Finite Group Databasebeta

← C2×#10593866 #11900846

Subgroups — C2×#10593866 #11900846

Order 1152.

2585 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#869C212yesmaximal, complemented
3C2×#63872C212yesmaximal, complemented
4C2×#63871C214yesmaximal
5C2×#63849C212yesmaximal
6C2×#63843C214yesmaximal, complemented
7#10593866C2116yesmaximal, direct product factor
8C2×#5728—32nomaximal
9C22×C4×C3⋊D3C2212yes—
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2214yes—
12C2×C32×C42C2211yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C42×C3⋊D3C2218yes—
16C2×C3×C4⋊Dic3C2214yes—
17C2×C3×C4⋊Dic3C2214yes—
18C3×#869C22116yescomplemented
19C2×Dic3⋊Dic3C2218yes—
20C2×#3722C2214yes—
21C2×Dic32C2214yes—
22#63872C22116yescomplemented
23#63871C22132yes—
24#63849C22116yes—
25#63843C22132yescomplemented
26C2×C3×C4⋊Q8—32no—
27C2×#946—34no—
28C2×Q8×Dic3—34no—
29#5728—332no—
30C2×#897—34no—
31C2×#892—34no—
32C2×#890—34no—
33C2×#887—34no—
34C2×C42×D3—32no—
35C2×C42×D3—61no—
36C2×#869D312yescomplemented
37C23×C3⋊D3C2311yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3C2312yes—
41C22×C3⋊Dic3C2311yescharacteristic
42C2×C4×C3⋊D3—28no—
43C2×C4×C3⋊D3Q818yescomplemented
44C2×C4×C3⋊D3C2318yes—
45C2×C4×C3⋊D3C2314yes—
46C22×C3×Dic3C2318yes—
47C2×C3×Dic6—216no—
48C2×C3×Dic6C23116yes—
49C32×C42C2314yes—
50C4×C3⋊Dic3C2318yes—
51C4×C3⋊Dic3C2314yes—
52C3×C4⋊Dic3C23116yes—
53C3×C4⋊Dic3C23116yes—
54Dic3⋊Dic3C23132yes—
55#3722C23116yes—
56Dic32C23116yes—
57C2×#533—91noSylow
58C22×C3×Q8—34no—
59C22×C4×D3—32no—
60C22×C4×D3—32no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C22×C4×D3—62no—
64C22×Dic6C2×D314yes—
65C3×C4⋊Q8—316no—
66C2×C3×C4⋊C4—34no—
67C2×C3×C4⋊C4—34no—
68C2×C3×C42—21no—
69C2×C3×C42C2×D312yes—
70#946—332no—
71Q8×Dic3—332no—
72C2×(C2×D3)⋊C4—38no—
73C2×C4⋊Dic3—38no—
74C2×C4⋊Dic3C2×D314yes—
75C2×C4⋊Dic3C2×D314yes—
76C2×Dic3⋊C4—38no—
77C2×C4×Dic3—32no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—38no—
81C2×C4×Dic3—62no—
82C2×C4×Dic3—61no—
83#897—332no—
84#892—332no—
85#890—332no—
86#887—332no—
87C42×D3—316no—
88C42×D3—68no—
89#869C2×D3116yescomplemented
90C23×C32C2411yescharacteristic
91C22×C3⋊D3—24no—
92C22×C3⋊D3C2×Q814yes—
93C22×C3⋊D3C2412yes—
94C2×C32×C4C2×Q814yes—
95C2×C32×C4#4118yes—
96C2×C32×C4C2412yes—
97C2×C32×C4C2414yes—
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3C2×Q814yes—
100C2×C3⋊Dic3C2414yes—
101C2×C3⋊Dic3C2412yes—
102C4×C3⋊D3—216no—
103C4×C3⋊D3C2×Q8116yescomplemented
104C2×C3×Dic3—216no—
105C2×C3×Dic3C24116yes—
106C3×Dic6—232no—
107#533—916no—
108C2×C4⋊Q8—32no—
109C2×#125—92no—
110C2×C22⋊Q8—94no—
111C2×C4×Q8—94no—
112C2×#117—92no—
113C22×C42—91no—
114C23×D3—32no—
115C23×D3—61no—
116C2×C3×Q8—316no—
117C2×C3×Q8—616no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—38no—
121C22×C3×C4C22×D312yes—
122C22×C3×C4C22×D312yes—
123C22×C3×C4C22×D312yes—
124C22×Dic3—32no—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—61no—
128C22×Dic3—62no—
129C22×Dic3C22×D318yes—
130C2×C4×D3—316no—
131C2×C4×D3—38no—
132C2×C4×D3—38no—
133C2×C4×D3—38no—
134C2×C4×D3—64no—
135C2×C4×D3—68no—
136C2×C4×D3—68no—
137C2×C4×D3—616no—
138C2×C4×D3—68no—
139C2×C4×D3—68no—
140C2×Dic6—216no—
141C2×Dic6C22×D3116yes—
142C3×C4⋊C4—316no—
143C3×C4⋊C4—316no—
144C3×C42—24no—
145C3×C42C22×D318yes—
146(C2×D3)⋊C4—332no—
147C4⋊Dic3—332no—
148C4⋊Dic3C22×D3116yes—
149C4⋊Dic3C22×D3116yes—
150Dic3⋊C4—332no—
151C4×Dic3—38no—
152C4×Dic3—38no—
153C4×Dic3—38no—
154C4×Dic3—332no—
155C4×Dic3—68no—
156C4×Dic3—64no—
157C22×C32C22×Q812yes—
158C22×C32C2×#4114yes—
159C22×C32C2511yescharacteristic
