Finite Group Databasebeta

← C2×#10594841 #11903406

Subgroups — C2×#10594841 #11903406

Order 1152.

2389 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×#64135C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C2×#63959C212yesmaximal
5C2×#63956C212yesmaximal, complemented
6C2×#63918C211yesmaximal, characteristic, complemented
7C2×#63862C212yesmaximal, complemented
8C2×#63856C211yesmaximal, characteristic, complemented
9#10594841C2116yesmaximal, direct product factor
10C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
11C2×#63841C211yesmaximal, characteristic, complemented
12C2×#63838C212yesmaximal, complemented
13C2×#5641—31nomaximal
14C2×#5542—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2212yes—
20C2×#3757C2212yes—
21#64135C2218yescomplemented
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2211yescharacteristic
27C3×C4×#67C2218yes—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2218yescomplemented
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39#63959C22116yes—
40#63956C22116yescomplemented
41C2×Dic32C2212yes—
42C2×Dic32C2212yes—
43#63918C2218yescomplemented
44#63862C22116yescomplemented
45#63856C2218yescomplemented
46Dic3×Dic6C2218yescomplemented
47#63841C2218yescomplemented
48#63838C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×D4—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×#936—32no—
54C2×C4×#67D311yescharacteristic
55C2×#926—31no—
56C2×#926—31no—
57C2×#926—31no—
58C2×#926—61no—
59C2×#924—31no—
60C2×#924D311yescharacteristic, complemented
61#5641—316no—
62#5542—316no—
63C2×#898—32no—
64C2×#892—31no—
65C2×#888—31no—
66C2×#887—32no—
67C2×#887—32no—
68C2×#885—32no—
69C2×#879—32no—
70C2×#879—32no—
71C2×#879—32no—
72C2×#869—31no—
73C2×C4×Dic6—31no—
74C24×C32C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2312yes—
82C2×C3×#67—24no—
83C2×C3×#67C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#627—28no—
94C2×#627C2318yes—
95#3757C2318yes—
96C4⋊(C3⋊Dic3)C2314yes—
97C4⋊(C3⋊Dic3)C2314yes—
98C4×C3⋊Dic3C2318yes—
99C3×#217C2318yes—
100C3×#217C2314yes—
101C3×(C2×D3)⋊C4C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2318yes—
104C3×Dic3⋊C4C2314yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×D4—31no—
116C23×C3×C4—21no—
117C23×C3×C4—31no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C2×D311yescharacteristic
120C22×#67C2×D311yescharacteristic
121C22×C4×D3C2×D311yescharacteristic
122C22×Dic6—32no—
123C22×Dic6—32no—
124C22×Dic6C2×D311yescharacteristic
125C3×C22⋊Q8—38no—
126C3×C4×D4—38no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C22⋊C4—31no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—31no—
133C2×C3×C42—31no—
134C2×#217—32no—
135C2×#217—32no—
136C2×#217—32no—
137C2×#217—32no—
138C2×#217—62no—
139C2×#217C2×D311yescharacteristic
140C2×#217C2×D312yes—
141#946—38no—
142Q8×Dic3—38no—
143#936—316no—
144C4×#67C2×D318yes—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4C2×D311yescharacteristic
148#926—38no—
149#926—38no—
150#926—38no—
151#926—68no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—32no—
157C2×C4⋊Dic3—32no—
158C2×C4⋊Dic3—61no—
159C2×C4⋊Dic3—61no—
160C2×C4⋊Dic3C2×D311yescharacteristic
161#924—38no—
162#924C2×D318yescomplemented
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4C2×D312yes—
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×C4×Dic3—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—32no—
175C2×C4×Dic3—62no—
176C2×C4×Dic3C2×D311yescharacteristic
177#898—316no—
178#892—38no—
179#888—38no—
180#887—316no—
181#887—316no—
182#885—316no—
183#879—316no—
184#879—316no—
185#879—316no—
186#869—38no—
187C4×Dic6—38no—
188C23×C32—22no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32C2412yes—
192C23×C32C2411yescharacteristic
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C2×C32×C4—22no—
198C2×C32×C4—28no—
199C2×C32×C4#4114yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2412yes—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3—24no—
