Finite Group Databasebeta

← C2×#10591106 #11857919

Subgroups — C2×#10591106 #11857919

Order 1152.

2077 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4#10591106C218yesmaximal, direct product factor
5C2×#63567C212yesmaximal, complemented
6C2×#63564C212yesmaximal, complemented
7C2×#5133—31nomaximal
8C2×#4966—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×#638—21no—
11C2×#3828—24no—
12C2×#3828—22no—
13C2×#3828C418yescomplemented
14C2×#3828C2214yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3—21no—
17C22×#634C2211yescharacteristic
18C23×C3×Dic3—21no—
19C2×C3×C4⋊Dic3—22no—
20C2×C3×C4⋊Dic3—21no—
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2214yescomplemented
23C2×C3×#208—24no—
24C2×C3×#208C2214yescomplemented
25C22×C3×C3⋊C8C2212yes—
26#63567C2218yescomplemented
27#63564C2218yescomplemented
28C22×#235—31no—
29C22×#235—31no—
30C22×#235—61no—
31C22×C3×M16—31no—
32C22×C3×C4⋊C4—31no—
33C22×C4⋊Dic3D311yescharacteristic, complemented
34C22×#208D311yescharacteristic, complemented
35#5133—38no—
36C2×#821—32no—
37C2×#816—32no—
38C2×#810—32no—
39#4966—38no—
40C2×#809—32no—
41C24×C32D411yescharacteristic
42C23×C3⋊D3—21no—
43C22×C32×C4C2×C414yes—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D412yes—
46C22×C32×C4D414yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2312yes—
49C2×#638—28no—
50C2×#638—24no—
51C22×C3⋊Dic3—21no—
52#3828—216no—
53#3828—28no—
54#3828C2×C4116yescomplemented
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yescomplemented
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—28no—
60C2×C4×C3⋊D3—24no—
61C2×#634—21no—
62C2×#634—22no—
63C2×#634C2×C414yescomplemented
64C2×#634C2312yes—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—24no—
67C22×C3×Dic3—44no—
68C3×C4⋊Dic3—22no—
69C3×C4⋊Dic3—24no—
70C3×C4⋊Dic3C2314yes—
71C3×#208—28no—
72C2×C3×C3⋊C8—24no—
73C2×C3×C3⋊C8C2314yes—
74C2×#417—91noSylow
75C23×C3×C4—21no—
76C23×C3×C4—61no—
77C23×C3×C4C2×D311yescharacteristic
78C23×C3×C4C2×D311yescharacteristic
79C22×#67—62no—
80C22×#67—61no—
81C22×#67—61no—
82C23×Dic3—21no—
83C2×#235—38no—
84C2×#235—38no—
85C2×#235—34no—
86C2×#235—34no—
87C2×#235—68no—
88C2×#235—64no—
89C2×#235—68no—
90C2×#235—64no—
91C2×#235—64no—
92C2×#235—62no—
93C2×#235—64no—
94C2×#235—62no—
95C22×D12—31no—
96C22×D12—31no—
97C22×D12—61no—
98C22×C4×D3—62no—
99C22×C4×D3—61no—
100C22×C4×D3—61no—
101C22×Dic6—31no—
102C22×Dic6—31no—
103C22×Dic6—61no—
104C2×C3×M16—34no—
105C2×C3×M16—64no—
106C22×C3×C8—32no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4—34no—
109C2×C3×C4⋊C4—61no—
110C2×C3×C4⋊C4—62no—
111C2×C4⋊Dic3—22no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3C2×D312yes—
114C2×C4⋊Dic3C2×D314yescomplemented
115C2×#208—24no—
116C2×#208C2×D314yescomplemented
117C22×C3⋊C8C2×D312yes—
118#821—38no—
119#816—38no—
120#810—38no—
121#809—38no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32C22⋊C414yes—
125C23×C32C2×D412yes—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—24no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—42no—
