Finite Group Databasebeta

← C2×#10591676 #11861062

Subgroups — C2×#10591676 #11861062

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591676C218yesmaximal, direct product factor
6C2×#63577C211yesmaximal, characteristic, complemented
7C2×#63569C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5197—31nomaximal
10C2×#4823—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64157—22no—
14#64157C2214yescomplemented
15C2×#3748—21no—
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)—21no—
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#950C414yescomplemented
20C3×#950C2214yes—
21C2×C3×#216C411yescharacteristic, complemented
22C2×C3×#215C411yescharacteristic, complemented
23C2×C3×#214C411yescharacteristic, complemented
24C2×C3×#213C411yescharacteristic, complemented
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3711—21no—
29#63815—22no—
30#63815C2214yescomplemented
31C2×D3×C3⋊C8—21no—
32C3×#837C2214yescomplemented
33#63577C2214yescomplemented
34#63569C2214yescomplemented
35#63554C2214yescomplemented
36C2×C3×#135—31no—
37C2×#950D311yescharacteristic
38C2×#948—31no—
39C2×#948—31no—
40C2×#948—31no—
41C2×#948—61no—
42C2×#907—31no—
43C2×C3×#104—31no—
44C2×#837—31no—
45C2×#837D311yescharacteristic, complemented
46#5197—38no—
47C2×#822—31no—
48C2×#819—31no—
49C2×#815—31no—
50C2×#805—31no—
51C2×#803—31no—
52#4823—38no—
53C32×#41—21no—
54C32×#41—21no—
55C32×#41C2×C412yes—
56C32×#41C2312yes—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2×C411yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67—21no—
63C22×C3×Dic3—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235C2×C412yes—
67C3×#235C2312yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2×C411yescharacteristic
71#3748—21no—
72#3748—24no—
73#3748C2312yes—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—24no—
76C2×C3⋊(C3⋊C8)D411yescharacteristic
77C2×C3⋊(C3⋊C8)D412yes—
78C2×C3⋊(C3⋊C8)D411yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#216C2×C414yescomplemented
81C3×#215C2×C414yescomplemented
82C3×#214C2×C414yescomplemented
83C3×#213C2×C414yescomplemented
84C3×C4×Dic3—21no—
85C3×C4×Dic3C2312yes—
86C3×#208—21no—
87C3×#208C2312yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8C2×C411yescharacteristic
90C2×C3×C3⋊C8C2×C411yescharacteristic
91C2×C3×C3⋊C8C2×C412yes—
92C2×C3×C3⋊C8C2312yes—
93#3711—24no—
94D3×C3⋊C8—24no—
95C2×#444—91noSylow
96C2×C3×#41—21no—
97C2×C3×#41—31no—
98C2×C3×#41C2×D311yescharacteristic
99C2×C3×#41C2×D311yescharacteristic
100C2×#235C2×D311yescharacteristic
101C3×#135—34no—
102C3×#135—34no—
103C2×C3×Q16—31no—
104C2×C3×SD16—31no—
105C2×C3×SD16—31no—
106C2×C3×D8—31no—
107C2×C3×M16—31no—
108C22×C3×C8—31no—
109C2×C3×C42—31no—
110#950Dic314yescomplemented
111#950C2×D314yes—
112#948—34no—
113#948—34no—
114#948—34no—
115#948—64no—
116#948—62no—
117#948—62no—
118#948—62no—
119#948—64no—
120C2×#216Dic311yescharacteristic, complemented
121C2×#215Dic311yescharacteristic, complemented
122C2×#214Dic311yescharacteristic, complemented
123C2×#213Dic311yescharacteristic, complemented
124C2×C4×Dic3C2×D311yescharacteristic
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C2×#208—61no—
