Finite Group Databasebeta

← C2×#10591407 #11867874

Subgroups — C2×#10591407 #11867874

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#833C211yesmaximal, characteristic, complemented
6#10591407C218yesmaximal, direct product factor
7C2×#63577C211yesmaximal, characteristic, complemented
8C2×#63560C211yesmaximal, characteristic, complemented
9C2×#5177—31nomaximal
10C2×#4748—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3754—21no—
15#64141—22no—
16#64141C2214yes—
17C2×#3753—21no—
18C2×#3748C2211yescharacteristic
19C2×C3×#214—21no—
20C2×C3×#214—22no—
21C2×C3×#214—21no—
22C2×C3×#214C2214yescomplemented
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3719—21no—
27#63833—22no—
28#63833C2214yescomplemented
29C2×#3717—21no—
30C2×#3712—21no—
31#63817—22no—
32#63817C2214yescomplemented
33C2×#3710—21no—
34C3×#833C2214yescomplemented
35#63577C2214yescomplemented
36#63560C2214yescomplemented
37C22×C3×SD16—31no—
38C2×#942—31no—
39C22×#214D311yescharacteristic, complemented
40C2×#932—31no—
41C2×#932—31no—
42C2×#932—61no—
43C2×#909—31no—
44C2×#907—31no—
45C2×#901—31no—
46C2×C3×#100—31no—
47C2×#836—31no—
48C2×#833D311yescharacteristic, complemented
49#5177—38no—
50C2×#824—31no—
51C2×#822—31no—
52C2×#819—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
62C2×#638—21no—
63#3828—21no—
64#3828—21no—
65#3828D412yes—
66#3828C2312yes—
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634D411yescharacteristic
70C22×C3×Dic3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2312yes—
77#3754—24no—
78#3753—24no—
79#3748—21no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C3×#214—24no—
83C3×#214—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#3719—24no—
95#3717—24no—
96#3712—24no—
97#3710—24no—
98C2×#471—91noSylow
99C22×C3×Q8—31no—
100C22×C3×D4—21no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C2×#235—31no—
104C2×#235—31no—
105C2×#235—61no—
106C22×Dic6C2×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—
115#942—34no—
116#942—62no—
117C2×#215—61no—
118C2×#214—21no—
119C2×#214—21no—
120C2×#214—22no—
121C2×#214—61no—
122C2×#214—61no—
123C2×#214—62no—
124C2×#214C2×D314yescomplemented
125#932—34no—
126#932—34no—
127#932—64no—
128#932—62no—
129#932—62no—
130#932—64no—
131C2×#213—61no—
132C2×#213—61no—
133C2×#213—62no—
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138C2×#208C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140#909—34no—
141#909—62no—
142#907—34no—
143#907—62no—
144C2×Dic12—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×#100—34no—
153#836—34no—
154#833C2×D314yescomplemented
155#824—34no—
156#822—34no—
157#819—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
174#638—22no—
175#638—22no—
176C2×C3⋊Dic3—21no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)C2×D412yes—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181#634—21no—
182#634C2×D412yes—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—41no—
185C2×C3×Dic3—41no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6—41no—
189C3×Dic6—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—91no—
202C2×#100—31no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—41no—
206C2×C3×Q8—32no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8—61no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
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—21no—
224C2×C3×D4—22no—
225C2×C3×D4—41no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4C22×D312yes—
229C2×C3×D4C22×D312yes—
230C22×C3×C4—21no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—61no—
235C2×#67—61no—
236C2×#67—121no—
237C22×Dic3—21no—
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—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—121no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—31no—
262C2×Dic6—31no—
263C2×Dic6—61no—
264C2×Dic6C22×D312yes—
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#215—64no—
279#214—24no—
280#214—24no—
281#214—64no—
282#214—64no—
283#214—68no—
284#213—64no—
285#213—64no—
286#213—68no—
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—
306Dic12—64no—
307#204—64no—
308ΓL(1,𝔽25)—64no—
309ΓL(1,𝔽25)—64no—
310D3×C8—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—22no—
327C3×Dic3—42no—
328C2×#41—91no—
329C22×Q8—31no—
330C22×D4D3211yescharacteristic
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—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—82no—
365C23×C3—82no—
366C23×C3—84no—
367C23×C3#23511yescharacteristic
368C23×C3#23711yescharacteristic
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—121no—
372C3×Q8—62no—
373C3×Q8—62no—
374C3×Q8—121no—
375C3×Q8—121no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—22no—
380C3×D4—22no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—42no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—41no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—62no—
395C2×C3×C4—121no—
396C2×C3×C4—121no—
