Finite Group Databasebeta

← C2×#10594397 #11900842

Subgroups — C2×#10594397 #11900842

Order 1152.

2497 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×#63888C212yesmaximal
5C2×C4×#624C211yesmaximal, characteristic
6C2×#63871C211yesmaximal, characteristic
7C2×#63866C211yesmaximal, characteristic, complemented
8C2×#63845C212yesmaximal, complemented
9C2×#63844C211yesmaximal, characteristic, complemented
10C2×Dic3×Dic6C212yesmaximal, complemented
11C2×#63836C212yesmaximal
12#10594397C2116yesmaximal, direct product factor
13C2×#5728—31nomaximal
14C2×#5578—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×Dic6C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×#624C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2212yes—
24#64106C2218yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#888C2218yescomplemented
32C3×#887C2218yescomplemented
33C2×#3724C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×#3722C2212yes—
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2211yescharacteristic
41#63888C22116yes—
42C4×#624C2218yes—
43#63871C2218yes—
44#63866C2218yescomplemented
45#63845C22116yescomplemented
46#63844C2218yescomplemented
47Dic3×Dic6C22116yescomplemented
48#63836C22116yes—
49C2×C3×C4⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#946—31no—
52C2×#946—32no—
53C2×Q8×Dic3—32no—
54C2×#944—31no—
55#5728—316no—
56#5578—316no—
57C2×#897—31no—
58C2×#897—31no—
59C2×#897—31no—
60C2×#897—61no—
61C2×#896—32no—
62C2×#892—32no—
63C2×#890—32no—
64C2×#889—32no—
65C2×#888D311yescharacteristic, complemented
66C2×#887—31no—
67C2×#887D311yescharacteristic, complemented
68C2×#872—32no—
69C2×C42×D3—31no—
70C2×C42×D3—31no—
71C2×#869—31no—
72C2×C4×Dic6—32no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3C2314yes—
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×Dic6—24no—
90C2×C3×Dic6—28no—
91C2×C3×Dic6C2314yes—
92C2×C3×Dic6C2318yes—
93C2×#624—24no—
94C2×#624Q818yescomplemented
95C2×#624C2314yes—
96C2×#624C2314yes—
97C32×C4⋊C4C2314yes—
98#3752C2318yes—
99C4⋊(C3⋊Dic3)C2318yes—
100C3×C4⋊Dic3C2314yes—
101C3×Dic3⋊C4C2318yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2318yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110#3722C2318yes—
111Dic32C2318yes—
112Dic32C2314yes—
113Dic32C2314yes—
114C2×#533—91noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—61no—
124C22×Dic6—31no—
125C22×Dic6—31no—
126C22×Dic6—61no—
127C22×Dic6C2×D312yes—
128C22×Dic6C2×D311yescharacteristic
129C3×C4⋊Q8—38no—
130C3×C4×Q8—38no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C42—31no—
138C2×C3×C42—32no—
139C2×C3×C42—31no—
140#946—38no—
141#946—316no—
142Q8×Dic3—316no—
143#944—38no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—62no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—62no—
155C2×C4⋊Dic3C2×D311yescharacteristic
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4C2×D312yes—
162C2×Dic3⋊C4C2×D312yes—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3C2×D311yescharacteristic
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D312yes—
172#897—38no—
173#897—38no—
174#897—38no—
175#897—68no—
176#896—316no—
177#892—316no—
178#890—316no—
179#889—316no—
180#888C2×D318yescomplemented
181#887—38no—
182#887C2×D318yescomplemented
183#872—316no—
184C42×D3—38no—
185C42×D3—38no—
186#869—38no—
187C4×Dic6—316no—
188C4×Dic6—38no—
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C2×Q814yes—
193C22×C3⋊D3C2412yes—
194C2×C32×C4—24no—
195C2×C32×C4#4114yes—
196C2×C32×C4C2414yes—
197C2×C32×C4C2412yes—
198C2×C3⋊Dic3—24no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3C2412yes—
201C2×C3⋊Dic3C2414yes—
202C4×C3⋊D3—28no—
203#634—28no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3C2×Q814yes—
208C2×C3×Dic3C2×Q814yes—
209C2×C3×Dic3#4114yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C3×Dic6—28no—
