—
71C2×C42×D3—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—32no—
74C23×C3×D3C2311yescharacteristic
75C2×C32×Q8—24no—
76C2×C32×Q8C2314yes—
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×#634—24no—
83C2×#634C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×#627—28no—
92C2×#627C2318yes—
93C2×D3×Dic3—24no—
94C2×D3×Dic3Q818yescomplemented
95C2×D3×Dic3C2314yes—
96C2×D3×Dic3C2314yes—
97#3750C2318yes—
98#3750C2318yes—
99C4×C3⋊Dic3C2314yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×C4⋊Dic3C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2314yes—
104C3×Dic3⋊C4C2318yes—
105C3×C4×Dic3C2318yes—
106C3×C4×Dic3C2314yes—
107#3724C2318yes—
108#3724C2318yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111Dic32C2314yes—
112Dic32C2318yes—
113Dic32C2314yes—
114C2×#533—91noSylow
115C22×C3×Q8—21no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C23×C3×C4—31no—
119C23×Dic3—31no—
120C23×Dic3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3C2×D311yescharacteristic
124C22×Dic6—31no—
125C22×Dic6—31no—
126C22×Dic6—32no—
127C22×Dic6—32no—
128C22×Dic6—61no—
129C3×C22⋊Q8—38no—
130C3×C4×Q8—38no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C42—31no—
137C2×C3×C42—32no—
138C2×#217—32no—
139#946C2×D318yes—
140Q8×Dic3C2×D318yescomplemented
141#944—38no—
142#944—38no—
143#944—68no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4C2×D312yes—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D312yes—
149C2×C4⋊Dic3C2×D311yescharacteristic
150#924—38no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—62no—
161C2×Dic3⋊C4—62no—
162C2×Dic3⋊C4C2×D312yes—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—38no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D312yes—
174C2×C4×Dic3C2×D311yescharacteristic
175#897—38no—
176#896—316no—
177#889—316no—
178#889—316no—
179#888—38no—
180#888—38no—
181#887—316no—
182#887—38no—
183#878—316no—
184#877—316no—
185#872—316no—
186C42×D3—38no—
187C4×Dic6—38no—
188C4×Dic6—316no—
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3C2×Q814yes—
193C22×C3×D3C2412yes—
194C32×Q8—28no—
195C2×C32×C4—24no—
196C2×C32×C4#4114yes—
197C2×C32×C4C2414yes—
198C2×C32×C4C2412yes—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3C2×Q814yes—
201C2×C3⋊Dic3#4114yes—
202C2×C3⋊Dic3C2414yes—
203C2×C3⋊Dic3C2412yes—
204C2×C3⋊Dic3C2412yes—
205#634—28no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3C2×Q814yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C3×C4×D3—28no—
217#627—216no—
218D3×Dic3—28no—
219D3×Dic3C2×Q8116yescomplemented
220#533—916no—
221C2×C4⋊Q8—91no—
222C2×C4⋊Q8—91no—
223C2×#125—92no—
224C2×C22⋊Q8—31no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—31no—
228C2×C4×Q8—92no—
229C2×C4×Q8—91no—
230C2×#117—92no—
231C22×C42—91no—
232C24×C3—31no—
233C23×D3C22×D311yescharacteristic
234C2×C3×Q8—24no—
235C2×C3×Q8—24no—
236C2×C3×Q8—24no—
237C2×C3×Q8—44no—
238C2×C3×Q8C22×D314yes—
239C2×C3×Q8C22×D314yes—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4—34no—
248C22×C3×C4—64no—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—38no—
258C22×Dic3—34no—
259C22×Dic3—32no—
260C22×Dic3—32no—
261C22×Dic3—34no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—62no—
265C22×Dic3—64no—
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D311yescharacteristic
271C2×C4×D3—24no—
272C2×C4×D3—38no—
