Finite Group Databasebeta

← C2×#10595411 #11903418

Subgroups — C2×#10595411 #11903418

Order 1152.

2385 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595411C2116yesmaximal, direct product factor
5C2×#63918C211yesmaximal, characteristic, complemented
6C2×C4×#626C211yesmaximal, characteristic
7C2×#63858C212yesmaximal, complemented
8C2×#63852C212yesmaximal
9C2×#63849C211yesmaximal, characteristic, complemented
10C2×#63848C212yesmaximal, complemented
11C2×#63841C211yesmaximal, characteristic, complemented
12C2×#63837C212yesmaximal, complemented
13C2×#5641—31nomaximal
14C2×#5584—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#627C2212yes—
19C22×#626C2211yescharacteristic
20#64155C2218yescomplemented
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2212yes—
24C3×#946C2218yescomplemented
25C3×Q8×Dic3C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2212yes—
41#63918C2218yescomplemented
42C4×#626C2218yes—
43#63858C22116yescomplemented
44#63852C22116yes—
45#63849C2218yescomplemented
46#63848C22116yescomplemented
47#63841C2218yescomplemented
48#63837C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#946—31no—
52C2×#946—31no—
53C2×#946—61no—
54C2×#946D311yescharacteristic, complemented
55C2×Q8×Dic3D311yescharacteristic, complemented
56C2×C4×#67—31no—
57C2×#926—31no—
58#5641—316no—
59#5584—316no—
60C2×#898—32no—
61C2×#898—32no—
62C2×#898—32no—
63C2×#892—31no—
64C2×#892—31no—
65C2×#892—31no—
66C2×#888—31no—
67C2×#887—32no—
68C2×#885—32no—
69C2×#879—32no—
70C2×#875—32no—
71C2×C4×D12—31no—
72C2×#869—31no—
73C2×C4×Dic6—32no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C2×C32×Q8—24no—
77C2×C32×Q8C2314yes—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3C2314yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×#627—28no—
92C2×#627C2318yes—
93C2×#626—24no—
94C2×#626C2314yes—
95#3752C2318yes—
96C4⋊(C3⋊Dic3)C2314yes—
97#3750C2318yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4⋊Dic3C2314yes—
100C3×C4⋊Dic3C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2318yes—
104C3×C4×Dic3C2314yes—
105Dic3⋊Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107#3722C2314yes—
108#3722C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—21no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C2×D311yescharacteristic
117C23×C3×C4—31no—
118C22×#67—31no—
119C22×D12—31no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—61no—
123C22×C4×D3C2×D311yescharacteristic
124C22×Dic6—32no—
125C22×Dic6—32no—
126C3×C22⋊Q8—38no—
127C3×C4×Q8—38no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—32no—
134C2×C3×C42—31no—
135C2×#217—31no—
136C2×#217—32no—
137#946—38no—
138#946—38no—
139#946—68no—
140#946C2×D318yescomplemented
141Q8×Dic3C2×D318yescomplemented
142C4×#67—38no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—62no—
152C2×(C2×D3)⋊C4C2×D312yes—
153#926—38no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—32no—
158C2×C4⋊Dic3—61no—
159C2×C4⋊Dic3C2×D311yescharacteristic
160C2×C4⋊Dic3C2×D312yes—
161C2×C4⋊Dic3C2×D311yescharacteristic
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—62no—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3C2×D312yes—
173C2×C4×Dic3C2×D311yescharacteristic
174#898—316no—
175#898—316no—
176#898—316no—
177#892—38no—
178#892—38no—
179#892—38no—
180#888—38no—
181#887—316no—
182#885—316no—
183#879—316no—
184#875—316no—
185C4×D12—38no—
186#869—38no—
187C4×Dic6—316no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C2412yes—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C32×Q8—28no—
198C2×C32×C4—24no—
199C2×C32×C4#4114yes—
200C2×C32×C4C2414yes—
201C2×C32×C4C2412yes—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3C2412yes—
205C2×C3⋊Dic3C2414yes—
206C4×C3⋊D3—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C3×C4×D3—28no—
218#627—216no—
219#626—28no—
220#556—916no—
221C2×C4⋊Q8—91no—
222C2×#126—92no—
223C2×#126—92no—
