Finite Group Databasebeta

← C2×#10594970 #11903028

Subgroups — C2×#10594970 #11903028

Order 1152.

2461 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C2×#63975C212yesmaximal
5C2×#63956C212yesmaximal, complemented
6#10594970C2116yesmaximal, direct product factor
7C2×#63900C211yesmaximal, characteristic, complemented
8C2×#63872C211yesmaximal, characteristic, complemented
9C2×#63871C211yesmaximal, characteristic, complemented
10C2×#63867C212yesmaximal, complemented
11C2×#63843C211yesmaximal, characteristic, complemented
12C2×#63836C212yesmaximal, complemented
13C2×#5639—31nomaximal
14C2×#5529—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#624C2212yes—
20C2×#3757C2211yescharacteristic
21C4×#638C2218yes—
22C2×#3752C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×#926C2218yescomplemented
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2218yescomplemented
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×C4×Dic3C2212yes—
34#63975C22116yes—
35C2×#3724C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×#3722C2212yes—
41#63956C22116yescomplemented
42C2×Dic32C2212yes—
43#63900C2218yescomplemented
44#63872C2218yescomplemented
45#63871C2218yescomplemented
46#63867C22116yescomplemented
47#63843C2218yescomplemented
48#63836C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×#117—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×C4×#67—31no—
54C2×C4×#67—31no—
55C2×C4×#67—61no—
56C2×#926D311yescharacteristic, complemented
57C2×#924D311yescharacteristic, complemented
58#5639—316no—
59#5529—316no—
60C2×#897—31no—
61C2×#892—32no—
62C2×D3×C4⋊C4—31no—
63C2×D3×C4⋊C4—31no—
64C2×#890—31no—
65C2×#890—31no—
66C2×#889—32no—
67C2×#887—31no—
68C2×#883—32no—
69C2×#883—32no—
70C2×#879—32no—
71C2×#879—32no—
72C2×#872—32no—
73C2×#870—32no—
74C24×C32C2311yescharacteristic
75C23×C3⋊D3C2311yescharacteristic
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C2×#638—24no—
81C2×#638C2314yes—
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3C2314yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#624—28no—
94C2×#624C2318yes—
95#3757C2314yes—
96#3752C2314yes—
97#3750C2314yes—
98C4×C3⋊Dic3C2314yes—
99C3×#217C2318yes—
100C3×#217C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2314yes—
104C3×Dic3⋊C4C2318yes—
105C3×C4×Dic3C2318yes—
106#3724C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111#3722C2318yes—
112Dic32C2318yes—
113C2×#552—91noSylow
114C22×C3×Q8—31no—
115C23×C3×C4—21no—
116C23×C3×C4C2×D311yescharacteristic
117C23×C3×C4C2×D311yescharacteristic
118C22×#67—31no—
119C22×#67—31no—
120C22×#67—61no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—32no—
124C22×C4×D3—32no—
125C22×C4×D3—61no—
126C22×Dic6C2×D311yescharacteristic
127C3×C22⋊Q8—38no—
128C3×#117—38no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—32no—
136C2×#217—31no—
137C2×#217—31no—
138C2×#217—61no—
139C2×#217C2×D312yes—
140C2×#217C2×D312yes—
141#946—38no—
142Q8×Dic3—38no—
143C4×#67—38no—
144C4×#67—38no—
145C4×#67—68no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—61no—
151#926C2×D318yescomplemented
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—32no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159#924C2×D318yescomplemented
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—32no—
168C2×Dic3⋊C4—61no—
169C2×Dic3⋊C4C2×D312yes—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3C2×D312yes—
176#897—38no—
177#892—316no—
178D3×C4⋊C4—38no—
179D3×C4⋊C4—38no—
180#890—38no—
181#890—38no—
182#889—316no—
183#887—38no—
184#883—316no—
185#883—316no—
186#879—316no—
187#879—316no—
188#872—316no—
189#870—316no—
190C23×C32—22no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32C2412yes—
194C23×C32C2411yescharacteristic
195C22×C3⋊D3—22no—
196C22×C3⋊D3—22no—
197C22×C3⋊D3#4114yes—
198C22×C3⋊D3C2412yes—
199C2×C32×C4—22no—
200C2×C32×C4—28no—
201C2×C32×C4#4114yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204#638—28no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3—22no—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3C2412yes—
209C2×C3⋊Dic3C2412yes—
210C2×C3⋊Dic3C2412yes—
211C4×C3⋊D3—28no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2414yes—
220C3×Dic6—28no—