273C2×C4×D3—34no—
274C2×C4×D3—34no—
275C2×C4×D3—64no—
276C2×C4×D3C22×D314yes—
277C2×Dic6—34no—
278C2×Dic6—34no—
279C2×Dic6—38no—
280C2×Dic6—38no—
281C2×Dic6—64no—
282C2×Dic6—68no—
283C2×Dic6—68no—
284C2×Dic6—64no—
285C2×Dic6—64no—
286C2×Dic6—124no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C22⋊C4—38no—
292C3×C42—34no—
293C3×C42—38no—
294#217—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4C22×D318yes—
297C4⋊Dic3—38no—
298C4⋊Dic3C22×D314yes—
299C4⋊Dic3C22×D318yes—
300C4⋊Dic3C22×D314yes—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—68no—
311Dic3⋊C4—68no—
312Dic3⋊C4C22×D318yes—
313C4×Dic3—34no—
314C4×Dic3—34no—
315C4×Dic3—34no—
316C4×Dic3—38no—
317C4×Dic3—34no—
318C4×Dic3—38no—
319C4×Dic3—34no—
320C4×Dic3—34no—
321C4×Dic3—64no—
322C4×Dic3C22×D318yes—
323C4×Dic3C22×D314yes—
324C22×C32C22×Q812yes—
325C22×C32C2×#4112yes—
326C22×C32C2×#4112yes—
327C22×C32C2511yescharacteristic
328C2×C3×D3—28no—
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3C22×Q814yes—
332C32×C4—24no—
333C32×C4C2×#4114yes—
334C3⋊Dic3—24no—
335C3⋊Dic3C22×Q814yes—
336C3⋊Dic3C2×#4114yes—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—24no—
340C3×Dic3—22no—
341C3×Dic3C22×Q814yes—
342C22×Q8—92no—
343C22×Q8—91no—
344C22×Q8D3211yescharacteristic
345C23×C4—31no—
346C23×C4—91no—
347C23×C4—91no—
348C4⋊Q8—98no—
349C4⋊Q8—98no—
350#125—916no—
351C22⋊Q8—38no—
352C22⋊Q8—916no—
353C22⋊Q8—98no—
354C4×Q8—38no—
355C4×Q8—98no—
356C4×Q8—916no—
357#117—916no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—92no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—92no—
369C2×C42—32no—
370C2×C42—31no—
371C2×C42—98no—
372C2×C42—92no—
373C2×C42—91no—
374C2×C42—91no—
375C2×C42—91no—
376C23×C3—21no—
377C23×C3—34no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C22×D3—22no—
384C22×D3—22no—
385C22×D3D3×Q814yes—
386C22×D3C23×D312yes—
387C3×Q8—28no—
388C3×Q8—28no—
389C3×Q8—48no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—44no—
402C2×C3×C4—62no—
403C2×C3×C4—64no—
404C2×C3×C4—64no—
405C2×C3×C4—62no—
406C2×C3×C4—68no—
407C2×C3×C4#23514yes—
408C2×C3×C4#23714yes—
409C2×C3×C4C23×D314yes—
410C2×C3×C4C23×D314yes—
411C2×C3×C4C23×D312yes—
412C2×C3×C4C23×D312yes—
413C2×Dic3—22no—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—22no—
417C2×Dic3—34no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—316no—
426C2×Dic3—34no—
427C2×Dic3—34no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—64no—
433C2×Dic3—68no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—124no—
437C2×Dic3D3×Q814yes—
438C2×Dic3C23×D312yes—
439C2×Dic3C23×D312yes—
440C2×Dic3C23×D314yes—
441C2×Dic3C23×D314yes—
442C2×Dic3C23×D312yes—
443C4×D3—28no—
444C4×D3—316no—
445C4×D3—68no—
446Dic6—616no—
447Dic6—616no—
448Dic6—68no—
449Dic6—68no—
450Dic6—128no—
451C2×C32#53314yescomplemented
452C2×C32C23×Q811yescharacteristic
453C2×C32C22×#4111yescharacteristic
454C2×C32C22×#4111yescharacteristic
455C3×D3—24no—
456C24—31no—
457C2×Q8—24no—
458C2×Q8—98no—
459C2×Q8—94no—
460C2×Q8—188no—
461C2×Q8—184no—
462C2×Q8C2×D3214yes—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—32no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—34no—
469C22×C4—64no—
470C22×C4—94no—
471C22×C4—98no—
472C22×C4—94no—
473C22×C4—91no—
474C22×C4—91no—
475C22×C4—92no—
476C22×C4—184no—
477C22×C4C2×D3212yes—
478C22×C4C2×D3211yescharacteristic