129C2×#208—61no—
130C2×#208—61no—
131C2×#208—62no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—61no—
136C22×C3⋊C8—61no—
137C22×C3⋊C8—61no—
138C22×C3⋊C8—61no—
139C22×C3⋊C8—62no—
140C22×C3⋊C8C2×D311yescharacteristic
141#907—34no—
142#907—62no—
143C2×ΓL(1,𝔽25)—61no—
144C2×D3×C8—61no—
145C3×#104—34no—
146#837—34no—
147#837C2×D314yescomplemented
148#822—34no—
149#819—34no—
150#815—34no—
151#805—34no—
152#803—34no—
153C23×C32—21no—
154C23×C32#4111yescharacteristic
155C22×C3×D3—21no—
156C32×Q8—21no—
157C32×Q8C22×C412yes—
158C32×D4—22no—
159C32×D4—22no—
160C32×D4—21no—
161C32×D4C22×C412yes—
162C2×C32×C4—21no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C411yescharacteristic
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4#4111yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C3×#67—22no—
172C3×#67—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C3×D12—21no—
177C3×D12C22×C412yes—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×Dic6—21no—
181C3×Dic6C22×C412yes—
182C3⋊(C3⋊C8)—22no—
183C3⋊(C3⋊C8)C2×D412yes—
184C3⋊(C3⋊C8)C2×D412yes—
185C3×C3⋊C8—22no—
186C3×C3⋊C8C22×C412yes—
187C3×C3⋊C8C22×C412yes—
188C2×#135—31no—
189C2×#131—91no—
190C2×#131—91no—
191#444—98no—
192C2×#108—91no—
193C2×#104—31no—
194C2×#104—91no—
195C2×#97—91no—
196C3×#41—22no—
197C3×#41—22no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—22no—
203C3×#41—22no—
204C3×#41—32no—
205C3×#41—32no—
206C3×#41—61no—
207C3×#41—61no—
208C3×#41C4×D312yes—
209C3×#41C2×Dic312yes—
210C3×#41C22×D312yes—
211C3×#41C22×D312yes—
212C2×C3×Q8—21no—
213C2×C3×Q8—31no—
214C2×C3×Q8C4×D311yescharacteristic
215C2×C3×Q8C2×Dic311yescharacteristic
216C2×C3×D4—22no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—31no—
221C2×C3×D4—61no—
222C2×C3×D4C4×D311yescharacteristic
223C2×C3×D4C2×Dic311yescharacteristic
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C22×Dic3—21no—
234#235—21no—
235#235—21no—
236#235C2×Dic312yes—
237#235C22×D312yes—
238C2×D12C2×Dic311yescharacteristic
239C2×C4×D3—21no—
240C2×Dic6C2×Dic311yescharacteristic
241C3×Q16—34no—
242C3×SD16—34no—
243C3×SD16—34no—
244C3×D8—34no—
245C3×M16—32no—
246C3×M16—61no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C2×C3×C8—32no—
250C2×C3×C8—32no—
251C2×C3×C8—61no—
252C3×C42—32no—
253C3×C42—61no—
254#216C2×Dic314yescomplemented
255#215C2×Dic314yescomplemented
256#214C2×Dic314yescomplemented
257#213C2×Dic314yescomplemented
258C4×Dic3—21no—
259C4×Dic3C22×D312yes—
260#208—21no—
261#208—32no—
262#208—32no—
263#208—62no—
264#208—64no—
265#208—64no—
266#208—64no—
267#208—68no—
268#208—62no—
269#208—61no—
270#208—61no—
271#208C22×D312yes—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—32no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8—64no—
286C2×C3⋊C8—64no—
287C2×C3⋊C8—64no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—68no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8C2×Dic311yescharacteristic
293C2×C3⋊C8C2×Dic311yescharacteristic
294C2×C3⋊C8C2×Dic312yes—
295C2×C3⋊C8C22×D312yes—
296ΓL(1,𝔽25)—64no—
297D3×C8—64no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—42no—
301C22×C32C4×D411yescharacteristic
302C22×C32C4×D411yescharacteristic