224C2×#124—92no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—31no—
228C2×C4×Q8—92no—
229C2×C4×D4—91no—
230C2×#117—91no—
231C2×#117—91no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—24no—
238C2×C3×Q8—24no—
239C2×C3×Q8—24no—
240C2×C3×Q8—44no—
241C2×C3×Q8C22×D314yes—
242C2×C3×Q8C22×D314yes—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—32no—
248C22×C3×C4—32no—
249C22×C3×C4—31no—
250C22×C3×C4—34no—
251C22×C3×C4—64no—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—34no—
257C2×#67—64no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—61no—
263C22×Dic3—62no—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C2×D12—34no—
270C2×D12—64no—
271C2×C4×D3—24no—
272C2×C4×D3—34no—
273C2×C4×D3—34no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3—124no—
278C2×C4×D3C22×D314yes—
279C2×Dic6—38no—
280C2×Dic6—38no—
281C2×Dic6—68no—
282C2×Dic6—68no—
283C3×C4⋊C4—38no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—34no—
286C3×C4⋊C4—38no—
287C3×C22⋊C4—38no—
288C3×C42—38no—
289C3×C42—34no—
290#217—34no—
291#217—38no—
292(C2×D3)⋊C4—34no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—68no—
301(C2×D3)⋊C4C22×D318yes—
302C4⋊Dic3—34no—
303C4⋊Dic3—34no—
304C4⋊Dic3—34no—
305C4⋊Dic3—38no—
306C4⋊Dic3—64no—
307C4⋊Dic3C22×D314yes—
308C4⋊Dic3C22×D318yes—
309C4⋊Dic3C22×D314yes—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—34no—
314Dic3⋊C4—68no—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3C22×D318yes—
321C4×Dic3C22×D314yes—
322C22×C32C2×#4112yes—
323C22×C32C2×#4112yes—
324C22×C322−1+412yes—
325C22×C32C2511yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—44no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—44no—
334C32×C4—24no—
335C32×C4C2×#4114yes—
336C3⋊Dic3—24no—
337C3⋊Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—24no—
341C3×Dic3—22no—
342C3×Dic3C2×#4114yes—
343C22×Q8—92no—
344C22×Q8D3211yescharacteristic
345C22×D4—91no—
346C23×C4—31no—
347C23×C4—91no—
348C4⋊Q8—98no—
349#126—916no—
350#126—916no—
351#124—916no—
352C22⋊Q8—38no—
353C22⋊Q8—98no—
354C4×Q8—38no—
355C4×Q8—916no—
356C4×D4—98no—
357#117—98no—
358#117—98no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—92no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—91no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—91no—
372C2×C22⋊C4—92no—
373C2×C42—31no—
374C2×C42—32no—
375C2×C42—92no—
376C2×C42—92no—
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3C23×D311yescharacteristic
383C23×C3C23×D311yescharacteristic
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—32no—
388C22×D3—32no—
389C22×D3—62no—
390C22×D3—64no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3C23×D312yes—
400C3×Q8—28no—
401C3×Q8—28no—
402C3×Q8—48no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—34no—
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—34no—
412C2×C3×C4—34no—
413C2×C3×C4—32no—
414C2×C3×C4—44no—
415C2×C3×C4—62no—
416C2×C3×C4—64no—
417C2×C3×C4—64no—
418C2×C3×C4—62no—
419C2×C3×C4—68no—
420C2×C3×C4#23514yes—
421C2×C3×C4#23714yes—
422C2×C3×C4C23×D314yes—
423C2×C3×C4C23×D314yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426#67—68no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—32no—
432C2×Dic3—32no—
433C2×Dic3—34no—
434C2×Dic3—34no—
435C2×Dic3—62no—
436C2×Dic3—64no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—64no—
440C2×Dic3—64no—
441C2×Dic3—122no—
442C2×Dic3—124no—
443C2×Dic3#23914yes—
444C2×Dic3C23×D314yes—
445C2×Dic3C23×D312yes—
446C2×Dic3C23×D314yes—
447C2×Dic3C23×D312yes—
448C2×Dic3C23×D312yes—
449D12—68no—
450C4×D3—28no—
451C4×D3—68no—
452C4×D3—68no—
453C4×D3—128no—
454Dic6—616no—
455Dic6—616no—
456C2×C32#55614yescomplemented
457C2×C32C22×#4111yescharacteristic
458C2×C32C22×#4111yescharacteristic
459C2×C32C2×2−1+411yescharacteristic
460C3⋊D3—42no—
461C3×D3—42no—
462C24—31no—
463C24—91no—
464C2×Q8—24no—
465C2×Q8—98no—
466C2×Q8—188no—
467C2×Q8C2×D3214yes—
468C2×D4—94no—
