Finite Group Databasebeta

← C2×#10591507 #11867873

Subgroups — C2×#10591507 #11867873

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×#3754C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×C3×#833C211yesmaximal, characteristic, complemented
6#10591507C218yesmaximal, direct product factor
7C2×#63578C211yesmaximal, characteristic, complemented
8C2×#63561C211yesmaximal, characteristic, complemented
9C2×#5200—31nomaximal
10C2×#4748—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×#3754—21no—
15C2×#3754—22no—
16C2×#3754—21no—
17C2×#3754C2214yescomplemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×#214—21no—
20C3×#932—22no—
21C3×#932C2214yes—
22C2×C3×#213—21no—
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3719—21no—
27#63831—22no—
28#63831C2214yescomplemented
29C2×#3716—21no—
30C2×#3711—21no—
31#63815—22no—
32#63815C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34C3×#833C2214yescomplemented
35#63578C2214yescomplemented
36#63561C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C2×#951—31no—
39C2×#948—31no—
40C22×#214—31no—
41C22×#214—31no—
42C22×#214—61no—
43C2×#932D311yescharacteristic
44C2×#909—31no—
45C2×#907—31no—
46C2×C3×#100—31no—
47C2×#833D311yescharacteristic, complemented
48#5200—38no—
49C2×#824—31no—
50C2×#824—31no—
51C2×#822—31no—
52C2×#822—31no—
53#4748—38no—
54C24×C32—21no—
55C2×C32×D4—21no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4—21no—
60C2×C32×D4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3—21no—
63C2×#634—21no—
64C2×#634—21no—
65C2×#634—21no—
66C2×#634—21no—
67C2×#634—21no—
68C2×#634C2312yes—
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#3754—24no—
78#3754—24no—
79C2×C3⋊(C3⋊C8)D411yescharacteristic
80C2×C3⋊(C3⋊C8)D412yes—
81C2×C3⋊(C3⋊C8)D411yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#214—24no—
84C3×#213—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#3719—24no—
95#3716—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#471—91noSylow
99C2×C3×#41—31no—
100C22×C3×D4—21no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C2×#235C2×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—
111C2×C3×M16—31no—
112C2×C3×M16—31no—
113C2×C3×M16—31no—
114#951—34no—
115#951—62no—
116#948—34no—
117#948—62no—
118C2×#216—61no—
119C2×#214—21no—
120C2×#214—34no—
121C2×#214—34no—
122C2×#214—64no—
123C2×#214—61no—
124C2×#214—61no—
125C2×#214—61no—
126C2×#214—62no—
127C2×#214—61no—
128C2×#214—61no—
129C2×#214—62no—
130C2×#214—62no—
131C2×#214—62no—
132C2×#214—64no—
133#932—22no—
134#932C2×D314yes—
135C2×#213—21no—
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#909—34no—
145#909—62no—
146#907—34no—
147#907—62no—
148C2×Dic12—61no—
149C2×#204—61no—
150C2×ΓL(1,𝔽25)—61no—
151C2×D3×C8—61no—
152C3×#100—34no—
153#833C2×D314yescomplemented
154#824—34no—
155#824—34no—
156#822—34no—
157#822—34no—
158C23×C32—22no—
159C23×C32—41no—
160C23×C32—41no—
161C23×C32—82no—
162C23×C32#4111yescharacteristic
163C22×C3×D3—21no—
164C32×D4—22no—
165C32×D4—22no—
166C32×D4—41no—
167C32×D4—41no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4111yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—41no—
176C2×C3⋊Dic3—41no—
177#634—22no—
178#634—22no—
179#634—41no—
180#634—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—91no—
196C2×AGL(1,ℤ/8)—31no—
197C22×SD16—91no—
198C2×#131—91no—
199#471—98no—
200C2×#108—91no—
201C2×#101—91no—
202C2×#100—31no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—41no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—61no—
209C3×#41—61no—
210C2×C3×Q8—31no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—22no—
224C2×C3×D4—31no—
225C2×C3×D4—41no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4—61no—
229C2×C3×D4C22×D312yes—
230C2×C3×D4C22×D312yes—
231C22×C3×C4—21no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—21no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—121no—
239#235—21no—
240#235—21no—
241#235#6712yes—
242#235C22×D312yes—
243C2×D12#6711yescharacteristic
244C2×C4×D3—21no—
245C2×Dic6—32no—
246C2×Dic6—32no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—61no—
251C2×Dic6—61no—
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—121no—
261C2×Dic6—121no—
262C2×Dic6—121no—
263C2×Dic6#6711yescharacteristic
264C3×SD16—64no—
265C3×D8—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—64no—
276#214—24no—
277#214—64no—
278#214—64no—
279#214—64no—
280#214—64no—
281#214—64no—
282#214—68no—
283#214—68no—
284#213—24no—
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—
308Dic12—64no—
309#204—64no—
310ΓL(1,𝔽25)—64no—
311D3×C8—64no—
312C22×C32—22no—
313C22×C32—42no—
314C22×C32—82no—
315C22×C32—82no—
316C22×C32—82no—
317C22×C32#12111yescharacteristic
318C22×C32#12111yescharacteristic
319C22×C32C2×#4111yescharacteristic
320C2×C3×D3—22no—
321C2×C3×D3—42no—
