Finite Group Databasebeta

← C2×#10591572 #11860077

Subgroups — C2×#10591572 #11860077

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591572C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8C2×#63555C211yesmaximal, characteristic, complemented
9C2×#5164—31nomaximal
10C2×#4817—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×D3×Dic3—21no—
14Q8×C3⋊Dic3—22no—
15Q8×C3⋊Dic3C2214yescomplemented
16C2×C4⋊(C3⋊Dic3)—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#215C418yescomplemented
21C2×C3×#215C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63898—22no—
27#63898C2214yes—
28C3×#835C2214yescomplemented
29#63575C2214yescomplemented
30#63563C2214yes—
31#63555C2214yescomplemented
32C22×C3×SD16—31no—
33C2×Q8×Dic3—31no—
34C2×Q8×Dic3—31no—
35C2×Q8×Dic3—61no—
36C22×#215D311yescharacteristic
37C2×D4×Dic3—31no—
38C2×#893—31no—
39C2×C3×#103—31no—
40C2×#835D311yescharacteristic, complemented
41C2×#832—31no—
42#5164—38no—
43C2×#821—31no—
44C2×#818—31no—
45C2×#815—31no—
46C2×#815—31no—
47C2×#807—31no—
48#4817—38no—
49C23×C3×D3—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2×C414yescomplemented
53C2×C32×Q8C2312yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3D411yescharacteristic
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3×Dic3—21no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—24no—
68C4⋊(C3⋊Dic3)C2312yes—
69C4×C3⋊Dic3—24no—
70C4×C3⋊Dic3D412yes—
71C4×C3⋊Dic3C2312yes—
72C3×#215C2×C4116yescomplemented
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2×C414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79(C2×D3)⋊Dic3—24no—
80C2×#440—91noSylow
81C22×C3×Q8—21no—
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×D4—31no—
85C23×Dic3—61no—
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C2×C3×SD16—38no—
89C2×C3×SD16—34no—
90C22×C3×C8—31no—
91C22×C3×C8—31no—
92C2×C3×C4⋊C4—31no—
93C2×#217—61no—
94Q8×Dic3—34no—
95Q8×Dic3—34no—
96Q8×Dic3—64no—
97Q8×Dic3—62no—
98Q8×Dic3—62no—
99Q8×Dic3—64no—
100C2×#215Dic318yescomplemented
101C2×#215C2×D314yes—
102D4×Dic3—34no—
103D4×Dic3—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3—62no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—62no—
118C22×C3⋊C8C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120#893—34no—
121#893—62no—
122C3×#103—34no—
123#835C2×D314yescomplemented
124#832—34no—
125#821—34no—
126#818—34no—
127#815—34no—
128#815—34no—
129#807—34no—
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—24no—
132C22×C3×D3—22no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C32×Q8—24no—
136C32×Q8—22no—
137C32×Q8C22×C414yescomplemented
138C2×C32×C4—24no—
139C2×C32×C4—22no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—42no—
148C2×C3⋊Dic3C2×D412yes—
149C2×C3⋊Dic3C2×D412yes—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12C22×C414yes—
155D3×Dic3—48no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8C22×C414yescomplemented
158C22×SD16—31no—
159C2×C4×Q8—91no—
160C2×C4×D4—91no—
161#440—98no—
162C2×#107—91no—
163C2×#103—31no—
164C2×#102—91no—
165C2×#97—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—24no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—24no—
175C2×C3×Q8—22no—
176C2×C3×Q8C4×D314yescomplemented
177C2×C3×Q8C2×Dic314yescomplemented
178C2×C3×Q8C22×D312yes—
179C2×C3×Q8C22×D312yes—
180C2×C3×D4—34no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—62no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—64no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—124no—
