Finite Group Databasebeta

← C2×#10594551 #11903077

Subgroups — C2×#10594551 #11903077

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#63905C212yesmaximal
5C2×C4×#625C211yesmaximal, characteristic
6C2×#63861C212yesmaximal, complemented
7C2×#63856C211yesmaximal, characteristic, complemented
8C2×#63847C212yesmaximal, complemented
9C2×#63843C211yesmaximal, characteristic, complemented
10C2×#63841C211yesmaximal, characteristic, complemented
11C2×#63841C212yesmaximal, complemented
12#10594551C2116yesmaximal, direct product factor
13C2×#5639—31nomaximal
14C2×#5513—31nomaximal
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#625C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64099C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C3×#897C2218yescomplemented
31C3×D3×C4⋊C4C2218yescomplemented
32C2×#3724C2211yescharacteristic
33C2×#3724C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2212yes—
41#63905C22116yes—
42C4×#625C2218yes—
43#63861C22116yescomplemented
44#63856C2218yescomplemented
45#63847C22116yescomplemented
46#63843C2218yescomplemented
47#63841C22116yescomplemented
48#63841C2218yescomplemented
49C2×C3×C22⋊Q8—31no—
50C22×C3×C4⋊C4—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×#929—32no—
54C2×C4×#67—31no—
55C2×C4×#67—31no—
56C2×#926—32no—
57C2×#926—31no—
58C2×#924—31no—
59#5639—316no—
60#5513—316no—
61C2×#898—32no—
62C2×#897D311yescharacteristic, complemented
63C2×#892—31no—
64C2×#892—32no—
65C2×D3×C4⋊C4D311yescharacteristic, complemented
66C2×#890—31no—
67C2×#890—31no—
68C2×#890—61no—
69C2×#889—32no—
70C2×#889—32no—
71C2×#887—31no—
72C2×#883—32no—
73C2×#879—32no—
74C23×C3×D3C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C2×C3×C4×D3—28no—
86C2×C3×C4×D3—24no—
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3C2318yes—
89C2×C3×C4×D3C2314yes—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#625—24no—
94C2×#625C2314yes—
95C32×C4⋊C4C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97C4⋊(C3⋊Dic3)C2318yes—
98#3750C2318yes—
99C4×C3⋊Dic3C2314yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2318yes—
103C3×Dic3⋊C4C2318yes—
104#3724C2314yes—
105#3724C2318yes—
106Dic3⋊Dic3C2318yes—
107(C2×D3)⋊Dic3C2314yes—
108(C2×D3)⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#552—91noSylow
114C22×C3×Q8—31no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×C3×C4—32no—
118C22×#67—31no—
119C22×#67—31no—
120C22×C4×D3C2×D312yes—
121C22×C4×D3C2×D311yescharacteristic
122C22×C4×D3C2×D311yescharacteristic
123C22×Dic6C2×D311yescharacteristic
124C3×C22⋊Q8—38no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—38no—
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C22⋊C4—32no—
133C2×#217—31no—
134C2×#217—32no—
135C2×#217—32no—
136C2×#217—31no—
137#946—38no—
138Q8×Dic3—38no—
139#929—316no—
140C4×#67—38no—
141C4×#67—38no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4C2×D312yes—
147#926—38no—
148#926—316no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—61no—
155C2×C4⋊Dic3—62no—
156C2×C4⋊Dic3C2×D312yes—
157C2×C4⋊Dic3C2×D311yescharacteristic
158#924—38no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—62no—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—61no—
175#898—316no—
176#897C2×D318yescomplemented
177#892—316no—
178#892—38no—
179D3×C4⋊C4C2×D318yescomplemented
180#890—38no—
181#890—38no—
182#890—68no—
183#889—316no—
184#889—316no—
185#887—38no—
186#883—316no—
187#879—316no—
188C23×C32C2411yescharacteristic
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—22no—
194C22×C3×D3#4114yes—
195C22×C3×D3C2412yes—
196C22×C3×D3C2412yes—
197C2×C32×C4—24no—
198C2×C32×C4#4114yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—24no—
204C2×C3⋊Dic3C2412yes—
205C2×C3⋊Dic3C2414yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C3×C4×D3—216no—
216C3×C4×D3—28no—
217C3×C4×D3—28no—
218C3×Dic6—28no—
219#625—28no—
220#552—916no—
221C2×#126—92no—
222C2×#125—92no—
223C2×#125—91no—
224C2×#123—92no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—91no—