204C2×C3⋊Dic3C2414yes—
205C2×C3⋊Dic3C2414yes—
206C3×#67—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C3×C4×D3—28no—
218C3×Dic6—28no—
219#627—216no—
220#556—916no—
221C2×C4⋊Q8—91no—
222C2×#126—92no—
223C2×#126—92no—
224C2×#124—92no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×Q8—92no—
229C2×C4×D4—31no—
230C2×#117—91no—
231C2×#117—91no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C22×D311yescharacteristic
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—34no—
238C2×C3×Q8—64no—
239C2×C3×D4—34no—
240C2×C3×D4—64no—
241C22×C3×C4—28no—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—32no—
250C22×C3×C4—32no—
251C22×C3×C4—31no—
252C22×C3×C4—34no—
253C22×C3×C4—64no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D314yes—
257C22×C3×C4C22×D314yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—24no—
261C2×#67C22×D314yes—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—32no—
265C22×Dic3—32no—
266C22×Dic3—62no—
267C22×Dic3—62no—
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D312yes—
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C2×C4×D3—24no—
274C2×C4×D3C22×D314yes—
275C2×Dic6—24no—
276C2×Dic6—38no—
277C2×Dic6—38no—
278C2×Dic6—68no—
279C2×Dic6—68no—
280C2×Dic6C22×D314yes—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—34no—
284C3×C22⋊C4—34no—
285C3×C22⋊C4—38no—
286C3×C22⋊C4—34no—
287C3×C42—34no—
288#217—38no—
289#217—38no—
290#217—38no—
291#217—38no—
292#217—68no—
293#217C22×D314yes—
294#217C22×D318yes—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4C22×D314yes—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305C4⋊Dic3—64no—
306C4⋊Dic3C22×D314yes—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4C22×D318yes—
312Dic3⋊C4C22×D314yes—
313C4×Dic3—38no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—68no—
320C4×Dic3C22×D314yes—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—44no—
325C22×C32C2×#4112yes—
326C22×C32C2×#4112yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—44no—
333C32×C4—22no—
334C32×C4C2×#4114yes—
335C3⋊Dic3—24no—
336C3⋊Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—92no—
344C22×D4—31no—
345C23×C4—31no—
346C23×C4D3211yescharacteristic
347C4⋊Q8—98no—
348#126—916no—
349#126—916no—
350#124—916no—
351C22⋊Q8—38no—
352C22⋊Q8—98no—
353C4×Q8—98no—
354C4×Q8—916no—
355C4×D4—38no—
356#117—98no—
357#117—98no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—91no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C42—31no—
373C2×C42—92no—
374C2×C42—92no—
375C2×C42—92no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—32no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3C23×D312yes—
392C23×C3C23×D312yes—
393C23×C3C23×D311yescharacteristic
394C23×C3C23×D311yescharacteristic
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3C23×D312yes—
399C3×Q8—68no—
400C3×D4—68no—
401C2×C3×C4—24no—
402C2×C3×C4—216no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—28no—
406C2×C3×C4—28no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—34no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—34no—
414C2×C3×C4—34no—
415C2×C3×C4—32no—
416C2×C3×C4—64no—
417C2×C3×C4—62no—
418C2×C3×C4—64no—
419C2×C3×C4—62no—
420C2×C3×C4—68no—
421C2×C3×C4#23714yes—
422C2×C3×C4#23714yes—
423C2×C3×C4C23×D312yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426C2×C3×C4C23×D312yes—
427#67—28no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—24no—
431C2×Dic3—22no—
432C2×Dic3—34no—
433C2×Dic3—34no—
434C2×Dic3—34no—
435C2×Dic3—34no—
436C2×Dic3—64no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—64no—
441C2×Dic3—64no—
442C2×Dic3—124no—
443C2×Dic3—124no—
444C2×Dic3#23514yes—
445C2×Dic3C23×D312yes—
446C2×Dic3C23×D314yes—
447C2×Dic3C23×D314yes—
448C2×Dic3C23×D312yes—
449C2×Dic3C23×D312yes—
450C4×D3—28no—
451Dic6—28no—
452Dic6—616no—
453Dic6—616no—
454C2×C32—42no—
455C2×C32#55614yescomplemented
456C2×C32C22×#4111yescharacteristic