322C32×C4#12111yescharacteristic
323C32×C4#12111yescharacteristic
324C32×C4C22×D411yescharacteristic
325C32×C4C22×D411yescharacteristic
326C3⋊Dic3—42no—
327C3×Dic3—22no—
328C2×#41—31no—
329C22×Q8—91no—
330C22×D4D3211yescharacteristic
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—181no—
341C2×SD16—182no—
342C2×D8—61no—
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—94no—
353#100—34no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—21no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—61no—
365C23×C3—82no—
366C23×C3—82no—
367C23×C3—84no—
368C23×C3#23511yescharacteristic
369C23×C3#23711yescharacteristic
370C22×D3—21no—
371C3×Q8—32no—
372C3×Q8—61no—
373C3×D4—24no—
374C3×D4—22no—
375C3×D4—22no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—32no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—61no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4#23511yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4#23711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—22no—
411#67—22no—
412C2×Dic3—21no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422D12—21no—
423D12C2×#6712yes—
424C4×D3—22no—
425C4×D3—22no—
426Dic6—21no—
427Dic6—64no—
428Dic6—62no—
429Dic6—62no—
430Dic6—62no—
431Dic6—62no—
432Dic6—122no—
433Dic6—122no—
434Dic6—122no—
435Dic6—121no—
436Dic6—121no—
437Dic6—121no—
438Dic6—121no—
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—82no—
455C2×C32#47112yescomplemented
456C2×C32C2×#12111yescharacteristic
457C3×D3—42no—
458C24—21no—
459#41—32no—
460#41—32no—
461#41—61no—
462#41—61no—
463C2×Q8—31no—
464C2×Q8—92no—
465C2×Q8—181no—
466C2×Q8—181no—
467C2×Q8—181no—
468C2×Q8—181no—
469C2×Q8—181no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—31no—
476C2×D4—61no—
477C2×D4C2×D3212yes—
478C22×C4—61no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481Q16—184no—
482SD16—64no—
483SD16—184no—
484SD16—184no—
485SD16—184no—
486D8—64no—
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—44no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3—62no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—84no—
515C22×C3—84no—
516C22×C3—82no—
517C22×C3—82no—
518C22×C3—84no—
519C22×C3—82no—
520C22×C3—82no—
521C22×C3—122no—
522C22×C3#88411yescharacteristic
523C22×C3#88411yescharacteristic
524C22×C3#93911yescharacteristic
525C22×C3#93911yescharacteristic
526C22×C3C2×#23511yescharacteristic
527C22×C3C2×#23711yescharacteristic
528C2×D3—22no—
529C2×D3—42no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—62no—
535C3×C4#88411yescharacteristic
536C3×C4#88411yescharacteristic
537C3×C4#93911yescharacteristic
538C3×C4#93911yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C22×#6711yescharacteristic
543Dic3—22no—
544Dic3—124no—
545Dic3—122no—
546Dic3—122no—
547C32C2×#47111yescharacteristic, complemented, Sylow
548C23—22no—
549C23—41no—
550C23—41no—
551C23—61no—
552C23—82no—
553C23#380411yescharacteristic
554Q8—32no—
555Q8—61no—
556Q8—182no—
557Q8—182no—
558Q8—361no—
559Q8—361no—
560D4—22no—
561D4—22no—
562D4—32no—
563D4—41no—
564D4—41no—
565D4—62no—
566D4—62no—
567D4—61no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—182no—
572C2×C4—361no—
573C2×C4—361no—
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—84no—
594C2×C3—82no—
595C2×C3—82no—
596C2×C3—122no—
597C2×C3#474812yescomplemented
598C2×C3#520012yescomplemented
599C2×C3C2×#88411yescharacteristic
600C2×C3C2×#93911yescharacteristic
601D3—42no—
602C22—22no—
603C22—42no—
604C22—62no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22—122no—
609C22#6397111yescharacteristic
610C22#6397111yescharacteristic
611C22C2×#380411yescharacteristic
612C4—62no—
613C4—362no—
614C4#6397111yescharacteristic
615C4#6397111yescharacteristic
616C4C2×D3×#6711yescharacteristic
617C4C2×#381111yescharacteristic
618C3—21no—
619C3C2×#474811yescharacteristic, complemented
620C3C2×#520011yescharacteristic, complemented
621C2—21no—
622C2—21no—
623C2—82no—
624C2—122no—
625C2#1059150712yesdirect product factor
626C2C2×#6397111yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×C3×#932C2
hypercenterC22×D4D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3754C2semidirect
3. C2×#63831C2semidirect
4. C2×#63815C2semidirect
5. C2×C3×#833C2semidirect
6. #10591507C2direct (N × H)
7. C2×#63578C2semidirect
8. C2×#63561C2semidirect
17. C2×#3754C22semidirect
28. #63831C22semidirect
32. #63815C22semidirect
34. C3×#833C22semidirect
35. #63578C22semidirect
36. #63561C22semidirect
47. C2×#833D3semidirect
153. #833C2×D3semidirect
455. C2×C32#471semidirect
547. C32C2×#471semidirect
597. C2×C3#4748semidirect
598. C2×C3#5200semidirect
619. C3C2×#4748semidirect
620. C3C2×#5200semidirect
625. C2#10591507direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9322
C2×#638312
C2×#638152
C2×C3×#8332
#105915072
C2×#635782
C2×#635612
C2×#52003
C2×#47483