Finite Group Databasebeta

← C2×#10594333 #11903036

Subgroups — C2×#10594333 #11903036

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic
5C2×#63871C211yesmaximal, characteristic, complemented
6C2×#63870C212yesmaximal, complemented
7C2×#63869C211yesmaximal, characteristic, complemented
8C2×#63868C212yesmaximal, complemented
9C2×#63856C211yesmaximal, characteristic, complemented
10C2×#63855C212yesmaximal, complemented
11C2×#63850C212yesmaximal
12#10594333C2116yesmaximal, direct product factor
13C2×#5581—31nomaximal
14C2×#5513—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2212yes—
24#64101C2218yescomplemented
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×D3×C4⋊C4C2218yescomplemented
31C3×#887C2218yescomplemented
32C2×#3724C2212yes—
33C2×#3724C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2212yes—
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C4×#626C2218yes—
42#63871C2218yescomplemented
43#63870C22116yescomplemented
44#63869C2218yescomplemented
45#63868C22116yescomplemented
46#63856C2218yescomplemented
47#63855C22116yescomplemented
48#63850C22116yes—
49C2×C3×C4×Q8—31no—
50C22×C3×C4⋊C4—31no—
51C2×#946—31no—
52C2×#946—31no—
53C2×#929—32no—
54C2×C4×#67—31no—
55C2×#926—32no—
56C2×#924—31no—
57#5581—316no—
58#5513—316no—
59C2×#898—32no—
60C2×#897—31no—
61C2×#894—32no—
62C2×#892—31no—
63C2×#892—31no—
64C2×#892—61no—
65C2×D3×C4⋊C4D311yescharacteristic, complemented
66C2×#890—31no—
67C2×#889—32no—
68C2×#889—32no—
69C2×#887D311yescharacteristic, complemented
70C2×#876—32no—
71C2×C4×D12—31no—
72C2×#872—32no—
73C2×#870—31no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3C2314yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×C4×D3—28no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3C2318yes—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#626—24no—
94C2×#626C2314yes—
95C32×C4⋊C4C2314yes—
96#3752C2318yes—
97C4⋊(C3⋊Dic3)C2314yes—
98C4×C3⋊Dic3C2318yes—
99C3×C4⋊Dic3C2314yes—
100C3×Dic3⋊C4C2318yes—
101C3×Dic3⋊C4C2318yes—
102C3×C4×Dic3C2318yes—
103C3×C4×Dic3C2314yes—
104#3724C2318yes—
105#3724C2318yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2314yes—
109#3722C2318yes—
110#3722C2314yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2314yes—
113C2×#552—91noSylow
114C22×C3×Q8—31no—
115C23×C3×C4—31no—
116C23×C3×C4—32no—
117C22×#67—31no—
118C22×D12—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—61no—
122C22×C4×D3C2×D312yes—
123C22×C4×D3C2×D311yescharacteristic
124C22×Dic6C2×D311yescharacteristic
125C3×C4×Q8—38no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—38no—
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C42—31no—
134C2×C3×C42—32no—
135C2×#217—32no—
136C2×#217—31no—
137#946—38no—
138#946—38no—
139#929—316no—
140C4×#67—38no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—62no—
150#926—316no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—32no—
156C2×C4⋊Dic3—61no—
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—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4C2×D312yes—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—62no—
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D312yes—
173#898—316no—
174#897—38no—
175#894—316no—
176#892—38no—
177#892—38no—
178#892—68no—
179D3×C4⋊C4C2×D318yescomplemented
180#890—38no—
181#889—316no—
182#889—316no—
183#887C2×D318yescomplemented
184#876—316no—
185C4×D12—38no—
186#872—316no—
187#870—38no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C2412yes—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3#4114yes—
196C22×C3×D3C2412yes—
197C2×C32×C4—24no—
198C2×C32×C4#4114yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3C2412yes—
204C2×C3⋊Dic3C2414yes—
205C4×C3⋊D3—28no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C3×C4×D3—216no—
217C3×C4×D3—28no—
218C3×Dic6—28no—
219#626—28no—
