Finite Group Databasebeta

← C2×#10594939 #11903029

Subgroups — C2×#10594939 #11903029

Order 1152.

2409 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63969C212yesmaximal
5C2×#63956C212yesmaximal, complemented
6#10594939C2116yesmaximal, direct product factor
7C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63877C212yesmaximal, complemented
9C2×#63869C211yesmaximal, characteristic, complemented
10C2×#63867C212yesmaximal, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5541—31nomaximal
14C2×#5529—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×#3757C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133C2218yescomplemented
23C2×#3750C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic
26C3×C4×#67C2218yes—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C3×#926C2218yescomplemented
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2212yes—
34#63969C22116yes—
35C2×#3724C2212yes—
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63956C22116yescomplemented
42C2×Dic32C2212yes—
43D3×C4⋊Dic3C2218yescomplemented
44#63877C22116yescomplemented
45#63869C2218yescomplemented
46#63867C22116yescomplemented
47#63857C2218yescomplemented
48#63844C2218yescomplemented
49C2×C3×C4×D4—31no—
50C2×C3×#117—31no—
51C2×#935—32no—
52C2×C4×#67D311yescharacteristic
53C2×#926D311yescharacteristic, complemented
54C22×C4⋊Dic3—31no—
55C2×#924—31no—
56C2×#924—31no—
57C2×#924—31no—
58C2×#924—61no—
59#5541—316no—
60#5529—316no—
61C2×#897—31no—
62C2×D3×C4⋊C4—31no—
63C2×#890—31no—
64C2×#889—32no—
65C2×#887—31no—
66C2×#883—32no—
67C2×#879—32no—
68C2×#879—32no—
69C2×#877—32no—
70C2×#872—32no—
71C2×#870—31no—
72C2×#870—32no—
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×#634—24no—
83C2×#634C2314yes—
84C2×C3×#67—24no—
85C2×C3×#67C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3C2318yes—
95#3757C2318yes—
96C4⋊(C3⋊Dic3)C2314yes—
97#3750C2318yes—
98C3×#217C2318yes—
99C3×#217C2314yes—
100C3×(C2×D3)⋊C4C2314yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2314yes—
104C3×C4×Dic3C2318yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113C2×#552—91noSylow
114C22×C3×D4—31no—
115C23×C3×C4—21no—
116C23×C3×C4—31no—
117C23×C3×C4C2×D311yescharacteristic
118C23×C3×C4C2×D311yescharacteristic
119C22×#67C2×D311yescharacteristic
120C23×Dic3—32no—
121C22×C4×D3—32no—
122C22×C4×D3C2×D311yescharacteristic
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—61no—
126C3×C4×D4—38no—
127C3×#117—38no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C22⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C42—31no—
135C2×C3×C42—32no—
136C2×#217—32no—
137C2×#217—32no—
138C2×#217—32no—
139C2×#217—62no—
140C2×#217C2×D311yescharacteristic
141C2×#217C2×D312yes—
142#935—316no—
143C4×#67C2×D318yes—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4C2×D311yescharacteristic
146#926C2×D318yescomplemented
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—38no—
153C2×C4⋊Dic3—61no—
154C2×C4⋊Dic3C2×D311yescharacteristic
155C2×C4⋊Dic3C2×D311yescharacteristic
156#924—38no—
157#924—38no—
158#924—38no—
159#924—68no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
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—32no—
169C2×Dic3⋊C4—62no—
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3C2×D312yes—
174C2×C4×Dic3C2×D311yescharacteristic
175#897—38no—
176D3×C4⋊C4—38no—
177#890—38no—
178#889—316no—
179#887—38no—
180#883—316no—
181#879—316no—
182#879—316no—
183#877—316no—
184#872—316no—
185#870—38no—
186#870—316no—
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#4114yes—
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—
206#634—28no—
207C3×#67—28no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C3×C4×D3—28no—
219D3×Dic3—216no—
220#552—916no—
221C2×#126—92no—
222C2×#125—92no—
223C2×#125—91no—
224C2×#123—92no—
225C2×C22⋊Q8—91no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—31no—
229C2×#117—31no—
230C2×#117—92no—
