Finite Group Databasebeta

← C2×#10590633 #11899565

Subgroups — C2×#10590633 #11899565

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2C22×C3×D24C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4C2×#63548C212yesmaximal, complemented
5#10590633C218yesmaximal, direct product factor
6C2×#63546C212yesmaximal, complemented
7C2×#5147—31nomaximal
8C2×#4908—31nomaximal
9C2×#3828—21no—
10C22×C3×D12—21no—
11C22×C32×C8C2211yescharacteristic
12C2×#3746C2211yescharacteristic, complemented
13#64113—22no—
14#64113C2214yescomplemented
15C2×#3745C2211yescharacteristic, complemented
16C2×#3744—21no—
17C2×C3×D24—22no—
18C2×C3×D24—21no—
19C2×C3×D24C2212yes—
20C2×C3×D24C2214yescomplemented
21C3×#812C2214yescomplemented
22C2×C3×C3⋊C16C2212yescomplemented
23#63548C2218yescomplemented
24#63546C2218yescomplemented
25C22×C3×D8—31no—
26C2×#904—31no—
27C2×#904—31no—
28C2×#904—61no—
29C22×D24D311yescharacteristic, complemented
30C2×C3×M32—31no—
31C2×#827—32no—
32#5147—38no—
33C2×#826—32no—
34C2×#812D311yescharacteristic, complemented
35#4908—38no—
36C2×#800—32no—
37C2×D48—32no—
38C23×C3×D3—41no—
39C22×C32×C4D411yescharacteristic
40C2×#638—41no—
41#3828—24no—
42#3828—42no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4×C3⋊D3—41no—
45C2×#634—21no—
46C2×C3×D12—22no—
47C2×C3×D12—24no—
48C2×C3×D12—41no—
49C2×C3×D12—42no—
50C2×C32×C8D411yescharacteristic
51C2×C32×C8D412yes—
52C2×C32×C8C2311yescharacteristic
53C2×C32×C8C2312yes—
54#3746—21no—
55#3746C2312yescomplemented
56#3745—21no—
57#3745C2312yescomplemented
58#3744—24no—
59C3×D24—22no—
60C3×D24—24no—
61C3×D24C2314yes—
62C3×C3⋊C16C2314yescomplemented
63C2×#509—91noSylow
64C22×C3×D4—61no—
65C2×#235—62no—
66C2×#235—61no—
67C2×#235—61no—
68C22×D12—21no—
69C2×C3×D8—32no—
70C2×C3×D8—34no—
71C2×C3×D8—61no—
72C2×C3×D8—62no—
73C22×C3×C8—21no—
74C22×C3×C8C2×D311yescharacteristic
75C22×C3×C8C2×D311yescharacteristic
76C2×Dic12—31no—
77C2×Dic12—31no—
78C2×Dic12—61no—
79#904—34no—
80#904—34no—
81#904—64no—
82#904—64no—
83#904—62no—
84#904—62no—
85C2×D24—22no—
86C2×D24—21no—
87C2×D24—31no—
88C2×D24—31no—
89C2×D24—61no—
90C2×D24C2×D312yes—
91C2×D24C2×D314yescomplemented
92C2×#204—62no—
93C2×#204—61no—
94C2×#204—61no—
95C3×M32—34no—
96C2×C3×C16—32no—
97#827—38no—
98#826—38no—
99#812C2×D314yescomplemented
100C2×C3⋊C16C2×D312yescomplemented
101#800—38no—
102D48—38no—
103C23×C32D811yescharacteristic
104C22×C3⋊D3—41no—
105C22×C3×D3—44no—
106C22×C3×D3—42no—
107C22×C3×D3—84no—
108C2×C32×C4D811yescharacteristic
109C2×C32×C4D812yes—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D412yes—
112#638—44no—
113C2×C3⋊Dic3—41no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—41no—
116C4×C3⋊D3—44no—
117#634—22no—
118#634—41no—
119C3×D12—24no—
120C3×D12—42no—
121C3×D12—44no—
122C32×C8C2×D412yes—
123C32×C8C2×D411yescharacteristic
124C32×C8C2411yescharacteristic
125C2×#135—91no—
126C22×D8—31no—
127#509—98no—
128C2×SD32—92no—
129C2×D16—92no—
130C2×M32—31no—
131C24×C3—121no—
132C23×D3—41no—
133C2×C3×D4—62no—
134C2×C3×D4—64no—
135C2×C3×D4—121no—
136C2×C3×D4—122no—
137C22×C3×C4—21no—
138C22×C3×C4D1211yescharacteristic