160C2×C3⋊D3—28no—
161C2×C3⋊D3—24no—
162C2×C3⋊D3C22×Q814yes—
163C32×C4C22×Q814yes—
164C32×C4C2×#4118yes—
165C3⋊Dic3—24no—
166C3⋊Dic3C22×Q814yes—
167C3×Dic3—216no—
168C22×Q8—34no—
169C23×C4—91no—
170C23×C4—92no—
171C4⋊Q8—316no—
172#125—916no—
173C22⋊Q8—932no—
174C4×Q8—932no—
175#117—916no—
176C2×C4⋊C4—34no—
177C2×C4⋊C4—34no—
178C2×C4⋊C4—98no—
179C2×C22⋊C4—94no—
180C2×C42—94no—
181C2×C42—92no—
182C2×C42—91no—
183C2×C42—98no—
184C2×C42D3211yescharacteristic
185C23×C3—21no—
186C23×C3C23×D312yes—
187C22×D3—38no—
188C22×D3—34no—
189C22×D3—64no—
190C22×D3—62no—
191C22×D3—68no—
192C22×D3—64no—
193C22×D3—64no—
194C3×Q8—632no—
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—28no—
198C2×C3×C4—24no—
199C2×C3×C4—316no—
200C2×C3×C4—616no—
201C2×C3×C4#23718yes—
202C2×C3×C4D3×Q818yes—
203C2×C3×C4#23918yes—
204C2×C3×C4C23×D314yes—
205C2×C3×C4C23×D314yes—
206C2×C3×C4C23×D314yes—
207C2×Dic3—216no—
208C2×Dic3—38no—
209C2×Dic3—34no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—64no—
213C2×Dic3—62no—
214C2×Dic3—64no—
215C2×Dic3—68no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3C23×D3116yes—
219C4×D3—332no—
220C4×D3—616no—
221C4×D3—632no—
222C4×D3—616no—
223C4×D3—616no—
224Dic6—232no—
225C2×C32#53314yescomplemented
226C2×C32C23×Q811yescharacteristic
227C2×C32C22×#4112yes—
228C3⋊D3—24no—
229C24—91no—
230C2×Q8—316no—
231C2×Q8—616no—
232C22×C4—38no—
233C22×C4—91no—
234C22×C4—94no—
235C22×C4—98no—
236C22×C4—92no—
237C22×C4—98no—
238C22×C4—188no—
239C22×C4C2×D3212yes—
240C22×C4C2×D3211yescharacteristic
241C4⋊C4—316no—
242C4⋊C4—316no—
243C4⋊C4—932no—
244C22⋊C4—916no—
245C42—916no—
246C42—98no—
247C42—94no—
248C42C2×D3214yes—
249C22×C3—24no—
250C22×C3—22no—
251C22×C3—21no—
252C22×C3C2×#23714yes—
253C22×C3C2×D3×Q814yes—
254C22×C3C2×#23914yes—
255C22×C3C24×D312yes—
256C2×D3—38no—
257C2×D3—64no—
258C2×D3—68no—
259C2×D3—616no—
260C2×D3—64no—
261C2×D3—64no—
262C2×D3—616no—
263C3×C4—28no—
264C3×C4—24no—
265C3×C4—616no—
266C3×C4C2×#23718yes—
267C3×C4C2×D3×Q818yes—
268C3×C4C2×#23918yes—
269Dic3—216no—
270Dic3—38no—
271Dic3—64no—
272Dic3—68no—
273Dic3—64no—
274Dic3—64no—
275C32C2×#53311yescharacteristic, complemented, Sylow
276C23—94no—
277C23—92no—
278C23—184no—
279C23C22×D3211yescharacteristic
280Q8—632no—
281C2×C4—316no—
282C2×C4—616no—
283C2×C4—94no—
284C2×C4—92no—
285C2×C4—916no—
286C2×C4—94no—
287C2×C4—184no—
288C2×C4—1816no—
289C2×C4#379618yes—
290C2×C4#379714yes—
291C2×C4C22×D3214yes—
292C2×C4C22×D3212yes—
293C2×C3—22no—
294C2×C3—21no—
295C2×C3—24no—
296C2×C3#572818yescomplemented
297C2×C3C22×#23712yes—
298C2×C3C22×D3×Q812yes—
299C2×C3C22×#23912yes—
300D3—68no—
301D3—68no—
302C22—94no—
303C22—184no—
304C22—188no—
305C22C2×#379614yes—
306C22C2×#379712yes—
307C22C23×D3211yescharacteristic
308C4—616no—
309C4—94no—
310C4—184no—
311C4C2×#379618yes—
312C4C2×#379714yes—
313C3—21no—
314C3C2×#572812yescomplemented
315C2—184no—
316C2#1059386614yesdirect product factor
317C2C22×#379612yes—
318C2C22×#379711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#869C2semidirect
3. C2×#63872C2semidirect
6. C2×#63843C2semidirect
7. #10593866C2direct (N × H)
18. C3×#869C22semidirect
22. #63872C22semidirect
25. #63843C22semidirect
36. C2×#869D3semidirect
43. C2×C4×C3⋊D3Q8semidirect
89. #869C2×D3semidirect
103. C4×C3⋊D3C2×Q8semidirect
225. C2×C32#533semidirect
275. C32C2×#533semidirect
296. C2×C3#5728semidirect
314. C3C2×#5728semidirect
316. C2#10593866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×C3×#8692
C2×#638722
C2×#638712
C2×#638492
C2×#638432
#105938662
C2×#57283