221#624—216no—
222#552—916no—
223C2×#126—92no—
224C2×#125—92no—
225C2×#125—91no—
226C2×#123—92no—
227C2×C22⋊Q8—31no—
228C2×C22⋊Q8—91no—
229C2×C4×Q8—91no—
230C2×C4×D4—91no—
231C2×#117—31no—
232C2×#117—92no—
233C22×C4⋊C4—91no—
234C24×C3—21no—
235C24×C3C22×D311yescharacteristic
236C24×C3C22×D311yescharacteristic
237C23×D3—31no—
238C23×D3—31no—
239C23×D3—61no—
240C2×C3×Q8—34no—
241C2×C3×Q8—64no—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—32no—
248C22×C3×C4—32no—
249C22×C3×C4—32no—
250C22×C3×C4—32no—
251C22×C3×C4—44no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D314yes—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—34no—
259C2×#67—34no—
260C2×#67—64no—
261C2×#67—64no—
262C2×#67—64no—
263C2×#67—68no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—61no—
271C22×Dic3—61no—
272C22×Dic3—61no—
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D312yes—
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D312yes—
277C2×C4×D3—34no—
278C2×C4×D3—34no—
279C2×C4×D3—38no—
280C2×C4×D3—38no—
281C2×C4×D3—64no—
282C2×C4×D3—68no—
283C2×C4×D3—68no—
284C2×C4×D3—64no—
285C2×C4×D3—64no—
286C2×C4×D3—124no—
287C2×Dic6—24no—
288C2×Dic6C22×D314yes—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—34no—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—38no—
295C3×C42—38no—
296#217—34no—
297#217—34no—
298#217—64no—
299#217C22×D318yes—
300#217C22×D318yes—
301(C2×D3)⋊C4—34no—
302(C2×D3)⋊C4—34no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—64no—
306C4⋊Dic3—38no—
307C4⋊Dic3—38no—
308C4⋊Dic3—38no—
309C4⋊Dic3—38no—
310C4⋊Dic3C22×D314yes—
311C4⋊Dic3C22×D314yes—
312C4⋊Dic3C22×D314yes—
313Dic3⋊C4—34no—
314Dic3⋊C4—34no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4—64no—
322Dic3⋊C4C22×D318yes—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—38no—
326C4×Dic3—38no—
327C4×Dic3—64no—
328C4×Dic3C22×D318yes—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—44no—
333C22×C32C2×#4112yes—
334C22×C32C2×#4112yes—
335C22×C322−1+412yes—
336C22×C32C2511yescharacteristic
337C2×C3⋊D3—28no—
338C2×C3⋊D3—22no—
339C2×C3⋊D3—22no—
340C2×C3⋊D3C2×#4114yes—
341C32×C4—22no—
342C32×C4C2×#4114yes—
343C3⋊Dic3—22no—
344C3⋊Dic3—22no—
345C3⋊Dic3—22no—
346C3×Dic3—24no—
347C3×Dic3—24no—
348C3×Dic3—24no—
349C3×Dic3—24no—
350C22×Q8—31no—
351C22×D4—91no—
352C23×C4—92no—
353C23×C4—91no—
354C23×C4D3211yescharacteristic
355#126—916no—
356#125—916no—
357#125—98no—
358#123—916no—
359C22⋊Q8—38no—
360C22⋊Q8—98no—
361C4×Q8—98no—
362C4×D4—98no—
363#117—38no—
364#117—916no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—98no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—92no—
372C2×C4⋊C4—92no—
373C2×C4⋊C4—92no—
374C2×C4⋊C4—92no—
375C2×C4⋊C4—91no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—92no—
379C2×C22⋊C4—91no—
380C2×C22⋊C4—91no—
381C2×C42—32no—
382C2×C42—92no—
383C2×C42—91no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—21no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3C23×D312yes—
396C23×C3C23×D312yes—
397C23×C3C23×D311yescharacteristic
398C23×C3C23×D311yescharacteristic
399C22×D3—34no—
400C22×D3—34no—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—64no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—122no—
410C22×D3—122no—
411C3×Q8—68no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—28no—
415C2×C3×C4—28no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—34no—
420C2×C3×C4—34no—
421C2×C3×C4—34no—
422C2×C3×C4—34no—
423C2×C3×C4—48no—
424C2×C3×C4—42no—
425C2×C3×C4—64no—
426C2×C3×C4—64no—
427C2×C3×C4—64no—
428C2×C3×C4—64no—
429C2×C3×C4#23514yes—
430C2×C3×C4#23714yes—
431C2×C3×C4C23×D312yes—
432C2×C3×C4C23×D312yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435#67—68no—
436#67—68no—
437#67—616no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—32no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—32no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—64no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—122no—
459C2×Dic3—122no—
460C2×Dic3C23×D314yes—
461C2×Dic3C23×D314yes—
462C2×Dic3C23×D314yes—
463C2×Dic3C23×D314yes—
464C4×D3—616no—
465C4×D3—616no—
466C4×D3—68no—
467C4×D3—68no—
468C4×D3—128no—
469Dic6—28no—
470C2×C32—42no—
471C2×C32#55214yescomplemented