397C2×C3×C4#23511yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4#23711yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409#67—62no—
410#67—62no—
411#67—62no—
412#67—62no—
413#67—122no—
414#67—122no—
415C2×Dic3—22no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421D12—32no—
422D12—32no—
423D12—62no—
424D12—61no—
425D12—61no—
426D12—121no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—122no—
432C4×D3—122no—
433Dic6—22no—
434Dic6—22no—
435Dic6—32no—
436Dic6—32no—
437Dic6—41no—
438Dic6—41no—
439Dic6—62no—
440Dic6—61no—
441Dic6—61no—
442Dic6—121no—
443C3×C8—32no—
444C3×C8—32no—
445C3×C8—62no—
446C3×C8—62no—
447C3⋊C8—22no—
448C3⋊C8—22no—
449C3⋊C8—64no—
450C3⋊C8—62no—
451C3⋊C8—62no—
452C3⋊C8C2×#6712yes—
453C3⋊C8C2×#6712yes—
454C2×C32—21no—
455C2×C32—21no—
456C2×C32—82no—
457C2×C32#47112yescomplemented
458C2×C32C2×#12111yescharacteristic
459C3⋊D3—42no—
460C24—21no—
461#41—92no—
462#41—92no—
463#41—181no—
464#41—181no—
465C2×Q8—32no—
466C2×Q8—61no—
467C2×Q8—61no—
468C2×Q8—61no—
469C2×Q8—61no—
470C2×Q8—61no—
471C2×Q8—91no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—91no—
478C2×D4—181no—
479C2×D4C2×D3212yes—
480C22×C4—61no—
481C22×C4—181no—
482C22×C4C2×D3211yescharacteristic
483Q16—184no—
484SD16—64no—
485SD16—64no—
486SD16—184no—
487SD16—184no—
488D8—184no—
489M16—32no—
490M16—32no—
491M16—61no—
492M16—61no—
493M16—92no—
494M16—184no—
495M16—181no—
496C2×C8—32no—
497C2×C8—31no—
498C2×C8—31no—
499C2×C8—32no—
500C2×C8—61no—
501C2×C8—61no—
502C2×C8—184no—
503C2×C8—181no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—42no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—82no—
514C22×C3—82no—
515C22×C3—82no—
516C22×C3—82no—
517C22×C3—84no—
518C22×C3—84no—
519C22×C3—84no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3#88411yescharacteristic
523C22×C3#88411yescharacteristic
524C22×C3#93811yescharacteristic
525C22×C3#93811yescharacteristic
526C22×C3C2×#23511yescharacteristic
527C22×C3C2×#23711yescharacteristic
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—242no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—122no—
539C3×C4#88411yescharacteristic
540C3×C4#88411yescharacteristic
541C3×C4#93811yescharacteristic
542C3×C4#93811yescharacteristic
543C3×C4C2×D3×D411yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C2×D3×D411yescharacteristic
546C3×C4C22×#6711yescharacteristic
547Dic3—42no—
548Dic3—62no—
549Dic3—62no—
550Dic3—122no—
551C32C2×#47111yescharacteristic, complemented, Sylow
552C23—22no—
553C23—41no—
554C23—41no—
555C23—82no—
556C23—181no—
557C23#380411yescharacteristic
558Q8—62no—
559Q8—62no—
560Q8—92no—
561Q8—121no—
562Q8—121no—
563Q8—181no—
564D4—22no—
565D4—22no—
566D4—41no—
567D4—41no—
568D4—92no—
569D4—182no—
570D4—182no—
571D4—181no—
572C2×C4—62no—
573C2×C4—121no—
574C2×C4—121no—
575C2×C4—181no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4#380411yescharacteristic
579C2×C4D3×#6711yescharacteristic
580C2×C4D3×#6711yescharacteristic
581C2×C4#381111yescharacteristic
582C2×C4#381111yescharacteristic
583C2×C4C22×D3211yescharacteristic
584C8—32no—
585C8—32no—
586C8—62no—
587C8—62no—
588C8—182no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—22no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—84no—
598C2×C3—82no—
599C2×C3—82no—
600C2×C3#474812yescomplemented
601C2×C3#517712yescomplemented
602C2×C3C2×#88411yescharacteristic
603C2×C3C2×#93811yescharacteristic
604D3—122no—
605D3—122no—
606D3—242no—
607C22—22no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—182no—
613C22—362no—
614C22#6395811yescharacteristic
615C22#6395811yescharacteristic
616C22C2×#380411yescharacteristic
617C4—122no—
618C4—182no—
619C4#6395811yescharacteristic
620C4#6395811yescharacteristic
621C4C2×D3×#6711yescharacteristic
622C4C2×#381111yescharacteristic
623C3—21no—
624C3C2×#474811yescharacteristic, complemented
625C3C2×#517711yescharacteristic, complemented
626C2—21no—
627C2—21no—
628C2—82no—
629C2—362no—
630C2#1059140712yesdirect product factor
631C2C2×#6395811yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×#64141C2
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
2. C22×C3×#214C2semidirect
3. C2×#63833C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#833C2semidirect
6. #10591407C2direct (N × H)
7. C2×#63577C2semidirect
8. C2×#63560C2semidirect
22. C2×C3×#214C22semidirect
28. #63833C22semidirect
32. #63817C22semidirect
34. C3×#833C22semidirect
35. #63577C22semidirect
36. #63560C22semidirect
39. C22×#214D3semidirect
48. C2×#833D3semidirect
124. C2×#214C2×D3semidirect
154. #833C2×D3semidirect
457. C2×C32#471semidirect
551. C32C2×#471semidirect
600. C2×C3#4748semidirect
601. C2×C3#5177semidirect
624. C3C2×#4748semidirect
625. C3C2×#5177semidirect
630. C2#10591407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641412
C22×C3×#2142
C2×#638332
C2×#638172
C2×C3×#8332
#105914072
C2×#635772
C2×#635602
C2×#51773
C2×#47483