Finite Group Databasebeta

← C2×#10595387 #11903426

Subgroups — C2×#10595387 #11903426

Order 1152.

2389 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4#10595387C2116yesmaximal, direct product factor
5C2×C4×#627C211yesmaximal, characteristic, complemented
6C2×#63895C212yesmaximal, complemented
7C2×#63894C211yesmaximal, characteristic
8C2×#63868C212yesmaximal, complemented
9C2×#63864C211yesmaximal, characteristic
10C2×#63848C212yesmaximal, complemented
11C2×#63843C211yesmaximal, characteristic, complemented
12C2×#63836C212yesmaximal, complemented
13C2×#5732—31nomaximal
14C2×#5568—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×#627C2211yescharacteristic
19C22×#624C2212yes—
20#64156C2218yes—
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C3×Q8×Dic3C2218yescomplemented
25C3×#944C2218yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2212yes—
38C2×#3722C2212yes—
39C2×#3722C2212yes—
40C2×Dic32C2212yes—
41C4×#627C2218yescomplemented
42#63895C22116yescomplemented
43#63894C2218yes—
44#63868C22116yescomplemented
45#63864C2218yes—
46#63848C22116yescomplemented
47#63843C2218yescomplemented
48#63836C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#947—31no—
52C2×#947—31no—
53C2×#947—31no—
54C2×#947—61no—
55C2×Q8×Dic3—31no—
56C2×Q8×Dic3D311yescharacteristic, complemented
57C2×#944D311yescharacteristic, complemented
58#5732—316no—
59#5568—316no—
60C2×#898—32no—
61C2×#898—32no—
62C2×#898—32no—
63C2×#897—32no—
64C2×#896—32no—
65C2×#893—31no—
66C2×#892—32no—
67C2×#887—31no—
68C2×#876—32no—
69C2×#875—31no—
70C2×C4×D12—31no—
71C2×#872—32no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2312yes—
75C2×C32×Q8—24no—
76C2×C32×Q8C2314yes—
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C4⋊(C3⋊D3)—24no—
82C2×C4⋊(C3⋊D3)C2314yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2314yes—
91C2×#627—24no—
92C2×#627C2314yes—
93C2×#624—28no—
94C2×#624C2318yes—
95#3752C2318yes—
96#3752C2318yes—
97C4×C3⋊Dic3C2314yes—
98C3×C4⋊Dic3C2314yes—
99C3×C4⋊Dic3C2318yes—
100C3×Dic3⋊C4C2318yes—
101C3×Dic3⋊C4C2318yes—
102C3×C4×Dic3C2314yes—
103C3×C4×Dic3C2318yes—
104C3×C4×Dic3C2314yes—
105#3724C2314yes—
106Dic3⋊Dic3C2314yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2314yes—
109#3722C2318yes—
110#3722C2318yes—
111#3722C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—21no—
115C22×C3×Q8—31no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C22×D12—31no—
119C22×D12—31no—
120C22×D12—61no—
121C22×C4×D3—32no—
122C22×C4×D3—32no—
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6C2×D311yescharacteristic
126C3×C4⋊Q8—38no—
127C3×C4×Q8—38no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C42—31no—
133C2×C3×C42—31no—
134C2×C3×C42—32no—
135#947—38no—
136#947—38no—
137#947—38no—
138#947—68no—
139Q8×Dic3—38no—
140Q8×Dic3C2×D318yescomplemented
141#944C2×D318yescomplemented
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—62no—
153C2×(C2×D3)⋊C4—62no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—32no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D312yes—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4C2×D312yes—
165C2×Dic3⋊C4C2×D312yes—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—61no—
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D312yes—
174#898—316no—
175#898—316no—
176#898—316no—
177#897—316no—
178#896—316no—
179#893—38no—
180#892—316no—
181#887—38no—
182#876—316no—
183#875—38no—
184C4×D12—38no—
185#872—316no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—24no—
190C22×C3⋊D3—24no—
191C22×C3⋊D3—24no—
192C22×C3⋊D3C2414yes—
193C32×Q8—28no—
194C2×C32×C4—24no—
195C2×C32×C4#4114yes—
196C2×C32×C4C2414yes—
197C2×C32×C4C2412yes—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3C2412yes—
201C2×C3⋊Dic3C2412yes—
202C4⋊(C3⋊D3)—28no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×Dic6—28no—