203C2×D12—21no—
204C2×D12—22no—
205C2×D12C2×Dic314yes—
206C2×D12C22×D312yes—
207C2×C4×D3—64no—
208C2×C4×D3—124no—
209C3×SD16—316no—
210C2×C3×C8—34no—
211C2×C3×C8—32no—
212C2×C3×C8—32no—
213C2×C3×C8—62no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—61no—
216#217—64no—
217#215C2×Dic3116yescomplemented
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—21no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—62no—
223C4⋊Dic3—64no—
224C4⋊Dic3—64no—
225C4⋊Dic3—68no—
226C4⋊Dic3—62no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3C22×D312yes—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—32no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—64no—
237C4×Dic3—64no—
238C4×Dic3—68no—
239C2×C3⋊C8—22no—
240C2×C3⋊C8C2×Dic314yescomplemented
241C2×C3⋊C8C22×D312yes—
242C2×C3⋊C8C22×D312yes—
243C22×C32C4×D412yes—
244C22×C32AGL(1,ℤ/8)12yes—
245C22×C32#13712yes—
246C22×C32C22×D411yescharacteristic
247C2×C3×D3—24no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—48no—
251C32×C4—24no—
252C32×C4C4×D412yes—
253C32×C4C23×C411yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—22no—
256C3⋊Dic3—22no—
257C3⋊Dic3—42no—
258C3×Dic3—42no—
259C22×Q8D3211yescharacteristic
260C22×D4—31no—
261C23×C4—181no—
262C2×SD16—38no—
263C2×SD16—34no—
264C22×C8—31no—
265C22×C8—31no—
266C4×Q8—94no—
267C4×Q8—182no—
268C4×D4—94no—
269C4×D4—182no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—181no—
273C2×C22⋊C4—181no—
274C2×C42—91no—
275C2×C42—181no—
276#107—94no—
277#103—34no—
278#102—94no—
279#97—94no—
280C23×C3—21no—
281C23×C3—64no—
282C23×C3—62no—
283C23×C3—122no—
284C23×C3—122no—
285C23×C3D3×D411yescharacteristic
286C23×C3D3×D411yescharacteristic
287C22×D3—24no—
288C22×D3—22no—
289C22×D3—42no—
290C22×D3—42no—
291C3×Q8—24no—
292C3×Q8—28no—
293C3×Q8—24no—
294C3×Q8—24no—
295C3×Q8—22no—
296C3×Q8—22no—
297C3×Q8—24no—
298C3×Q8C2×C4×D314yescomplemented
299C3×Q8C22×Dic314yescomplemented
300C3×D4—34no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—24no—
304C2×C3×C4—28no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—62no—
314C2×C3×C4—122no—
315C2×C3×C4C2×C4×D312yes—
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4#23712yes—
319C2×C3×C4#23712yes—
320C2×C3×C4C22×Dic312yes—
321C2×C3×C4C23×D311yescharacteristic
322C2×C3×C4C23×D311yescharacteristic
323C2×Dic3—22no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—42no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—64no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—122no—
340C2×Dic3—128no—
341C2×Dic3—124no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344D12—24no—
345D12—22no—
346D12C22×Dic314yes—
347C4×D3—128no—
348C3×C8—34no—
349C3×C8—62no—
350C3⋊C8—22no—
351C3⋊C8C22×Dic314yescomplemented
352C2×C32#44014yescomplemented
353C2×C32C2×C4×D411yescharacteristic
354C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
355C2×C32C2×#13711yescharacteristic
356C3×D3—44no—
357C24—61no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8D3×Dic314yescomplemented
361C2×Q8C2×D3212yes—
362C2×D4—32no—
363C2×D4—34no—
364C2×D4—62no—
365C2×D4—61no—
366C22×C4—21no—
367C22×C4—61no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—184no—
371C22×C4—181no—
372C22×C4—364no—
373C22×C4C2×D3211yescharacteristic
374SD16—316no—
375C2×C8—32no—
376C2×C8—34no—
377C2×C8—32no—
378C2×C8—62no—
379C4⋊C4—32no—
380C4⋊C4—61no—
381C4⋊C4—92no—
382C4⋊C4—184no—
383C4⋊C4—181no—
384C22⋊C4—184no—