303C22×C32C2×#4111yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—42no—
306C32×C4—22no—
307C32×C4C4×D411yescharacteristic
308C32×C4C4×D411yescharacteristic
309C32×C4C23×C411yescharacteristic
310C32×C4C22×D411yescharacteristic
311C3×Dic3—22no—
312C3×Dic3—42no—
313C2×#41—31no—
314C2×#41D3211yescharacteristic
315#135—34no—
316#135—34no—
317C2×Q16—31no—
318C2×SD16—31no—
319C2×SD16—31no—
320C2×D8—31no—
321#131—94no—
322#131—94no—
323#131—182no—
324#131—182no—
325C2×M16—31no—
326C2×M16—91no—
327C2×M16—181no—
328C2×M16—181no—
329C22×C8—31no—
330C22×C8—91no—
331C22×C8—181no—
332C22×C8—181no—
333C2×C42—31no—
334#108—94no—
335#104—34no—
336#104—94no—
337#97—94no—
338C23×C3—22no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—61no—
343C23×C3#23711yescharacteristic
344C23×C3#23711yescharacteristic
345C22×D3—21no—
346C3×Q8—22no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×Q8—22no—
350C3×Q8—32no—
351C3×Q8—61no—
352C3×Q8C2×C4×D312yes—
353C3×Q8C22×Dic312yes—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—22no—
364C3×D4—32no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—61no—
368C3×D4C2×C4×D312yes—
369C3×D4C22×Dic312yes—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—122no—
390C2×C3×C4C2×C4×D311yescharacteristic
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4#23711yescharacteristic
397C2×C3×C4#23711yescharacteristic
398C2×C3×C4C22×Dic311yescharacteristic
399C2×C3×C4C22×Dic311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—22no—
403#67—22no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—42no—
407D12—21no—
408D12C22×Dic312yes—
409C4×D3—22no—
410C4×D3—22no—
411Dic6—21no—
412Dic6C22×Dic312yes—
413C3×C8—32no—
414C3×C8—32no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—32no—
418C3⋊C8—32no—
419C3⋊C8—32no—
420C3⋊C8—32no—
421C3⋊C8—62no—
422C3⋊C8—62no—
423C3⋊C8—64no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C3⋊C8C22×Dic312yes—
427C3⋊C8C22×Dic312yes—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32—42no—
431C2×C32#44412yescomplemented
432C2×C32C2×C4×D411yescharacteristic
433C3×D3—42no—
434#41—21no—
435#41—21no—
436#41—32no—
437#41—32no—
438#41—61no—
439#41—61no—
440#41D3×Dic312yes—
441#41C2×D3212yes—
442C2×Q8—31no—
443C2×Q8D3×Dic311yescharacteristic
444C2×D4—21no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4D3×Dic311yescharacteristic
448C22×C4—21no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4C2×D3211yescharacteristic
452Q16—34no—
453SD16—34no—
454SD16—34no—
455D8—34no—
456M16—32no—
457M16—61no—
458M16—92no—
459M16—184no—
460M16—184no—
461M16—181no—
462C2×C8—32no—
463C2×C8—31no—
464C2×C8—31no—
465C2×C8—32no—
466C2×C8—61no—
467C2×C8—92no—
468C2×C8—92no—
469C2×C8—91no—
470C2×C8—91no—
471C2×C8—184no—
472C2×C8—184no—
473C2×C8—181no—
474C42—32no—
475C42—61no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—24no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—42no—
485C22×C3—44no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—62no—
489C22×C3—122no—
490C22×C3#67⋊C411yescharacteristic
491C22×C3#67⋊C411yescharacteristic
492C22×C3D4×Dic311yescharacteristic
493C22×C3D4×Dic311yescharacteristic
494C22×C3C2×#23711yescharacteristic
