Finite Group Databasebeta

← C2×#10591542 #11867883

Subgroups — C2×#10591542 #11867883

Order 1152.

1065 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#836C211yesmaximal, characteristic, complemented
6#10591542C218yesmaximal, direct product factor
7C2×#63577C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5177—31nomaximal
10C2×#4754—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×#3756—21no—
15#64151—22no—
16#64151C2214yescomplemented
17C2×#3755—21no—
18C2×#3748C2211yescharacteristic
19C2×C3×#215—21no—
20C2×C3×#215—22no—
21C2×C3×#215—21no—
22C2×C3×#215C2214yescomplemented
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63830—22no—
27#63830C2214yes—
28C2×#3716—21no—
29C2×#3714—21no—
30C2×#3712—21no—
31#63817—22no—
32#63817C2214yescomplemented
33C2×#3710—21no—
34C3×#836C2214yescomplemented
35#63577C2214yescomplemented
36#63558C2214yescomplemented
37C22×C3×SD16—31no—
38C2×#942—31no—
39C2×#942—31no—
40C2×#942—61no—
41C22×#215D311yescharacteristic, complemented
42C2×#932—31no—
43C2×#908—31no—
44C2×#907—31no—
45C2×#901—31no—
46C2×C3×#101—31no—
47C2×#836D311yescharacteristic, complemented
48C2×#833—31no—
49#5177—38no—
50C2×#823—31no—
51C2×#822—31no—
52C2×#819—31no—
53#4754—38no—
54C23×C3×D3—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C2×C32×Q8—21no—
58C2×C32×Q8—21no—
59C2×C32×Q8—21no—
60C2×C32×Q8C2312yes—
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64#3828—21no—
65#3828—21no—
66#3828D412yes—
67#3828C2312yes—
68C2×C4⋊(C3⋊D3)D411yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77#3756—24no—
78#3755—24no—
79#3748—21no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C3×#215—24no—
83C3×#215—24no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208C2312yes—
87C3×#208C2312yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D412yes—
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94#3716—24no—
95#3714—24no—
96#3712—24no—
97#3710—24no—
98C2×#471—91noSylow
99C22×C3×Q8—21no—
100C22×C3×Q8C2×D311yescharacteristic
101C22×C3×Q8C2×D311yescharacteristic
102C22×C3×D4—31no—
103C2×#235—31no—
104C2×#235—31no—
105C2×#235—61no—
106C22×D12C2×D311yescharacteristic
107C2×C3×SD16—34no—
108C2×C3×SD16—61no—
109C2×C3×SD16—61no—
110C2×C3×SD16—62no—
111C2×C3×M16—31no—
112C2×C3×M16—31no—
113C22×C3×C8—31no—
114C2×#216—61no—
115C2×#216—61no—
116C2×#216—62no—
117#942—34no—
118#942—34no—
119#942—64no—
120#942—62no—
121#942—62no—
122#942—64no—
123C2×#215—21no—
124C2×#215—21no—
125C2×#215—22no—
126C2×#215—61no—
127C2×#215—61no—
128C2×#215—62no—
129C2×#215C2×D314yescomplemented
130C2×#214—61no—
131#932—34no—
132#932—62no—
133C2×#213—61no—
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138C2×#208C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140#908—34no—
141#908—62no—
142#907—34no—
143#907—62no—
144C2×D24—61no—
145C2×#204—61no—
146#901—34no—
147#901—62no—
148C2×ΓL(1,𝔽25)—61no—
149C2×ΓL(1,𝔽25)—61no—
150C2×D3×C8—61no—
151C2×D3×C8—61no—
152C3×#101—34no—
153#836C2×D314yescomplemented
154#833—34no—
155#823—34no—
156#822—34no—
157#819—34no—
158C23×C32#4111yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3×D3—22no—
161C22×C3×D3—41no—
162C22×C3×D3—41no—
163C22×C3×D3—82no—
164C32×Q8—22no—
165C32×Q8—22no—
166C32×Q8—41no—
167C32×Q8—41no—
168C2×C32×C4—22no—
169C2×C32×C4—41no—
170C2×C32×C4—41no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4111yescharacteristic
176C2×C32×C4C2411yescharacteristic
177#638—22no—
178#638—22no—
179C2×C3⋊Dic3—21no—
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)C2×D412yes—
182C4×C3⋊D3—22no—
183C4×C3⋊D3—22no—
184#634—21no—
185#634C2×D412yes—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—41no—
189C3×D12—41no—
190C3⋊(C3⋊C8)—22no—
191C3×C3⋊C8—22no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8C2×D412yes—
194C3×C3⋊C8C2×D412yes—
195C2×#137—91no—
196C2×AGL(1,ℤ/8)—91no—
197C22×SD16—31no—
198C2×#131—91no—
199#471—98no—
200C2×#108—91no—
201C2×#101—31no—
