Finite Group Databasebeta

← C2×#10595395 #11901694

Subgroups — C2×#10595395 #11901694

Order 1152.

2425 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×#64155C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595395C2116yesmaximal, direct product factor
5C2×#63918C211yesmaximal, characteristic, complemented
6C2×#63916C211yesmaximal, characteristic
7C2×#63899C212yesmaximal, complemented
8C2×Dic3×D12C211yesmaximal, characteristic, complemented
9C2×#63890C212yesmaximal, complemented
10C2×#63874C211yesmaximal, characteristic, complemented
11C2×#63859C212yesmaximal, complemented
12C2×#63852C212yesmaximal, complemented
13C2×#5682—31nomaximal
14C2×#5582—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×#627C2212yes—
19C22×#626C2212yes—
20C22×D3×Dic3C2212yes—
21#64155C2218yescomplemented
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C3×#947C2218yescomplemented
26C3×Q8×Dic3C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2212yes—
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63918C2218yescomplemented
42#63916C2218yes—
43#63899C22116yescomplemented
44Dic3×D12C2218yescomplemented
45#63890C22116yescomplemented
46#63874C2218yescomplemented
47#63859C22116yescomplemented
48#63852C22116yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×Q8—31no—
51C2×#947D311yescharacteristic, complemented
52C2×#946—31no—
53C2×#946—31no—
54C2×#946—61no—
55C2×Q8×Dic3D311yescharacteristic, complemented
56C2×#938—31no—
57C2×D4×Dic3—31no—
58#5682—316no—
59#5582—316no—
60C2×#896—32no—
61C2×#895—31no—
62C2×#894—32no—
63C2×#888—31no—
64C2×#886—32no—
65C2×#885—32no—
66C2×#879—32no—
67C2×#878—32no—
68C2×#876—32no—
69C2×#875—32no—
70C2×C4×D12—31no—
71C2×#872—31no—
72C2×#872—31no—
73C2×#869—31no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2312yes—
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×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×D12—24no—
90C2×C3×D12C2314yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C2×#626—44no—
94C2×#626C2318yes—
95C2×D3×Dic3—44no—
96C2×D3×Dic3C2318yes—
97#3752C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×C4⋊Dic3C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4×Dic3C2318yes—
105C3×C4×Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107#3724C2314yes—
108#3724C2314yes—
109Dic3⋊Dic3C2318yes—
110#3722C2314yes—
111#3722C2314yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—21no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C22×C3×D4—31no—
119C22×#67—32no—
120C23×Dic3—32no—
121C22×D12—32no—
122C22×D12C2×D311yescharacteristic
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—32no—
126C22×C4×D3—61no—
127C22×Dic6—32no—
128C22×Dic6—32no—
129C3×#124—38no—
130C3×C4×Q8—38no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—32no—
138C2×#217—32no—
139C2×#217—32no—
140#947C2×D318yescomplemented
141#946—38no—
142#946—38no—
143#946—68no—
144Q8×Dic3C2×D318yescomplemented
145#938—38no—
146D4×Dic3—38no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—62no—
156C2×(C2×D3)⋊C4C2×D312yes—
157C2×(C2×D3)⋊C4C2×D312yes—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3—61no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×C4⋊Dic3C2×D312yes—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—62no—
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D312yes—
175#896—316no—
176#895—38no—
177#894—316no—
178#888—38no—
179#886—316no—
180#885—316no—
181#879—316no—
182#878—316no—
183#876—316no—
184#875—316no—
185C4×D12—38no—
186#872—38no—
187#872—38no—
188#869—38no—
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3—22no—
193C22×C3⋊D3C2412yes—
194C22×C3×D3—24no—
195C22×C3×D3—24no—
196C22×C3×D3—24no—
197C22×C3×D3C2414yes—
198C32×Q8—28no—
199C2×C32×C4—24no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2414yes—
207C4×C3⋊D3—28no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C3×D12—28no—
219#627—48no—
220#626—48no—
