Finite Group Databasebeta

← C2×#10590573 #11858403

Subgroups — C2×#10590573 #11858403

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C2×C3×#807C212yesmaximal, complemented
5C2×#63575C212yesmaximal, complemented
6#10590573C218yesmaximal, direct product factor
7C2×D3×#107—32nomaximal
8C22×C4×C3⋊D3—21no—
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#624—21no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3750—21no—
14C4⋊C4×C3⋊D3—22no—
15C4⋊C4×C3⋊D3C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63900—22no—
20#63900C2214yes—
21C2×#3710C418yescomplemented
22C2×#3710C2214yes—
23C3×#807C2218yescomplemented
24#63575C2218yescomplemented
25C22×D3×C8—32no—
26C2×D3×C4⋊C4—32no—
27C2×D3×C4⋊C4—32no—
28C2×D3×C4⋊C4—61no—
29C2×C3×#107—32no—
30C2×#818—32no—
31C2×#807—32no—
32C2×#807D312yescomplemented
33D3×#107—316no—
34C23×C3⋊D3D411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3—24no—
40C2×C4×C3⋊D3—44no—
41C2×C4×C3⋊D3C2×C414yes—
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3Q814yes—
44C2×C4×C3⋊D3C2312yes—
45C22×C3×Dic3—22no—
46C2×#624—24no—
47C2×#624—44no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2312yes—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)C2312yes—
52#3750—24no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3C2314yes—
55C2×C3×C3⋊C8C2×C418yescomplemented
56C2×C3×C3⋊C8C2314yes—
57#3724—24no—
58#3710C2×C4116yescomplemented
59C22×#107—91noSylow
60C22×C4×D3—32no—
61C22×C4×D3—61no—
62C22×C4×D3—62no—
63C22×C4×D3—62no—
64C22×C4×D3—62no—
65C22×C3×C8—32no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4C2×D312yes—
69C2×C4⋊Dic3—32no—
70C2×C4⋊Dic3—61no—
71C2×C4⋊Dic3C2×D312yes—
72C2×Dic3⋊C4—62no—
73C2×Dic3⋊C4—62no—
74C2×Dic3⋊C4—62no—
75C22×C3⋊C8C2×D312yes—
76C2×D3×C8—316no—
77C2×D3×C8—38no—
78D3×C4⋊C4—38no—
79D3×C4⋊C4—38no—
80D3×C4⋊C4—64no—
81D3×C4⋊C4—64no—
82D3×C4⋊C4—64no—
83D3×C4⋊C4—64no—
84C3×#107—38no—
85#818—38no—
86#807—38no—
87#807C2×D318yescomplemented
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3C4⋊C414yes—
90C22×C3⋊D3D814yes—
91C22×C3⋊D3Q1614yes—
92C22×C3⋊D3C2×D412yes—
93C2×C32×C4—22no—
94C2×C32×C4—42no—
95C2×C32×C4C22×C412yes—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×Q812yes—
98C2×C32×C4C2411yescharacteristic
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—42no—
101C2×C3⋊Dic3C4⋊C414yes—
102C2×C3⋊Dic3C2×D412yes—
103C4×C3⋊D3—48no—
104C4×C3⋊D3C4⋊C418yes—
105C4×C3⋊D3C22×C414yes—
106C4×C3⋊D3C2×Q814yes—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—44no—
109#624—48no—
110C3×C3⋊C8C22×C418yescomplemented
111C23×C8—91no—
112C22×C4⋊C4—91no—
113C22×C4⋊C4—91no—
114C2×#107—32no—
115C2×#107—98no—
116C2×#107—92no—
117C23×D3—32no—
118C23×D3—61no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4C22×D312yes—
124C22×Dic3—22no—
125C22×Dic3—32no—
126C22×Dic3—61no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C2×C4×D3—38no—
130C2×C4×D3—34no—
131C2×C4×D3—38no—
132C2×C4×D3—34no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—68no—
138C2×C4×D3—68no—
139C2×C4×D3—68no—
140C2×C4×D3—128no—
141C2×C4×D3—128no—
142C2×C4×D3—128no—
143C2×C3×C8—38no—
144C2×C3×C8—34no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—34no—
149C3×C4⋊C4—62no—
150C3×C4⋊C4C22×D314yes—
151C4⋊Dic3—22no—
152C4⋊Dic3—34no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156C4⋊Dic3C22×D314yes—
157Dic3⋊C4—68no—
158Dic3⋊C4—68no—
159Dic3⋊C4—68no—
160C2×C3⋊C8C4×D318yescomplemented
161C2×C3⋊C8C22×D314yes—
162D3×C8—332no—
163C22×C32C2×C4⋊C412yes—
164C22×C32C2×D812yes—
165C22×C32C2×Q1612yes—
166C22×C32C22×D411yescharacteristic
167C2×C3⋊D3#107116yescomplemented
168C2×C3⋊D3C2×C4⋊C414yes—
169C2×C3⋊D3C2×D814yes—
170C2×C3⋊D3C2×Q1614yes—
171C32×C4—42no—
172C32×C4C2×C4⋊C412yes—
173C32×C4C23×C411yescharacteristic
174C32×C4C22×Q811yescharacteristic
175C3⋊Dic3—42no—
176C3⋊Dic3C2×C4⋊C414yes—
177C3×Dic3—44no—
178C23×C4—91no—
179C23×C4—181no—
180C23×C4—181no—
181C22×C8—32no—
182C22×C8—98no—
183C22×C8—94no—