229C2×#117—91no—
230C2×#117—92no—
231C22×C4⋊C4—31no—
232C24×C3—31no—
233C24×C3—31no—
234C23×D3C22×D311yescharacteristic
235C23×D3C22×D311yescharacteristic
236C2×C3×Q8—34no—
237C2×C3×Q8—64no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4—31no—
244C22×C3×C4—34no—
245C22×C3×C4—34no—
246C22×C3×C4—38no—
247C22×C3×C4—68no—
248C22×C3×C4—64no—
249C22×C3×C4—64no—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—34no—
255C2×#67—34no—
256C2×#67—64no—
257C2×#67—64no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—61no—
265C22×Dic3—61no—
266C22×Dic3—62no—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D311yescharacteristic
271C2×C4×D3—28no—
272C2×C4×D3—24no—
273C2×C4×D3—24no—
274C2×C4×D3C22×D318yes—
275C2×C4×D3C22×D314yes—
276C2×C4×D3C22×D314yes—
277C2×Dic6—24no—
278C2×Dic6C22×D314yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4—38no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4C22×D314yes—
284C3×C4⋊C4C22×D314yes—
285C3×C22⋊C4—38no—
286#217—34no—
287#217—38no—
288#217—38no—
289#217—34no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—34no—
294(C2×D3)⋊C4C22×D318yes—
295C4⋊Dic3—38no—
296C4⋊Dic3—34no—
297C4⋊Dic3—38no—
298C4⋊Dic3—34no—
299C4⋊Dic3—38no—
300C4⋊Dic3—64no—
301C4⋊Dic3—68no—
302C4⋊Dic3C22×D318yes—
303C4⋊Dic3C22×D314yes—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—34no—
309Dic3⋊C4—34no—
310Dic3⋊C4—38no—
311Dic3⋊C4—68no—
312Dic3⋊C4C22×D318yes—
313C4×Dic3—34no—
314C4×Dic3—34no—
315C4×Dic3—38no—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—64no—
320C22×C32C2×#4112yes—
321C22×C32C2×#4112yes—
322C22×C322−1+412yes—
323C22×C32C2511yescharacteristic
324C2×C3×D3—28no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3—44no—
331C2×C3×D3C2×#4114yes—
332C32×C4—24no—
333C32×C4C2×#4114yes—
334C3⋊Dic3—22no—
335C3⋊Dic3—22no—
336C3⋊Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3—22no—
340C3×Dic3—24no—
341C22×Q8—31no—
342C22×D4—91no—
343C23×C4—32no—
344C23×C4—31no—
345C23×C4—31no—
346#126—916no—
347#125—916no—
348#125—98no—
349#123—916no—
350C22⋊Q8—38no—
351C22⋊Q8—98no—
352C4×Q8—98no—
353C4×D4—98no—
354#117—98no—
355#117—916no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—38no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4D3211yescharacteristic
367C2×C22⋊C4—32no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—91no—
372C2×C42—92no—
373C2×C42—92no—
374C2×C42—91no—
375C23×C3—21no—
376C23×C3—34no—
377C23×C3—32no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3—62no—
383C23×C3—62no—
384C23×C3C23×D311yescharacteristic
385C23×C3C23×D311yescharacteristic
386C22×D3—22no—
387C22×D3—22no—
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3#23714yes—
392C22×D3C23×D312yes—
393C22×D3C23×D312yes—
394C3×Q8—68no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—32no—
401C2×C3×C4—34no—
402C2×C3×C4—34no—
403C2×C3×C4—32no—
404C2×C3×C4—44no—
405C2×C3×C4—616no—
406C2×C3×C4—62no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—64no—
410C2×C3×C4—68no—
411C2×C3×C4—68no—
412C2×C3×C4#23514yes—
413C2×C3×C4#23714yes—
414C2×C3×C4C23×D314yes—
415C2×C3×C4C23×D314yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418#67—68no—
419#67—68no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—22no—
423C2×Dic3—24no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—34no—
429C2×Dic3—34no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—64no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—64no—
436C2×Dic3—62no—
437C2×Dic3—64no—
438C2×Dic3—62no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—124no—
442C2×Dic3C23×D312yes—
443C2×Dic3C23×D314yes—
444C2×Dic3C23×D314yes—
445C2×Dic3C23×D312yes—
446C4×D3—216no—
447C4×D3—28no—
448C4×D3—28no—
449Dic6—28no—
450C2×C32#55214yescomplemented
451C2×C32C22×#4111yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C2×C32C2×2−1+411yescharacteristic
454C3×D3—24no—
455C3×D3—42no—
456C24—31no—
457C24—31no—
458C2×Q8—34no—
459C2×Q8—64no—
460C2×D4—94no—
461C2×D4—184no—
462C22×C4—31no—
463C22×C4—32no—
464C22×C4—32no—