221D3×Dic3—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—31no—
226C2×#124—92no—
227C2×#123—92no—
228C2×C22⋊Q8—92no—
229C2×C22⋊Q8—91no—
230C2×#121—91no—
231C2×C4×Q8—31no—
232C2×C4×D4—91no—
233C2×#117—91no—
234C24×C3—32no—
235C23×D3—31no—
236C23×D3—31no—
237C23×D3—61no—
238C23×D3C22×D312yes—
239C2×C3×Q8—24no—
240C2×C3×Q8—24no—
241C2×C3×Q8—24no—
242C2×C3×Q8—44no—
243C2×C3×Q8C22×D314yes—
244C2×C3×Q8C22×D314yes—
245C2×C3×D4—34no—
246C2×C3×D4—64no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
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—32no—
263C22×Dic3—32no—
264C22×Dic3—38no—
265C22×Dic3—61no—
266C22×Dic3—62no—
267C22×Dic3—124no—
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D311yescharacteristic
270C22×Dic3C22×D311yescharacteristic
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D312yes—
273C2×D12—24no—
274C2×D12—38no—
275C2×D12—124no—
276C2×D12C22×D314yes—
277C2×C4×D3—34no—
278C2×C4×D3—34no—
279C2×C4×D3—38no—
280C2×C4×D3—64no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—124no—
284C2×C4×D3—124no—
285C2×Dic6—38no—
286C2×Dic6—38no—
287C2×Dic6—124no—
288C2×Dic6—124no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C22⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C42—34no—
294C3×C42—34no—
295C3×C42—38no—
296#217—38no—
297#217—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—34no—
303(C2×D3)⋊C4—34no—
304(C2×D3)⋊C4—34no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—68no—
307(C2×D3)⋊C4C22×D318yes—
308(C2×D3)⋊C4C22×D318yes—
309C4⋊Dic3—34no—
310C4⋊Dic3—34no—
311C4⋊Dic3—38no—
312C4⋊Dic3—64no—
313C4⋊Dic3C22×D314yes—
314C4⋊Dic3C22×D318yes—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—34no—
320Dic3⋊C4—34no—
321Dic3⋊C4—38no—
322Dic3⋊C4—68no—
323C4×Dic3C22×D314yes—
324C4×Dic3C22×D314yes—
325C4×Dic3C22×D318yes—
326C22×C32C2×#4112yes—
327C22×C32H(5,𝔽2)12yes—
328C22×C322−1+412yes—
329C22×C32C2511yescharacteristic
330C2×C3⋊D3—22no—
331C2×C3⋊D3—22no—
332C2×C3⋊D3—22no—
333C2×C3⋊D3—44no—
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—48no—
338C32×C4—24no—
339C32×C4C2×#4114yes—
340C3⋊Dic3—22no—
341C3⋊Dic3—24no—
342C3×Dic3—22no—
343C3×Dic3—24no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C22×Q8—92no—
348C22×Q8D3211yescharacteristic
349C22×D4—31no—
350C22×D4—92no—
351C23×C4—92no—
352C23×C4—91no—
353C4⋊Q8—98no—
354#126—916no—
355#124—38no—
356#124—916no—
357#123—916no—
358C22⋊Q8—916no—
359C22⋊Q8—98no—
360#121—98no—
361C4×Q8—38no—
362C4×D4—98no—
363#117—98no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—92no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—91no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—32no—
381C23×C3—21no—
382C23×C3—34no—
383C23×C3—64no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3C23×D311yescharacteristic
387C23×C3C23×D311yescharacteristic
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—32no—
392C22×D3—32no—
393C22×D3—62no—
394C22×D3—64no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3—62no—
401C22×D3—122no—
402C22×D3—122no—
403C22×D3C23×D314yes—
404C3×Q8—28no—
405C3×Q8—28no—
406C3×Q8—48no—
407C3×D4—68no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—34no—
417C2×C3×C4—32no—
418C2×C3×C4—44no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
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—22no—
435C2×Dic3—22no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—34no—
439C2×Dic3—34no—
440C2×Dic3—62no—
441C2×Dic3—64no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—64no—
446C2×Dic3—122no—
447C2×Dic3—124no—
448C2×Dic3—128no—
449C2×Dic3C23×D312yes—
450C2×Dic3C23×D312yes—
451C2×Dic3C23×D312yes—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D314yes—
454D12—28no—
455D12—128no—
456C4×D3—68no—
457C4×D3—68no—
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—42no—
467C3×D3—44no—
468C24—32no—
469C24—91no—
470C2×Q8—24no—
471C2×Q8—98no—
472C2×Q8—364no—
473C2×Q8C2×D3214yes—
474C2×D4—34no—
475C2×D4—64no—
476C2×D4—98no—