231C22×C4⋊C4—91no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C22×D311yescharacteristic
236C23×D3C22×D311yescharacteristic
237C2×C3×D4—34no—
238C2×C3×D4—64no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—24no—
244C22×C3×C4—31no—
245C22×C3×C4—32no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—34no—
250C22×C3×C4—44no—
251C22×C3×C4—64no—
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—24no—
259C2×#67C22×D314yes—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—38no—
265C22×Dic3—62no—
266C22×Dic3—62no—
267C22×Dic3—68no—
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D312yes—
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C2×C4×D3—24no—
274C2×C4×D3—38no—
275C2×C4×D3—68no—
276C2×C4×D3C22×D314yes—
277C2×Dic6—34no—
278C2×Dic6—34no—
279C2×Dic6—64no—
280C2×Dic6—64no—
281C2×Dic6—64no—
282C2×Dic6—124no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—34no—
286C3×C22⋊C4—34no—
287C3×C22⋊C4—38no—
288C3×C22⋊C4—34no—
289C3×C42—34no—
290C3×C42—38no—
291#217—38no—
292#217—38no—
293#217—38no—
294#217—68no—
295#217C22×D314yes—
296#217C22×D318yes—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4C22×D314yes—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—38no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305C4⋊Dic3C22×D314yes—
306C4⋊Dic3C22×D314yes—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—68no—
317Dic3⋊C4C22×D314yes—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3C22×D318yes—
321C4×Dic3C22×D314yes—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—44no—
326C22×C32C2×#4112yes—
327C22×C32C2×#4112yes—
328C22×C322−1+412yes—
329C22×C32C2511yescharacteristic
330C2×C3×D3—28no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3C2×#4114yes—
334C32×C4—22no—
335C32×C4C2×#4114yes—
336C3⋊Dic3—24no—
337C3⋊Dic3—24no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C3×Dic3—22no—
342C3×Dic3—24no—
343C22×Q8—91no—
344C22×D4—31no—
345C23×C4—31no—
346C23×C4—92no—
347C23×C4D3211yescharacteristic
348#126—916no—
349#125—916no—
350#125—98no—
351#123—916no—
352C22⋊Q8—98no—
353C22⋊Q8—98no—
354C4×Q8—98no—
355C4×D4—38no—
356#117—38no—
357#117—916no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—98no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—92no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C42—32no—
375C2×C42—31no—
376C2×C42—92no—
377C23×C3—24no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—21no—
386C23×C3—34no—
387C23×C3—32no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3C23×D312yes—
393C23×C3C23×D312yes—
394C23×C3C23×D311yescharacteristic
395C23×C3C23×D311yescharacteristic
396C22×D3—22no—
397C22×D3—22no—
398C22×D3#23514yes—
399C22×D3C23×D312yes—
400C3×D4—68no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—28no—
404C2×C3×C4—28no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—32no—
409C2×C3×C4—34no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—34no—
413C2×C3×C4—48no—
414C2×C3×C4—42no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—64no—
420C2×C3×C4—68no—
421C2×C3×C4#23514yes—
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—22no—
429C2×Dic3—22no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—34no—
434C2×Dic3—34no—
435C2×Dic3—34no—
436C2×Dic3—34no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—616no—
440C2×Dic3—64no—
441C2×Dic3—64no—
442C2×Dic3—64no—
443C2×Dic3—64no—
444C2×Dic3—124no—
445C2×Dic3—124no—
446C2×Dic3C23×D312yes—
447C2×Dic3C23×D314yes—
448C2×Dic3C23×D314yes—
449C2×Dic3C23×D312yes—
450C2×Dic3C23×D312yes—
451C4×D3—28no—
452C4×D3—616no—
453Dic6—68no—
454Dic6—68no—
455Dic6—128no—
456C2×C32—42no—
457C2×C32#55214yescomplemented
458C2×C32C22×#4111yescharacteristic
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×2−1+411yescharacteristic
461C3×D3—24no—
462C24—31no—
463C24C2×D3211yescharacteristic
464C2×Q8—94no—
465C2×Q8—184no—
466C2×D4—34no—
467C2×D4—64no—
468C22×C4—24no—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—34no—