457C2×C32C22×#4111yescharacteristic
458C2×C32C2×2−1+411yescharacteristic
459C3×D3—42no—
460C24—31no—
461C24C2×D3211yescharacteristic
462C2×Q8—34no—
463C2×Q8—64no—
464C2×Q8—98no—
465C2×Q8—188no—
466C2×D4—34no—
467C2×D4—64no—
468C22×C4—24no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—34no—
475C22×C4—64no—
476C22×C4—92no—
477C22×C4—92no—
478C22×C4C2×D3214yes—
479C22×C4C2×D3211yescharacteristic
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—34no—
483C4⋊C4—38no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—98no—
487C4⋊C4—94no—
488C4⋊C4—94no—
489C22⋊C4—34no—
490C22⋊C4—38no—
491C22⋊C4—34no—
492C22⋊C4—98no—
493C22⋊C4—98no—
494C22⋊C4—98no—
495C42—34no—
496C42—98no—
497C42—98no—
498C42—98no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—48no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—124no—
519C22×C3C2×#23512yes—
520C22×C3C2×#23712yes—
521C22×C3C2×#23712yes—
522C22×C3#100712yes—
523C22×C3D3×#4112yes—
524C22×C3#101012yes—
525C22×C3C24×D311yescharacteristic
526C22×C3C24×D311yescharacteristic
527C2×D3—22no—
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—44no—
531C3×C4—24no—
532C3×C4—22no—
533C3×C4—22no—
534C3×C4—24no—
535C3×C4—34no—
536C3×C4—64no—
537C3×C4—62no—
538C3×C4—64no—
539C3×C4—62no—
540C3×C4C2×#23714yes—
541C3×C4C2×#23714yes—
542Dic3—24no—
543Dic3—22no—
544Dic3—24no—
545Dic3—22no—
546Dic3—64no—
547Dic3—64no—
548Dic3—64no—
549Dic3—64no—
550Dic3—124no—
551Dic3—124no—
552Dic3C2×#23514yes—
553C32C2×#55611yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—32no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23C22×D3212yes—
562C23C22×D3211yescharacteristic
563Q8—68no—
564Q8—1816no—
565D4—68no—
566C2×C4—22no—
567C2×C4—28no—
568C2×C4—34no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—34no—
573C2×C4—34no—
574C2×C4—62no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—68no—
579C2×C4—94no—
580C2×C4—94no—
581C2×C4—184no—
582C2×C4—184no—
583C2×C4#380514yes—
584C2×C4C22×D3212yes—
585C2×C4C22×D3212yes—
586C2×C3—24no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—44no—
591C2×C3—42no—
592C2×C3—42no—
593C2×C3—122no—
594C2×C3#554214yescomplemented
595C2×C3#564114yescomplemented
596C2×C3C22×#23511yescharacteristic
597C2×C3C22×#23711yescharacteristic
598C2×C3C22×#23711yescharacteristic
599C2×C3C2×#100711yescharacteristic
600C2×C3C2×D3×#4111yescharacteristic
601C2×C3C2×#101011yescharacteristic
602D3—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—44no—
607C22—62no—
608C22—62no—
609C22—62no—
610C22—124no—
611C22#6429712yes—
612C22D3×#23512yes—
613C22C2×#380512yes—
614C22C23×D3211yescharacteristic
615C4—22no—
616C4—34no—
617C4—62no—
618C4—64no—
619C4—62no—
620C4—64no—
621C4—184no—
622C4—184no—
623C4C2×#380514yes—
624C3—21no—
625C3C2×#554211yescharacteristic, complemented
626C3C2×#564111yescharacteristic, complemented
627C2—42no—
628C2—122no—
629C2#1059484114yesdirect product factor
630C2C2×#6429711yescharacteristic
631C2C2×D3×#23511yescharacteristic
632C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
3. C2×C3×#924C2semidirect
5. C2×#63956C2semidirect
6. C2×#63918C2semidirect
7. C2×#63862C2semidirect
8. C2×#63856C2semidirect
9. #10594841C2direct (N × H)
10. C2×Dic3×Dic6C2semidirect
11. C2×#63841C2semidirect
12. C2×#63838C2semidirect
21. #64135C22semidirect
30. C3×#924C22semidirect
40. #63956C22semidirect
43. #63918C22semidirect
44. #63862C22semidirect
45. #63856C22semidirect
46. Dic3×Dic6C22semidirect
47. #63841C22semidirect
48. #63838C22semidirect
60. C2×#924D3semidirect
162. #924C2×D3semidirect
455. C2×C32#556semidirect
553. C32C2×#556semidirect
594. C2×C3#5542semidirect
595. C2×C3#5641semidirect
625. C3C2×#5542semidirect
626. C3C2×#5641semidirect
629. C2#10594841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×C4×#672
C2×C3×#9242
C2×#639592
C2×#639562
C2×#639182
C2×#638622
C2×#638562
#105948412
C2×Dic3×Dic62
C2×#638412
C2×#638382
C2×#56413
C2×#55423