Finite Group Databasebeta

← C2×#10591173 #11863786

Subgroups — C2×#10591173 #11863786

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C2×#64133C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#830C211yesmaximal, characteristic, complemented
6#10591173C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5239—31nomaximal
10C2×#4733—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C2×C3×#235—22no—
15C2×C3×#235—24no—
16C2×C3×#235—24no—
17C2×C3×#235C2214yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C22×C3×Dic6C2211yescharacteristic
21C2×#3757—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23#64133—22no—
24#64133C2214yescomplemented
25C2×#3750—21no—
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#830C2214yescomplemented
33#63566C2214yescomplemented
34#63563C2214yescomplemented
35C22×C3×#41—31no—
36C22×#235D311yescharacteristic
37C22×#216—31no—
38C22×#214—31no—
39C2×#924—31no—
40C2×#924—31no—
41C2×#924—61no—
42C22×Dic12—31no—
43C22×#204—31no—
44C2×C3×C22⋊C8—31no—
45#5239—38no—
46C2×#835—31no—
47C2×#832—31no—
48C2×#830D311yescharacteristic, complemented
49C2×#821—31no—
50C2×#816—31no—
51#4733—38no—
52C24×C32D411yescharacteristic
53C23×C3×D3—21no—
54C22×C32×C4—22no—
55C22×C32×C4—22no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D412yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3—21no—
62C2×#634—22no—
63C2×#634—22no—
64C2×#634—21no—
65C2×#634C2312yes—
66C2×C3×#67—28no—
67C2×C3×#67—24no—
68C22×C3×Dic3—21no—
69C3×#235—216no—
70C3×#235—28no—
71C3×#235—28no—
72C2×C3×D12—21no—
73C2×C3×D12—22no—
74C2×C3×D12D414yes—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3—28no—
77C2×C3×C4×D3—24no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6D414yes—
81C2×C3×Dic6C2312yes—
82#3757—24no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—24no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3719—28no—
91#3716—28no—
92C2×#452—91noSylow
93C2×C3×#41—34no—
94C2×C3×#41—64no—
95C2×C3×#41—64no—
96C2×C3×#41—62no—
97C22×C3×Q8—31no—
98C22×C3×D4—31no—
99C22×C3×D4—61no—
100C23×C3×C4—21no—
101C23×C3×C4—61no—
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C2×D311yescharacteristic
104C22×#67—21no—
105C2×#235—22no—
106C2×#235—24no—
107C2×#235—24no—
108C2×#235C2×D314yes—
109C22×D12C2×D311yescharacteristic
110C22×C4×D3—21no—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6C2×D311yescharacteristic
115C22×C3×C8—31no—
116C22×C3×C8—31no—
117C2×#217—62no—
118C2×#217—61no—
119C2×#217—61no—
120C2×#216—34no—
121C2×#216—64no—
122C2×#214—34no—
123C2×#214—64no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—61no—
127#924—34no—
128#924—34no—
129#924—64no—
130#924—64no—
131#924—62no—
132#924—62no—
133C2×Dic3⋊C4—62no—
134C2×Dic3⋊C4—61no—
135C2×Dic3⋊C4—61no—
136C22×C3⋊C8C2×D311yescharacteristic
137C22×C3⋊C8C2×D311yescharacteristic
138C2×Dic12—34no—
139C2×Dic12—64no—
140C2×#204—34no—
141C2×#204—64no—
142C3×C22⋊C8—34no—
143#835—34no—
144#832—34no—
145#830C2×D314yescomplemented
146#821—34no—
147#816—34no—
148C23×C32—22no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32C2×D412yes—
152C23×C32C2×D411yescharacteristic
153C22×C3×D3—24no—
154C22×C3×D3—22no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C2×C32×C4—22no—
158C2×C32×C4—24no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—42no—
169C2×C3⋊Dic3—42no—
170#634—22no—
171#634—22no—
172#634—42no—
173C3×#67—216no—
174C2×C3×Dic3—24no—
175C2×C3×Dic3—22no—
176C3×D12—24no—
177C3×D12—22no—
178C3×D12C2×D414yes—
179C3×C4×D3—216no—
180C3×Dic6—24no—
181C3×Dic6—22no—
182C3×Dic6C2×D414yes—
183C3×C3⋊C8—22no—
184C3×C3⋊C8—22no—
185C22×#41—31no—
186C22×Q16—91no—
187C22×SD16—91no—
188C2×C22⋊Q8—91no—
189#452—98no—
190C2×#103—91no—
191C2×#102—91no—
192C2×C22⋊C8—31no—
193C24×C3—21no—
194C24×C3—61no—
195C24×C3D1211yescharacteristic
196C24×C3#6711yescharacteristic
197C23×D3—21no—
198C3×#41—68no—