469C2×D4—184no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—32no—
475C22×C4—34no—
476C22×C4—64no—
477C22×C4—91no—
478C22×C4—92no—
479C22×C4—94no—
480C22×C4—184no—
481C22×C4C2×D3212yes—
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—34no—
484C4⋊C4—34no—
485C4⋊C4—38no—
486C4⋊C4—38no—
487C4⋊C4—94no—
488C4⋊C4—98no—
489C4⋊C4—94no—
490C4⋊C4—98no—
491C22⋊C4—38no—
492C22⋊C4—98no—
493C22⋊C4—94no—
494C22⋊C4—98no—
495C22⋊C4—94no—
496C22⋊C4—98no—
497C42—34no—
498C42—38no—
499C42—98no—
500C42—98no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—62no—
508C22×C3—124no—
509C22×C3C2×#23512yes—
510C22×C3C2×#23712yes—
511C22×C3C2×#23912yes—
512C22×C3#100712yes—
513C22×C3D3×#4112yes—
514C22×C3#101012yes—
515C22×C3C24×D311yescharacteristic
516C22×C3C24×D311yescharacteristic
517C2×D3—22no—
518C2×D3—22no—
519C2×D3—22no—
520C2×D3—44no—
521C2×D3—64no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—128no—
531C2×D3—124no—
532C2×D3—124no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—34no—
537C3×C4—44no—
538C3×C4—62no—
539C3×C4—64no—
540C3×C4—64no—
541C3×C4—62no—
542C3×C4C2×#23514yes—
543C3×C4C2×#23714yes—
544Dic3—22no—
545Dic3—24no—
546Dic3—24no—
547Dic3—22no—
548Dic3—62no—
549Dic3—62no—
550Dic3—64no—
551Dic3—64no—
552Dic3—122no—
553Dic3—124no—
554Dic3C2×#23914yes—
555C32C2×#55611yescharacteristic, complemented, Sylow
556C23—32no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—92no—
561C23—182no—
562C23—182no—
563C23—182no—
564C23C22×D3211yescharacteristic
565Q8—28no—
566Q8—1816no—
567D4—188no—
568C2×C4—24no—
569C2×C4—34no—
570C2×C4—32no—
571C2×C4—34no—
572C2×C4—32no—
573C2×C4—32no—
574C2×C4—34no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—62no—
579C2×C4—68no—
580C2×C4—92no—
581C2×C4—94no—
582C2×C4—184no—
583C2×C4—182no—
584C2×C4—188no—
585C2×C4#380414yes—
586C2×C4C22×D3214yes—
587C2×C4C22×D3212yes—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—24no—
591C2×C3—21no—
592C2×C3—122no—
593C2×C3#558414yescomplemented
594C2×C3#564114yescomplemented
595C2×C3C22×#23511yescharacteristic
596C2×C3C22×#23711yescharacteristic
597C2×C3C22×#23911yescharacteristic
598C2×C3C2×#100711yescharacteristic
599C2×C3C2×D3×#4111yescharacteristic
600C2×C3C2×#101011yescharacteristic
601D3—42no—
602D3—124no—
603D3—122no—
604D3—122no—
605C22—62no—
606C22—62no—
607C22—62no—
608C22—124no—
609C22—182no—
610C22—182no—
611C22—182no—
612C22—364no—
613C22#6431512yes—
614C22D3×#23912yes—
615C22C2×#380412yes—
616C22C23×D3211yescharacteristic
617C4—24no—
618C4—34no—
619C4—64no—
620C4—62no—
621C4—64no—
622C4—62no—
623C4—184no—
624C4—182no—
625C4C2×#380414yes—
626C3—21no—
627C3C2×#558411yescharacteristic, complemented
628C3C2×#564111yescharacteristic, complemented
629C2—122no—
630C2—362no—
631C2#1059541114yesdirect product factor
632C2C2×#6431511yescharacteristic
633C2C2×D3×#23911yescharacteristic
634C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×#626C22
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
1. C2×#64155C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595411C2direct (N × H)
5. C2×#63918C2semidirect
7. C2×#63858C2semidirect
9. C2×#63849C2semidirect
10. C2×#63848C2semidirect
11. C2×#63841C2semidirect
12. C2×#63837C2semidirect
20. #64155C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
41. #63918C22semidirect
43. #63858C22semidirect
45. #63849C22semidirect
46. #63848C22semidirect
47. #63841C22semidirect
48. #63837C22semidirect
54. C2×#946D3semidirect
55. C2×Q8×Dic3D3semidirect
140. #946C2×D3semidirect
141. Q8×Dic3C2×D3semidirect
456. C2×C32#556semidirect
555. C32C2×#556semidirect
593. C2×C3#5584semidirect
594. C2×C3#5641semidirect
627. C3C2×#5584semidirect
628. C3C2×#5641semidirect
631. C2#10595411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C2×C3×#9462
C2×C3×Q8×Dic32
#105954112
C2×#639182
C2×C4×#6262
C2×#638582
C2×#638522
C2×#638492
C2×#638482
C2×#638412
C2×#638372
C2×#56413
C2×#55843