Finite Group Databasebeta

← C2×#10591679 #11867881

Subgroups — C2×#10591679 #11867881

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×#64160C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5#10591679C218yesmaximal, direct product factor
6C2×#63577C211yesmaximal, characteristic, complemented
7C2×#63561C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5200—31nomaximal
10C2×#5141—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14#64160—22no—
15#64160C2214yescomplemented
16C2×#3756—21no—
17C2×#3754—21no—
18C2×#3748C2211yescharacteristic
19C3×#949—22no—
20C3×#949C2214yes—
21C3×#948—22no—
22C3×#948C2214yescomplemented
23C2×C3×#215—21no—
24C2×C3×#213—21no—
25C2×C3×#208—21no—
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8—21no—
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3716—21no—
31C2×#3716—21no—
32C2×#3716—22no—
33C2×#3716C2214yescomplemented
34#63577C2214yescomplemented
35#63561C2214yescomplemented
36#63558C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C2×C3×#131—31no—
39C2×#951—31no—
40C2×#951—31no—
41C2×#951—61no—
42C2×#949D311yescharacteristic
43C2×#948D311yescharacteristic, complemented
44C22×#214—31no—
45C22×#204—31no—
46C2×#833—31no—
47#5200—38no—
48#5141—38no—
49C2×#824—31no—
50C2×#824—31no—
51C2×#823—31no—
52C2×#822—31no—
53C2×#819—31no—
54C23×C3×D3—21no—
55C32×#41—21no—
56C32×#41—21no—
57C32×#41D412yes—
58C32×#41C2312yes—
59C2×C32×Q8D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4D411yescharacteristic
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—21no—
65C2×#634—21no—
66C2×#634—21no—
67C2×#634—21no—
68C2×#634—21no—
69C2×#634—21no—
70C2×#634C2312yes—
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#3754—24no—
79#3748—21no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C3×#215—24no—
83C3×#213—24no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208—24no—
87C3×#208C2312yes—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8—21no—
91C2×C3×C3⋊C8—24no—
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8D411yescharacteristic
94C2×C3×C3⋊C8D412yes—
95C2×C3×C3⋊C8C2312yes—
96#3716—24no—
97#3716—24no—
98C2×#471—91noSylow
99C2×C3×#41—21no—
100C2×C3×#41C2×D311yescharacteristic
101C2×C3×#41C2×D311yescharacteristic
102C22×C3×D4—31no—
103C22×D12C2×D311yescharacteristic
104C22×Dic6—31no—
105C22×Dic6—31no—
106C22×Dic6—61no—
107C3×AGL(1,ℤ/8)—34no—
108C3×AGL(1,ℤ/8)—62no—
109C2×C3×SD16—61no—
110C2×C3×D8—61no—
111C3×#131—34no—
112C3×#131—62no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C2×C3×M16—61no—
116C22×C3×C8—31no—
117C22×C3×C8—61no—
118#951—34no—
119#951—34no—
120#951—64no—
121#951—64no—
122#951—62no—
123#951—62no—
124#949—22no—
125#949C2×D314yes—
126#948—22no—
127#948C2×D314yescomplemented
128C2×#216—62no—
129C2×#216—61no—
130C2×#216—61no—
131C2×#215—21no—
132C2×#214—34no—
133C2×#214—62no—
134C2×#214—61no—
135C2×#214—61no—
136C2×#214—61no—
137C2×#214—61no—
138C2×#214—62no—
139C2×#213—21no—
140C2×#208—21no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×#208C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—21no—
147C22×C3⋊C8C2×D311yescharacteristic
148C2×#204—34no—
149C2×#204—61no—
150C2×#204—61no—
151C2×#204—62no—
152#833—34no—
153#824—34no—
154#824—34no—
155#823—34no—
156#822—34no—
157#819—34no—
158C23×C32—21no—
159C23×C32#4111yescharacteristic
160C22×C3×D3—22no—
161C22×C3×D3—41no—
162C22×C3×D3—41no—
163C22×C3×D3—82no—
164C32×Q8—21no—
165C32×Q8C2×D412yes—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—21no—
169C32×D4C2×D412yes—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4111yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—41no—
181C2×C3⋊Dic3—41no—
182#634—22no—
183#634—22no—
184#634—41no—
185#634—41no—
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)—31no—
197C22×SD16—91no—
198C2×#131—31no—
