Finite Group Databasebeta

← C2×#10590406 #11857526

Subgroups — C2×#10590406 #11857526

Order 1152.

1741 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic
2C2×#64086C211yesmaximal, characteristic, complemented
3C2×#63957C211yesmaximal, characteristic, complemented
4C2×C3×#806C212yesmaximal, complemented
5C2×#63580C212yesmaximal, complemented
6#10590406C218yesmaximal, direct product factor
7C2×#4740—32nomaximal
8C23×C3⋊Dic3C2211yescharacteristic
9C22×C3×#67C2212yes—
10C22×#627C411yescharacteristic, complemented
11C22×#625C411yescharacteristic, complemented
12C2×#3805—22no—
13C2×#3805—21no—
14C2×#3805—21no—
15C2×#3805—21no—
16C2×#3805—22no—
17C2×#3805—21no—
18C2×#3805C414yescomplemented
19C2×#3805C2214yes—
20C22×D3×Dic3C412yescomplemented
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3750—21no—
24C2×C4×C3⋊Dic3—21no—
25#64086—22no—
26#64086C2214yescomplemented
27C2×C3×#217C2212yes—
28C2×#3724—21no—
29#63957—22no—
30#63957C2214yescomplemented
31C2×Dic32—21no—
32C3×#806C2218yescomplemented
33#63580C2218yescomplemented
34C22×#237—32no—
35C2×#877—32no—
36C2×#877—32no—
37C2×#877—61no—
38C2×C3×#99—32no—
39C2×#834—32no—
40C2×#806—32no—
41C2×#806D312yescomplemented
42#4740—316no—
43C24×C32C2311yescharacteristic
44C23×C3×D3C2×C412yes—
45C22×C32×C4—21no—
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3⋊Dic3C2×C412yes—
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3D412yes—
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D412yes—
55C22×C3⋊Dic3D411yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C2×C3×#67—22no—
58C2×C3×#67—22no—
59C2×C3×#67—22no—
60C2×C3×#67—22no—
61C2×C3×#67C2×C414yes—
62C2×C3×#67C2314yes—
63C22×C3×Dic3—22no—
64C22×C3×Dic3C2×C412yes—
65C2×#627—22no—
66C2×#627—21no—
67C2×#627—21no—
68C2×#627C2×C414yescomplemented
69C2×#625—22no—
70C2×#625—21no—
71C2×#625—21no—
72C2×#625C2×C414yescomplemented
73#3805—24no—
74#3805—24no—
75#3805—24no—
76#3805—24no—
77#3805—24no—
78#3805—24no—
79#3805—24no—
80#3805—24no—
81C2×D3×Dic3—24no—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3C2×C418yescomplemented
85C32×C22⋊C4—21no—
86C32×C22⋊C4C2312yes—
87#3757—21no—
88#3757C2312yes—
89#3750—24no—
90C4×C3⋊Dic3—24no—
91C3×#217—22no—
92C3×#217C2314yes—
93#3724—24no—
94Dic32—24no—
95C2×#410—91noSylow
96C22×C3×D4—32no—
97C22×#67—32no—
98C22×#67C2×D312yes—
99C23×Dic3—32no—
100C23×Dic3—32no—
101C23×Dic3—61no—
102C2×#237—38no—
103C2×#237—38no—
104C2×#237—64no—
105C2×#237—64no—
106C2×#237—62no—
107C2×#237—62no—
108C2×#237—62no—
109C2×#237—62no—
110C22×C4×D3—32no—
111C22×Dic6—32no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4C2×D312yes—
115C2×#217—32no—
116C2×#217—61no—
117C2×#217C2×D312yes—
118C2×Dic3⋊C4—62no—
119C2×Dic3⋊C4—62no—
120C2×Dic3⋊C4—62no—
121C2×C4×Dic3—62no—
122C2×C4×Dic3—62no—
123C2×C4×Dic3—62no—
124#877—38no—
125#877—38no—
126#877—64no—
127#877—64no—
128#877—64no—
129#877—64no—
130C3×#99—38no—
131#834—38no—
132#806—38no—
133#806C2×D318yescomplemented