130C22×C3⋊D3—42no—
131C2×C32×C4C22⋊C414yes—
132C2×C32×C4C22⋊C418yes—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C22×C414yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D412yes—
137C2×C32×C4C2×D412yes—
138C2×C32×C4C2×D414yes—
139C2×C32×C4C2411yescharacteristic
140#638—216no—
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3—22no—
143C4⋊(C3⋊D3)—24no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)C22×C414yescomplemented
146C4×C3⋊D3—216no—
147#634—24no—
148#634—22no—
149#634C22×C414yescomplemented
150C2×C3×Dic3—24no—
151C2×C3×Dic3—48no—
152C2×C3×Dic3—44no—
153C3×C3⋊C8—24no—
154C22×#41—91no—
155C22×M16—31no—
156C22×C4⋊C4—31no—
157#417—98no—
158C2×#103—92no—
159C2×#102—92no—
160C24×C3—21no—
161C24×C3D1211yescharacteristic
162C24×C3#6711yescharacteristic
163C23×D3—62no—
164C23×D3—61no—
165C23×D3—61no—
166C22×C3×C4—24no—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—24no—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—64no—
173C22×C3×C4—62no—
174C22×C3×C4—124no—
175C22×C3×C4C4×D314yes—
176C22×C3×C4C4×D314yes—
177C22×C3×C4D1211yescharacteristic
178C22×C3×C4D1212yes—
179C22×C3×C4D1214yes—
180C22×C3×C4#6711yescharacteristic
181C22×C3×C4#6712yes—
182C22×C3×C4#6714yes—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D312yes—
187C2×#67—616no—
188C2×#67—68no—
189C2×#67—68no—
190C2×#67—68no—
191C2×#67—64no—
192C2×#67—64no—
193C22×Dic3—22no—
194C22×Dic3—24no—
195C22×Dic3—44no—
196C22×Dic3—62no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199#235—316no—
200#235—316no—
201#235—616no—
202#235—632no—
203#235—616no—
204#235—616no—
205#235—616no—
206#235—68no—
207#235—68no—
208C2×D12—34no—
209C2×D12—34no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12—62no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—62no—
220C2×C4×D3—616no—
221C2×C4×D3—68no—
222C2×C4×D3—68no—
223C2×C4×D3—68no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×Dic6—34no—
227C2×Dic6—34no—
228C2×Dic6—32no—
229C2×Dic6—32no—
230C2×Dic6—64no—
231C2×Dic6—62no—
232C2×Dic6—62no—
233C2×Dic6—64no—
234C2×Dic6—61no—
235C2×Dic6—62no—
236C2×Dic6—61no—
237C2×Dic6—62no—
238C3×M16—68no—
239C2×C3×C8—34no—
240C2×C3×C8—64no—
241C3×C4⋊C4—34no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—64no—
244C4⋊Dic3—22no—
245C4⋊Dic3—24no—
246C4⋊Dic3C22×D314yes—
247#208—28no—
248C2×C3⋊C8—24no—
249C2×C3⋊C8C22×D314yes—
250C22×C32—22no—
251C22×C32—22no—
252C22×C32—28no—
253C22×C32C2×C22⋊C414yes—
254C22×C32C2×C22⋊C412yes—
255C22×C32AGL(1,ℤ/8)12yes—
256C22×C32#13712yes—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—24no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—48no—
262C32×C4C2×C22⋊C412yes—
263C32×C4C2×C22⋊C414yes—
264C32×C4C23×C411yescharacteristic
265C32×C4C22×D411yescharacteristic
266C3⋊Dic3—24no—
267C3×Dic3—44no—
268C2×#41—98no—
269C2×#41—94no—
270C2×#41—184no—
271C2×#41—182no—
272C22×Q8—91no—
273C22×D4—91no—
274C22×D4—181no—
275C23×C4—61no—
276C23×C4—181no—
277C23×C4D3211yescharacteristic
278C2×M16—34no—
279C2×M16—64no—