217C3×Dic6—216no—
218#624—28no—
219#624C2×Q8116yescomplemented
220#533—916no—
221C2×C4⋊Q8—31no—
222C2×C4⋊Q8—91no—
223C2×#125—92no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—91no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—31no—
228C2×C4×Q8—91no—
229C2×C4×Q8—92no—
230C2×#117—92no—
231C22×C42—91no—
232C23×D3—31no—
233C23×D3—31no—
234C23×D3—61no—
235C2×C3×Q8—34no—
236C2×C3×Q8—38no—
237C2×C3×Q8—68no—
238C2×C3×Q8—64no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—61no—
256C22×Dic3—62no—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D311yescharacteristic
263C2×C4×D3—38no—
264C2×C4×D3—38no—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—34no—
269C2×C4×D3—34no—
270C2×C4×D3—34no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—124no—
277C2×Dic6—24no—
278C2×Dic6—28no—
279C2×Dic6—34no—
280C2×Dic6—34no—
281C2×Dic6—64no—
282C2×Dic6—64no—
283C2×Dic6—64no—
284C2×Dic6—124no—
285C2×Dic6C22×D318yes—
286C2×Dic6C22×D314yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—38no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4C22×D314yes—
292C3×C4⋊C4C22×D314yes—
293C3×C42—34no—
294C3×C42—38no—
295C3×C42—34no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—68no—
301C4⋊Dic3—38no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—38no—
305C4⋊Dic3—38no—
306C4⋊Dic3—68no—
307C4⋊Dic3C22×D314yes—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4C22×D318yes—
314Dic3⋊C4C22×D318yes—
315C4×Dic3—34no—
316C4×Dic3—38no—
317C4×Dic3—34no—
318C4×Dic3—34no—
319C4×Dic3—34no—
320C4×Dic3—38no—
321C4×Dic3C22×D314yes—
322C4×Dic3C22×D314yes—
323C4×Dic3C22×D318yes—
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⋊Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3—24no—
338C3×Dic3—24no—
339C3×Dic3C22×Q814yes—
340C3×Dic3C22×Q814yes—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—32no—
344C22×Q8—91no—
345C23×C4—91no—
346C23×C4—91no—
347C23×C4—91no—
348C4⋊Q8—38no—
349C4⋊Q8—98no—
350#125—916no—
351C22⋊Q8—916no—
352C22⋊Q8—98no—
353C22⋊Q8—98no—
354C4×Q8—38no—
355C4×Q8—98no—
356C4×Q8—916no—
357#117—916no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4D3211yescharacteristic
367C2×C22⋊C4—92no—
368C2×C22⋊C4—92no—
369C2×C42—32no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—98no—
373C2×C42—92no—
374C2×C42—91no—
375C2×C42—91no—
376C23×C3—21no—
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D311yescharacteristic
379C22×D3—34no—
380C22×D3—34no—
381C22×D3—32no—
382C22×D3—32no—
383C22×D3—64no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—122no—
390C22×D3—122no—
391C3×Q8—616no—
392C3×Q8—68no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—32no—
402C2×C3×C4—32no—
403C2×C3×C4—32no—
404C2×C3×C4—32no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—44no—
408C2×C3×C4—62no—
409C2×C3×C4—64no—
410C2×C3×C4—64no—
411C2×C3×C4#23514yes—
412C2×C3×C4#23914yes—
413C2×C3×C4C23×D314yes—
414C2×C3×C4C23×D314yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—22no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—62no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—62no—
428C2×Dic3—64no—
429C2×Dic3—62no—
430C2×Dic3—124no—
431C2×Dic3—122no—
432C2×Dic3#23714yes—
433C2×Dic3D3×Q814yes—
434C2×Dic3D3×Q814yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D314yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D312yes—
439C2×Dic3C23×D312yes—
440C2×Dic3C23×D312yes—
441C4×D3—316no—
442C4×D3—316no—
443C4×D3—68no—
444C4×D3—68no—
445C4×D3—68no—
446C4×D3—68no—
447C4×D3—128no—
448Dic6—28no—
449Dic6—216no—
450Dic6—68no—
451Dic6—68no—
452Dic6—128no—
453C2×C32#53314yescomplemented
454C2×C32C23×Q811yescharacteristic
455C2×C32C22×#4111yescharacteristic
456C2×C32C22×#4111yescharacteristic
457C3⋊D3—24no—
458C24—91no—
459C2×Q8—34no—
