Finite Group Databasebeta

← C2×#10590356 #11865546

Subgroups — C2×#10590356 #11865546

Order 1152.

1341 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590356C218yesmaximal, direct product factor
9C2×#5057—31nomaximal
10C2×#4844—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C4×C4⋊(C3⋊D3)—22no—
19C4×C4⋊(C3⋊D3)C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×(C2×D3)⋊C4—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#875—22no—
25C3×#875C2214yescomplemented
26C2×#3717—24no—
27C2×#3717C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yes—
30C3×C4⋊(C3⋊C8)C2214yescomplemented
31#63566C2214yescomplemented
32#63563C2214yescomplemented
33C2×C3×#124—31no—
34C22×#215—31no—
35C22×#213—31no—
36C22×D24—31no—
37C22×#204—31no—
38C2×#875D311yescharacteristic, complemented
39C2×C4×D12—31no—
40C2×C4×D12—31no—
41C2×C4×D12—61no—
42C2×C3×C4⋊C8—31no—
43C2×#835—31no—
44C2×#832—31no—
45C2×#821—31no—
46C2×#816—31no—
47#5057—38no—
48C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
49#4844—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—24no—
61C2×C4×C3⋊D3—44no—
62C22×C3×Dic3—21no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C32×C42D412yes—
72C32×C42C2312yes—
73#3752—24no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C3×(C2×D3)⋊C4—24no—
77C3×(C2×D3)⋊C4—24no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3717—28no—
83#3714—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—62no—
92C22×C4×D3—61no—
93C22×C4×D3—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C3×#124—34no—
98C3×#124—62no—
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—21no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C2×D311yescharacteristic
104C2×#215—34no—
105C2×#215—64no—
106C2×#213—34no—
107C2×#213—64no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—62no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—61no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117C22×C3⋊C8C2×D311yescharacteristic
118C2×D24—34no—
119C2×D24—64no—
120C2×#204—34no—
121C2×#204—64no—
122#875—22no—
123#875C2×D314yescomplemented
124C4×D12—34no—
125C4×D12—34no—
126C4×D12—64no—
127C4×D12—64no—
128C4×D12—62no—
129C4×D12—62no—
130C3×C4⋊C8—34no—
131#835—34no—
132#832—34no—
133#821—34no—
134#816—34no—
135C4⋊(C3⋊C8)C2×D314yescomplemented
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—24no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3—42no—
141C22×C3×D3—22no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—42no—
155C4⋊(C3⋊D3)—24no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)C2×D414yes—
158C4×C3⋊D3—48no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—42no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C22×SD16—91no—
170C22×D8—91no—
171C2×#124—31no—
172C2×C4×D4—91no—
173#463—98no—
174C2×C4⋊C8—31no—
175C2×#103—91no—
176C2×#102—91no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—62no—
180C23×D3—61no—
181C23×D3—61no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×D4—32no—
187C2×C3×D4—61no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4D1211yescharacteristic
195C22×C3×C4D1211yescharacteristic
196C22×C3×C4#6711yescharacteristic
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—62no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C2×D12—22no—
205C2×D12—22no—
206C2×D12—21no—
207C2×D12—34no—
208C2×D12—34no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12—61no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12C22×D312yes—
220C2×C4×D3—68no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—128no—
224C2×C4×D3—124no—
225C2×C4×D3—124no—
226C2×Dic6—22no—
227C2×Dic6—22no—
228C2×Dic6—21no—
229C2×Dic6C22×D312yes—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C2×C3×C8—62no—
234C3×C22⋊C4—64no—
235C3×C22⋊C4—64no—
236C3×C42—22no—
237C3×C42—22no—
238C3×C42D1212yes—
239C3×C42#6712yes—
240C3×C42C22×D312yes—
241C3×C42C22×D312yes—
242#215—68no—
243#213—68no—
244(C2×D3)⋊C4—24no—
245(C2×D3)⋊C4—24no—
246(C2×D3)⋊C4—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8C22×D312yes—
258C2×C3⋊C8C22×D312yes—
259D24—68no—
260#204—68no—
261C22×C32#12112yes—
262C22×C32#13512yes—
263C22×C32AGL(1,ℤ/8)12yes—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—24no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—48no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—84no—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—42no—
279C3×Dic3—42no—
280C22×Q8—31no—
281C22×D4—31no—
282C22×D4—91no—
283C23×C4—181no—
284C2×SD16—94no—
285C2×SD16—184no—
286C2×D8—94no—
287C2×D8—184no—
288C22×C8—31no—
289C22×C8—31no—
290#124—34no—
291#124—62no—
292C4×D4—94no—
293C4×D4—182no—
294C2×C4⋊C4—91no—
295C2×C22⋊C4—61no—
296C2×C22⋊C4—61no—
297C2×C22⋊C4—181no—
298C2×C42D3211yescharacteristic
299C4⋊C8—34no—
300#103—94no—
301#102—94no—
302C23×C3—21no—
303C23×C3—62no—
304C23×C3—122no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3C2×D1211yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—22no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—42no—
313C22×D3—64no—
314C22×D3—68no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—124no—
