Finite Group Databasebeta

← C2×#10594387 #11900843

Subgroups — C2×#10594387 #11900843

Order 1152.

2485 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×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63887C212yesmaximal
5C2×#63878C212yesmaximal
6C2×C4×D3×Dic3C211yesmaximal, characteristic
7C2×#63866C211yesmaximal, characteristic, complemented
8C2×#63857C211yesmaximal, characteristic
9C2×#63846C212yesmaximal, complemented
10C2×#63843C212yesmaximal, complemented
11C2×#63843C211yesmaximal, characteristic, complemented
12#10594387C2116yesmaximal, direct product factor
13C2×#5728—31nomaximal
14C2×#5622—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3750C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2212yes—
25#64096C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#897C2218yes—
32C3×#888C2218yescomplemented
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2211yescharacteristic
41#63887C22116yes—
42#63878C22116yes—
43C4×D3×Dic3C2218yes—
44#63866C2218yescomplemented
45#63857C2218yes—
46#63846C22116yescomplemented
47#63843C2218yescomplemented
48#63843C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×C22⋊Q8—31no—
51C2×#946—32no—
52C2×Q8×Dic3—32no—
53C2×Q8×Dic3—31no—
54C2×#944—31no—
55C2×#924—31no—
56C22×C4×Dic3—31no—
57#5728—316no—
58#5622—316no—
59C2×#897—31no—
60C2×#897D311yescharacteristic
61C2×#892—32no—
62C2×#890—32no—
63C2×#889—32no—
64C2×#888D311yescharacteristic, complemented
65C2×#887—31no—
66C2×#887—32no—
67C2×#887—31no—
68C2×#887—31no—
69C2×#887—61no—
70C2×#878—32no—
71C2×#877—32no—
72C2×C42×D3—31no—
73C2×#869—31no—
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C2×#634—24no—
81C2×#634C2314yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3C2314yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6—28no—
91C2×C3×Dic6C2318yes—
92C2×C3×Dic6C2314yes—
93C2×D3×Dic3—24no—
94C2×D3×Dic3Q818yescomplemented
95C2×D3×Dic3C2314yes—
96C2×D3×Dic3C2314yes—
97C32×C4⋊C4C2314yes—
98#3750C2318yes—
99C4×C3⋊Dic3C2314yes—
100C4×C3⋊Dic3C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2318yes—
104C3×Dic3⋊C4C2318yes—
105C3×C4×Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111Dic32C2314yes—
112Dic32C2318yes—
113Dic32C2314yes—
114C2×#533—91noSylow
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C23×C3×C4—31no—
118C23×Dic3—31no—
119C23×Dic3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3C2×D311yescharacteristic
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—61no—
126C22×Dic6C2×D311yescharacteristic
127C22×Dic6C2×D312yes—
128C3×C4⋊Q8—38no—
129C3×C22⋊Q8—38no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4—32no—
137C2×C3×C42—31no—
138C2×#217—32no—
139#946—316no—
140Q8×Dic3—316no—
141Q8×Dic3—38no—
142#944—38no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4C2×D312yes—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D312yes—
151#924—38no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—62no—
159C2×Dic3⋊C4C2×D312yes—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3—32no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—38no—
171C2×C4×Dic3—62no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D311yescharacteristic
174#897—38no—
175#897C2×D318yes—
176#892—316no—
177#890—316no—
178#889—316no—
179#888C2×D318yescomplemented
180#887—38no—
181#887—316no—
182#887—38no—
183#887—38no—
184#887—68no—
185#878—316no—
186#877—316no—
187C42×D3—38no—
188#869—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⋊Dic3C2×Q814yes—
201C2×C3⋊Dic3C2412yes—
202C2×C3⋊Dic3C2414yes—
203C2×C3⋊Dic3C2412yes—
204#634—28no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3C2×Q814yes—
209C2×C3×Dic3#4114yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×C4×D3—28no—