199C3×#41—68no—
200C3×#41—616no—
201C2×C3×Q8—34no—
202C2×C3×Q8—32no—
203C2×C3×Q8—61no—
204C2×C3×Q8—62no—
205C2×C3×D4—34no—
206C2×C3×D4—32no—
207C2×C3×D4—68no—
208C2×C3×D4—64no—
209C2×C3×D4—61no—
210C2×C3×D4—62no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—68no—
222C22×C3×C4—61no—
223C22×C3×C4—64no—
224C22×C3×C4D1211yescharacteristic
225C22×C3×C4D1212yes—
226C22×C3×C4#6711yescharacteristic
227C22×C3×C4#6712yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D312yes—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—28no—
233C2×#67—24no—
234C22×Dic3—21no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241#235—216no—
242#235—28no—
243#235—28no—
244C2×D12—21no—
245C2×D12—22no—
246C2×D12#6714yes—
247C2×D12C22×D312yes—
248C2×C4×D3—28no—
249C2×C4×D3—24no—
250C2×Dic6—21no—
251C2×Dic6—22no—
252C2×Dic6—32no—
253C2×Dic6—32no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—62no—
257C2×Dic6—62no—
258C2×Dic6—62no—
259C2×Dic6—62no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×Dic6—122no—
263C2×Dic6—122no—
264C2×Dic6#6714yes—
265C2×Dic6C22×D312yes—
266C2×C3×C8—32no—
267C2×C3×C8—32no—
268C2×C3×C8—62no—
269C2×C3×C8—62no—
270#217—68no—
271#217—64no—
272#217—64no—
273#216—68no—
274#214—68no—
275C4⋊Dic3—32no—
276C4⋊Dic3—32no—
277C4⋊Dic3—62no—
278C4⋊Dic3—62no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281Dic3⋊C4—68no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8C22×D312yes—
287C2×C3⋊C8C22×D312yes—
288Dic12—68no—
289#204—68no—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—44no—
294C22×C32#12012yes—
295C22×C32#13512yes—
296C22×C32#13712yes—
297C22×C32C22×D411yescharacteristic
298C2×C3×D3—24no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—48no—
302C32×C4—22no—
303C32×C4#12012yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3⋊Dic3—42no—
307C3⋊Dic3—42no—
308C3×Dic3—24no—
309C2×#41—34no—
310C2×#41—64no—
311C2×#41—64no—
312C2×#41—62no—
313C22×Q8—31no—
314C22×Q8—91no—
315C22×D4—31no—
316C22×D4—61no—
317C23×C4—61no—
318C23×C4D3211yescharacteristic
319C2×Q16—94no—
320C2×Q16—184no—
321C2×SD16—94no—
322C2×SD16—184no—
323C22×C8—31no—
324C22×C8—31no—
325C22⋊Q8—94no—
326C22⋊Q8—182no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—181no—
329C2×C22⋊C4—181no—
330#103—94no—
331#102—94no—
332C22⋊C8—34no—
333C23×C3—24no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—64no—
345C23×C3—62no—
346C23×C3—122no—
347C23×C3—122no—
348C23×C3C2×D1212yes—
349C23×C3C2×D1211yescharacteristic
350C23×C3C2×#6712yes—
351C23×C3C2×#6711yescharacteristic
352C22×D3—24no—
353C22×D3—22no—
354C22×D3—42no—
355C22×D3—42no—
356C3×Q8—34no—
357C3×Q8—64no—
358C3×Q8—62no—
359C3×D4—34no—
360C3×D4—616no—
361C3×D4—64no—
362C3×D4—62no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—44no—
379C2×C3×C4—42no—
380C2×C3×C4—616no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4C2×D1212yes—
384C2×C3×C4C2×D1211yescharacteristic
385C2×C3×C4D3×D412yes—
386C2×C3×C4D3×D412yes—
387C2×C3×C4C2×#6712yes—
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×#6712yes—
390C2×C3×C4C2×#6712yes—
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393#67—216no—
394C2×Dic3—24no—
395C2×Dic3—22no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—124no—
403C2×Dic3—124no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408D12—24no—
409D12—22no—
410D12C2×#6714yes—
411C4×D3—216no—
412Dic6—24no—
413Dic6—22no—
414Dic6—62no—
415Dic6—62no—
416Dic6—62no—
417Dic6—62no—
418Dic6—122no—
419Dic6—122no—
420Dic6—124no—
421Dic6—122no—
422Dic6—122no—
423Dic6C2×#6714yes—
424C3×C8—62no—
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—22no—
428C2×C32—42no—
429C2×C32#45214yescomplemented
430C2×C32C2×#12011yescharacteristic
431C2×C32C2×#13511yescharacteristic
432C2×C32C2×#13711yescharacteristic
433C3×D3—44no—
434C24—61no—
435C24#62611yescharacteristic
436#41—68no—
437#41—68no—
438#41—616no—
439C2×Q8—32no—