479C4⋊C4—38no—
480C4⋊C4—34no—
481C4⋊C4—38no—
482C4⋊C4—34no—
483C4⋊C4—98no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—98no—
487C4⋊C4—98no—
488C22⋊C4—38no—
489C22⋊C4—98no—
490C42—34no—
491C42—38no—
492C42—94no—
493C42—94no—
494C42—98no—
495C42—94no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—21no—
500C22×C3—34no—
501C22×C3—62no—
502C22×C3—62no—
503C22×C3—68no—
504C22×C3C2×#23512yes—
505C22×C3C2×#23712yes—
506C22×C3C2×D3×Q812yes—
507C22×C3C2×D3×Q812yes—
508C22×C3D3×#4112yes—
509C22×C3D3×#4112yes—
510C22×C3C24×D311yescharacteristic
511C22×C3C24×D311yescharacteristic
512C2×D3—22no—
513C2×D3—22no—
514C2×D3—28no—
515C2×D3C2×D3×Q814yes—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—24no—
519C3×C4—34no—
520C3×C4—44no—
521C3×C4—62no—
522C3×C4—64no—
523C3×C4—64no—
524C3×C4—62no—
525C3×C4C2×#23514yes—
526C3×C4C2×#23714yes—
527Dic3—22no—
528Dic3—24no—
529Dic3—24no—
530Dic3—22no—
531Dic3—34no—
532Dic3—34no—
533Dic3—34no—
534Dic3—34no—
535Dic3—64no—
536Dic3—64no—
537Dic3—64no—
538Dic3—64no—
539Dic3—124no—
540Dic3C2×D3×Q814yes—
541C32C2×#53311yescharacteristic, complemented, Sylow
542C23—34no—
543C23—32no—
544C23—62no—
545C23—62no—
546C23C22×D3211yescharacteristic
547Q8—28no—
548Q8—1816no—
549Q8—188no—
550C2×C4—24no—
551C2×C4—34no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—34no—
555C2×C4—32no—
556C2×C4—34no—
557C2×C4—62no—
558C2×C4—64no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—68no—
562C2×C4—916no—
563C2×C4—94no—
564C2×C4—94no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—94no—
568C2×C4—188no—
569C2×C4—184no—
570C2×C4#380414yes—
571C2×C4C22×D3214yes—
572C2×C4C22×D3212yes—
573C2×C3—24no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—64no—
578C2×C3#557814yescomplemented
579C2×C3#562214yescomplemented
580C2×C3C22×#23511yescharacteristic
581C2×C3C22×#23711yescharacteristic
582C2×C3C22×D3×Q811yescharacteristic
583C2×C3C22×D3×Q811yescharacteristic
584C2×C3C2×D3×#4111yescharacteristic
585C2×C3C2×D3×#4111yescharacteristic
586D3—24no—
587C22—34no—
588C22—68no—
589C22—62no—
590C22—62no—
591C22D32×Q812yes—
592C22#6431912yes—
593C22C2×#380412yes—
594C22C23×D3211yescharacteristic
595C4—24no—
596C4—34no—
597C4—62no—
598C4—64no—
599C4—64no—
600C4—62no—
601C4—94no—
602C4—94no—
603C4—184no—
604C4C2×#380414yes—
605C3—21no—
606C3C2×#557811yescharacteristic, complemented
607C3C2×#562211yescharacteristic, complemented
608C2—64no—
609C2#1059536714yesdirect product factor
610C2C2×D32×Q811yescharacteristic
611C2C2×#6431911yescharacteristic
612C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595367C2direct (N × H)
5. C2×#63919C2semidirect
10. C2×#63847C2semidirect
11. C2×#63844C2semidirect
12. C2×#63837C2semidirect
21. #64153C22semidirect
26. C3×Q8×Dic3C22semidirect
41. #63919C22semidirect
46. #63847C22semidirect
47. #63844C22semidirect
48. #63837C22semidirect
52. C2×Q8×Dic3D3semidirect
94. C2×D3×Dic3Q8semidirect
140. Q8×Dic3C2×D3semidirect
219. D3×Dic3C2×Q8semidirect
451. C2×C32#533semidirect
541. C32C2×#533semidirect
578. C2×C3#5578semidirect
579. C2×C3#5622semidirect
606. C3C2×#5578semidirect
607. C3C2×#5622semidirect
609. C2#10595367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9462
C2×C3×Q8×Dic32
#105953672
C2×#639192
C2×#638992
C2×#638772
C2×C4×D3×Dic32
C2×#638572
C2×#638472
C2×#638442
C2×#638372
C2×#56223
C2×#55783