216C3×Dic6—28no—
217C3×Dic6—216no—
218D3×Dic3—28no—
219D3×Dic3C2×Q8116yescomplemented
220#533—916no—
221C2×C4⋊Q8—31no—
222C2×C4⋊Q8—91no—
223C2×#125—92no—
224C2×C22⋊Q8—31no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×Q8—92no—
229C2×C4×Q8—91no—
230C2×#117—92no—
231C22×C42—91no—
232C24×C3—31no—
233C23×D3C22×D311yescharacteristic
234C2×C3×Q8—34no—
235C2×C3×Q8—38no—
236C2×C3×Q8—68no—
237C2×C3×Q8—64no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—34no—
246C22×C3×C4—64no—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—38no—
254C22×Dic3—34no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—32no—
258C22×Dic3—32no—
259C22×Dic3—34no—
260C22×Dic3—61no—
261C22×Dic3—62no—
262C22×Dic3—61no—
263C22×Dic3—64no—
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C2×C4×D3—24no—
270C2×C4×D3—38no—
271C2×C4×D3—34no—
272C2×C4×D3—34no—
273C2×C4×D3—64no—
274C2×C4×D3C22×D314yes—
275C2×Dic6—24no—
276C2×Dic6—28no—
277C2×Dic6—34no—
278C2×Dic6—34no—
279C2×Dic6—64no—
280C2×Dic6—68no—
281C2×Dic6—64no—
282C2×Dic6—64no—
283C2×Dic6C22×D314yes—
284C2×Dic6C22×D318yes—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—38no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4C22×D314yes—
290C3×C4⋊C4C22×D314yes—
291C3×C22⋊C4—38no—
292C3×C42—34no—
293#217—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4C22×D318yes—
296C4⋊Dic3—38no—
297C4⋊Dic3—38no—
298C4⋊Dic3—38no—
299C4⋊Dic3—38no—
300C4⋊Dic3C22×D314yes—
301C4⋊Dic3C22×D318yes—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—68no—
309Dic3⋊C4C22×D318yes—
310C4×Dic3—34no—
311C4×Dic3—38no—
312C4×Dic3—38no—
313C4×Dic3—34no—
314C4×Dic3—34no—
315C4×Dic3—34no—
316C4×Dic3—38no—
317C4×Dic3—34no—
318C4×Dic3—38no—
319C4×Dic3—34no—
320C4×Dic3—64no—
321C4×Dic3—68no—
322C4×Dic3C22×D314yes—
323C22×C32C22×Q812yes—
324C22×C32C2×#4112yes—
325C22×C32C2×#4112yes—
326C22×C32C2511yescharacteristic
327C2×C3×D3—28no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3C22×Q814yes—
331C32×C4—24no—
332C32×C4C2×#4114yes—
333C3⋊Dic3—24no—
334C3⋊Dic3—22no—
335C3⋊Dic3C22×Q814yes—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3C22×Q814yes—
340C3×Dic3C2×#4114yes—
341C22×Q8—31no—
342C22×Q8—32no—
343C22×Q8—91no—
344C23×C4—31no—
345C23×C4—91no—
346C23×C4—91no—
347C4⋊Q8—38no—
348C4⋊Q8—98no—
349#125—916no—
350C22⋊Q8—38no—
351C22⋊Q8—916no—
352C22⋊Q8—98no—
353C4×Q8—916no—
354C4×Q8—98no—
355C4×Q8—98no—
356#117—916no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4D3211yescharacteristic
366C2×C22⋊C4—32no—
367C2×C22⋊C4—92no—
368C2×C42—31no—
369C2×C42—98no—
370C2×C42—92no—
371C2×C42—91no—
372C2×C42—91no—
373C2×C42—92no—
374C2×C42—91no—
375C23×C3—21no—
376C23×C3—34no—
377C23×C3—32no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3C23×D311yescharacteristic
381C23×C3C23×D311yescharacteristic
382C22×D3—22no—
383C22×D3—22no—
384C22×D3D3×Q814yes—
385C22×D3C23×D312yes—
386C3×Q8—616no—
387C3×Q8—68no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—44no—
401C2×C3×C4—62no—
402C2×C3×C4—64no—
403C2×C3×C4—64no—
404C2×C3×C4—68no—
405C2×C3×C4#23714yes—
406C2×C3×C4#23914yes—
407C2×C3×C4C23×D314yes—
408C2×C3×C4C23×D314yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—316no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—68no—
428C2×Dic3—64no—
429C2×Dic3—62no—
430C2×Dic3—64no—
431C2×Dic3—62no—
432C2×Dic3—68no—
433C2×Dic3—122no—
434C2×Dic3#23714yes—
435C2×Dic3D3×Q814yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D314yes—
439C2×Dic3C23×D312yes—
440C2×Dic3C23×D312yes—
441C4×D3—28no—
442C4×D3—316no—
443C4×D3—68no—
444Dic6—28no—
445Dic6—216no—
446Dic6—616no—
447Dic6—68no—
448Dic6—68no—
449C2×C32#53314yescomplemented
450C2×C32C23×Q811yescharacteristic