472C2×C32C22×#4111yescharacteristic
473C2×C32C22×#4111yescharacteristic
474C2×C32C2×2−1+411yescharacteristic
475C3⋊D3—24no—
476C24—91no—
477C24C2×D3211yescharacteristic
478C2×Q8—34no—
479C2×Q8—64no—
480C2×D4—94no—
481C2×D4—184no—
482C22×C4—24no—
483C22×C4—32no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—98no—
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—91no—
491C22×C4—94no—
492C22×C4—188no—
493C22×C4—184no—
494C22×C4C2×D3214yes—
495C22×C4C2×D3211yescharacteristic
496C22×C4C2×D3211yescharacteristic
497C4⋊C4—34no—
498C4⋊C4—34no—
499C4⋊C4—34no—
500C4⋊C4—38no—
501C4⋊C4—98no—
502C4⋊C4—98no—
503C4⋊C4—98no—
504C4⋊C4—98no—
505C4⋊C4—98no—
506C4⋊C4—94no—
507C22⋊C4—38no—
508C22⋊C4—38no—
509C22⋊C4—98no—
510C22⋊C4—94no—
511C22⋊C4—94no—
512C42—38no—
513C42—98no—
514C42—94no—
515C22×C3—24no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—48no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3C2×#23512yes—
532C22×C3C2×#23712yes—
533C22×C3#100712yes—
534C22×C3D3×#4112yes—
535C22×C3D3×#4112yes—
536C22×C3#101012yes—
537C22×C3C24×D311yescharacteristic
538C22×C3C24×D311yescharacteristic
539C2×D3—34no—
540C2×D3—34no—
541C2×D3—64no—
542C2×D3—68no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—68no—
548C2×D3—122no—
549C2×D3—122no—
550C2×D3—128no—
551C3×C4—22no—
552C3×C4—22no—
553C3×C4—24no—
554C3×C4—42no—
555C3×C4—64no—
556C3×C4—64no—
557C3×C4—64no—
558C3×C4—64no—
559C3×C4C2×#23514yes—
560C3×C4C2×#23714yes—
561Dic3—24no—
562Dic3—24no—
563Dic3—24no—
564Dic3—24no—
565Dic3—64no—
566Dic3—62no—
567Dic3—62no—
568Dic3—62no—
569Dic3—62no—
570Dic3—62no—
571Dic3—62no—
572Dic3—122no—
573Dic3—122no—
574C32C2×#55211yescharacteristic, complemented, Sylow
575C23—22no—
576C23—22no—
577C23—22no—
578C23—94no—
579C23—92no—
580C23—182no—
581C23—182no—
582C23C22×D3212yes—
583C23C22×D3211yescharacteristic
584Q8—68no—
585D4—188no—
586C2×C4—22no—
587C2×C4—28no—
588C2×C4—34no—
589C2×C4—34no—
590C2×C4—34no—
591C2×C4—34no—
592C2×C4—64no—
593C2×C4—64no—
594C2×C4—64no—
595C2×C4—64no—
596C2×C4—92no—
597C2×C4—92no—
598C2×C4—92no—
599C2×C4—1816no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—182no—
603C2×C4—188no—
604C2×C4#380414yes—
605C2×C4C22×D3212yes—
606C2×C4C22×D3212yes—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—24no—
611C2×C3—44no—
612C2×C3—42no—
613C2×C3—42no—
614C2×C3#552914yescomplemented
615C2×C3#563914yescomplemented
616C2×C3C22×#23511yescharacteristic
617C2×C3C22×#23711yescharacteristic
618C2×C3C2×#100711yescharacteristic
619C2×C3C2×D3×#4111yescharacteristic
620C2×C3C2×D3×#4111yescharacteristic
621C2×C3C2×#101011yescharacteristic
622D3—64no—
623D3—64no—
624D3—124no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—44no—
629C22—94no—
630C22—182no—
631C22—182no—
632C22—188no—
633C22#6429712yes—
634C22#6430612yes—
635C22C2×#380412yes—
636C22C23×D3211yescharacteristic
637C4—22no—
638C4—64no—
639C4—64no—
640C4—64no—
641C4—64no—
642C4—182no—
643C4—182no—
644C4—182no—
645C4C2×#380414yes—
646C3—21no—
647C3C2×#552911yescharacteristic, complemented
648C3C2×#563911yescharacteristic, complemented
649C2—42no—
650C2—184no—
651C2#1059497014yesdirect product factor
652C2C2×#6429711yescharacteristic
653C2C2×#6430611yescharacteristic
654C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×C3×#924C2semidirect
5. C2×#63956C2semidirect
6. #10594970C2direct (N × H)
7. C2×#63900C2semidirect
8. C2×#63872C2semidirect
9. C2×#63871C2semidirect
10. C2×#63867C2semidirect
11. C2×#63843C2semidirect
12. C2×#63836C2semidirect
27. C3×#926C22semidirect
31. C3×#924C22semidirect
41. #63956C22semidirect
43. #63900C22semidirect
44. #63872C22semidirect
45. #63871C22semidirect
46. #63867C22semidirect
47. #63843C22semidirect
48. #63836C22semidirect
56. C2×#926D3semidirect
57. C2×#924D3semidirect
151. #926C2×D3semidirect
159. #924C2×D3semidirect
471. C2×C32#552semidirect
574. C32C2×#552semidirect
614. C2×C3#5529semidirect
615. C2×C3#5639semidirect
647. C3C2×#5529semidirect
648. C3C2×#5639semidirect
651. C2#10594970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9262
C2×C3×#9242
C2×#639752
C2×#639562
#105949702
C2×#639002
C2×#638722
C2×#638712
C2×#638672
C2×#638432
C2×#638362
C2×#56393
C2×#55293