134C23×C32—42no—
135C23×C32C22×C411yescharacteristic
136C23×C32C22×C411yescharacteristic
137C23×C32C2×D411yescharacteristic
138C23×C32C2×D411yescharacteristic
139C23×C32C2×D411yescharacteristic
140C23×C32C2×D411yescharacteristic
141C23×C32C2411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—44no—
145C22×C3×D3C22×C414yes—
146C2×C32×C4—22no—
147C2×C32×C4—42no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C2×C3⋊Dic3C22⋊C412yes—
151C2×C3⋊Dic3C22⋊C411yescharacteristic
152C2×C3⋊Dic3C22⋊C411yescharacteristic
153C2×C3⋊Dic3C22⋊C412yes—
154C2×C3⋊Dic3C22⋊C412yes—
155C2×C3⋊Dic3C22⋊C412yes—
156C2×C3⋊Dic3C22⋊C412yes—
157C2×C3⋊Dic3C22⋊C412yes—
158C2×C3⋊Dic3C22⋊C411yescharacteristic
159C2×C3⋊Dic3C22⋊C411yescharacteristic
160C2×C3⋊Dic3C22×C412yes—
161C2×C3⋊Dic3C22×C412yes—
162C2×C3⋊Dic3C2×D412yes—
163C2×C3⋊Dic3C2×D412yes—
164C2×C3⋊Dic3C2×D412yes—
165C2×C3⋊Dic3C2×D412yes—
166C3×#67—24no—
167C3×#67—24no—
168C3×#67—24no—
169C3×#67—24no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—24no—
173C2×C3×Dic3—44no—
174C2×C3×Dic3C22×C414yes—
175#627—24no—
176#627—24no—
177#625—24no—
178#625—24no—
179D3×Dic3—28no—
180D3×Dic3—28no—
181C22×#41—91no—
182C2×#117—91no—
183C2×#117—91no—
184#410—98no—
185C2×#99—32no—
186C2×#99—92no—
187C24×C3—21no—
188C24×C3—32no—
189C24×C3C22×D312yes—
190C23×D3C4×D312yes—
191C2×C3×D4—34no—
192C2×C3×D4—34no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—32no—
200C22×C3×C4—62no—
201C2×#67—22no—
202C2×#67—22no—
203C2×#67—22no—
204C2×#67—22no—
205C2×#67—38no—
206C2×#67—64no—
207C2×#67—62no—
208C2×#67—62no—
209C2×#67C4×D314yes—
210C2×#67C22×D314yes—
211C22×Dic3—22no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—34no—
215C22×Dic3—34no—
216C22×Dic3—34no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—34no—
222C22×Dic3—38no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—62no—
233C22×Dic3—64no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—62no—
238C22×Dic3C4×D312yes—
239#237—68no—
240#237—68no—
241#237—68no—
242#237—68no—
243#237—68no—
244#237—68no—
245#237—68no—
246#237—68no—
247C2×C4×D3—38no—
248C2×C4×D3—64no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×Dic6—38no—
252C2×Dic6—64no—
253C2×Dic6—62no—
254C2×Dic6—62no—
255C3×C22⋊C4—22no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—34no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4C22×D314yes—
261#217—22no—
262#217—34no—
263#217—62no—
264#217—62no—
265#217—62no—
266#217C22×D314yes—
267Dic3⋊C4—68no—
268Dic3⋊C4—68no—
269Dic3⋊C4—68no—
270C4×Dic3—68no—
271C4×Dic3—68no—
272C4×Dic3—68no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32—22no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32C2×C22⋊C411yescharacteristic
281C22×C32C2×C22⋊C411yescharacteristic
282C22×C32C2×C22⋊C411yescharacteristic
283C22×C32C2×C22⋊C411yescharacteristic
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—24no—
288C2×C3×D3—44no—
289C2×C3×D3—44no—
290C2×C3×D3—44no—
291C32×C4—42no—
