Finite Group Databasebeta

← C2×#10591643 #11867882

Subgroups — C2×#10591643 #11867882

Order 1152.

1085 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
1C22×#3755C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×C3×#836C211yesmaximal, characteristic, complemented
6#10591643C218yesmaximal, direct product factor
7C2×#63578C211yesmaximal, characteristic, complemented
8C2×#63559C211yesmaximal, characteristic, complemented
9C2×#5203—31nomaximal
10C2×#4754—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×#3755—21no—
15C2×#3755—22no—
16C2×#3755—21no—
17C2×#3755C2214yescomplemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×#216—21no—
20C3×#942—22no—
21C3×#942C2214yescomplemented
22C2×C3×#215—21no—
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3717—21no—
27#63825—22no—
28#63825C2214yes—
29C2×#3714—21no—
30C2×#3711—21no—
31#63815—22no—
32#63815C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34C3×#836C2214yescomplemented
35#63578C2214yescomplemented
36#63559C2214yescomplemented
37C2×C3×#137—31no—
38C2×#949—31no—
39C2×#948—31no—
40C2×#942D311yescharacteristic, complemented
41C22×#215—31no—
42C22×#215—31no—
43C22×#215—61no—
44C2×#908—31no—
45C2×#907—31no—
46C2×C3×#101—31no—
47C2×#836D311yescharacteristic, complemented
48#5203—38no—
49C2×#823—31no—
50C2×#823—31no—
51C2×#822—31no—
52C2×#822—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×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235D412yes—
73C3×#235C2312yes—
74C2×C3×D12D411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77#3755—24no—
78#3755—24no—
79C2×C3⋊(C3⋊C8)D411yescharacteristic
80C2×C3⋊(C3⋊C8)D412yes—
81C2×C3⋊(C3⋊C8)D411yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#216—24no—
84C3×#215—24no—
85C3×#208—21no—
86C3×#208—21no—
87C3×#208—21no—
88C3×#208C2312yes—
89C3×#208C2312yes—
90C3×#208C2312yes—
91C2×C3×C3⋊C8—21no—
92C2×C3×C3⋊C8—21no—
93C2×C3×C3⋊C8—21no—
94#3717—24no—
95#3714—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#471—91noSylow
99C2×C3×#41—31no—
100C22×C3×Q8—21no—
101C22×C3×Q8C2×D311yescharacteristic
102C22×C3×Q8C2×D311yescharacteristic
103C2×#235C2×D311yescharacteristic
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—61no—
107C3×#137—34no—
108C3×#137—62no—
109C2×C3×Q16—61no—
110C2×C3×SD16—61no—
111C2×C3×M16—31no—
112C2×C3×M16—31no—
113C2×C3×M16—31no—
114#949—34no—
115#949—62no—
116#948—34no—
117#948—62no—
118C2×#216—21no—
119#942—22no—
120#942C2×D314yescomplemented
121C2×#215—21no—
122C2×#215—34no—
123C2×#215—34no—
124C2×#215—64no—
125C2×#215—61no—
126C2×#215—61no—
127C2×#215—61no—
128C2×#215—62no—
129C2×#215—61no—
130C2×#215—61no—
131C2×#215—62no—
132C2×#215—62no—
133C2×#215—62no—
134C2×#215—64no—
135C2×#213—61no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138C2×#208C2×D311yescharacteristic
139C2×#208C2×D311yescharacteristic
140C22×C3⋊C8—31no—
141C22×C3⋊C8—31no—
142C22×C3⋊C8—61no—
143C22×C3⋊C8—61no—
144#908—34no—
145#908—62no—
146#907—34no—
147#907—62no—
148C2×D24—61no—
149C2×#204—61no—
150C2×ΓL(1,𝔽25)—61no—
151C2×D3×C8—61no—
152C3×#101—34no—
153#836C2×D314yescomplemented
154#823—34no—
155#823—34no—
156#822—34no—
157#822—34no—
158C23×C32#4111yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3⋊D3—41no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—82no—
163C22×C3×D3—21no—
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
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—41no—
180C4⋊(C3⋊D3)—41no—
181C3×#67—22no—
182C3×#67—22no—
183C2×C3×Dic3—21no—
184C3×D12—21no—
185C3×D12C2×D412yes—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×Dic6—21no—
189C3×Dic6C2×D412yes—
190C3⋊(C3⋊C8)C2×D412yes—
191C3⋊(C3⋊C8)C2×D412yes—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—22no—
195C2×#137—31no—
196C2×AGL(1,ℤ/8)—91no—
197C22×SD16—91no—
198C2×#131—91no—
199#471—98no—
200C2×#108—91no—
201C2×#101—31no—
202C2×#100—91no—
203C23×D3—61no—