320C22×D3—124no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—122no—
325C3×Q8—62no—
326C3×Q8—62no—
327C3×Q8—122no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—122no—
331C2×C3×C4—24no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—122no—
345C2×C3×C4C2×D1212yes—
346C2×C3×C4C2×D1212yes—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4D3×D412yes—
349C2×C3×C4D3×D412yes—
350C2×C3×C4#23712yes—
351C2×C3×C4#23912yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—42no—
359C2×Dic3—64no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—124no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365D12—22no—
366D12—22no—
367D12—34no—
368D12—34no—
369D12—42no—
370D12—64no—
371D12—64no—
372D12—68no—
373D12—64no—
374D12—64no—
375D12—62no—
376D12—62no—
377C4×D3—1216no—
378C4×D3—128no—
379C4×D3—128no—
380Dic6—22no—
381Dic6—22no—
382Dic6—42no—
383C3×C8—62no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—22no—
387C2×C32#46314yescomplemented
388C2×C32C2×#12111yescharacteristic
389C2×C32C2×#13511yescharacteristic
390C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
391C3⋊D3—44no—
392C3×D3—82no—
393C24—61no—
394C24—181no—
395C2×Q8—32no—
396C2×Q8—61no—
397C2×Q8—62no—
398C2×Q8—62no—
399C2×D4—32no—
400C2×D4—62no—
401C2×D4—62no—
402C2×D4—61no—
403C2×D4—92no—
404C2×D4—94no—
405C2×D4—182no—
406C2×D4—181no—
407C22×C4—61no—
408C22×C4—181no—
409C22×C4—184no—
410C22×C4—364no—
411C22×C4#62611yescharacteristic
412C22×C4#62611yescharacteristic
413C22×C4C2×D3211yescharacteristic
414SD16—188no—
415D8—188no—
416C2×C8—32no—
417C2×C8—32no—
418C2×C8—62no—
419C2×C8—62no—
420C4⋊C4—92no—
421C4⋊C4—181no—
422C22⋊C4—64no—
423C22⋊C4—64no—
424C22⋊C4—184no—
425C42#62612yes—
426C42C2×D3212yes—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—244no—
435C22×C3#89512yes—
436C22×C3#90412yes—
437C22×C3#90812yes—
438C22×C3#93812yes—
439C22×C3#94912yes—
440C22×C3#95012yes—
441C22×C3C22×D1211yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—68no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—84no—
450C2×D3—124no—
451C2×D3—1216no—
452C2×D3—124no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—128no—
458C2×D3—128no—
459C3×C4—24no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—42no—
468C3×C4—122no—
469C3×C4#89512yes—
470C3×C4#93812yes—
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C2×D3×D411yescharacteristic
473C3×C4C2×#23711yescharacteristic
474C3×C4C2×#23911yescharacteristic
475Dic3—42no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479C32C2×#46311yescharacteristic, complemented, Sylow
480C23—62no—
481C23—122no—
482C23—122no—
483C23—122no—
484C23—182no—
485C23—184no—
486C23—362no—
487C23—362no—
488C23C2×#62611yescharacteristic
489Q8—62no—
490Q8—62no—
491Q8—122no—
492D4—62no—
493D4—62no—
494D4—94no—
495D4—122no—
496D4—182no—
497D4—184no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—62no—
501C2×C4—122no—
502C2×C4—182no—
503C2×C4—368no—
504C2×C4—362no—
505C2×C4#379612yes—
506C2×C4#380212yes—
507C2×C4C2×#62612yes—
508C2×C4C2×#62612yes—
509C2×C4C2×#62611yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—62no—
512C8—62no—
513C2×C3—24no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—242no—
518C2×C3#484414yescomplemented
519C2×C3#505714yescomplemented
520C2×C3C2×#89511yescharacteristic
521C2×C3C2×#90411yescharacteristic
522C2×C3C2×#90811yescharacteristic
523C2×C3C2×#93811yescharacteristic
524C2×C3C2×#94911yescharacteristic
525C2×C3C2×#95011yescharacteristic
526D3—82no—
527D3—128no—
528D3—124no—
529D3—124no—
530C22—122no—
531C22—122no—
532C22—122no—
533C22—184no—
534C22—244no—
535C22—368no—
536C22—362no—
537C22—362no—
538C22#6382512yes—
539C22#6382912yes—
540C22#6391612yes—
541C22C22×#62611yescharacteristic
542C4—22no—
543C4—22no—
544C4—122no—
545C4—362no—
546C4#6391612yes—
547C4C2×#379611yescharacteristic
548C4C2×#380211yescharacteristic
549C3—21no—
550C3C2×#484411yescharacteristic, complemented
551C3C2×#505711yescharacteristic, complemented
552C2—242no—
553C2—364no—
554C2#1059035614yesdirect product factor
555C2C2×#6382511yescharacteristic
556C2C2×#6382911yescharacteristic
557C2C2×#6391611yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC2×C42D32
hypocenterC32C2×#463
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×#875C2semidirect
3. C22×#3717C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. C2×#63566C2semidirect
7. C2×#63563C2semidirect
8. #10590356C2direct (N × H)
19. C4×C4⋊(C3⋊D3)C22semidirect
25. C3×#875C22semidirect
27. C2×#3717C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63566C22semidirect
32. #63563C22semidirect
38. C2×#875D3semidirect
48. C2×C4⋊(C3⋊C8)D3semidirect
123. #875C2×D3semidirect
135. C4⋊(C3⋊C8)C2×D3semidirect
387. C2×C32#463semidirect
479. C32C2×#463semidirect
518. C2×C3#4844semidirect
519. C2×C3#5057semidirect
550. C3C2×#4844semidirect
551. C3C2×#5057semidirect
554. C2#10590356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8752
C22×#37172
C22×#37142
C2×C3×C4⋊(C3⋊C8)2
C2×#635662
C2×#635632
#105903562
C2×#50573
C2×#48443