220#552—916no—
221C2×#126—92no—
222C2×#125—91no—
223C2×#125—92no—
224C2×#123—92no—
225C2×C22⋊Q8—91no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—31no—
228C2×C4×D4—91no—
229C2×#117—92no—
230C2×#117—91no—
231C22×C4⋊C4—31no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—34no—
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—32no—
245C22×C3×C4—32no—
246C22×C3×C4—34no—
247C22×C3×C4—38no—
248C22×C3×C4—68no—
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—64no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—32no—
259C22×Dic3—32no—
260C22×Dic3—61no—
261C22×Dic3—62no—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D311yescharacteristic
267C2×D12—34no—
268C2×D12—64no—
269C2×C4×D3—28no—
270C2×C4×D3—24no—
271C2×C4×D3—34no—
272C2×C4×D3—34no—
273C2×C4×D3—64no—
274C2×C4×D3—68no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3C22×D318yes—
278C2×C4×D3C22×D314yes—
279C2×Dic6—24no—
280C2×Dic6C22×D314yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—38no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4C22×D314yes—
286C3×C4⋊C4C22×D314yes—
287C3×C42—34no—
288C3×C42—38no—
289#217—38no—
290#217—34no—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—68no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—38no—
304C4⋊Dic3—38no—
305C4⋊Dic3—64no—
306C4⋊Dic3C22×D314yes—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—34no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4C22×D318yes—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—68no—
319C4×Dic3C22×D314yes—
320C4×Dic3C22×D318yes—
321C22×C32C2×#4112yes—
322C22×C32C2×#4112yes—
323C22×C322−1+412yes—
324C22×C32C2511yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—44no—
329C2×C3×D3—28no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3C2×#4114yes—
333C32×C4—24no—
334C32×C4C2×#4114yes—
335C3⋊Dic3—22no—
336C3⋊Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—24no—
341C3×Dic3—22no—
342C22×Q8—31no—
343C22×D4—91no—
344C23×C4—32no—
345C23×C4—31no—
346C23×C4—91no—
347#126—916no—
348#125—98no—
349#125—916no—
350#123—916no—
351C22⋊Q8—98no—
352C22⋊Q8—98no—
353C4×Q8—38no—
354C4×D4—98no—
355#117—916no—
356#117—98no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—38no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4D3211yescharacteristic
368C2×C22⋊C4—91no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C42—32no—
374C2×C42—31no—
375C2×C42—92no—
376C23×C3—21no—
377C23×C3—34no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—32no—
386C22×D3—32no—
387C22×D3—62no—
388C22×D3—64no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3#23714yes—
398C22×D3C23×D312yes—
399C3×Q8—68no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—34no—
409C2×C3×C4—34no—
410C2×C3×C4—44no—
411C2×C3×C4—616no—
412C2×C3×C4—62no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—64no—
417C2×C3×C4—68no—
418C2×C3×C4#23514yes—
419C2×C3×C4#23514yes—
420C2×C3×C4C23×D314yes—
421C2×C3×C4C23×D314yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424#67—68no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—24no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—34no—
433C2×Dic3—34no—
434C2×Dic3—62no—
435C2×Dic3—64no—
436C2×Dic3—64no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—64no—
440C2×Dic3—64no—
441C2×Dic3—124no—
442C2×Dic3C23×D312yes—
443C2×Dic3C23×D312yes—
444C2×Dic3C23×D314yes—
445C2×Dic3C23×D314yes—
446C2×Dic3C23×D312yes—
447D12—68no—
448C4×D3—216no—
449C4×D3—28no—
450C4×D3—616no—
451C4×D3—68no—
452C4×D3—68no—
453Dic6—28no—
454C2×C32#55214yescomplemented
455C2×C32C22×#4111yescharacteristic
456C2×C32C22×#4111yescharacteristic
457C2×C32C2×2−1+411yescharacteristic
458C3⋊D3—42no—
459C3×D3—24no—
460C24—31no—
461C24—91no—
462C2×Q8—34no—
463C2×Q8—64no—
464C2×D4—94no—
465C2×D4—184no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—38no—
