Finite Group Databasebeta

← C2×#10590360 #11860070

Subgroups — C2×#10590360 #11860070

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×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic
4C2×C3×#803C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590360C218yesmaximal, direct product factor
9C2×#5018—31nomaximal
10C2×#4710—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×C42C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3—21no—
18C4×#634—22no—
19C4×#634C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×C4×D12—22no—
25C3×C4×D12C2214yes—
26C2×#3716C418yescomplemented
27C2×#3716C2214yes—
28C3×#803C2214yescomplemented
29#63575C2214yescomplemented
30#63567C2214yescomplemented
31#63563C2214yes—
32C2×C3×C4×D4—31no—
33C22×#214—31no—
34C22×#204—31no—
35C2×C4×D12D311yescharacteristic
36C2×C4×Dic6—31no—
37C2×C4×Dic6—31no—
38C2×C4×Dic6—61no—
39C2×C3×#97—31no—
40C2×#832—31no—
41C2×#821—31no—
42C2×#818—31no—
43C2×#816—31no—
44#5018—38no—
45C2×#810—31no—
46C2×#807—31no—
47C2×#803D311yescharacteristic, complemented
48#4710—38no—
49C23×C3×D3—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C2×#634—21no—
56C2×#634—22no—
57C2×#634C2×C414yescomplemented
58C2×#634C2312yes—
59C22×C3×Dic3—21no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C2×C3×C4×D3—44no—
66C32×C42D412yes—
67C32×C42C2312yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70#3750—24no—
71C4×C3⋊Dic3—24no—
72C3×(C2×D3)⋊C4—24no—
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#3716C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×D4—31no—
82C23×C3×C4—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—21no—
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C3×C4×D4—34no—
91C3×C4×D4—62no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C2×D311yescharacteristic
97C2×#214—38no—
98C2×#214—34no—
99C2×(C2×D3)⋊C4—21no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—62no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C2×C4×Dic3—62no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×#204—38no—
113C2×#204—34no—
114C4×D12—22no—
115C4×D12C2×D314yes—
116C4×Dic6—34no—
117C4×Dic6—34no—
118C4×Dic6—64no—
119C4×Dic6—64no—
120C4×Dic6—62no—
121C4×Dic6—62no—
122C3×#97—34no—
123#832—34no—
124#821—34no—
125#818—34no—
126#816—34no—
127#810—34no—
128#807—34no—
129#803C2×D314yescomplemented
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—24no—
132C22×C3×D3—22no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—24no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147#634—24no—
148#634—22no—
149#634C22×C414yescomplemented
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12C22×C414yes—
155C3×C4×D3—48no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8C22×C414yescomplemented
158C22×SD16—91no—
159C2×C4×Q8—91no—
160C2×C4×D4—31no—
161#440—98no—
162C2×#107—91no—
163C2×#103—91no—
164C2×#102—91no—
165C2×#97—31no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×D4—34no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—62no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—61no—
176C22×C3×C4—64no—
177C22×C3×C4—124no—
178C22×C3×C4D1211yescharacteristic
179C22×C3×C4D1211yescharacteristic
180C22×C3×C4#6711yescharacteristic
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—62no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C2×D12—22no—