477C2×D4—364no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—32no—
483C22×C4—98no—
484C22×C4—91no—
485C22×C4—92no—
486C22×C4—94no—
487C22×C4—184no—
488C22×C4—364no—
489C22×C4C2×D3212yes—
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—34no—
492C4⋊C4—38no—
493C4⋊C4—94no—
494C4⋊C4—94no—
495C4⋊C4—98no—
496C4⋊C4—94no—
497C4⋊C4—98no—
498C22⋊C4—38no—
499C22⋊C4—38no—
500C22⋊C4—94no—
501C22⋊C4—94no—
502C22⋊C4—98no—
503C22⋊C4—98no—
504C22⋊C4—98no—
505C42—34no—
506C42—34no—
507C42—38no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—64no—
513C22×C3—64no—
514C22×C3—64no—
515C22×C3—128no—
516C22×C3C2×#23512yes—
517C22×C3C2×#23712yes—
518C22×C3#100712yes—
519C22×C3#100912yes—
520C22×C3#100912yes—
521C22×C3#101012yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C24×D311yescharacteristic
524C2×D3—24no—
525C2×D3—24no—
526C2×D3—24no—
527C2×D3—48no—
528C2×D3—64no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—128no—
538C2×D3—124no—
539C2×D3—124no—
540C3×C4—24no—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—44no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—64no—
547C3×C4—62no—
548C3×C4—62no—
549C3×C4C2×#23514yes—
550C3×C4C2×#23714yes—
551Dic3—22no—
552Dic3—22no—
553Dic3—24no—
554Dic3—22no—
555Dic3—22no—
556Dic3—62no—
557Dic3—62no—
558Dic3—64no—
559Dic3—64no—
560Dic3—122no—
561Dic3—124no—
562C32C2×#54211yescharacteristic, complemented, Sylow
563C23—34no—
564C23—64no—
565C23—64no—
566C23—64no—
567C23—92no—
568C23—182no—
569C23—182no—
570C23—182no—
571C23C22×D3211yescharacteristic
572Q8—28no—
573Q8—368no—
574D4—68no—
575D4—368no—
576C2×C4—24no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—34no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—64no—
586C2×C4—62no—
587C2×C4—92no—
588C2×C4—94no—
589C2×C4—184no—
590C2×C4—182no—
591C2×C4—188no—
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—124no—
601C2×C3#558214yescomplemented
602C2×C3#568214yescomplemented
603C2×C3C22×#23511yescharacteristic
604C2×C3C22×#23711yescharacteristic
605C2×C3C2×#100711yescharacteristic
606C2×C3C2×#100911yescharacteristic
607C2×C3C2×#100911yescharacteristic
608C2×C3C2×#101011yescharacteristic
609D3—44no—
610D3—124no—
611D3—122no—
612D3—122no—
613C22—64no—
614C22—64no—
615C22—64no—
616C22—128no—
617C22—182no—
618C22—182no—
619C22—182no—
620C22—364no—
621C22#6431512yes—
622C22#6432012yes—
623C22C2×#380412yes—
624C22C23×D3211yescharacteristic
625C4—24no—
626C4—62no—
627C4—62no—
628C4—62no—
629C4—64no—
630C4—62no—
631C4—184no—
632C4—182no—
633C4C2×#380414yes—
634C3—21no—
635C3C2×#558211yescharacteristic, complemented
636C3C2×#568211yescharacteristic, complemented
637C2—124no—
638C2—362no—
639C2#1059539514yesdirect product factor
640C2C2×#6431511yescharacteristic
641C2C2×#6432011yescharacteristic
642C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC2×#63916C2
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×#64155C2semidirect
2. C2×C3×#947C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595395C2direct (N × H)
5. C2×#63918C2semidirect
7. C2×#63899C2semidirect
8. C2×Dic3×D12C2semidirect
9. C2×#63890C2semidirect
10. C2×#63874C2semidirect
11. C2×#63859C2semidirect
12. C2×#63852C2semidirect
21. #64155C22semidirect
25. C3×#947C22semidirect
26. C3×Q8×Dic3C22semidirect
41. #63918C22semidirect
43. #63899C22semidirect
44. Dic3×D12C22semidirect
45. #63890C22semidirect
46. #63874C22semidirect
47. #63859C22semidirect
48. #63852C22semidirect
51. C2×#947D3semidirect
55. C2×Q8×Dic3D3semidirect
140. #947C2×D3semidirect
144. Q8×Dic3C2×D3semidirect
462. C2×C32#542semidirect
562. C32C2×#542semidirect
601. C2×C3#5582semidirect
602. C2×C3#5682semidirect
635. C3C2×#5582semidirect
636. C3C2×#5682semidirect
639. C2#10595395direct (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×#9472
C2×C3×Q8×Dic32
#105953952
C2×#639182
C2×#639162
C2×#638992
C2×Dic3×D122
C2×#638902
C2×#638742
C2×#638592
C2×#638522
C2×#56823
C2×#55823