Finite Group Databasebeta

← C2×#10595346 #11901695

Subgroups — C2×#10595346 #11901695

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595346C2116yesmaximal, direct product factor
5C2×#63919C211yesmaximal, characteristic, complemented
6C2×#63909C211yesmaximal, characteristic
7C2×#63895C212yesmaximal, complemented
8C2×#63894C211yesmaximal, characteristic, complemented
9C2×#63868C212yesmaximal, complemented
10C2×#63855C211yesmaximal, characteristic, complemented
11C2×#63854C212yesmaximal, complemented
12C2×#63852C212yesmaximal, complemented
13C2×#5643—31nomaximal
14C2×#5582—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#627C2212yes—
19C22×#626C2212yes—
20C22×#624C2212yes—
21#64156C2218yescomplemented
22C2×#3752C2212yes—
23C2×#3752C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C3×#946C2218yescomplemented
26C3×Q8×Dic3C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2212yes—
38C2×#3722C2212yes—
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41#63919C2218yescomplemented
42#63909C2218yes—
43#63895C22116yescomplemented
44#63894C2218yescomplemented
45#63868C22116yescomplemented
46#63855C2218yescomplemented
47#63854C22116yescomplemented
48#63852C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#947—31no—
52C2×#947—31no—
53C2×#947—61no—
54C2×#946D311yescharacteristic, complemented
55C2×Q8×Dic3D311yescharacteristic, complemented
56C2×#930—31no—
57C2×#926—31no—
58#5643—316no—
59#5582—316no—
60C2×#898—32no—
61C2×#897—32no—
62C2×#896—32no—
63C2×#895—31no—
64C2×#894—32no—
65C2×#893—31no—
66C2×#888—31no—
67C2×#888—31no—
68C2×#885—32no—
69C2×#883—32no—
70C2×#876—32no—
71C2×#875—32no—
72C2×C4×D12—31no—
73C2×#872—31no—
74C23×C3⋊D3C2312yes—
75C23×C3×D3C2311yescharacteristic
76C2×C32×Q8—24no—
77C2×C32×Q8C2314yes—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C2×#626—44no—
94C2×#626C2318yes—
95C2×#624—44no—
96C2×#624C2318yes—
97#3752C2318yes—
98#3752C2318yes—
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—
108Dic3⋊Dic3C2314yes—
109Dic3⋊Dic3C2314yes—
110#3722C2318yes—
111#3722C2318yes—
112(C2×D3)⋊Dic3C2314yes—
113(C2×D3)⋊Dic3C2314yes—
114C2×#542—91noSylow
115C22×C3×Q8—21no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C23×C3×C4—31no—
119C22×#67—32no—
120C22×D12—31no—
121C22×D12—31no—
122C22×D12—32no—
123C22×D12—61no—
124C22×C4×D3—32no—
125C22×C4×D3—32no—
126C22×C4×D3C2×D311yescharacteristic
127C22×Dic6—32no—
128C22×Dic6—32no—
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—31no—
139C2×#217—31no—
140#947—38no—
141#947—38no—
142#947—68no—
143#946C2×D318yescomplemented
144Q8×Dic3C2×D318yescomplemented
145#930—38no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
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—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—62no—
157C2×(C2×D3)⋊C4—62no—
158C2×(C2×D3)⋊C4C2×D312yes—
159#926—38no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×C4⋊Dic3C2×D312yes—
164C2×C4⋊Dic3C2×D311yescharacteristic
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—32no—
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4C2×D312yes—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D312yes—
174C2×C4×Dic3C2×D311yescharacteristic
175#898—316no—
176#897—316no—
177#896—316no—
178#895—38no—
179#894—316no—
180#893—38no—
181#888—38no—
182#888—38no—
183#885—316no—
184#883—316no—
185#876—316no—
186#875—316no—
187C4×D12—38no—
188#872—38no—
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—24no—
191C22×C3⋊D3—24no—
192C22×C3⋊D3—24no—
193C22×C3⋊D3C2414yes—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3C2412yes—
198C32×Q8—28no—
199C2×C32×C4—24no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2412yes—
207C4⋊(C3⋊D3)—28no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2414yes—
218C3×C4×D3—28no—
219#627—48no—
220#626—48no—
221#624—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—92no—
226C2×#124—91no—
227C2×#123—92no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8—92no—
230C2×#121—91no—
231C2×C4×Q8—31no—
232C2×C4×D4—91no—
233C2×#117—91no—
234C24×C3—31no—
235C23×D3—32no—