451C2×C32C22×#4111yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C3×D3—24no—
454C24—31no—
455C2×Q8—34no—
456C2×Q8—38no—
457C2×Q8—68no—
458C2×Q8—64no—
459C2×Q8—94no—
460C2×Q8—184no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—32no—
465C22×C4—32no—
466C22×C4—34no—
467C22×C4—64no—
468C22×C4—94no—
469C22×C4—98no—
470C22×C4—94no—
471C22×C4—91no—
472C22×C4—91no—
473C22×C4—92no—
474C22×C4—184no—
475C22×C4C2×D3212yes—
476C22×C4C2×D3211yescharacteristic
477C4⋊C4—38no—
478C4⋊C4—38no—
479C4⋊C4—34no—
480C4⋊C4—98no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—98no—
484C4⋊C4—98no—
485C4⋊C4C2×D3214yes—
486C22⋊C4—38no—
487C22⋊C4—98no—
488C42—34no—
489C42—94no—
490C42—94no—
491C42—98no—
492C42—94no—
493C42—98no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—34no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—68no—
502C22×C3C2×#23712yes—
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—22no—
511C2×D3—22no—
512C2×D3—28no—
513C2×D3C2×D3×Q814yes—
514C3×C4—24no—
515C3×C4—24no—
516C3×C4—24no—
517C3×C4—34no—
518C3×C4—34no—
519C3×C4—44no—
520C3×C4—62no—
521C3×C4—64no—
522C3×C4—64no—
523C3×C4C2×#23714yes—
524C3×C4C2×#23914yes—
525Dic3—24no—
526Dic3—24no—
527Dic3—22no—
528Dic3—34no—
529Dic3—34no—
530Dic3—64no—
531Dic3—68no—
532Dic3—64no—
533Dic3—62no—
534Dic3—64no—
535Dic3—62no—
536Dic3—122no—
537Dic3C2×#23714yes—
538Dic3C2×D3×Q814yes—
539C32C2×#53311yescharacteristic, complemented, Sylow
540C23—34no—
541C23—32no—
542C23—62no—
543C23—62no—
544C23C22×D3211yescharacteristic
545Q8—616no—
546Q8—68no—
547Q8—188no—
548C2×C4—24no—
549C2×C4—34no—
550C2×C4—34no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—34no—
555C2×C4—34no—
556C2×C4—62no—
557C2×C4—64no—
558C2×C4—64no—
559C2×C4—68no—
560C2×C4—916no—
561C2×C4—94no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—94no—
565C2×C4—188no—
566C2×C4—184no—
567C2×C4—182no—
568C2×C4#379614yes—
569C2×C4C22×D3214yes—
570C2×C4C22×D3212yes—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—24no—
575C2×C3—64no—
576C2×C3#562214yescomplemented
577C2×C3#572814yescomplemented
578C2×C3C22×#23711yescharacteristic
579C2×C3C22×#23711yescharacteristic
580C2×C3C22×D3×Q811yescharacteristic
581C2×C3C22×D3×Q811yescharacteristic
582C2×C3C22×#23911yescharacteristic
583C2×C3C2×D3×#4111yescharacteristic
584D3—24no—
585C22—34no—
586C22—62no—
587C22—62no—
588C22—68no—
589C22C2×#379612yes—
590C22D3×#23712yes—
591C22D32×Q812yes—
592C22C23×D3211yescharacteristic
593C4—24no—
594C4—34no—
595C4—34no—
596C4—62no—
597C4—64no—
598C4—64no—
599C4—94no—
600C4—184no—
601C4—182no—
602C4C2×#379614yes—
603C3—21no—
604C3C2×#562211yescharacteristic, complemented
605C3C2×#572811yescharacteristic, complemented
606C2—64no—
607C2#1059438714yesdirect product factor
608C2C22×#379611yescharacteristic
609C2C2×D3×#23711yescharacteristic
610C2C2×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
1. C2×#64096C2semidirect
3. C2×C3×#888C2semidirect
7. C2×#63866C2semidirect
9. C2×#63846C2semidirect
10. C2×#63843C2semidirect
11. C2×#63843C2semidirect
12. #10594387C2direct (N × H)
25. #64096C22semidirect
32. C3×#888C22semidirect
44. #63866C22semidirect
46. #63846C22semidirect
47. #63843C22semidirect
48. #63843C22semidirect
64. C2×#888D3semidirect
94. C2×D3×Dic3Q8semidirect
179. #888C2×D3semidirect
219. D3×Dic3C2×Q8semidirect
449. C2×C32#533semidirect
539. C32C2×#533semidirect
576. C2×C3#5622semidirect
577. C2×C3#5728semidirect
604. C3C2×#5622semidirect
605. C3C2×#5728semidirect
607. C2#10594387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8972
C2×C3×#8882
C2×#638872
C2×#638782
C2×C4×D3×Dic32
C2×#638662
C2×#638572
C2×#638462
C2×#638432
#105943872
C2×#57283
C2×#56223