292C3⋊Dic3—42no—
293C3⋊Dic3C2×C22⋊C412yes—
294C3⋊Dic3C2×C22⋊C412yes—
295C3⋊Dic3C2×C22⋊C412yes—
296C3⋊Dic3C2×C22⋊C412yes—
297C3×Dic3—24no—
298C3×Dic3—44no—
299C2×#41—94no—
300C2×#41—94no—
301C2×#41—181no—
302C2×#41—181no—
303C2×#41—182no—
304C2×#41—181no—
305C2×#41—181no—
306C2×#41—182no—
307C22×Q8—91no—
308C22×D4—32no—
309C22×D4—91no—
310C23×C4—92no—
311C23×C4—91no—
312#117—94no—
313#117—94no—
314#117—182no—
315#117—182no—
316C2×C4⋊C4—181no—
317C2×C4⋊C4—181no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4D3211yescharacteristic
321C2×C42—181no—
322C2×C42—181no—
323#99—38no—
324#99—98no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—34no—
333C23×C3—44no—
334C23×C3—44no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3—124no—
338C23×C3C2×C4×D312yes—
339C23×C3C2×C4×D312yes—
340C23×C3D3×D412yes—
341C23×C3D3×D412yes—
342C23×C3D3×D412yes—
343C23×C3D3×D412yes—
344C23×C3C23×D312yes—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—44no—
348C22×D3C2×C4×D314yes—
349C3×D4—64no—
350C3×D4—64no—
351C3×D4—64no—
352C3×D4—64no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—34no—
356C2×C3×C4—44no—
357C2×C3×C4—44no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—64no—
361C2×C3×C4—124no—
362#67—24no—
363#67—24no—
364#67—24no—
365#67—24no—
366#67—68no—
367#67—68no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—24no—
371C2×Dic3—34no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—34no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—34no—
383C2×Dic3—34no—
384C2×Dic3—34no—
385C2×Dic3—34no—
386C2×Dic3—34no—
387C2×Dic3—44no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—68no—
405C2×Dic3—68no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—124no—
409C2×Dic3—124no—
410C2×Dic3C2×C4×D314yes—
411C4×D3—68no—
412C4×D3—68no—
413Dic6—68no—
414Dic6—68no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32—21no—
418C2×C32—21no—
419C2×C32—21no—
420C2×C32—21no—
421C2×C32#41012yescomplemented
422C2×C32C22×C22⋊C411yescharacteristic
423C3×D3—44no—
424C24—32no—
425C24C2×D3211yescharacteristic
426#41—184no—
427#41—184no—
428#41—184no—
429#41—184no—
430#41—184no—
431#41—184no—
432#41—184no—
433#41—184no—
434C2×Q8—94no—
435C2×Q8—182no—
436C2×Q8—181no—
437C2×Q8—181no—
438C2×D4—34no—
439C2×D4—34no—
440C2×D4—62no—
441C2×D4—62no—
442C2×D4—62no—
443C2×D4—62no—
444C2×D4—94no—
445C2×D4—182no—
446C2×D4—181no—
447C2×D4—181no—
448C22×C4—21no—
449C22×C4—32no—
450C22×C4—62no—
451C22×C4—98no—
452C22×C4—92no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—92no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—92no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—92no—
462C22×C4—184no—
463C22×C4—182no—
464C22×C4—182no—
465C22×C4—181no—
466C4⋊C4—184no—
467C4⋊C4—184no—
468C22⋊C4—21no—
469C22⋊C4—34no—
470C22⋊C4—62no—
471C22⋊C4—92no—
472C22⋊C4—181no—
473C22⋊C4C2×D3212yes—
474C42—184no—
475C42—184no—
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—64no—
498C22×C3—124no—
