Finite Group Databasebeta

← C2×#10591105 #11857799

Subgroups — C2×#10591105 #11857799

Order 1152.

2029 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591105C218yesmaximal, direct product factor
5C2×#63567C212yesmaximal, complemented
6C2×#63564C212yesmaximal, complemented
7C2×#5113—31nomaximal
8C2×#5002—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
18C2×C3×#217—21no—
19C3×#926—22no—
20C3×#926C2214yescomplemented
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4×Dic3—21no—
23C22×C3×C3⋊C8—24no—
24C22×C3×C3⋊C8C2212yes—
25C22×C3×C3⋊C8C2214yescomplemented
26#63567C2218yescomplemented
27#63564C2218yescomplemented
28C22×#235—31no—
29C22×#235—31no—
30C22×#235—61no—
31C23×C3×C8—31no—
32C2×C3×#117—31no—
33C2×#926D311yescharacteristic, complemented
34C23×C3⋊C8D311yescharacteristic, complemented
35#5113—38no—
36C2×#821—32no—
37C2×#816—32no—
38#5002—38no—
39C2×#810—32no—
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×C414yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—28no—
60C2×C4×C3⋊D3—24no—
61C2×#634—21no—
62C2×#634—22no—
63C2×#634C2×C414yes—
64C2×#634C2312yes—
65C22×C3×Dic3—22no—
66C3×#217—24no—
67C3×C4⋊Dic3—22no—
68C3×C4⋊Dic3C2314yes—
69C3×C4×Dic3—24no—
70C2×C3×C3⋊C8—24no—
71C2×C3×C3⋊C8—28no—
72C2×C3×C3⋊C8C2314yes—
73C2×#416—91noSylow
74C23×C3×C4—21no—
75C23×C3×C4C2×D311yescharacteristic
76C23×C3×C4C2×D311yescharacteristic
77C22×#67—62no—
78C22×#67—61no—
79C22×#67—61no—
80C2×#235—38no—
81C2×#235—38no—
82C2×#235—34no—
83C2×#235—34no—
84C2×#235—68no—
85C2×#235—64no—
86C2×#235—68no—
87C2×#235—64no—
88C2×#235—64no—
89C2×#235—62no—
90C2×#235—64no—
91C2×#235—62no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×C4×D3—62no—
96C22×C4×D3—61no—
97C22×C4×D3—61no—
98C22×Dic6—31no—
99C22×Dic6—31no—
100C22×Dic6—61no—
101C22×C3×C8—32no—
102C22×C3×C8—34no—
103C22×C3×C8—64no—
104C3×#117—34no—
105C3×#117—62no—
106C2×C3×C4⋊C4—32no—
107C2×C3×C22⋊C4—61no—
108C2×C3×C42—61no—
109C2×#217—21no—
110#926—22no—
111#926C2×D314yescomplemented
112C2×C4⋊Dic3C2×D312yes—
113C2×C4×Dic3—21no—
114C22×C3⋊C8—24no—
115C22×C3⋊C8C2×D312yes—
116C22×C3⋊C8C2×D314yescomplemented
117#821—38no—
118#816—38no—
119#810—38no—
120#809—38no—
121C23×C32—24no—
122C23×C32C22⋊C414yes—
123C23×C32C2×D412yes—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—24no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—44no—
128C2×C32×C4C22⋊C414yes—
129C2×C32×C4C22⋊C418yes—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C22×C414yes—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D414yes—
136C2×C32×C4C2411yescharacteristic
137#638—216no—
138C2×C3⋊Dic3—24no—
139C2×C3⋊Dic3—22no—
140C4⋊(C3⋊D3)—24no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)C22×C414yes—
143C4×C3⋊D3—216no—
144#634—24no—
145#634—22no—
146#634C22×C414yes—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—44no—
149C3×C3⋊C8—24no—
150C22×#41—91no—
151C23×C8—31no—
152C2×#117—31no—
153#416—98no—
154C2×#103—92no—
155C2×#102—92no—
156C24×C3—21no—
157C24×C3D1211yescharacteristic
158C24×C3#6711yescharacteristic
159C23×D3—62no—
160C23×D3—61no—
161C23×D3—61no—
162C22×C3×C4—24no—
163C22×C3×C4—22no—
164C22×C3×C4—24no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—22no—
168C22×C3×C4—62no—
169C22×C3×C4C4×D314yes—
170C22×C3×C4C4×D314yes—
171C22×C3×C4D1212yes—
172C22×C3×C4D1214yes—
173C22×C3×C4D1211yescharacteristic
174C22×C3×C4#6712yes—
175C22×C3×C4#6714yes—
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D312yes—
181C2×#67—616no—
182C2×#67—68no—
183C2×#67—68no—
184C2×#67—68no—
185C2×#67—64no—