460C2×Q8—38no—
461C2×Q8—68no—
462C2×Q8—64no—
463C2×Q8—94no—
464C2×Q8—184no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—94no—
472C22×C4—98no—
473C22×C4—94no—
474C22×C4—91no—
475C22×C4—92no—
476C22×C4—94no—
477C22×C4—184no—
478C22×C4—184no—
479C22×C4C2×D3212yes—
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—38no—
482C4⋊C4—38no—
483C4⋊C4—34no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—98no—
487C4⋊C4—98no—
488C4⋊C4—98no—
489C4⋊C4C2×D3214yes—
490C22⋊C4—98no—
491C22⋊C4—98no—
492C42—34no—
493C42—34no—
494C42—38no—
495C42—94no—
496C42—94no—
497C42—98no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3C2×#23512yes—
503C22×C3C2×#23712yes—
504C22×C3C2×D3×Q812yes—
505C22×C3C2×D3×Q812yes—
506C22×C3C2×#23912yes—
507C22×C3D3×#4112yes—
508C22×C3C24×D311yescharacteristic
509C22×C3C24×D311yescharacteristic
510C2×D3—34no—
511C2×D3—34no—
512C2×D3—64no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—62no—
517C2×D3—68no—
518C2×D3—68no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—128no—
522C3×C4—24no—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—34no—
526C3×C4—34no—
527C3×C4—34no—
528C3×C4—44no—
529C3×C4—62no—
530C3×C4—64no—
531C3×C4—64no—
532C3×C4C2×#23514yes—
533C3×C4C2×#23914yes—
534Dic3—24no—
535Dic3—24no—
536Dic3—22no—
537Dic3—64no—
538Dic3—62no—
539Dic3—64no—
540Dic3—62no—
541Dic3—124no—
542Dic3—122no—
543Dic3C2×#23714yes—
544Dic3C2×D3×Q814yes—
545Dic3C2×D3×Q814yes—
546C32C2×#53311yescharacteristic, complemented, Sylow
547C23—94no—
548C23—92no—
549C23—182no—
550C23—182no—
551C23C22×D3211yescharacteristic
552Q8—616no—
553Q8—68no—
554Q8—188no—
555C2×C4—24no—
556C2×C4—34no—
557C2×C4—34no—
558C2×C4—34no—
559C2×C4—32no—
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—34no—
564C2×C4—34no—
565C2×C4—64no—
566C2×C4—62no—
567C2×C4—64no—
568C2×C4—916no—
569C2×C4—92no—
570C2×C4—94no—
571C2×C4—188no—
572C2×C4—182no—
573C2×C4—184no—
574C2×C4—188no—
575C2×C4#379914yes—
576C2×C4C22×D3214yes—
577C2×C4C22×D3212yes—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—24no—
582C2×C3#557814yescomplemented
583C2×C3#572814yescomplemented
584C2×C3C22×#23511yescharacteristic
585C2×C3C22×#23711yescharacteristic
586C2×C3C22×D3×Q811yescharacteristic
587C2×C3C22×D3×Q811yescharacteristic
588C2×C3C22×#23911yescharacteristic
589C2×C3C2×D3×#4111yescharacteristic
590D3—64no—
591D3—64no—
592D3—124no—
593C22—94no—
594C22—182no—
595C22—182no—
596C22—188no—
597C22C2×#379912yes—
598C22D3×#23712yes—
599C22D32×Q812yes—
600C22C23×D3211yescharacteristic
601C4—24no—
602C4—34no—
603C4—34no—
604C4—34no—
605C4—64no—
606C4—62no—
607C4—64no—
608C4—182no—
609C4—184no—
610C4C2×#379914yes—
611C3—21no—
612C3C2×#557811yescharacteristic, complemented
613C3C2×#572811yescharacteristic, complemented
614C2—184no—
615C2#1059439714yesdirect product factor
616C2C22×#379911yescharacteristic
617C2C2×D3×#23711yescharacteristic
618C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#888C2semidirect
3. C2×C3×#887C2semidirect
7. C2×#63866C2semidirect
8. C2×#63845C2semidirect
9. C2×#63844C2semidirect
10. C2×Dic3×Dic6C2semidirect
12. #10594397C2direct (N × H)
31. C3×#888C22semidirect
32. C3×#887C22semidirect
44. #63866C22semidirect
45. #63845C22semidirect
46. #63844C22semidirect
47. Dic3×Dic6C22semidirect
65. C2×#888D3semidirect
67. C2×#887D3semidirect
94. C2×#624Q8semidirect
180. #888C2×D3semidirect
182. #887C2×D3semidirect
219. #624C2×Q8semidirect
453. C2×C32#533semidirect
546. C32C2×#533semidirect
582. C2×C3#5578semidirect
583. C2×C3#5728semidirect
612. C3C2×#5578semidirect
613. C3C2×#5728semidirect
615. C2#10594397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8882
C2×C3×#8872
C2×#638882
C2×C4×#6242
C2×#638712
C2×#638662
C2×#638452
C2×#638442
C2×Dic3×Dic62
C2×#638362
#105943972
C2×#57283
C2×#55783