236C23×D3—32no—
237C23×D3—62no—
238C23×D3C22×D311yescharacteristic
239C2×C3×Q8—24no—
240C2×C3×Q8—24no—
241C2×C3×Q8—24no—
242C2×C3×Q8—44no—
243C2×C3×Q8C22×D314yes—
244C2×C3×Q8C22×D314yes—
245C22×C3×C4—21no—
246C22×C3×C4—22no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—31no—
250C22×C3×C4—32no—
251C22×C3×C4—31no—
252C22×C3×C4—34no—
253C22×C3×C4—64no—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D312yes—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—38no—
259C2×#67—124no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—61no—
265C22×Dic3—61no—
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D311yescharacteristic
270C22×Dic3C22×D312yes—
271C2×D12—34no—
272C2×D12—34no—
273C2×D12—38no—
274C2×D12—64no—
275C2×D12—64no—
276C2×D12—64no—
277C2×D12—124no—
278C2×D12—124no—
279C2×C4×D3—24no—
280C2×C4×D3—38no—
281C2×C4×D3—38no—
282C2×C4×D3—124no—
283C2×C4×D3—124no—
284C2×C4×D3C22×D314yes—
285C2×Dic6—38no—
286C2×Dic6—38no—
287C2×Dic6—124no—
288C2×Dic6—124no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—38no—
292C3×C4⋊C4—38no—
293C3×C22⋊C4—38no—
294C3×C42—34no—
295C3×C42—38no—
296#217—34no—
297#217—34no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—68no—
309(C2×D3)⋊C4—68no—
310(C2×D3)⋊C4C22×D318yes—
311C4⋊Dic3—34no—
312C4⋊Dic3—34no—
313C4⋊Dic3C22×D314yes—
314C4⋊Dic3C22×D318yes—
315C4⋊Dic3C22×D314yes—
316Dic3⋊C4—34no—
317Dic3⋊C4—34no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320Dic3⋊C4C22×D318yes—
321C4×Dic3—34no—
322C4×Dic3—34no—
323C4×Dic3—64no—
324C4×Dic3C22×D318yes—
325C4×Dic3C22×D314yes—
326C22×C32C2×#4112yes—
327C22×C32H(5,𝔽2)12yes—
328C22×C322−1+412yes—
329C22×C32C2511yescharacteristic
330C2×C3⋊D3—24no—
331C2×C3⋊D3—24no—
332C2×C3⋊D3—24no—
333C2×C3⋊D3—48no—
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—22no—
337C2×C3×D3—44no—
338C32×C4—24no—
339C32×C4C2×#4114yes—
340C3⋊Dic3—22no—
341C3⋊Dic3—22no—
342C3×Dic3—22no—
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—24no—
346C3×Dic3—22no—
347C22×Q8—92no—
348C22×Q8D3211yescharacteristic
349C22×D4—92no—
350C22×D4—91no—
351C23×C4—31no—
352C23×C4—92no—
353C4⋊Q8—98no—
354#126—916no—
355#124—916no—
356#124—98no—
357#123—916no—
358C22⋊Q8—38no—
359C22⋊Q8—916no—
360#121—98no—
361C4×Q8—38no—
362C4×D4—98no—
363#117—98no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—92no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C42—31no—
379C2×C42—32no—
380C2×C42—91no—
381C23×C3—21no—
382C23×C3—32no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3—62no—
386C23×C3C23×D311yescharacteristic
387C23×C3C23×D311yescharacteristic
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—34no—
392C22×D3—34no—
393C22×D3—64no—
394C22×D3—64no—
395C22×D3—64no—
396C22×D3—64no—
397C22×D3—64no—
398C22×D3—64no—
399C22×D3—64no—
400C22×D3—124no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3C23×D312yes—
404C3×Q8—28no—
405C3×Q8—28no—
406C3×Q8—48no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—32no—
413C2×C3×C4—34no—
414C2×C3×C4—32no—
415C2×C3×C4—34no—
416C2×C3×C4—32no—
417C2×C3×C4—44no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—64no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4—68no—
424C2×C3×C4#23514yes—
425C2×C3×C4#23714yes—
426C2×C3×C4C23×D314yes—
427C2×C3×C4C23×D314yes—
428C2×C3×C4C23×D312yes—
429C2×C3×C4C23×D312yes—
430#67—128no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—22no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448C2×Dic3C23×D312yes—
449C2×Dic3C23×D314yes—
450C2×Dic3C23×D312yes—
451C2×Dic3C23×D312yes—
452C2×Dic3C23×D314yes—
453D12—68no—
454D12—68no—
455D12—128no—
456D12—128no—
457C4×D3—28no—
458C4×D3—128no—
459C4×D3—128no—
460Dic6—128no—
461Dic6—128no—
462C2×C32#54214yescomplemented
463C2×C32C22×#4111yescharacteristic
464C2×C32C2×H(5,𝔽2)11yescharacteristic
465C2×C32C2×2−1+411yescharacteristic
466C3⋊D3—44no—
467C3×D3—42no—
468C24—31no—
469C24—92no—
470C2×Q8—24no—
471C2×Q8—98no—
472C2×Q8—364no—
473C2×Q8C2×D3214yes—
474C2×D4—98no—
475C2×D4—94no—
476C2×D4—184no—
477C2×D4—364no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—32no—