440C2×Q8—34no—
441C2×Q8—61no—
442C2×Q8—62no—
443C2×Q8—92no—
444C2×Q8—181no—
445C2×Q8—182no—
446C2×Q8—182no—
447C2×D4—32no—
448C2×D4—34no—
449C2×D4—68no—
450C2×D4—64no—
451C2×D4—61no—
452C2×D4—62no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—68no—
456C22×C4—61no—
457C22×C4—64no—
458C22×C4—181no—
459C22×C4—181no—
460C22×C4#62612yes—
461C22×C4#62611yescharacteristic
462C22×C4C2×D3212yes—
463C22×C4C2×D3211yescharacteristic
464Q16—188no—
465SD16—188no—
466C2×C8—32no—
467C2×C8—32no—
468C2×C8—62no—
469C2×C8—62no—
470C4⋊C4—92no—
471C4⋊C4—181no—
472C4⋊C4—184no—
473C22⋊C4—184no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—48no—
488C22×C3—44no—
489C22×C3—44no—
490C22×C3—64no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—128no—
494C22×C3#88212yes—
495C22×C3#90412yes—
496C22×C3#90912yes—
497C22×C3#95012yes—
498C22×C3#95112yes—
499C22×C3#95312yes—
500C22×C3C22×D1211yescharacteristic
501C22×C3C22×#6711yescharacteristic
502C2×D3—24no—
503C2×D3—48no—
504C2×D3—42no—
505C2×D3—42no—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—42no—
512C3×C4—64no—
513C3×C4#88212yes—
514C3×C4#95312yes—
515C3×C4C2×D3×D411yescharacteristic
516C3×C4C2×D3×D411yescharacteristic
517C3×C4C22×#6711yescharacteristic
518C3×C4C22×#6711yescharacteristic
519Dic3—24no—
520Dic3—124no—
521Dic3—124no—
522Dic3—122no—
523Dic3—122no—
524Dic3—122no—
525Dic3—122no—
526C32C2×#45211yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—22no—
530C23—62no—
531C23—64no—
532C23—122no—
533C23—122no—
534C23C2×#62612yes—
535C23C2×#62611yescharacteristic
536Q8—34no—
537Q8—62no—
538Q8—64no—
539Q8—182no—
540Q8—182no—
541Q8—362no—
542D4—34no—
543D4—616no—
544D4—62no—
545D4—64no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—616no—
551C2×C4—62no—
552C2×C4—64no—
553C2×C4—182no—
554C2×C4—182no—
555C2×C4—362no—
556C2×C4—362no—
557C2×C4C2×#62612yes—
558C2×C4C2×#62611yescharacteristic
559C2×C4D3×#6712yes—
560C2×C4D3×#6712yes—
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—62no—
564C2×C3—21no—
565C2×C3—24no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—44no—
569C2×C3—42no—
570C2×C3—42no—
571C2×C3—124no—
572C2×C3#473314yescomplemented
573C2×C3#523914yescomplemented
574C2×C3C2×#88211yescharacteristic
575C2×C3C2×#90411yescharacteristic
576C2×C3C2×#90911yescharacteristic
577C2×C3C2×#95011yescharacteristic
578C2×C3C2×#95111yescharacteristic
579C2×C3C2×#95311yescharacteristic
580D3—44no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—44no—
585C22—64no—
586C22—128no—
587C22—122no—
588C22—122no—
589C22#6382912yes—
590C22#6383112yes—
591C22#6397712yes—
592C22C22×#62611yescharacteristic
593C4—22no—
594C4—64no—
595C4—362no—
596C4—362no—
597C4#6397712yes—
598C4C2×D3×#6711yescharacteristic
599C4C2×D3×#6711yescharacteristic
600C3—21no—
601C3C2×#473311yescharacteristic, complemented
602C3C2×#523911yescharacteristic, complemented
603C2—42no—
604C2—124no—
605C2#1059117314yesdirect product factor
606C2C2×#6382911yescharacteristic
607C2C2×#6383111yescharacteristic
608C2C2×#6397711yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×C3×#235C2
hypercenterC23×C4D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64133C2semidirect
3. C22×#3719C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#830C2semidirect
6. #10591173C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×#63563C2semidirect
24. #64133C22semidirect
29. C2×#3719C22semidirect
31. C2×#3716C22semidirect
32. C3×#830C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
48. C2×#830D3semidirect
145. #830C2×D3semidirect
429. C2×C32#452semidirect
526. C32C2×#452semidirect
572. C2×C3#4733semidirect
573. C2×C3#5239semidirect
601. C3C2×#4733semidirect
602. C3C2×#5239semidirect
605. C2#10591173direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#641332
C22×#37192
C22×#37162
C2×C3×#8302
#105911732
C2×#635662
C2×#635632
C2×#52393
C2×#47333