139C22×C3×C4#6711yescharacteristic
140C2×#67—122no—
141C2×#67—121no—
142C2×#67—121no—
143#235—68no—
144#235—64no—
145#235—64no—
146#235—124no—
147#235—122no—
148#235—122no—
149C2×D12—22no—
150C2×D12—24no—
151C2×D12—41no—
152C2×D12—42no—
153C2×D12—62no—
154C2×D12—61no—
155C2×D12—61no—
156C2×C4×D3—122no—
157C2×C4×D3—121no—
158C2×C4×D3—121no—
159C2×Dic6—62no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C3×D8—34no—
163C3×D8—64no—
164C3×D8—62no—
165C2×C3×C8—21no—
166C2×C3×C8—22no—
167C2×C3×C8—21no—
168C2×C3×C8—22no—
169C2×C3×C8D1211yescharacteristic
170C2×C3×C8D1212yes—
171C2×C3×C8#6711yescharacteristic
172C2×C3×C8#6712yes—
173C2×C3×C8C22×D311yescharacteristic
174C2×C3×C8C22×D312yes—
175C2×C3×C8C22×D311yescharacteristic
176C2×C3×C8C22×D312yes—
177Dic12—32no—
178Dic12—32no—
179Dic12—62no—
180Dic12—62no—
181Dic12—61no—
182Dic12—61no—
183D24—22no—
184D24—24no—
185D24—32no—
186D24—32no—
187D24—62no—
188D24—62no—
189D24—61no—
190D24—61no—
191D24C22×D314yes—
192#204—68no—
193#204—64no—
194#204—64no—
195C3×C16—34no—
196C3⋊C16C22×D314yescomplemented
197C22×C32—22no—
198C22×C32C2×D812yes—
199C22×C32C2×D811yescharacteristic
200C2×C3⋊D3—42no—
201C2×C3⋊D3—82no—
202C2×C3×D3—44no—
203C2×C3×D3—88no—
204C2×C3×D3—84no—
205C32×C4C2×D811yescharacteristic
206C32×C4C2×D812yes—
207C32×C4C22×D411yescharacteristic
208C3⋊Dic3—42no—
209C2×#41—181no—
210C22×D4—61no—
211#135—94no—
212#135—182no—
213C2×Q16—91no—
214C2×SD16—181no—
215C2×D8—32no—
216C2×D8—34no—
217C2×D8—61no—
218C2×D8—62no—
219C2×D8—91no—
220C22×C8D3211yescharacteristic
221SD32—98no—
222D16—98no—
223M32—34no—
224C2×C16—32no—
225C23×C3—21no—
226C23×C3—124no—
227C23×C3—122no—
228C23×C3—244no—
229C23×C3D2411yescharacteristic
230C23×C3#21311yescharacteristic
231C22×D3—44no—
232C22×D3—42no—
233C22×D3—84no—
234C22×D3—122no—
235C22×D3—121no—
236C22×D3—121no—
237C3×D4—64no—
238C3×D4—122no—
239C3×D4—124no—
240C2×C3×C4—21no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—22no—
244C2×C3×C4D2411yescharacteristic
245C2×C3×C4D2412yes—
246C2×C3×C4#21311yescharacteristic
247C2×C3×C4#21312yes—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4C2×D1212yes—
250C2×C3×C4C2×#6711yescharacteristic
251C2×C3×C4C2×#6712yes—
252#67—128no—
253#67—124no—
254#67—124no—
255C2×Dic3—122no—
256C2×Dic3—121no—
257C2×Dic3—121no—
258D12—24no—
259D12—42no—
260D12—44no—
261D12—64no—
262D12—62no—
263D12—62no—
264D12—122no—
265D12—121no—
266D12—121no—
267C4×D3—128no—
268C4×D3—124no—
269C4×D3—124no—
270Dic6—64no—
271Dic6—62no—
272Dic6—62no—
273Dic6—122no—
274Dic6—121no—
275Dic6—121no—
276C3×C8—21no—
277C3×C8—22no—
278C3×C8—21no—
279C3×C8C2×D1212yes—
280C3×C8C2×D1211yescharacteristic
281C3×C8C2×#6712yes—
282C3×C8C2×#6711yescharacteristic
283C3×C8C23×D311yescharacteristic
284C3×C8C23×D311yescharacteristic
285C2×C32—22no—
286C2×C32#50912yescomplemented
287C2×C32C22×D811yescharacteristic
288C3⋊D3—82no—
289C3×D3—84no—
290C24—121no—
291#41—184no—
292#41—362no—
293C2×Q8—181no—
294C2×D4—64no—
295C2×D4—62no—
296C2×D4—122no—
297C2×D4—121no—
298C2×D4—181no—
299C2×D4—361no—
300C22×C4—361no—
301C22×C4#62611yescharacteristic
302Q16—92no—
303Q16—181no—
304SD16—184no—