199#471—98no—
200C2×#108—91no—
201C2×#101—91no—
202C2×#100—91no—
203C24×C3—61no—
204C23×D3—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—41no—
212C3×#41—41no—
213C3×#41D1212yes—
214C3×#41#6712yes—
215C3×#41C22×D312yes—
216C3×#41C22×D312yes—
217C2×C3×Q8—21no—
218C2×C3×Q8D1211yescharacteristic
219C2×C3×Q8#6711yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—32no—
224C2×C3×D4—41no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4D1211yescharacteristic
231C2×C3×D4#6711yescharacteristic
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—41no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—121no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12C22×D312yes—
247C2×Dic6—32no—
248C2×Dic6—32no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—62no—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6—61no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×Dic6—121no—
263C2×Dic6—121no—
264C2×Dic6—121no—
265C3×SD16—64no—
266C3×D8—64no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—64no—
270C3×M16—61no—
271C3×M16—61no—
272C2×C3×C8—31no—
273C2×C3×C8—31no—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C2×C3×C8—64no—
277C2×C3×C8—61no—
278C2×C3×C8—61no—
279#216—68no—
280#216—64no—
281#216—64no—
282#215—24no—
283#214—68no—
284#214—64no—
285#214—64no—
286#214—64no—
287#214—64no—
288#213—24no—
289#208—21no—
290#208—21no—
291#208—24no—
292#208—32no—
293#208—32no—
294#208—62no—
295#208—62no—
296#208—61no—
297#208—61no—
298#208C22×D312yes—
299#208C22×D312yes—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—24no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8#6711yescharacteristic
307C2×C3⋊C8#6711yescharacteristic
308C2×C3⋊C8#6712yes—
309C2×C3⋊C8C22×D312yes—
310#204—64no—
311#204—64no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—42no—
315C22×C32#12111yescharacteristic
316C22×C32#12111yescharacteristic
317C22×C32C2×#4111yescharacteristic
318C2×C3×D3—42no—
319C2×C3×D3—82no—
320C2×C3×D3—82no—
321C2×C3×D3—82no—
322C32×C4—22no—
323C32×C4#12111yescharacteristic
324C32×C4#12111yescharacteristic
325C32×C4C22×D411yescharacteristic
326C32×C4C22×D411yescharacteristic
327C3⋊Dic3—42no—
328C2×#41D3211yescharacteristic
329C22×Q8—91no—
330C22×D4—31no—
331#137—94no—
332#137—182no—
333AGL(1,ℤ/8)—34no—
334AGL(1,ℤ/8)—62no—
335C2×Q16—181no—
336C2×SD16—61no—
337C2×SD16—94no—
338C2×SD16—181no—
339C2×SD16—181no—
340C2×SD16—182no—
341C2×SD16—181no—
342C2×D8—61no—
343#131—34no—
344#131—62no—
345C2×M16—31no—
346C2×M16—31no—
347C2×M16—61no—
348C2×M16—91no—
349C22×C8—31no—
350C22×C8—61no—
351#108—94no—
352#101—94no—
353#100—94no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—41no—
358C23×C3—62no—
359C23×C3—121no—
360C23×C3—121no—
361C23×C3—242no—
362C23×C3#23511yescharacteristic
363C23×C3#23711yescharacteristic
364C22×D3—22no—
365C22×D3—41no—
366C22×D3—41no—
367C22×D3—82no—
368C3×Q8—21no—
369C3×Q8—21no—
370C3×Q8—22no—
371C3×Q8—41no—
372C3×Q8C2×D1212yes—
373C3×Q8C2×#6712yes—
374C3×D4—22no—
375C3×D4—22no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—21no—
379C3×D4—21no—
380C3×D4—22no—
381C3×D4—41no—
382C3×D4—42no—
383C3×D4—42no—
384C3×D4—62no—
385C3×D4—62no—
386C3×D4—121no—
387C3×D4—121no—
388C3×D4C2×D1212yes—
389C3×D4C2×#6712yes—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4#23511yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4#23711yescharacteristic
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426D12—22no—
427D12—22no—
428D12—41no—
429D12—41no—
430Dic6—64no—
431Dic6—62no—
432Dic6—62no—
433Dic6—62no—
434Dic6—62no—
435Dic6—122no—
436Dic6—122no—
437Dic6—122no—
438Dic6—121no—
439Dic6—121no—
440Dic6—121no—
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—42no—
456C2×C32#47112yescomplemented
457C2×C32C2×#12111yescharacteristic
458C3×D3—82no—
459C24—61no—