216#627—28no—
217#624—216no—
218#556—916no—
219C2×C4⋊Q8—31no—
220C2×#126—92no—
221C2×#126—92no—
222C2×#124—91no—
223C2×#124—91no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—31no—
226C2×C4×Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—91no—
229C2×#117—92no—
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—62no—
233C2×C3×Q8—24no—
234C2×C3×Q8—24no—
235C2×C3×Q8—24no—
236C2×C3×Q8—34no—
237C2×C3×Q8—44no—
238C2×C3×Q8—64no—
239C2×C3×Q8C22×D314yes—
240C2×C3×Q8C22×D314yes—
241C22×C3×C4—21no—
242C22×C3×C4—22no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
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—61no—
258C22×Dic3—61no—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C2×D12—34no—
266C2×D12—34no—
267C2×D12—64no—
268C2×D12—64no—
269C2×D12—64no—
270C2×D12—124no—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—68no—
274C2×C4×D3—68no—
275C2×Dic6—24no—
276C2×Dic6—34no—
277C2×Dic6—34no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6C22×D314yes—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—38no—
284C3×C4⋊C4—38no—
285C3×C42—34no—
286C3×C42—34no—
287C3×C42—38no—
288(C2×D3)⋊C4—38no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—68no—
299(C2×D3)⋊C4—68no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—38no—
303C4⋊Dic3C22×D314yes—
304C4⋊Dic3C22×D318yes—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—34no—
308Dic3⋊C4—34no—
309Dic3⋊C4—38no—
310Dic3⋊C4C22×D318yes—
311Dic3⋊C4C22×D318yes—
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—64no—
317C4×Dic3C22×D314yes—
318C4×Dic3C22×D314yes—
319C4×Dic3C22×D318yes—
320C22×C32C2×#4112yes—
321C22×C32C2×#4112yes—
322C22×C322−1+412yes—
323C22×C32C2511yescharacteristic
324C2×C3⋊D3—24no—
325C2×C3⋊D3—24no—
326C2×C3⋊D3—24no—
327C2×C3⋊D3—48no—
328C32×C4—24no—
329C32×C4C2×#4114yes—
330C3⋊Dic3—22no—
331C3⋊Dic3—22no—
332C3×Dic3—24no—
333C3×Dic3—22no—
334C3×Dic3—24no—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3C2×#4114yes—
338C22×Q8—31no—
339C22×Q8—91no—
340C22×Q8D3211yescharacteristic
341C22×D4—91no—
342C23×C4—92no—
343C4⋊Q8—38no—
344#126—916no—
345#126—916no—
346#124—98no—
347#124—98no—
348C22⋊Q8—916no—
349C4×Q8—38no—
350C4×Q8—98no—
351C4×Q8—98no—
352C4×D4—98no—
353#117—916no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—91no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C42—32no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—92no—
371C2×C42—91no—
372C23×C3—21no—
373C23×C3C23×D311yescharacteristic
374C23×C3C23×D311yescharacteristic
375C22×D3—34no—
376C22×D3—34no—
377C22×D3—64no—
378C22×D3—64no—
379C22×D3—64no—
380C22×D3—64no—
381C22×D3—64no—
382C22×D3—64no—
383C22×D3—64no—
384C22×D3—124no—
385C22×D3—124no—
386C22×D3—124no—
387C3×Q8—28no—
388C3×Q8—28no—
389C3×Q8—48no—
390C3×Q8—68no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—34no—
397C2×C3×C4—32no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—32no—
401C2×C3×C4—32no—
402C2×C3×C4—32no—
403C2×C3×C4—44no—
404C2×C3×C4—64no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4#23514yes—
410C2×C3×C4#23714yes—
411C2×C3×C4C23×D314yes—
412C2×C3×C4C23×D314yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×Dic3—24no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—24no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3#23914yes—
433C2×Dic3C23×D314yes—
434C2×Dic3C23×D314yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D312yes—
438C2×Dic3C23×D312yes—
439D12—68no—
440D12—68no—
441D12—128no—
442C4×D3—616no—
443C4×D3—616no—
444Dic6—28no—
445Dic6—68no—
446Dic6—68no—
447C2×C32#55614yescomplemented
448C2×C32C22×#4111yescharacteristic
449C2×C32C22×#4111yescharacteristic
450C2×C32C2×2−1+411yescharacteristic
451C3⋊D3—44no—
452C24—92no—
453C2×Q8—24no—
454C2×Q8—34no—
455C2×Q8—64no—
456C2×Q8—94no—