184C2×C4⋊C4—32no—
185C2×C4⋊C4—94no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—94no—
188C2×C4⋊C4—182no—
189C2×C4⋊C4—182no—
190C2×C4⋊C4—181no—
191C2×C4⋊C4—181no—
192C2×C4⋊C4D3211yescharacteristic
193#107—38no—
194#107—98no—
195C23×C3—21no—
196C23×C3D3×D412yes—
197C22×D3—38no—
198C22×D3—38no—
199C22×D3—38no—
200C22×D3—34no—
201C22×D3—64no—
202C22×D3—64no—
203C22×D3—64no—
204C22×D3—62no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—44no—
212C2×C3×C4—44no—
213C2×C3×C4—64no—
214C2×C3×C4—124no—
215C2×C3×C4C2×C4×D314yes—
216C2×C3×C4D3×D412yes—
217C2×C3×C4D3×Q814yes—
218C2×C3×C4C23×D312yes—
219C2×Dic3—24no—
220C2×Dic3—38no—
221C2×Dic3—34no—
222C2×Dic3—44no—
223C2×Dic3—64no—
224C2×Dic3—62no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229C4×D3—316no—
230C4×D3—38no—
231C4×D3—38no—
232C4×D3—68no—
233C4×D3—64no—
234C4×D3—64no—
235C4×D3—1216no—
236C4×D3—1216no—
237C4×D3—1216no—
238C3×C8—38no—
239C3⋊C8C2×C4×D318yescomplemented
240C2×C32C2×#10714yescomplemented
241C2×C32C22×C4⋊C411yescharacteristic
242C2×C32C22×D811yescharacteristic
243C2×C32C22×Q1611yescharacteristic
244C3⋊D3C2×#10718yescomplemented
245C24—91no—
246C22×C4—21no—
247C22×C4—62no—
248C22×C4—91no—
249C22×C4—92no—
250C22×C4—94no—
251C22×C4—94no—
252C22×C4—92no—
253C22×C4—184no—
254C22×C4—184no—
255C22×C4—181no—
256C22×C4—364no—
257C22×C4—364no—
258C22×C4C2×D3211yescharacteristic
259C2×C8—34no—
260C2×C8—38no—
261C2×C8—916no—
262C4⋊C4—21no—
263C4⋊C4—34no—
264C4⋊C4—62no—
265C4⋊C4—92no—
266C4⋊C4—184no—
267C4⋊C4—184no—
268C4⋊C4—181no—
269C4⋊C4C2×D3212yes—
270C22×C3—21no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3D3×C4⋊C414yes—
275C22×C3D3×D814yes—
276C22×C3D3×Q1614yes—
277C22×C3C2×D3×D412yes—
278C2×D3—332no—
279C2×D3—38no—
280C2×D3—38no—
281C2×D3—38no—
282C2×D3—64no—
283C2×D3—64no—
284C2×D3—616no—
285C2×D3—64no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—22no—
289C3×C4—44no—
290C3×C4—44no—
291C3×C4—124no—
292C3×C4D3×C4⋊C414yes—
293C3×C4C22×C4×D312yes—
294C3×C4C2×D3×Q812yes—
295Dic3—38no—
296Dic3—44no—
297Dic3—64no—
298Dic3—124no—
299Dic3—124no—
300C32C22×#10711yescharacteristic, complemented, Sylow
301C23—92no—
302C23—94no—
303C23—94no—
304C23—94no—
305C23#381111yescharacteristic
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—64no—
309C2×C4—92no—
310C2×C4—94no—
311C2×C4—94no—
312C2×C4—94no—
313C2×C4—98no—
314C2×C4—124no—
315C2×C4—182no—
316C2×C4—368no—
317C2×C4—368no—
318C2×C4—362no—
319C2×C4#379712yes—
320C2×C4C4×D3212yes—
321C2×C4#381111yescharacteristic
322C2×C4C22×D3211yescharacteristic
323C8—38no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—24no—
328C2×C3D3×#10718yescomplemented
329C2×C3C2×D3×C4⋊C412yes—
330C2×C3C2×D3×D812yes—
331C2×C3C2×D3×Q1612yes—
332D3—316no—
333D3—68no—
334C22—94no—
335C22—94no—
336C22—94no—
337C22—916no—
338C22#6388312yes—
339C22#6392612yes—
340C22#6394412yes—
341C22C2×#381111yescharacteristic
342C4—42no—
343C4—94no—
344C4—124no—
345C4—362no—
346C4#6388312yes—
347C4C2×#379711yescharacteristic
348C4C2×C4×D3211yescharacteristic
349C3—21no—
350C3C2×D3×#10712yescomplemented
351C2—98no—
352C2#1059057314yesdirect product factor
353C2C2×#6388311yescharacteristic
354C2C2×#6392611yescharacteristic
355C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C22×#107
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×#807C2semidirect
5. C2×#63575C2semidirect
6. #10590573C2direct (N × H)
21. C2×#3710C4semidirect
23. C3×#807C22semidirect
24. #63575C22semidirect
32. C2×#807D3semidirect
55. C2×C3×C3⋊C8C2×C4semidirect
58. #3710C2×C4semidirect
87. #807C2×D3semidirect
110. C3×C3⋊C8C22×C4semidirect
160. C2×C3⋊C8C4×D3semidirect
167. C2×C3⋊D3#107semidirect
239. C3⋊C8C2×C4×D3semidirect
240. C2×C32C2×#107semidirect
244. C3⋊D3C2×#107semidirect
300. C32C22×#107semidirect
328. C2×C3D3×#107semidirect
350. C3C2×D3×#107semidirect
352. C2#10590573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639002
C22×#37102
C2×C3×#8072
C2×#635752
#105905732
C2×D3×#1073