186C2×#67—64no—
187C22×Dic3—22no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191#235—316no—
192#235—316no—
193#235—616no—
194#235—632no—
195#235—616no—
196#235—616no—
197#235—616no—
198#235—68no—
199#235—68no—
200C2×D12—34no—
201C2×D12—34no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—64no—
205C2×D12—62no—
206C2×D12—64no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—62no—
212C2×C4×D3—616no—
213C2×C4×D3—68no—
214C2×C4×D3—68no—
215C2×C4×D3—68no—
216C2×C4×D3—64no—
217C2×C4×D3—64no—
218C2×Dic6—34no—
219C2×Dic6—34no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—64no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—64no—
226C2×Dic6—61no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×C3×C8—34no—
231C2×C3×C8—64no—
232C2×C3×C8—68no—
233C3×C4⋊C4—34no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—64no—
236C3×C42—64no—
237#217—24no—
238C4⋊Dic3—22no—
239C4⋊Dic3C22×D314yes—
240C4×Dic3—24no—
241C2×C3⋊C8—24no—
242C2×C3⋊C8—28no—
243C2×C3⋊C8C22×D314yes—
244C22×C32—24no—
245C22×C32—28no—
246C22×C32C2×C22⋊C414yes—
247C22×C32C2×C22⋊C412yes—
248C22×C32#13514yes—
249C22×C32C22×D411yescharacteristic
250C2×C3⋊D3—24no—
251C2×C3⋊D3—44no—
252C2×C3⋊D3—48no—
253C32×C4C2×C22⋊C412yes—
254C32×C4C2×C22⋊C414yes—
255C32×C4C23×C411yescharacteristic
256C32×C4C22×D411yescharacteristic
257C3⋊Dic3—24no—
258C3×Dic3—44no—
259C2×#41—98no—
260C2×#41—94no—
261C2×#41—184no—
262C2×#41—182no—
263C22×Q8—91no—
264C22×D4—91no—
265C22×D4—181no—
266C23×C4—181no—
267C23×C4D3211yescharacteristic
268C22×C8—32no—
269C22×C8—34no—
270C22×C8—64no—
271#117—34no—
272#117—62no—
273C2×C4⋊C4—32no—
274C2×C22⋊C4—61no—
275C2×C42—61no—
276#103—98no—
277#102—98no—
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—21no—
282C23×C3—22no—
283C23×C3—44no—
284C23×C3(C2×D3)⋊C414yes—
285C23×C3(C2×D3)⋊C414yes—
286C23×C3C2×D1212yes—
287C23×C3C2×D1211yescharacteristic
288C23×C3C2×#6712yes—
289C23×C3C2×#6711yescharacteristic
290C22×D3—64no—
291C22×D3—68no—
292C22×D3—64no—
293C22×D3—64no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—128no—
297C22×D3—124no—
298C22×D3—124no—
299C2×C3×C4—21no—
300C2×C3×C4—24no—
301C2×C3×C4—28no—
302C2×C3×C4—22no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308C2×C3×C4—64no—
309C2×C3×C4—124no—
310C2×C3×C4(C2×D3)⋊C414yes—
311C2×C3×C4(C2×D3)⋊C414yes—
312C2×C3×C4(C2×D3)⋊C418yes—
313C2×C3×C4(C2×D3)⋊C418yes—
314C2×C3×C4C2×C4×D312yes—
315C2×C3×C4C2×C4×D312yes—
316C2×C3×C4C2×C4×D314yes—
317C2×C3×C4C2×C4×D314yes—
318C2×C3×C4C2×D1212yes—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4C2×D1212yes—
321C2×C3×C4C2×D1214yes—
322C2×C3×C4C2×#6712yes—
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6712yes—
325C2×C3×C4C2×#6714yes—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—632no—
329#67—616no—
330#67—616no—
331C2×Dic3—24no—
332C2×Dic3—44no—
333C2×Dic3—64no—
334C2×Dic3—68no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339D12—34no—
340D12—34no—
341D12—64no—
342D12—64no—
343D12—68no—
344D12—64no—
345D12—64no—
346D12—62no—
347D12—62no—
348C4×D3—632no—
349C4×D3—616no—
350C4×D3—616no—
351Dic6—34no—
352Dic6—34no—
353Dic6—64no—
354Dic6—64no—
355Dic6—68no—
356Dic6—64no—
357Dic6—64no—
358Dic6—62no—
359Dic6—62no—
360C3×C8—64no—
361C3⋊C8—24no—
362C2×C32—24no—
363C2×C32#41614yescomplemented
364C2×C32C22×C22⋊C411yescharacteristic
365C2×C32C2×#13512yes—
366C3⋊D3—44no—
367C24—181no—
368C24#62611yescharacteristic
369#41—916no—
370#41—1816no—
371#41—188no—
372C2×Q8—92no—
373C2×Q8—94no—
374C2×Q8—181no—
375C2×Q8—182no—
376C2×D4—92no—
377C2×D4—94no—