192C2×D12—21no—
193C2×D12C4×D314yes—
194C2×D12C22×D312yes—
195C2×C4×D3—24no—
196C2×C4×D3—44no—
197C2×Dic6—34no—
198C2×Dic6—34no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—62no—
202C2×Dic6—64no—
203C2×Dic6—62no—
204C2×Dic6—64no—
205C2×Dic6—61no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—61no—
209C2×C3×C8—34no—
210C2×C3×C8—32no—
211C2×C3×C8—32no—
212C2×C3×C8—62no—
213C3×C4⋊C4—32no—
214C3×C4⋊C4—61no—
215C3×C22⋊C4—64no—
216C3×C42—22no—
217C3×C42—22no—
218C3×C42D1212yes—
219C3×C42#6712yes—
220C3×C42C22×D312yes—
221C3×C42C22×D312yes—
222#214—316no—
223(C2×D3)⋊C4—24no—
224C4⋊Dic3—21no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—68no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235C4×Dic3—68no—
236C4×Dic3—64no—
237C4×Dic3—64no—
238C2×C3⋊C8—22no—
239C2×C3⋊C8C4×D314yescomplemented
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D312yes—
242#204—316no—
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—22no—
252C32×C4—22no—
253C32×C4C4×D412yes—
254C32×C4C23×C411yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—24no—
257C3⋊Dic3—42no—
258C3×Dic3—42no—
259C22×Q8—91no—
260C22×D4—31no—
261C23×C4—61no—
262C2×SD16—98no—
263C2×SD16—94no—
264C22×C8—31no—
265C22×C8—31no—
266C4×Q8—94no—
267C4×Q8—182no—
268C4×D4—34no—
269C4×D4—62no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—181no—
273C2×C22⋊C4—61no—
274C2×C42—181no—
275C2×C42D3211yescharacteristic
276#107—94no—
277#103—94no—
278#102—94no—
279#97—34no—
280C23×C3—21no—
281C23×C3—64no—
282C23×C3—62no—
283C23×C3—122no—
284C23×C3—122no—
285C23×C3C2×D1211yescharacteristic
286C23×C3C2×#6711yescharacteristic
287C22×D3—24no—
288C22×D3—22no—
289C22×D3—42no—
290C22×D3—42no—
291C3×D4—34no—
292C3×D4—64no—
293C3×D4—62no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—42no—
306C2×C3×C4—62no—
307C2×C3×C4—128no—
308C2×C3×C4—122no—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4C2×D1212yes—
312C2×C3×C4C2×D1212yes—
313C2×C3×C4C2×D1211yescharacteristic
314C2×C3×C4#23512yes—
315C2×C3×C4#23512yes—
316C2×C3×C4C2×#6712yes—
317C2×C3×C4C2×#6712yes—
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×Dic3—22no—
322C2×Dic3—42no—
323C2×Dic3—64no—
324C2×Dic3—68no—
325C2×Dic3—64no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—64no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—124no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335D12—24no—
336D12—22no—
337D12C2×C4×D314yes—
338C4×D3—48no—
339Dic6—34no—
340Dic6—34no—
341Dic6—64no—
342Dic6—64no—
343Dic6—68no—
344Dic6—64no—
345Dic6—64no—
346Dic6—62no—
347Dic6—62no—
348C3×C8—34no—
349C3×C8—62no—
350C3⋊C8—22no—
351C3⋊C8C2×C4×D314yescomplemented
352C2×C32#44014yescomplemented
353C2×C32C2×C4×D411yescharacteristic
354C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
355C2×C32C2×#13711yescharacteristic
356C3×D3—44no—
357C24—61no—
358C2×Q8—92no—
359C2×Q8—94no—
360C2×Q8—182no—
361C2×Q8—181no—
362C2×D4—32no—
363C2×D4—34no—
364C2×D4—62no—
365C2×D4—61no—
366C22×C4—61no—
367C22×C4—64no—
368C22×C4—124no—
369C22×C4—181no—
370C22×C4—181no—
371C22×C4#62611yescharacteristic
372C22×C4#62611yescharacteristic
373C22×C4C2×D3211yescharacteristic
374SD16—916no—
375C2×C8—32no—
376C2×C8—34no—
377C2×C8—32no—
378C2×C8—62no—
379C4⋊C4—32no—