202C2×#100—91no—
203C24×C3—61no—
204C23×D3—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—22no—
218C2×C3×Q8—41no—
219C2×C3×Q8—41no—
220C2×C3×Q8—41no—
221C2×C3×Q8C22×D312yes—
222C2×C3×Q8C22×D312yes—
223C2×C3×D4—32no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—41no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—121no—
238#235—32no—
239#235—32no—
240#235—32no—
241#235—32no—
242#235—62no—
243#235—62no—
244#235—61no—
245#235—61no—
246#235—61no—
247#235—61no—
248#235—121no—
249#235—121no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—31no—
256C2×D12—31no—
257C2×D12—61no—
258C2×D12C22×D312yes—
259C2×C4×D3—61no—
260C2×C4×D3—61no—
261C2×C4×D3—121no—
262C2×Dic6—31no—
263C2×Dic6—31no—
264C2×Dic6—61no—
265C3×SD16—64no—
266C3×SD16—64no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—61no—
270C3×M16—61no—
271C2×C3×C8—31no—
272C2×C3×C8—31no—
273C2×C3×C8—32no—
274C2×C3×C8—32no—
275C2×C3×C8—61no—
276C2×C3×C8—61no—
277#216—64no—
278#216—64no—
279#216—68no—
280#215—24no—
281#215—24no—
282#215—64no—
283#215—64no—
284#215—68no—
285#214—64no—
286#213—64no—
287#208—21no—
288#208—21no—
289#208—32no—
290#208—32no—
291#208—62no—
292#208—62no—
293#208—61no—
294#208—61no—
295#208C22×D312yes—
296#208C22×D312yes—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—61no—
301C2×C3⋊C8—61no—
302C2×C3⋊C8#6711yescharacteristic
303C2×C3⋊C8#6711yescharacteristic
304C2×C3⋊C8#6712yes—
305C2×C3⋊C8C22×D312yes—
306D24—64no—
307#204—64no—
308ΓL(1,𝔽25)—64no—
309ΓL(1,𝔽25)—64no—
310D3×C8—64no—
311D3×C8—64no—
312C22×C32—22no—
313C22×C32#12111yescharacteristic
314C22×C32#12111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C2×C3⋊D3—22no—
317C2×C3⋊D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—82no—
320C2×C3×D3—82no—
321C2×C3×D3—82no—
322C32×C4—42no—
323C32×C4#12111yescharacteristic
324C32×C4#12111yescharacteristic
325C32×C4C22×D411yescharacteristic
326C32×C4C22×D411yescharacteristic
327C3⋊Dic3—22no—
328C2×#41—91no—
329C22×Q8D3211yescharacteristic
330C22×D4—31no—
331#137—94no—
332#137—182no—
333AGL(1,ℤ/8)—94no—
334AGL(1,ℤ/8)—182no—
335C2×Q16—181no—
336C2×SD16—34no—
337C2×SD16—61no—
338C2×SD16—61no—
339C2×SD16—62no—
340C2×SD16—181no—
341C2×SD16—181no—
342C2×D8—181no—
343#131—94no—
344#131—182no—
345C2×M16—31no—
346C2×M16—31no—
347C2×M16—91no—
348C2×M16—181no—
349C22×C8—31no—
350C22×C8—181no—
351#108—94no—
352#101—34no—
353#100—94no—
354C23×C3—21no—
355C23×C3—62no—
356C23×C3—121no—
357C23×C3—121no—
358C23×C3—242no—
359C23×C3#23511yescharacteristic
360C23×C3#23711yescharacteristic
361C22×D3—22no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—82no—
367C22×D3—121no—
368C3×Q8—24no—
369C3×Q8—22no—
370C3×Q8—22no—
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—42no—
374C3×Q8—42no—
375C3×Q8—42no—
376C3×Q8—41no—
377C3×Q8—41no—
378C3×Q8—41no—
379C3×Q8—41no—
380C3×D4—62no—
381C3×D4—62no—
382C3×D4—121no—
383C3×D4—121no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4#23511yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4#23711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—62no—
412#67—62no—
413#67—62no—
414#67—62no—
415#67—122no—
416#67—122no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—121no—
420D12—22no—
421D12—22no—
422D12—32no—
423D12—32no—
424D12—41no—
425D12—41no—
426D12—62no—
427D12—61no—
428D12—61no—
429D12—121no—
430C4×D3—62no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—62no—
434C4×D3—122no—
435C4×D3—122no—
436Dic6—32no—
437Dic6—32no—
438Dic6—62no—
439Dic6—61no—
440Dic6—61no—
441Dic6—121no—
442C3×C8—32no—
443C3×C8—32no—
444C3×C8—62no—
445C3×C8—62no—
446C3⋊C8—22no—
447C3⋊C8—22no—
448C3⋊C8—64no—
449C3⋊C8—62no—
450C3⋊C8—62no—
451C3⋊C8C2×#6712yes—
452C3⋊C8C2×#6712yes—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32#47112yescomplemented
456C2×C32C2×#12111yescharacteristic
457C3⋊D3—42no—
458C3×D3—82no—
459C24—61no—
460#41—92no—
461#41—92no—
462#41—181no—