378C2×D4—188no—
379C2×D4—184no—
380C2×D4—182no—
381C2×D4—181no—
382C22×C4—62no—
383C22×C4—181no—
384C22×C4—188no—
385C22×C4—184no—
386C22×C4#62414yes—
387C22×C4#62612yes—
388C22×C4#62614yes—
389C22×C4#62611yescharacteristic
390C22×C4C2×D3211yescharacteristic
391C22×C4C2×D3212yes—
392C2×C8—34no—
393C2×C8—64no—
394C2×C8—68no—
395C4⋊C4—34no—
396C4⋊C4—62no—
397C22⋊C4—64no—
398C42—64no—
399C22×C3—24no—
400C22×C3—28no—
401C22×C3—24no—
402C22×C3—28no—
403C22×C3—21no—
404C22×C3—24no—
405C22×C3—22no—
406C22×C3—24no—
407C22×C3—48no—
408C22×C3—44no—
409C22×C3#90414yes—
410C22×C3C2×(C2×D3)⋊C414yes—
411C22×C3C2×(C2×D3)⋊C414yes—
412C22×C3C2×(C2×D3)⋊C412yes—
413C22×C3C2×(C2×D3)⋊C412yes—
414C22×C3#95014yes—
415C22×C3C22×D1211yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—68no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—1216no—
421C2×D3—128no—
422C2×D3—124no—
423C2×D3—128no—
424C2×D3—124no—
425C2×D3—128no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—24no—
430C3×C4—124no—
431C3×C4C2×(C2×D3)⋊C412yes—
432C3×C4C2×(C2×D3)⋊C412yes—
433C3×C4C2×(C2×D3)⋊C414yes—
434C3×C4C2×(C2×D3)⋊C414yes—
435C3×C4C22×C4×D311yescharacteristic
436C3×C4C22×C4×D311yescharacteristic
437C3×C4C22×D1211yescharacteristic
438C3×C4C22×#6711yescharacteristic
439Dic3—44no—
440Dic3—68no—
441Dic3—64no—
442Dic3—64no—
443C32C2×#41611yescharacteristic, complemented, Sylow
444C23—24no—
445C23—182no—
446C23—184no—
447C23—364no—
448C23#372214yes—
449C23C2×#62612yes—
450C23C2×#62611yescharacteristic
451Q8—94no—
452Q8—182no—
453Q8—184no—
454D4—94no—
455D4—1816no—
456D4—182no—
457D4—184no—
458C2×C4—64no—
459C2×C4—124no—
460C2×C4—182no—
461C2×C4—184no—
462C2×C4—1816no—
463C2×C4#372214yes—
464C2×C4#372218yes—
465C2×C4C2×#62412yes—
466C2×C4C2×#62414yes—
467C2×C4C2×#62612yes—
468C2×C4C2×#62614yes—
469C2×C4C2×#62612yes—
470C2×C4C2×#62611yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—64no—
473C2×C3—24no—
474C2×C3—24no—
475C2×C3—24no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—44no—
479C2×C3#500214yescomplemented
480C2×C3#511314yescomplemented
481C2×C3C2×#90412yes—
482C2×C3C22×(C2×D3)⋊C411yescharacteristic
483C2×C3C22×(C2×D3)⋊C411yescharacteristic
484C2×C3C2×#95012yes—
485D3—128no—
486D3—124no—
487D3—124no—
488C22—28no—
489C22—24no—
490C22—184no—
491C22—368no—
492C22—364no—
493C22#6382914yes—
494C22C2×#372214yes—
495C22C2×#372212yes—
496C22C22×#62611yescharacteristic
497C4—124no—
498C4—184no—
499C4C2×#372214yes—
500C4C2×#372212yes—
501C4C22×#62411yescharacteristic
502C4C22×#62611yescharacteristic
503C3—21no—
504C3C2×#500211yescharacteristic, complemented
505C3C2×#511311yescharacteristic, complemented
506C2—24no—
507C2—364no—
508C2#1059110514yesdirect product factor
509C2C2×#6382912yes—
510C2C22×#372211yescharacteristic
subgroupG/H
centerC22×C4#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×#3828C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. #10591105C2direct (N × H)
5. C2×#63567C2semidirect
6. C2×#63564C2semidirect
13. C2×#3828C4semidirect
20. C3×#926C22semidirect
25. C22×C3×C3⋊C8C22semidirect
26. #63567C22semidirect
27. #63564C22semidirect
33. C2×#926D3semidirect
34. C23×C3⋊C8D3semidirect
54. #3828C2×C4semidirect
111. #926C2×D3semidirect
116. C22×C3⋊C8C2×D3semidirect
363. C2×C32#416semidirect
443. C32C2×#416semidirect
479. C2×C3#5002semidirect
480. C2×C3#5113semidirect
504. C3C2×#5002semidirect
505. C3C2×#5113semidirect
508. C2#10591105direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9262
C23×C3×C3⋊C82
#105911052
C2×#635672
C2×#635642
C2×#51133
C2×#50023