475C22×C4—64no—
476C22×C4—98no—
477C22×C4—92no—
478C22×C4—92no—
479C22×C4—188no—
480C22×C4C2×D3214yes—
481C22×C4C2×D3211yescharacteristic
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—34no—
484C4⋊C4—34no—
485C4⋊C4—34no—
486C4⋊C4—98no—
487C4⋊C4—98no—
488C4⋊C4—98no—
489C4⋊C4—98no—
490C4⋊C4—98no—
491C4⋊C4—94no—
492C4⋊C4—98no—
493C22⋊C4—38no—
494C22⋊C4—34no—
495C22⋊C4—34no—
496C22⋊C4—98no—
497C22⋊C4—98no—
498C42—38no—
499C42—34no—
500C42—98no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—34no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—48no—
516C22×C3—44no—
517C22×C3—44no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—68no—
521C22×C3C2×#23512yes—
522C22×C3C2×#23512yes—
523C22×C3C2×#23712yes—
524C22×C3D3×#4112yes—
525C22×C3#101012yes—
526C22×C3#101012yes—
527C22×C3C24×D311yescharacteristic
528C22×C3C24×D311yescharacteristic
529C2×D3—22no—
530C2×D3—22no—
531C2×D3—28no—
532C2×D3C2×#23514yes—
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—24no—
536C3×C4—42no—
537C3×C4—64no—
538C3×C4—62no—
539C3×C4—62no—
540C3×C4—62no—
541C3×C4—64no—
542C3×C4C2×#23514yes—
543C3×C4C2×#23714yes—
544Dic3—22no—
545Dic3—22no—
546Dic3—24no—
547Dic3—24no—
548Dic3—22no—
549Dic3—64no—
550Dic3—64no—
551Dic3—64no—
552Dic3—64no—
553Dic3—124no—
554Dic3—124no—
555C32C2×#55211yescharacteristic, complemented, Sylow
556C23—22no—
557C23—22no—
558C23—22no—
559C23—34no—
560C23—32no—
561C23—62no—
562C23—62no—
563C23C22×D3212yes—
564C23C22×D3211yescharacteristic
565Q8—188no—
566D4—68no—
567C2×C4—22no—
568C2×C4—28no—
569C2×C4—32no—
570C2×C4—34no—
571C2×C4—34no—
572C2×C4—32no—
573C2×C4—32no—
574C2×C4—62no—
575C2×C4—64no—
576C2×C4—64no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—68no—
580C2×C4—94no—
581C2×C4—94no—
582C2×C4—1816no—
583C2×C4—184no—
584C2×C4—184no—
585C2×C4#380414yes—
586C2×C4C22×D3212yes—
587C2×C4C22×D3212yes—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—24no—
592C2×C3—44no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—64no—
596C2×C3#552914yescomplemented
597C2×C3#554114yescomplemented
598C2×C3C22×#23511yescharacteristic
599C2×C3C22×#23511yescharacteristic
600C2×C3C22×#23711yescharacteristic
601C2×C3C2×D3×#4111yescharacteristic
602C2×C3C2×#101011yescharacteristic
603C2×C3C2×#101011yescharacteristic
604D3—24no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—34no—
609C22—44no—
610C22—62no—
611C22—62no—
612C22—68no—
613C22#6429812yes—
614C22D3×#23512yes—
615C22C2×#380412yes—
616C22C23×D3211yescharacteristic
617C4—22no—
618C4—62no—
619C4—64no—
620C4—64no—
621C4—62no—
622C4—62no—
623C4—184no—
624C4—184no—
625C4C2×#380414yes—
626C3—21no—
627C3C2×#552911yescharacteristic, complemented
628C3C2×#554111yescharacteristic, complemented
629C2—42no—
630C2—64no—
631C2#1059493914yesdirect product factor
632C2C2×#6429811yescharacteristic
633C2C2×D3×#23511yescharacteristic
634C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
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
1. C2×#64133C2semidirect
3. C2×C3×#926C2semidirect
5. C2×#63956C2semidirect
6. #10594939C2direct (N × H)
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×#63877C2semidirect
9. C2×#63869C2semidirect
10. C2×#63867C2semidirect
11. C2×#63857C2semidirect
12. C2×#63844C2semidirect
22. #64133C22semidirect
28. C3×#926C22semidirect
41. #63956C22semidirect
43. D3×C4⋊Dic3C22semidirect
44. #63877C22semidirect
45. #63869C22semidirect
46. #63867C22semidirect
47. #63857C22semidirect
48. #63844C22semidirect
53. C2×#926D3semidirect
146. #926C2×D3semidirect
457. C2×C32#552semidirect
555. C32C2×#552semidirect
596. C2×C3#5529semidirect
597. C2×C3#5541semidirect
627. C3C2×#5529semidirect
628. C3C2×#5541semidirect
631. C2#10594939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×C4×#672
C2×C3×#9262
C2×#639692
C2×#639562
#105949392
C2×D3×C4⋊Dic32
C2×#638772
C2×#638692
C2×#638672
C2×#638572
C2×#638442
C2×#55413
C2×#55293