499C22×C3—124no—
500C22×C3—124no—
501C22×C3D3×C22⋊C412yes—
502C22×C3D3×C22⋊C412yes—
503C22×C3D3×C22⋊C412yes—
504C22×C3D3×C22⋊C412yes—
505C22×C3C22×C4×D312yes—
506C22×C3C2×D3×D412yes—
507C22×C3C2×D3×D412yes—
508C2×D3—24no—
509C2×D3—44no—
510C2×D3—44no—
511C2×D3—44no—
512C3×C4—44no—
513C3×C4—44no—
514C3×C4—64no—
515C3×C4—124no—
516Dic3—24no—
517Dic3—34no—
518Dic3—34no—
519Dic3—34no—
520Dic3—34no—
521Dic3—44no—
522Dic3—62no—
523Dic3—62no—
524Dic3—62no—
525Dic3—62no—
526Dic3—124no—
527Dic3—124no—
528C32C2×#41011yescharacteristic, complemented, Sylow
529C23—34no—
530C23—42no—
531C23—62no—
532C23—62no—
533C23—124no—
534C23C4×D3211yescharacteristic
535C23C4×D3211yescharacteristic
536C23#380211yescharacteristic
537C23#380211yescharacteristic
538C23#381111yescharacteristic
539C23#381111yescharacteristic
540C23C22×D3211yescharacteristic
541Q8—184no—
542Q8—184no—
543D4—64no—
544D4—64no—
545D4—64no—
546D4—64no—
547D4—184no—
548D4—184no—
549C2×C4—22no—
550C2×C4—34no—
551C2×C4—42no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—64no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—91no—
568C2×C4—91no—
569C2×C4—91no—
570C2×C4—91no—
571C2×C4—124no—
572C2×C4—188no—
573C2×C4—188no—
574C2×C4—182no—
575C2×C4—362no—
576C2×C3—22no—
577C2×C3—22no—
578C2×C3—22no—
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—22no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—21no—
586C2×C3—41no—
587C2×C3—41no—
588C2×C3—41no—
589C2×C3—41no—
590C2×C3—124no—
591C2×C3#474014yescomplemented
592C2×C3C2×D3×C22⋊C412yes—
593D3—44no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—64no—
602C22—124no—
603C22—124no—
604C22—124no—
605C22#6392111yescharacteristic
606C22#6392111yescharacteristic
607C22#6392111yescharacteristic
608C22#6392111yescharacteristic
609C22C2×C4×D3211yescharacteristic
610C22C2×#380211yescharacteristic
611C22C2×#381111yescharacteristic
612C4—42no—
613C4—64no—
614C4—92no—
615C4—92no—
616C4—92no—
617C4—92no—
618C4—124no—
619C4—362no—
620C3—21no—
621C3C2×#474012yescomplemented
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—124no—
629C2#1059040612yesdirect product factor
630C2C2×#6392111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3805C2
cosocleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64086C2semidirect
3. C2×#63957C2semidirect
4. C2×C3×#806C2semidirect
5. C2×#63580C2semidirect
6. #10590406C2direct (N × H)
10. C22×#627C4semidirect
11. C22×#625C4semidirect
18. C2×#3805C4semidirect
20. C22×D3×Dic3C4semidirect
26. #64086C22semidirect
30. #63957C22semidirect
32. C3×#806C22semidirect
33. #63580C22semidirect
41. C2×#806D3semidirect
68. C2×#627C2×C4semidirect
72. C2×#625C2×C4semidirect
84. C2×D3×Dic3C2×C4semidirect
133. #806C2×D3semidirect
421. C2×C32#410semidirect
528. C32C2×#410semidirect
591. C2×C3#4740semidirect
621. C3C2×#4740semidirect
629. C2#10590406direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C2×#640862
C2×#639572
C2×C3×#8062
C2×#635802
#105904062
C2×#47403