495C22×C3C2×#23711yescharacteristic
496C2×D3—22no—
497C2×D3—42no—
498C3×C4—24no—
499C3×C4—22no—
500C3×C4—22no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—62no—
506C3×C4—122no—
507C3×C4#67⋊C411yescharacteristic
508C3×C4#67⋊C411yescharacteristic
509C3×C4D4×Dic311yescharacteristic
510C3×C4D4×Dic311yescharacteristic
511C3×C4C22×C4×D311yescharacteristic
512C3×C4C2×D3×D411yescharacteristic
513C3×C4C2×D3×D411yescharacteristic
514C3×C4C23×Dic311yescharacteristic
515Dic3—22no—
516Dic3—42no—
517C32C2×#44411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—61no—
520C23#380511yescharacteristic
521Q8—21no—
522Q8—32no—
523Q8—61no—
524Q8C2×D3×Dic312yes—
525D4—22no—
526D4—22no—
527D4—21no—
528D4—32no—
529D4—62no—
530D4—62no—
531D4—61no—
532D4C2×D3×Dic312yes—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—122no—
541C2×C4C2×D3×Dic311yescharacteristic
542C2×C4C2×D3×Dic311yescharacteristic
543C2×C4#380511yescharacteristic
544C2×C4#381111yescharacteristic
545C2×C4#381111yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—32no—
548C8—32no—
549C8—62no—
550C8—92no—
551C8—92no—
552C8—182no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—22no—
559C2×C3—41no—
560C2×C3—41no—
561C2×C3—44no—
562C2×C3—42no—
563C2×C3—42no—
564C2×C3—122no—
565C2×C3#482312yescomplemented
566C2×C3#519712yescomplemented
567C2×C3C2×#67⋊C411yescharacteristic
568C2×C3C2×D4×Dic311yescharacteristic
569D3—42no—
570C22—22no—
571C22—22no—
572C22—42no—
573C22—62no—
574C22—122no—
575C22#67⋊Dic311yescharacteristic
576C22#67⋊Dic311yescharacteristic
577C22C2×#380511yescharacteristic
578C4—22no—
579C4—62no—
580C4—122no—
581C4#67⋊Dic311yescharacteristic
582C4#67⋊Dic311yescharacteristic
583C4C22×D3×Dic311yescharacteristic
584C4C2×#381111yescharacteristic
585C3—21no—
586C3C2×#482311yescharacteristic, complemented
587C3C2×#519711yescharacteristic, complemented
588C2—21no—
589C2—21no—
590C2—42no—
591C2—122no—
592C2#1059167612yesdirect product factor
593C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
3. C2×#63815C2semidirect
4. C2×C3×#837C2semidirect
5. #10591676C2direct (N × H)
6. C2×#63577C2semidirect
7. C2×#63569C2semidirect
8. C2×#63554C2semidirect
14. #64157C22semidirect
19. C3×#950C4semidirect
21. C2×C3×#216C4semidirect
22. C2×C3×#215C4semidirect
23. C2×C3×#214C4semidirect
24. C2×C3×#213C4semidirect
30. #63815C22semidirect
32. C3×#837C22semidirect
33. #63577C22semidirect
34. #63569C22semidirect
35. #63554C22semidirect
45. C2×#837D3semidirect
80. C3×#216C2×C4semidirect
81. C3×#215C2×C4semidirect
82. C3×#214C2×C4semidirect
83. C3×#213C2×C4semidirect
110. #950Dic3semidirect
120. C2×#216Dic3semidirect
121. C2×#215Dic3semidirect
122. C2×#214Dic3semidirect
123. C2×#213Dic3semidirect
147. #837C2×D3semidirect
254. #216C2×Dic3semidirect
255. #215C2×Dic3semidirect
256. #214C2×Dic3semidirect
257. #213C2×Dic3semidirect
431. C2×C32#444semidirect
517. C32C2×#444semidirect
565. C2×C3#4823semidirect
566. C2×C3#5197semidirect
586. C3C2×#4823semidirect
587. C3C2×#5197semidirect
592. C2#10591676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C3×#9502
C2×#638152
C2×C3×#8372
#105916762
C2×#635772
C2×#635692
C2×#635542
C2×#51973
C2×#48233