472C22×C4—34no—
473C22×C4—68no—
474C22×C4—64no—
475C22×C4—91no—
476C22×C4—92no—
477C22×C4—94no—
478C22×C4—184no—
479C22×C4C2×D3212yes—
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—38no—
483C4⋊C4—38no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—94no—
487C4⋊C4—98no—
488C4⋊C4—98no—
489C4⋊C4—94no—
490C4⋊C4C2×D3214yes—
491C22⋊C4—94no—
492C22⋊C4—98no—
493C22⋊C4—94no—
494C22⋊C4—98no—
495C22⋊C4—98no—
496C42—38no—
497C42—34no—
498C42—98no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—34no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—68no—
507C22×C3C2×#23512yes—
508C22×C3C2×#23512yes—
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—64no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—128no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3C2×#23714yes—
531C3×C4—24no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—44no—
535C3×C4—62no—
536C3×C4—64no—
537C3×C4—62no—
538C3×C4—62no—
539C3×C4—64no—
540C3×C4C2×#23514yes—
541C3×C4C2×#23514yes—
542Dic3—24no—
543Dic3—22no—
544Dic3—24no—
545Dic3—22no—
546Dic3—22no—
547Dic3—64no—
548Dic3—62no—
549Dic3—62no—
550Dic3—64no—
551Dic3—64no—
552Dic3—124no—
553C32C2×#55211yescharacteristic, complemented, Sylow
554C23—34no—
555C23—32no—
556C23—62no—
557C23—62no—
558C23—92no—
559C23—182no—
560C23—182no—
561C23—182no—
562C23C22×D3211yescharacteristic
563Q8—68no—
564D4—188no—
565C2×C4—24no—
566C2×C4—32no—
567C2×C4—34no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—34no—
571C2×C4—616no—
572C2×C4—62no—
573C2×C4—64no—
574C2×C4—64no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—68no—
578C2×C4—92no—
579C2×C4—94no—
580C2×C4—182no—
581C2×C4—184no—
582C2×C4—188no—
583C2×C4#379814yes—
584C2×C4C22×D3214yes—
585C2×C4C22×D3212yes—
586C2×C3—24no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—64no—
591C2×C3#551314yescomplemented
592C2×C3#558114yescomplemented
593C2×C3C22×#23511yescharacteristic
594C2×C3C22×#23511yescharacteristic
595C2×C3C22×#23711yescharacteristic
596C2×C3C2×#100711yescharacteristic
597C2×C3C2×#100711yescharacteristic
598C2×C3C2×D3×#4111yescharacteristic
599D3—24no—
600D3—124no—
601D3—122no—
602D3—122no—
603C22—34no—
604C22—68no—
605C22—62no—
606C22—62no—
607C22—182no—
608C22—182no—
609C22—182no—
610C22—364no—
611C22C2×#379812yes—
612C22D3×#23712yes—
613C22#6431612yes—
614C22C23×D3211yescharacteristic
615C4—24no—
616C4—62no—
617C4—64no—
618C4—64no—
619C4—62no—
620C4—62no—
621C4—182no—
622C4—184no—
623C4C2×#379814yes—
624C3—21no—
625C3C2×#551311yescharacteristic, complemented
626C3C2×#558111yescharacteristic, complemented
627C2—64no—
628C2—362no—
629C2#1059433314yesdirect product factor
630C2C22×#379811yescharacteristic
631C2C2×D3×#23711yescharacteristic
632C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
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×#64101C2semidirect
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×C3×#887C2semidirect
5. C2×#63871C2semidirect
6. C2×#63870C2semidirect
7. C2×#63869C2semidirect
8. C2×#63868C2semidirect
9. C2×#63856C2semidirect
10. C2×#63855C2semidirect
12. #10594333C2direct (N × H)
24. #64101C22semidirect
30. C3×D3×C4⋊C4C22semidirect
31. C3×#887C22semidirect
42. #63871C22semidirect
43. #63870C22semidirect
44. #63869C22semidirect
45. #63868C22semidirect
46. #63856C22semidirect
47. #63855C22semidirect
65. C2×D3×C4⋊C4D3semidirect
69. C2×#887D3semidirect
179. D3×C4⋊C4C2×D3semidirect
183. #887C2×D3semidirect
454. C2×C32#552semidirect
553. C32C2×#552semidirect
591. C2×C3#5513semidirect
592. C2×C3#5581semidirect
625. C3C2×#5513semidirect
626. C3C2×#5581semidirect
629. C2#10594333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×C3×D3×C4⋊C42
C2×C3×#8872
C2×C4×#6262
C2×#638712
C2×#638702
C2×#638692
C2×#638682
C2×#638562
C2×#638552
C2×#638502
#105943332
C2×#55813
C2×#55133