204C23×D3—61no—
205C23×D3—121no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—61no—
209C3×#41—61no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—22no—
213C2×C3×Q8—22no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—22no—
223C2×C3×Q8—31no—
224C2×C3×Q8—41no—
225C2×C3×Q8—41no—
226C2×C3×Q8—41no—
227C2×C3×Q8C22×D312yes—
228C2×C3×Q8C22×D312yes—
229C2×C3×D4—31no—
230C2×C3×D4—61no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—41no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239#235—21no—
240#235—21no—
241#235#6712yes—
242#235C22×D312yes—
243C2×D12—32no—
244C2×D12—32no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—61no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—121no—
259C2×D12—121no—
260C2×D12—121no—
261C2×D12#6711yescharacteristic
262C2×C4×D3—21no—
263C2×Dic6#6711yescharacteristic
264C3×Q16—64no—
265C3×SD16—64no—
266C3×M16—32no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—61no—
270C3×M16—61no—
271C3×M16—61no—
272C2×C3×C8—61no—
273C2×C3×C8—61no—
274C2×C3×C8—61no—
275#216—24no—
276#215—24no—
277#215—64no—
278#215—64no—
279#215—64no—
280#215—64no—
281#215—64no—
282#215—68no—
283#215—68no—
284#213—64no—
285#208—21no—
286#208—21no—
287#208—21no—
288#208—64no—
289#208C22×D312yes—
290#208C22×D312yes—
291#208C22×D312yes—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—31no—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—61no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8—64no—
308D24—64no—
309#204—64no—
310ΓL(1,𝔽25)—64no—
311D3×C8—64no—
312C22×C32—22no—
313C22×C32#12111yescharacteristic
314C22×C32#12111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C2×C3⋊D3—42no—
317C2×C3⋊D3—82no—
318C2×C3⋊D3—82no—
319C2×C3⋊D3—82no—
320C2×C3×D3—22no—
321C2×C3×D3—42no—
322C32×C4—42no—
323C32×C4#12111yescharacteristic
324C32×C4#12111yescharacteristic
325C32×C4C22×D411yescharacteristic
326C32×C4C22×D411yescharacteristic
327C3×Dic3—22no—
328C2×#41—31no—
329C22×Q8D3211yescharacteristic
330C22×D4—91no—
331#137—34no—
332#137—62no—
333AGL(1,ℤ/8)—94no—
334AGL(1,ℤ/8)—182no—
335C2×Q16—61no—
336C2×SD16—61no—
337C2×SD16—94no—
338C2×SD16—181no—
339C2×SD16—181no—
340C2×SD16—181no—
341C2×SD16—182no—
342C2×D8—181no—
343#131—94no—
344#131—182no—
345C2×M16—31no—
346C2×M16—31no—
347C2×M16—31no—
348C2×M16—181no—
349C22×C8—91no—
350C22×C8—181no—
351#108—94no—
352#101—34no—
353#100—94no—
354C23×C3—21no—
355C23×C3—61no—
356C23×C3#23511yescharacteristic
357C23×C3#23711yescharacteristic
358C22×D3—21no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—122no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—121no—
365C22×D3—121no—
366C22×D3—121no—
367C22×D3—121no—
368C22×D3—244no—
369C22×D3—242no—
370C22×D3—242no—
371C3×Q8—24no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8—22no—
375C3×Q8—22no—
376C3×Q8—32no—
377C3×Q8—42no—
378C3×Q8—42no—
379C3×Q8—42no—
380C3×Q8—41no—
381C3×Q8—41no—
382C3×Q8—41no—
383C3×Q8—41no—
384C3×Q8—61no—
385C3×D4—32no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—61no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4#23511yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4#23711yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—22no—
420#67—22no—
421C2×Dic3—21no—
422D12—21no—
423D12—64no—
424D12—62no—
425D12—62no—
426D12—62no—
427D12—62no—
428D12—122no—
429D12—122no—
430D12—122no—
431D12—121no—
432D12—121no—
433D12—121no—
434D12—121no—
435D12C2×#6712yes—
436C4×D3—22no—
437C4×D3—22no—
438Dic6—21no—
439Dic6C2×#6712yes—
440C3×C8—62no—
441C3×C8—62no—
442C3×C8—62no—
443C3⋊C8—22no—
444C3⋊C8—22no—
445C3⋊C8—22no—
446C3⋊C8—32no—
447C3⋊C8—32no—
448C3⋊C8—32no—
449C3⋊C8—32no—
450C3⋊C8—62no—
451C3⋊C8—62no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32#47112yescomplemented
455C2×C32C2×#12111yescharacteristic
456C3⋊D3—82no—
457C3×D3—42no—
458C24—181no—
459#41—32no—
460#41—32no—
461#41—61no—