465C22×C4—31no—
466C22×C4—38no—
467C22×C4—34no—
468C22×C4—34no—
469C22×C4—68no—
470C22×C4—64no—
471C22×C4—64no—
472C22×C4—91no—
473C22×C4—92no—
474C22×C4—91no—
475C22×C4C2×D3212yes—
476C22×C4C2×D3211yescharacteristic
477C4⋊C4—34no—
478C4⋊C4—38no—
479C4⋊C4—38no—
480C4⋊C4—94no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—94no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4C2×D3214yes—
487C22⋊C4—38no—
488C22⋊C4—94no—
489C22⋊C4—98no—
490C22⋊C4—98no—
491C22⋊C4—94no—
492C42—98no—
493C42—98no—
494C42—94no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—34no—
500C22×C3—68no—
501C22×C3—62no—
502C22×C3—62no—
503C22×C3—62no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—124no—
507C22×C3C2×#23512yes—
508C22×C3C2×#23712yes—
509C22×C3C2×#23712yes—
510C22×C3#100712yes—
511C22×C3#100712yes—
512C22×C3D3×#4112yes—
513C22×C3C24×D311yescharacteristic
514C22×C3C24×D311yescharacteristic
515C2×D3—22no—
516C2×D3—22no—
517C2×D3—28no—
518C2×D3—22no—
519C2×D3—22no—
520C2×D3—22no—
521C2×D3—44no—
522C2×D3C2×#23714yes—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—24no—
526C3×C4—44no—
527C3×C4—62no—
528C3×C4—64no—
529C3×C4—62no—
530C3×C4—64no—
531C3×C4C2×#23514yes—
532C3×C4C2×#23714yes—
533Dic3—22no—
534Dic3—24no—
535Dic3—22no—
536Dic3—24no—
537Dic3—62no—
538Dic3—62no—
539Dic3—64no—
540Dic3—62no—
541Dic3—64no—
542Dic3—62no—
543Dic3—122no—
544Dic3—122no—
545Dic3—124no—
546C32C2×#55211yescharacteristic, complemented, Sylow
547C23—34no—
548C23—32no—
549C23—32no—
550C23—62no—
551C23—62no—
552C23—62no—
553C23—62no—
554C23—62no—
555C23C22×D3211yescharacteristic
556Q8—68no—
557D4—188no—
558C2×C4—24no—
559C2×C4—32no—
560C2×C4—34no—
561C2×C4—34no—
562C2×C4—32no—
563C2×C4—616no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—64no—
567C2×C4—64no—
568C2×C4—68no—
569C2×C4—68no—
570C2×C4—92no—
571C2×C4—94no—
572C2×C4—92no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—184no—
576C2×C4#379514yes—
577C2×C4C22×D3214yes—
578C2×C4C22×D3212yes—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—24no—
583C2×C3—64no—
584C2×C3—122no—
585C2×C3#551314yescomplemented
586C2×C3#563914yescomplemented
587C2×C3C22×#23511yescharacteristic
588C2×C3C22×#23711yescharacteristic
589C2×C3C22×#23711yescharacteristic
590C2×C3C2×#100711yescharacteristic
591C2×C3C2×#100711yescharacteristic
592C2×C3C2×D3×#4111yescharacteristic
593D3—24no—
594D3—42no—
595C22—34no—
596C22—62no—
597C22—62no—
598C22—68no—
599C22—62no—
600C22—62no—
601C22—62no—
602C22—124no—
603C22C2×#379512yes—
604C22D3×#23712yes—
605C22#6431612yes—
606C22C23×D3211yescharacteristic
607C4—24no—
608C4—62no—
609C4—62no—
610C4—64no—
611C4—64no—
612C4—182no—
613C4—182no—
614C4—184no—
615C4C2×#379514yes—
616C3—21no—
617C3C2×#551311yescharacteristic, complemented
618C3C2×#563911yescharacteristic, complemented
619C2—64no—
620C2—122no—
621C2#1059455114yesdirect product factor
622C2C22×#379511yescharacteristic
623C2C2×D3×#23711yescharacteristic
624C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#552
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×#64099C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
6. C2×#63861C2semidirect
7. C2×#63856C2semidirect
8. C2×#63847C2semidirect
9. C2×#63843C2semidirect
10. C2×#63841C2semidirect
11. C2×#63841C2semidirect
12. #10594551C2direct (N × H)
25. #64099C22semidirect
30. C3×#897C22semidirect
31. C3×D3×C4⋊C4C22semidirect
43. #63861C22semidirect
44. #63856C22semidirect
45. #63847C22semidirect
46. #63843C22semidirect
47. #63841C22semidirect
48. #63841C22semidirect
62. C2×#897D3semidirect
65. C2×D3×C4⋊C4D3semidirect
176. #897C2×D3semidirect
179. D3×C4⋊C4C2×D3semidirect
450. C2×C32#552semidirect
546. C32C2×#552semidirect
585. C2×C3#5513semidirect
586. C2×C3#5639semidirect
617. C3C2×#5513semidirect
618. C3C2×#5639semidirect
621. C2#10594551direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×C3×#8972
C2×C3×D3×C4⋊C42
C2×#639052
C2×C4×#6252
C2×#638612
C2×#638562
C2×#638472
C2×#638432
C2×#638412
#105945512
C2×#56393
C2×#55133