460#41—21no—
461#41—21no—
462#41#62612yes—
463#41C2×D3212yes—
464C2×Q8—92no—
465C2×Q8—181no—
466C2×Q8—181no—
467C2×Q8—181no—
468C2×Q8—181no—
469C2×Q8—181no—
470C2×Q8#62611yescharacteristic
471C2×D4—21no—
472C2×D4—32no—
473C2×D4—61no—
474C2×D4—61no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4#62611yescharacteristic
479C22×C4—21no—
480C22×C4—181no—
481C22×C4C2×D3211yescharacteristic
482Q16—184no—
483SD16—64no—
484SD16—184no—
485SD16—184no—
486SD16—184no—
487D8—64no—
488M16—32no—
489M16—32no—
490M16—64no—
491M16—61no—
492M16—61no—
493M16—92no—
494M16—181no—
495C2×C8—32no—
496C2×C8—31no—
497C2×C8—31no—
498C2×C8—32no—
499C2×C8—64no—
500C2×C8—61no—
501C2×C8—61no—
502C2×C8—181no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—82no—
515C22×C3—122no—
516C22×C3—242no—
517C22×C3—242no—
518C22×C3—242no—
519C22×C3#93011yescharacteristic
520C22×C3#93011yescharacteristic
521C22×C3#93911yescharacteristic
522C22×C3#93911yescharacteristic
523C22×C3C2×#23511yescharacteristic
524C22×C3C2×#23711yescharacteristic
525C2×D3—42no—
526C2×D3—82no—
527C2×D3—82no—
528C2×D3—82no—
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—42no—
536C3×C4#93011yescharacteristic
537C3×C4#93011yescharacteristic
538C3×C4#93911yescharacteristic
539C3×C4#93911yescharacteristic
540C3×C4C22×D1211yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C22×#6711yescharacteristic
543C3×C4C22×#6711yescharacteristic
544Dic3—124no—
545Dic3—122no—
546Dic3—122no—
547C32C2×#47111yescharacteristic, complemented, Sylow
548C23—21no—
549C23—62no—
550C23—121no—
551C23—121no—
552C23—242no—
553C23#380411yescharacteristic
554Q8—21no—
555Q8—182no—
556Q8—182no—
557Q8—361no—
558Q8—361no—
559Q8C2×#62612yes—
560D4—22no—
561D4—22no—
562D4—21no—
563D4—62no—
564D4—62no—
565D4—121no—
566D4—121no—
567D4C2×#62612yes—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—182no—
572C2×C4—361no—
573C2×C4—361no—
574C2×C4#380411yescharacteristic
575C2×C4C2×#62611yescharacteristic
576C2×C4C2×#62611yescharacteristic
577C2×C4D3×#6711yescharacteristic
578C2×C4D3×#6711yescharacteristic
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—21no—
590C2×C3—22no—
591C2×C3—41no—
592C2×C3—41no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—82no—
596C2×C3—242no—
597C2×C3#514112yescomplemented
598C2×C3#520012yescomplemented
599C2×C3C2×#93011yescharacteristic
600C2×C3C2×#93911yescharacteristic
601D3—82no—
602C22—22no—
603C22—22no—
604C22—42no—
605C22—122no—
606C22—242no—
607C22—242no—
608C22—242no—
609C22#6397811yescharacteristic
610C22#6397811yescharacteristic
611C22C2×#380411yescharacteristic
612C4—22no—
613C4—362no—
614C4#6397811yescharacteristic
615C4#6397811yescharacteristic
616C4C22×#62611yescharacteristic
617C4C2×D3×#6711yescharacteristic
618C3—21no—
619C3C2×#514111yescharacteristic, complemented
620C3C2×#520011yescharacteristic, complemented
621C2—21no—
622C2—21no—
623C2—42no—
624C2—242no—
625C2#1059167912yesdirect product factor
626C2C2×#6397811yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×C3×#949C2
hypercenterC2×#41D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64160C2semidirect
3. C2×C3×#948C2semidirect
4. C22×#3716C2semidirect
5. #10591679C2direct (N × H)
6. C2×#63577C2semidirect
7. C2×#63561C2semidirect
8. C2×#63558C2semidirect
15. #64160C22semidirect
22. C3×#948C22semidirect
33. C2×#3716C22semidirect
34. #63577C22semidirect
35. #63561C22semidirect
36. #63558C22semidirect
43. C2×#948D3semidirect
127. #948C2×D3semidirect
456. C2×C32#471semidirect
547. C32C2×#471semidirect
597. C2×C3#5141semidirect
598. C2×C3#5200semidirect
619. C3C2×#5141semidirect
620. C3C2×#5200semidirect
625. C2#10591679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641602
C2×C3×#9492
C2×C3×#9482
C22×#37162
#105916792
C2×#635772
C2×#635612
C2×#635582
C2×#52003
C2×#51413