305D8—34no—
306D8—62no—
307D8—64no—
308D8—92no—
309D8—181no—
310C2×C8#62611yescharacteristic
311C2×C8#62612yes—
312C2×C8C2×D3211yescharacteristic
313C2×C8C2×D3212yes—
314C16—34no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—42no—
320C22×C3—124no—
321C22×C3—248no—
322C22×C3—244no—
323C22×C3C2×D2412yes—
324C22×C3C2×D2411yescharacteristic
325C22×C3C2×#21312yes—
326C22×C3C2×#21311yescharacteristic
327C2×D3—44no—
328C2×D3—88no—
329C2×D3—84no—
330C2×D3—124no—
331C2×D3—122no—
332C2×D3—122no—
333C2×D3—244no—
334C2×D3—242no—
335C2×D3—242no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—22no—
339C3×C4C2×D2411yescharacteristic
340C3×C4C2×D2412yes—
341C3×C4C2×#21311yescharacteristic
342C3×C4C2×#21312yes—
343C3×C4C22×D1211yescharacteristic
344C3×C4C22×#6711yescharacteristic
345Dic3—124no—
346Dic3—122no—
347Dic3—122no—
348C32C2×#50911yescharacteristic, complemented, Sylow
349C23—124no—
350C23—122no—
351C23—244no—
352C23—361no—
353C23#371411yescharacteristic
354Q8—182no—
355Q8—361no—
356D4—64no—
357D4—124no—
358D4—122no—
359D4—182no—
360D4—364no—
361D4—361no—
362C2×C4—361no—
363C2×C4—364no—
364C2×C4#371412yes—
365C2×C4#371411yescharacteristic
366C2×C4C2×#62612yes—
367C2×C4C2×#62611yescharacteristic
368C8C2×#62611yescharacteristic
369C8C2×#62612yes—
370C8C22×D3211yescharacteristic
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—42no—
376C2×C3—244no—
377C2×C3#490812yescomplemented
378C2×C3#514712yescomplemented
379C2×C3C22×D2411yescharacteristic
380C2×C3C22×#21311yescharacteristic
381D3—84no—
382D3—244no—
383D3—242no—
384D3—242no—
385C22—22no—
386C22—124no—
387C22—248no—
388C22—244no—
389C22—362no—
390C22—722no—
391C22C2×#371412yes—
392C22C2×#371411yescharacteristic
393C4—362no—
394C4C2×#371412yes—
395C4C2×#371411yescharacteristic
396C4C22×#62611yescharacteristic
397C3—21no—
398C3C2×#490811yescharacteristic, complemented
399C3C2×#514711yescharacteristic, complemented
400C2—22no—
401C2—244no—
402C2—722no—
403C2#1059063312yesdirect product factor
404C2C22×#371411yescharacteristic
subgroupG/H
centerC22C2×#3714
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC22×C32×C8C22
socleC22×C32C2×D8
hypercenterC22×C8D32
hypocenterC32C2×#509
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C22×C3×D24C2semidirect
3. C2×C3×#812C2semidirect
4. C2×#63548C2semidirect
5. #10590633C2direct (N × H)
6. C2×#63546C2semidirect
12. C2×#3746C22semidirect
14. #64113C22semidirect
15. C2×#3745C22semidirect
20. C2×C3×D24C22semidirect
21. C3×#812C22semidirect
22. C2×C3×C3⋊C16C22semidirect
23. #63548C22semidirect
24. #63546C22semidirect
29. C22×D24D3semidirect
34. C2×#812D3semidirect
55. #3746C23semidirect
57. #3745C23semidirect
62. C3×C3⋊C16C23semidirect
91. C2×D24C2×D3semidirect
99. #812C2×D3semidirect
100. C2×C3⋊C16C2×D3semidirect
196. C3⋊C16C22×D3semidirect
286. C2×C32#509semidirect
348. C32C2×#509semidirect
377. C2×C3#4908semidirect
378. C2×C3#5147semidirect
398. C3C2×#4908semidirect
399. C3C2×#5147semidirect
403. C2#10590633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641132
C22×C3×D242
C2×C3×#8122
C2×#635482
#105906332
C2×#635462
C2×#51473
C2×#49083