280C22×C8—32no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4—34no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—61no—
285#103—98no—
286#102—98no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—24no—
292C23×C3—22no—
293C23×C3—21no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3(C2×D3)⋊C414yes—
297C23×C3(C2×D3)⋊C414yes—
298C23×C3C2×D1212yes—
299C23×C3C2×D1211yescharacteristic
300C23×C3C2×#6712yes—
301C23×C3C2×#6711yescharacteristic
302C22×D3—64no—
303C22×D3—68no—
304C22×D3—64no—
305C22×D3—64no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—124no—
309C22×D3—124no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C2×C3×C4—21no—
315C2×C3×C4—24no—
316C2×C3×C4—28no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—24no—
323C2×C3×C4—64no—
324C2×C3×C4—128no—
325C2×C3×C4—124no—
326C2×C3×C4(C2×D3)⋊C414yes—
327C2×C3×C4(C2×D3)⋊C414yes—
328C2×C3×C4(C2×D3)⋊C418yes—
329C2×C3×C4(C2×D3)⋊C418yes—
330C2×C3×C4C2×C4×D312yes—
331C2×C3×C4C2×C4×D312yes—
332C2×C3×C4C2×C4×D314yes—
333C2×C3×C4C2×C4×D314yes—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1212yes—
336C2×C3×C4C2×D1212yes—
337C2×C3×C4C2×D1214yes—
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C2×#6712yes—
341C2×C3×C4C2×#6714yes—
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344#67—632no—
345#67—616no—
346#67—616no—
347C2×Dic3—24no—
348C2×Dic3—48no—
349C2×Dic3—44no—
350C2×Dic3—64no—
351C2×Dic3—68no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356D12—34no—
357D12—34no—
358D12—64no—
359D12—64no—
360D12—68no—
361D12—64no—
362D12—64no—
363D12—62no—
364D12—62no—
365C4×D3—632no—
366C4×D3—616no—
367C4×D3—616no—
368Dic6—34no—
369Dic6—34no—
370Dic6—64no—
371Dic6—64no—
372Dic6—68no—
373Dic6—64no—
374Dic6—64no—
375Dic6—62no—
376Dic6—62no—
377C3×C8—64no—
378C3⋊C8—24no—
379C2×C32—24no—
380C2×C32#41714yescomplemented
381C2×C32C22×C22⋊C411yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C3⋊D3—44no—
385C24—181no—
386C24#62611yescharacteristic
387#41—916no—
388#41—1816no—
389#41—188no—
390C2×Q8—92no—
391C2×Q8—94no—
392C2×Q8—181no—
393C2×Q8—182no—
394C2×D4—92no—
395C2×D4—94no—
396C2×D4—188no—
397C2×D4—184no—
398C2×D4—182no—
399C2×D4—181no—
400C22×C4—64no—
401C22×C4—62no—
402C22×C4—124no—
403C22×C4—181no—
404C22×C4—188no—
405C22×C4—184no—
406C22×C4#62414yes—
407C22×C4#62612yes—
408C22×C4#62611yescharacteristic
409C22×C4#62614yes—
410C22×C4C2×D3212yes—
411C22×C4C2×D3211yescharacteristic
412M16—68no—
413C2×C8—34no—
414C2×C8—64no—
415C4⋊C4—34no—
416C4⋊C4—64no—
417C4⋊C4—62no—
418C22×C3—28no—
419C22×C3—28no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—24no—
429C22×C3—48no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3#90812yes—
433C22×C3#90912yes—
434C22×C3C2×(C2×D3)⋊C414yes—
435C22×C3C2×(C2×D3)⋊C414yes—
436C22×C3C2×(C2×D3)⋊C412yes—
437C22×C3C2×(C2×D3)⋊C412yes—
438C22×C3#93212yes—
439C22×C3#94212yes—
440C22×C3C22×D1211yescharacteristic
441C22×C3C22×#6711yescharacteristic
442C2×D3—68no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—1216no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—128no—