380C4⋊C4—61no—
381C4⋊C4—92no—
382C4⋊C4—181no—
383C4⋊C4—184no—
384C22⋊C4—64no—
385C42—184no—
386C42#62612yes—
387C42C2×D3212yes—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—64no—
393C22×C3—128no—
394C22×C3—122no—
395C22×C3—122no—
396C22×C3C4×D1212yes—
397C22×C3#90812yes—
398C22×C3#90912yes—
399C22×C3C4×#6712yes—
400C22×C3#93212yes—
401C22×C3#95112yes—
402C22×C3C22×D1211yescharacteristic
403C22×C3C22×#6711yescharacteristic
404C2×D3—24no—
405C2×D3—48no—
406C2×D3—42no—
407C2×D3—42no—
408C3×C4—24no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—42no—
417C3×C4—122no—
418C3×C4C4×D1212yes—
419C3×C4C4×#6712yes—
420C3×C4C22×C4×D311yescharacteristic
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C2×#23511yescharacteristic
423C3×C4C2×#23511yescharacteristic
424Dic3—42no—
425Dic3—68no—
426Dic3—64no—
427Dic3—64no—
428Dic3—124no—
429Dic3—122no—
430Dic3—122no—
431C32C2×#44011yescharacteristic, complemented, Sylow
432C23—62no—
433C23—64no—
434C23—122no—
435C23—122no—
436C23C2×#62611yescharacteristic
437Q8—94no—
438Q8—182no—
439Q8—184no—
440D4—34no—
441D4—62no—
442D4—64no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—62no—
446C2×C4—128no—
447C2×C4—122no—
448C2×C4—182no—
449C2×C4—184no—
450C2×C4—182no—
451C2×C4—362no—
452C2×C4#379812yes—
453C2×C4C4×D3212yes—
454C2×C4C2×#62612yes—
455C2×C4C2×#62612yes—
456C2×C4C2×#62611yescharacteristic
457C2×C4C22×D3211yescharacteristic
458C8—34no—
459C8—62no—
460C2×C3—24no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—124no—
465C2×C3#471014yescomplemented
466C2×C3#501814yescomplemented
467C2×C3C2×C4×D1211yescharacteristic
468C2×C3C2×#90811yescharacteristic
469C2×C3C2×#90911yescharacteristic
470C2×C3C2×C4×#6711yescharacteristic
471C2×C3C2×#93211yescharacteristic
472C2×C3C2×#95111yescharacteristic
473D3—44no—
474C22—64no—
475C22—128no—
476C22—122no—
477C22—122no—
478C22#6383012yes—
479C22#6383112yes—
480C22C4×#62612yes—
481C22C22×#62611yescharacteristic
482C4—22no—
483C4—22no—
484C4—122no—
485C4—184no—
486C4—362no—
487C4C4×#62612yes—
488C4C2×#379811yescharacteristic
489C4C2×C4×D3211yescharacteristic
490C3—21no—
491C3C2×#471011yescharacteristic, complemented
492C3C2×#501811yescharacteristic, complemented
493C2—124no—
494C2#1059036014yesdirect product factor
495C2C2×#6383011yescharacteristic
496C2C2×#6383111yescharacteristic
497C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#440
LCSG ▷ 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×#634C2semidirect
4. C2×C3×#803C2semidirect
5. C2×#63575C2semidirect
6. C2×#63567C2semidirect
8. #10590360C2direct (N × H)
19. C4×#634C22semidirect
26. C2×#3716C4semidirect
28. C3×#803C22semidirect
29. #63575C22semidirect
30. #63567C22semidirect
47. C2×#803D3semidirect
57. C2×#634C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
79. #3716C2×C4semidirect
129. #803C2×D3semidirect
149. #634C22×C4semidirect
157. C3×C3⋊C8C22×C4semidirect
239. C2×C3⋊C8C4×D3semidirect
351. C3⋊C8C2×C4×D3semidirect
352. C2×C32#440semidirect
431. C32C2×#440semidirect
465. C2×C3#4710semidirect
466. C2×C3#5018semidirect
491. C3C2×#4710semidirect
492. C3C2×#5018semidirect
494. C2#10590360direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×C4×D122
C22×#37162
C2×C3×#8032
C2×#635752
C2×#635672
C2×#635632
#105903602
C2×#50183
C2×#47103