463#41—181no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—91no—
470C2×Q8C2×D3212yes—
471C2×D4—32no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—61no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—91no—
478C2×D4—181no—
479C22×C4—21no—
480C22×C4—181no—
481C22×C4C2×D3211yescharacteristic
482Q16—184no—
483SD16—64no—
484SD16—64no—
485SD16—184no—
486SD16—184no—
487D8—184no—
488M16—32no—
489M16—32no—
490M16—61no—
491M16—61no—
492M16—92no—
493M16—184no—
494M16—181no—
495C2×C8—32no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8—32no—
499C2×C8—61no—
500C2×C8—61no—
501C2×C8—184no—
502C2×C8—181no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—42no—
509C22×C3—122no—
510C22×C3—242no—
511C22×C3—242no—
512C22×C3—242no—
513C22×C3#88411yescharacteristic
514C22×C3#88411yescharacteristic
515C22×C3#93811yescharacteristic
516C22×C3#93811yescharacteristic
517C22×C3C2×#23511yescharacteristic
518C22×C3C2×#23711yescharacteristic
519C2×D3—42no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—82no—
523C2×D3—82no—
524C2×D3—82no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—242no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—44no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4#88411yescharacteristic
537C3×C4#88411yescharacteristic
538C3×C4#93811yescharacteristic
539C3×C4#93811yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C22×#6711yescharacteristic
544Dic3—62no—
545Dic3—62no—
546Dic3—122no—
547C32C2×#47111yescharacteristic, complemented, Sylow
548C23—62no—
549C23—121no—
550C23—121no—
551C23—181no—
552C23—242no—
553C23#380411yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—41no—
557Q8—41no—
558Q8—92no—
559Q8—181no—
560D4—62no—
561D4—62no—
562D4—92no—
563D4—121no—
564D4—121no—
565D4—182no—
566D4—182no—
567D4—181no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—181no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4#380411yescharacteristic
575C2×C4D3×#6711yescharacteristic
576C2×C4D3×#6711yescharacteristic
577C2×C4#381111yescharacteristic
578C2×C4#381111yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—32no—
581C8—32no—
582C8—62no—
583C8—62no—
584C8—182no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—41no—
592C2×C3—41no—
593C2×C3—242no—
594C2×C3#475412yescomplemented
595C2×C3#517712yescomplemented
596C2×C3C2×#88411yescharacteristic
597C2×C3C2×#93811yescharacteristic
598D3—82no—
599D3—122no—
600D3—122no—
601D3—242no—
602C22—22no—
603C22—122no—
604C22—182no—
605C22—242no—
606C22—242no—
607C22—242no—
608C22—362no—
609C22#6395811yescharacteristic
610C22#6395811yescharacteristic
611C22C2×#380411yescharacteristic
612C4—42no—
613C4—182no—
614C4#6395811yescharacteristic
615C4#6395811yescharacteristic
616C4C2×D3×#6711yescharacteristic
617C4C2×#381111yescharacteristic
618C3—21no—
619C3C2×#475411yescharacteristic, complemented
620C3C2×#517711yescharacteristic, complemented
621C2—21no—
622C2—21no—
623C2—242no—
624C2—362no—
625C2#1059154212yesdirect product factor
626C2C2×#6395811yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32#121
prime radicalC2×#63830C2
hypercenterC22×Q8D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64151C2semidirect
2. C22×C3×#215C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#836C2semidirect
6. #10591542C2direct (N × H)
7. C2×#63577C2semidirect
8. C2×#63558C2semidirect
16. #64151C22semidirect
22. C2×C3×#215C22semidirect
32. #63817C22semidirect
34. C3×#836C22semidirect
35. #63577C22semidirect
36. #63558C22semidirect
41. C22×#215D3semidirect
47. C2×#836D3semidirect
129. C2×#215C2×D3semidirect
153. #836C2×D3semidirect
455. C2×C32#471semidirect
547. C32C2×#471semidirect
594. C2×C3#4754semidirect
595. C2×C3#5177semidirect
619. C3C2×#4754semidirect
620. C3C2×#5177semidirect
625. C2#10591542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641512
C22×C3×#2152
C2×#638302
C2×#638172
C2×C3×#8362
#105915422
C2×#635772
C2×#635582
C2×#51773
C2×#47543