449C2×D3—128no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—24no—
458C3×C4—124no—
459C3×C4C2×(C2×D3)⋊C412yes—
460C3×C4C2×(C2×D3)⋊C412yes—
461C3×C4C2×(C2×D3)⋊C414yes—
462C3×C4C2×(C2×D3)⋊C414yes—
463C3×C4C22×C4×D311yescharacteristic
464C3×C4C22×C4×D311yescharacteristic
465C3×C4C22×D1211yescharacteristic
466C3×C4C22×#6711yescharacteristic
467Dic3—44no—
468Dic3—68no—
469Dic3—64no—
470Dic3—64no—
471C32C2×#41711yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—182no—
475C23—184no—
476C23—362no—
477C23—362no—
478C23#372214yes—
479C23C2×#62612yes—
480C23C2×#62611yescharacteristic
481Q8—94no—
482Q8—182no—
483Q8—184no—
484D4—94no—
485D4—1816no—
486D4—182no—
487D4—184no—
488C2×C4—64no—
489C2×C4—128no—
490C2×C4—124no—
491C2×C4—182no—
492C2×C4—184no—
493C2×C4—1816no—
494C2×C4#372214yes—
495C2×C4#372218yes—
496C2×C4C2×#62412yes—
497C2×C4C2×#62414yes—
498C2×C4C2×#62612yes—
499C2×C4C2×#62614yes—
500C2×C4C2×#62612yes—
501C2×C4C2×#62611yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—64no—
504C2×C3—24no—
505C2×C3—24no—
506C2×C3—24no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—44no—
511C2×C3#496614yescomplemented
512C2×C3#513314yescomplemented
513C2×C3C2×#90811yescharacteristic
514C2×C3C2×#90911yescharacteristic
515C2×C3C22×(C2×D3)⋊C411yescharacteristic
516C2×C3C22×(C2×D3)⋊C411yescharacteristic
517C2×C3C2×#93211yescharacteristic
518C2×C3C2×#94211yescharacteristic
519D3—128no—
520D3—124no—
521D3—124no—
522C22—28no—
523C22—22no—
524C22—22no—
525C22—184no—
526C22—368no—
527C22—362no—
528C22—362no—
529C22#6383012yes—
530C22#6383312yes—
531C22C2×#372214yes—
532C22C2×#372212yes—
533C22C22×#62611yescharacteristic
534C4—124no—
535C4—184no—
536C4C2×#372214yes—
537C4C2×#372212yes—
538C4C22×#62411yescharacteristic
539C4C22×#62611yescharacteristic
540C3—21no—
541C3C2×#496611yescharacteristic, complemented
542C3C2×#513311yescharacteristic, complemented
543C2—24no—
544C2—364no—
545C2#1059110614yesdirect product factor
546C2C2×#6383011yescharacteristic
547C2C2×#6383311yescharacteristic
548C2C22×#372211yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×#3828C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
3. C22×C3×#208C2semidirect
4. #10591106C2direct (N × H)
5. C2×#63567C2semidirect
6. C2×#63564C2semidirect
13. C2×#3828C4semidirect
22. C2×C3×C4⋊Dic3C22semidirect
24. C2×C3×#208C22semidirect
26. #63567C22semidirect
27. #63564C22semidirect
33. C22×C4⋊Dic3D3semidirect
34. C22×#208D3semidirect
54. #3828C2×C4semidirect
57. C2×C4⋊(C3⋊D3)C2×C4semidirect
63. C2×#634C2×C4semidirect
114. C2×C4⋊Dic3C2×D3semidirect
116. C2×#208C2×D3semidirect
145. C4⋊(C3⋊D3)C22×C4semidirect
149. #634C22×C4semidirect
380. C2×C32#417semidirect
471. C32C2×#417semidirect
511. C2×C3#4966semidirect
512. C2×C3#5133semidirect
541. C3C2×#4966semidirect
542. C3C2×#5133semidirect
545. C2#10591106direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×C4⋊Dic32
C22×C3×#2082
#105911062
C2×#635672
C2×#635642
C2×#51333
C2×#49663