462#41—61no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—31no—
469C2×Q8C2×D3212yes—
470C2×D4—31no—
471C2×D4—61no—
472C2×D4—92no—
473C2×D4—181no—
474C2×D4—181no—
475C2×D4—181no—
476C2×D4—181no—
477C2×D4—181no—
478C22×C4—21no—
479C22×C4—61no—
480C22×C4C2×D3211yescharacteristic
481Q16—64no—
482SD16—64no—
483SD16—184no—
484SD16—184no—
485SD16—184no—
486D8—184no—
487M16—32no—
488M16—32no—
489M16—32no—
490M16—61no—
491M16—61no—
492M16—61no—
493M16—184no—
494C2×C8—61no—
495C2×C8—61no—
496C2×C8—61no—
497C2×C8—92no—
498C2×C8—91no—
499C2×C8—91no—
500C2×C8—92no—
501C2×C8—184no—
502C22×C3—24no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—62no—
509C22×C3—122no—
510C22×C3#88411yescharacteristic
511C22×C3#88411yescharacteristic
512C22×C3#93911yescharacteristic
513C22×C3#93911yescharacteristic
514C22×C3C2×#23511yescharacteristic
515C22×C3C2×#23711yescharacteristic
516C2×D3—22no—
517C2×D3—42no—
518C2×D3—124no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—244no—
522C2×D3—244no—
523C2×D3—242no—
524C2×D3—242no—
525C2×D3—244no—
526C2×D3—242no—
527C2×D3—242no—
528C2×D3—242no—
529C2×D3—242no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—44no—
535C3×C4—42no—
536C3×C4—42no—
537C3×C4—62no—
538C3×C4#88411yescharacteristic
539C3×C4#88411yescharacteristic
540C3×C4#93911yescharacteristic
541C3×C4#93911yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C2×D3×D411yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C22×#6711yescharacteristic
546Dic3—22no—
547C32C2×#47111yescharacteristic, complemented, Sylow
548C23—61no—
549C23—182no—
550C23—361no—
551C23—361no—
552C23—722no—
553C23#380411yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—32no—
557Q8—41no—
558Q8—41no—
559Q8—61no—
560D4—32no—
561D4—62no—
562D4—62no—
563D4—61no—
564D4—182no—
565D4—182no—
566D4—361no—
567D4—361no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—61no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4#380411yescharacteristic
575C2×C4D3×#6711yescharacteristic
576C2×C4D3×#6711yescharacteristic
577C2×C4#381111yescharacteristic
578C2×C4#381111yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—62no—
581C8—62no—
582C8—62no—
583C8—92no—
584C8—92no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—122no—
594C2×C3#475412yescomplemented
595C2×C3#520312yescomplemented
596C2×C3C2×#88411yescharacteristic
597C2×C3C2×#93911yescharacteristic
598D3—42no—
599D3—244no—
600D3—242no—
601D3—242no—
602C22—22no—
603C22—62no—
604C22—122no—
605C22—362no—
606C22—722no—
607C22—722no—
608C22—722no—
609C22#6397111yescharacteristic
610C22#6397111yescharacteristic
611C22C2×#380411yescharacteristic
612C4—42no—
613C4—62no—
614C4#6397111yescharacteristic
615C4#6397111yescharacteristic
616C4C2×D3×#6711yescharacteristic
617C4C2×#381111yescharacteristic
618C3—21no—
619C3C2×#475411yescharacteristic, complemented
620C3C2×#520311yescharacteristic, complemented
621C2—21no—
622C2—21no—
623C2—122no—
624C2—722no—
625C2#1059164312yesdirect product factor
626C2C2×#6397111yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32#121
prime radicalC2×#63825C2
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. C22×#3755C2semidirect
2. C2×C3×#942C2semidirect
4. C2×#63815C2semidirect
5. C2×C3×#836C2semidirect
6. #10591643C2direct (N × H)
7. C2×#63578C2semidirect
8. C2×#63559C2semidirect
17. C2×#3755C22semidirect
21. C3×#942C22semidirect
32. #63815C22semidirect
34. C3×#836C22semidirect
35. #63578C22semidirect
36. #63559C22semidirect
40. C2×#942D3semidirect
47. C2×#836D3semidirect
120. #942C2×D3semidirect
153. #836C2×D3semidirect
454. C2×C32#471semidirect
547. C32C2×#471semidirect
594. C2×C3#4754semidirect
595. C2×C3#5203semidirect
619. C3C2×#4754semidirect
620. C3C2×#5203semidirect
625. C2#10591643direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×#9422
C2×#638252
C2×#638152
C2×C3×#8362
#105916432
C2×#635782
C2×#635592
C2×#52033
C2×#47543