481C22×C4—32no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—64no—
485C22×C4—98no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—364no—
489C22×C4C2×D3212yes—
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—34no—
492C4⋊C4—34no—
493C4⋊C4—38no—
494C4⋊C4—38no—
495C4⋊C4—94no—
496C4⋊C4—94no—
497C4⋊C4—98no—
498C22⋊C4—38no—
499C22⋊C4—98no—
500C22⋊C4—98no—
501C22⋊C4—94no—
502C22⋊C4—94no—
503C22⋊C4—98no—
504C22⋊C4—98no—
505C42—34no—
506C42—38no—
507C42—94no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—62no—
515C22×C3—124no—
516C22×C3C2×#23512yes—
517C22×C3C2×#23712yes—
518C22×C3#100712yes—
519C22×C3#100712yes—
520C22×C3#100912yes—
521C22×C3#100912yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C24×D311yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—22no—
527C2×D3—44no—
528C2×D3—64no—
529C2×D3—64no—
530C2×D3—64no—
531C2×D3—64no—
532C2×D3—64no—
533C2×D3—64no—
534C2×D3—124no—
535C2×D3—124no—
536C2×D3—124no—
537C2×D3—128no—
538C2×D3—128no—
539C2×D3—248no—
540C3×C4—24no—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—44no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—64no—
547C3×C4—64no—
548C3×C4—62no—
549C3×C4C2×#23514yes—
550C3×C4C2×#23714yes—
551Dic3—22no—
552Dic3—22no—
553Dic3—24no—
554Dic3—24no—
555Dic3—22no—
556Dic3—62no—
557Dic3—62no—
558Dic3—62no—
559Dic3—62no—
560Dic3—122no—
561Dic3—122no—
562C32C2×#54211yescharacteristic, complemented, Sylow
563C23—32no—
564C23—62no—
565C23—62no—
566C23—62no—
567C23—94no—
568C23—184no—
569C23—184no—
570C23—184no—
571C23C22×D3211yescharacteristic
572Q8—28no—
573Q8—368no—
574D4—188no—
575D4—368no—
576C2×C4—24no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—34no—
580C2×C4—34no—
581C2×C4—32no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—64no—
585C2×C4—64no—
586C2×C4—62no—
587C2×C4—68no—
588C2×C4—92no—
589C2×C4—92no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4—368no—
593C2×C4#380414yes—
594C2×C4C22×D3214yes—
595C2×C4C22×D3212yes—
596C2×C3—24no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—122no—
601C2×C3#558214yescomplemented
602C2×C3#564314yescomplemented
603C2×C3C22×#23511yescharacteristic
604C2×C3C22×#23711yescharacteristic
605C2×C3C2×#100711yescharacteristic
606C2×C3C2×#100711yescharacteristic
607C2×C3C2×#100911yescharacteristic
608C2×C3C2×#100911yescharacteristic
609D3—42no—
610D3—124no—
611D3—124no—
612D3—244no—
613C22—62no—
614C22—62no—
615C22—62no—
616C22—124no—
617C22—184no—
618C22—184no—
619C22—184no—
620C22—368no—
621C22#6431612yes—
622C22#6432012yes—
623C22C2×#380412yes—
624C22C23×D3211yescharacteristic
625C4—24no—
626C4—62no—
627C4—62no—
628C4—64no—
629C4—64no—
630C4—62no—
631C4—182no—
632C4—182no—
633C4C2×#380414yes—
634C3—21no—
635C3C2×#558211yescharacteristic, complemented
636C3C2×#564311yescharacteristic, complemented
637C2—122no—
638C2—364no—
639C2#1059534614yesdirect product factor
640C2C2×#6431611yescharacteristic
641C2C2×#6432011yescharacteristic
642C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC2×#63909C2
hypercenterC22×Q8D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64156C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595346C2direct (N × H)
5. C2×#63919C2semidirect
7. C2×#63895C2semidirect
8. C2×#63894C2semidirect
9. C2×#63868C2semidirect
10. C2×#63855C2semidirect
11. C2×#63854C2semidirect
12. C2×#63852C2semidirect
21. #64156C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
41. #63919C22semidirect
43. #63895C22semidirect
44. #63894C22semidirect
45. #63868C22semidirect
46. #63855C22semidirect
47. #63854C22semidirect
48. #63852C22semidirect
54. C2×#946D3semidirect
55. C2×Q8×Dic3D3semidirect
143. #946C2×D3semidirect
144. Q8×Dic3C2×D3semidirect
462. C2×C32#542semidirect
562. C32C2×#542semidirect
601. C2×C3#5582semidirect
602. C2×C3#5643semidirect
635. C3C2×#5582semidirect
636. C3C2×#5643semidirect
639. C2#10595346direct (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×#9462
C2×C3×Q8×Dic32
#105953462
C2×#639192
C2×#639092
C2×#638952
C2×#638942
C2×#638682
C2×#638552
C2×#638542
C2×#638522
C2×#56433
C2×#55823