457C2×Q8—184no—
458C2×Q8C2×D3214yes—
459C2×D4—94no—
460C2×D4—184no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—32no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—32no—
467C22×C4—98no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—188no—
471C22×C4C2×D3212yes—
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—38no—
474C4⋊C4—34no—
475C4⋊C4—38no—
476C4⋊C4—38no—
477C4⋊C4—94no—
478C4⋊C4—98no—
479C4⋊C4—94no—
480C4⋊C4—94no—
481C22⋊C4—98no—
482C22⋊C4—98no—
483C22⋊C4—98no—
484C22⋊C4—98no—
485C22⋊C4—98no—
486C42—38no—
487C42—34no—
488C42—34no—
489C42—98no—
490C42—94no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3C2×#23512yes—
496C22×C3C2×#23712yes—
497C22×C3C2×#23912yes—
498C22×C3#100712yes—
499C22×C3#100712yes—
500C22×C3D3×#4112yes—
501C22×C3C24×D311yescharacteristic
502C22×C3C24×D311yescharacteristic
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—124no—
510C2×D3—124no—
511C2×D3—124no—
512C2×D3—128no—
513C2×D3—128no—
514C2×D3—248no—
515C3×C4—24no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—34no—
519C3×C4—44no—
520C3×C4—64no—
521C3×C4—62no—
522C3×C4—64no—
523C3×C4—62no—
524C3×C4—62no—
525C3×C4C2×#23514yes—
526C3×C4C2×#23714yes—
527Dic3—24no—
528Dic3—22no—
529Dic3—22no—
530Dic3—22no—
531Dic3—24no—
532Dic3—62no—
533Dic3—62no—
534Dic3—62no—
535Dic3—62no—
536Dic3—122no—
537Dic3—122no—
538Dic3C2×#23914yes—
539C32C2×#55611yescharacteristic, complemented, Sylow
540C23—94no—
541C23—184no—
542C23—184no—
543C23—184no—
544C23C22×D3211yescharacteristic
545Q8—28no—
546Q8—68no—
547Q8—188no—
548D4—188no—
549C2×C4—24no—
550C2×C4—34no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—34no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—34no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—64no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—1816no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4#380414yes—
568C2×C4C22×D3214yes—
569C2×C4C22×D3212yes—
570C2×C3—24no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3#556814yescomplemented
575C2×C3#573214yescomplemented
576C2×C3C22×#23511yescharacteristic
577C2×C3C22×#23711yescharacteristic
578C2×C3C22×#23911yescharacteristic
579C2×C3C2×#100711yescharacteristic
580C2×C3C2×#100711yescharacteristic
581C2×C3C2×D3×#4111yescharacteristic
582D3—124no—
583D3—124no—
584D3—244no—
585C22—184no—
586C22—184no—
587C22—184no—
588C22—368no—
589C22#6431612yes—
590C22D3×#23912yes—
591C22C2×#380412yes—
592C22C23×D3211yescharacteristic
593C4—24no—
594C4—34no—
595C4—62no—
596C4—62no—
597C4—64no—
598C4—62no—
599C4—64no—
600C4—182no—
601C4—182no—
602C4C2×#380414yes—
603C3—21no—
604C3C2×#556811yescharacteristic, complemented
605C3C2×#573211yescharacteristic, complemented
606C2—364no—
607C2#1059538714yesdirect product factor
608C2C2×#6431611yescharacteristic
609C2C2×D3×#23911yescharacteristic
610C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Q8×Dic3C2semidirect
3. C2×C3×#944C2semidirect
4. #10595387C2direct (N × H)
5. C2×C4×#627C2semidirect
6. C2×#63895C2semidirect
8. C2×#63868C2semidirect
10. C2×#63848C2semidirect
11. C2×#63843C2semidirect
12. C2×#63836C2semidirect
24. C3×Q8×Dic3C22semidirect
25. C3×#944C22semidirect
41. C4×#627C22semidirect
42. #63895C22semidirect
44. #63868C22semidirect
46. #63848C22semidirect
47. #63843C22semidirect
48. #63836C22semidirect
56. C2×Q8×Dic3D3semidirect
57. C2×#944D3semidirect
140. Q8×Dic3C2×D3semidirect
141. #944C2×D3semidirect
447. C2×C32#556semidirect
539. C32C2×#556semidirect
574. C2×C3#5568semidirect
575. C2×C3#5732semidirect
604. C3C2×#5568semidirect
605. C3C2×#5732semidirect
607. C2#10595387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×C3×Q8×Dic32
C2×C3×#9442
#105953872
C2×C4×#6272
C2×#638952
C2×#638942
C2×#638682
C2×#638642
C2×#638482
C2×#638432
C2×#638362
C2×#57323
C2×#55683