385C42—92no—
386C42—92no—
387C42—184no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—64no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3—128no—
396C22×C3#67⋊C412yes—
397C22×C3#91412yes—
398C22×C3#91412yes—
399C22×C3#91512yes—
400C22×C3#91812yes—
401C22×C3D4×Dic312yes—
402C22×C3C2×D3×D411yescharacteristic
403C22×C3C2×D3×D411yescharacteristic
404C2×D3—24no—
405C2×D3—48no—
406C2×D3—42no—
407C2×D3—42no—
408C3×C4—28no—
409C3×C4—24no—
410C3×C4—24no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—22no—
414C3×C4—122no—
415C3×C4#67⋊C412yes—
416C3×C4D4×Dic312yes—
417C3×C4C22×C4×D311yescharacteristic
418C3×C4C2×#23711yescharacteristic
419C3×C4C2×#23711yescharacteristic
420C3×C4C23×Dic311yescharacteristic
421Dic3—42no—
422Dic3—64no—
423Dic3—62no—
424Dic3—62no—
425Dic3—62no—
426Dic3—62no—
427Dic3—122no—
428Dic3—124no—
429Dic3—122no—
430Dic3—122no—
431C32C2×#44011yescharacteristic, complemented, Sylow
432C23—62no—
433C23—64no—
434C23—122no—
435C23—122no—
436C23#381111yescharacteristic
437Q8—22no—
438Q8—24no—
439Q8C2×D3×Dic314yescomplemented
440D4—34no—
441D4—62no—
442D4—64no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—62no—
446C2×C4—92no—
447C2×C4—92no—
448C2×C4—122no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—368no—
453C2×C4—362no—
454C2×C4C2×D3×Dic312yes—
455C2×C4#380512yes—
456C2×C4#381111yescharacteristic
457C2×C4C22×D3211yescharacteristic
458C8—34no—
459C8—62no—
460C2×C3—21no—
461C2×C3—24no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—124no—
465C2×C3#481714yescomplemented
466C2×C3#516414yescomplemented
467C2×C3C2×#67⋊C411yescharacteristic
468C2×C3C2×#91411yescharacteristic
469C2×C3C2×#91411yescharacteristic
470C2×C3C2×#91511yescharacteristic
471C2×C3C2×#91811yescharacteristic
472C2×C3C2×D4×Dic311yescharacteristic
473D3—44no—
474C22—64no—
475C22—122no—
476C22—128no—
477C22—122no—
478C22#6394112yes—
479C22#6395112yes—
480C22#67⋊Dic312yes—
481C22C2×#381111yescharacteristic
482C4—24no—
483C4—122no—
484C4—182no—
485C4—182no—
486C4—362no—
487C4#67⋊Dic312yes—
488C4C22×D3×Dic311yescharacteristic
489C4C2×#380511yescharacteristic
490C3—21no—
491C3C2×#481711yescharacteristic, complemented
492C3C2×#516411yescharacteristic, complemented
493C2—124no—
494C2#1059157214yesdirect product factor
495C2C2×#6394111yescharacteristic
496C2C2×#6395111yescharacteristic
497C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
4. C2×C3×#835C2semidirect
5. #10591572C2direct (N × H)
6. C2×#63575C2semidirect
8. C2×#63555C2semidirect
15. Q8×C3⋊Dic3C22semidirect
20. C2×C3×#215C4semidirect
28. C3×#835C22semidirect
29. #63575C22semidirect
31. #63555C22semidirect
40. C2×#835D3semidirect
52. C2×C32×Q8C2×C4semidirect
72. C3×#215C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
100. C2×#215Dic3semidirect
123. #835C2×D3semidirect
137. C32×Q8C22×C4semidirect
157. C3×C3⋊C8C22×C4semidirect
176. C2×C3×Q8C4×D3semidirect
177. C2×C3×Q8C2×Dic3semidirect
217. #215C2×Dic3semidirect
240. C2×C3⋊C8C2×Dic3semidirect
298. C3×Q8C2×C4×D3semidirect
299. C3×Q8C22×Dic3semidirect
351. C3⋊C8C22×Dic3semidirect
352. C2×C32#440semidirect
360. C2×Q8D3×Dic3semidirect
431. C32C2×#440semidirect
439. Q8C2×D3×Dic3semidirect
465. C2×C3#4817semidirect
466. C2×C3#5164semidirect
491. C3C2×#4817semidirect
492. C3C2×#5164semidirect
494. C2#10591572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C22×C3×#2152
C2×#638982
C2×C3×#8352
#105915722
C2×#635752
C2×#635632
C2×#635552
C2×#51643
C2×#48173