Finite Group Databasebeta

← C2×#10593198 #11922094

Subgroups — C2×#10593198 #11922094

Order 1152.

585 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 585 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#226C211yesmaximal, characteristic
2C2×Dic3×SL(2,𝔽3)C211yesmaximal, characteristic
3C2×C3⋊#859C211yesmaximal, characteristic
4#10593198C214yesmaximal, direct product factor
5C2×#5388—31nomaximal
6C2×#5184—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3×#226C414yescomplemented
9C2×C3×#226C2212yes—
10C2×Dic3⋊Dic3—41nomaximal
11Dic3×SL(2,𝔽3)C2212yes—
12C3⋊#859C2212yes—
13C22×#226D311yescharacteristic
14C22×C3×Q16—31no—
15C2×Q8×Dic3—31no—
16C2×Q8×Dic3D311yescharacteristic
17C2×C4×SL(2,𝔽3)—31no—
18C2×#859—31no—
19C2×#859—61no—
20#5388—34no—
21C2×#835—31no—
22C2×#835—31no—
23#5184—34no—
24#5184—34no—
25C2×#817—31no—
26C2×#815—31no—
27C22×C3⋊Dic3—41no—
28C22×C3×Dic3—41no—
29C22×C3×Dic3—41no—
30C2×C3×SL(2,𝔽3)C2×C412yes—
31C2×C3×SL(2,𝔽3)C2311yescharacteristic
32C3×#226C2×C414yescomplemented
33Dic3⋊Dic3—44no—
34C2×#441—91noSylow
35C22×C3×Q8—31no—
36C22×C3×Q8C2×D311yescharacteristic
37C22×SL(2,𝔽3)—21no—
38C22×SL(2,𝔽3)C2×D311yescharacteristic
39C2×#226Dic314yescomplemented
40C2×#226C2×D312yes—
41C2×C3×Q16—34no—
42C2×C3×Q16—32no—
43C2×C3×Q16—34no—
44C2×C3×Q16—32no—
45C22×C3×C8—31no—
46Q8×Dic3—32no—
47Q8×Dic3—34no—
48Q8×Dic3—62no—
49Q8×Dic3C2×D312yes—
50C2×C4⋊Dic3—31no—
51C2×C4⋊Dic3—31no—
52C2×C4⋊Dic3—61no—
53C2×Dic3⋊C4—121no—
54C2×C4×Dic3—31no—
55C2×C4×Dic3—61no—
56C22×C3⋊C8—31no—
57C4×SL(2,𝔽3)—32no—
58#859—32no—
59#859—62no—
60#835—34no—
61#835—32no—
62#835—32no—
63#817—34no—
64#815—34no—
65C23×C32—41no—
66C2×C3⋊Dic3—42no—
67C2×C3⋊Dic3—82no—
68C2×C3×Dic3—42no—
69C2×C3×Dic3—44no—
70C2×C3×Dic3—42no—
71C2×C3×Dic3—82no—
72C3×SL(2,𝔽3)C22×C411yescharacteristic
73C22×Q16—31no—
74C2×C4×Q8—31no—
75C2×C4×Q8—91no—
76#441—94no—
77#441—94no—
78C2×#106—91no—
79C2×#103—91no—
80C2×#103—91no—
81C2×#97—91no—
82C2×C3×Q8—31no—
83C2×C3×Q8—32no—
84C2×C3×Q8—32no—
85C2×C3×Q8—34no—
86C2×C3×Q8—61no—
87C2×C3×Q8—62no—
88C2×C3×Q8C4×D312yes—
89C2×C3×Q8C22×D311yescharacteristic
90C22×C3×C4—31no—
91C22×C3×C4—61no—
92C22×C3×C4—121no—
93C22×Dic3—31no—
94C22×Dic3—41no—
95C22×Dic3—61no—
96C22×Dic3—121no—
97C22×Dic3—241no—
98C22×Dic3S411yescharacteristic
99C2×SL(2,𝔽3)—22no—
100C2×SL(2,𝔽3)—21no—
101C2×SL(2,𝔽3)C2×Dic312yes—
102C2×SL(2,𝔽3)C22×D311yescharacteristic
103#226C2×Dic314yescomplemented
104C3×Q16—38no—
105C3×Q16—34no—
106C3×Q16—34no—
107C2×C3×C8—32no—
108C2×C3×C8—34no—
109C4⋊Dic3—32no—
110C4⋊Dic3—32no—
111C4⋊Dic3—61no—
112C4⋊Dic3—61no—
113C4⋊Dic3—64no—
114Dic3⋊C4—124no—
115C4×Dic3—32no—
116C4×Dic3—32no—
117C4×Dic3—64no—
118C2×C3⋊C8—32no—
119C2×C3⋊C8—62no—
120C22×C32—42no—
121C22×C32—42no—
122C22×C32—42no—
123C22×C32—41no—
124C3⋊Dic3—82no—
125C3×Dic3—44no—
126C3×Dic3—82no—
127C22×Q8—31no—
128C22×Q8D3211yescharacteristic
129C2×Q16—32no—
130C2×Q16—34no—
131C2×Q16—34no—
132C2×Q16—32no—
133C22×C8—31no—
134C22×C8—91no—
135C4×Q8—32no—
136C4×Q8—92no—
137C4×Q8—94no—
138C4×Q8—182no—
139C2×C4⋊C4—91no—
140C2×C4⋊C4—91no—
141C2×C4⋊C4—181no—
142C2×C42—91no—
143C2×C42—181no—
144#106—94no—
145#103—94no—
146#103—92no—
147#103—92no—
148#97—94no—
149C23×C3—41no—
150C23×C3—81no—
151C23×C3C2×S411yescharacteristic
152C3×Q8—32no—
153C3×Q8—31no—
154C3×Q8—34no—
155C3×Q8—61no—
156C3×Q8—62no—
157C3×Q8—64no—
158C3×Q8C2×C4×D311yescharacteristic
159C2×C3×C4—32no—
160C2×C3×C4—32no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—64no—
164C2×C3×C4—62no—
165C2×C3×C4—122no—
166C2×C3×C4—242no—
167C2×Dic3—22no—
168C2×Dic3—32no—
169C2×Dic3—42no—
170C2×Dic3—44no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—122no—
174C2×Dic3—122no—
175C2×Dic3—242no—
176C2×Dic3—242no—
177C2×Dic3—244no—
178C2×Dic3C2×S412yes—
179SL(2,𝔽3)—21no—
180SL(2,𝔽3)C22×Dic311yescharacteristic
181C3×C8—34no—
182C3⋊C8—62no—
183C2×C32—44no—
184C2×C32—41no—
185C2×C32—41no—
186C2×C32—41no—
187C2×Q8—31no—
188C2×Q8—32no—
189C2×Q8—32no—
190C2×Q8—34no—
191C2×Q8—61no—
192C2×Q8—62no—
193C2×Q8D3×Dic312yes—
194C2×Q8C2×D3211yescharacteristic
195C22×C4—31no—
196C22×C4—31no—
197C22×C4—61no—
198C22×C4—91no—
199C22×C4—181no—
200Q16—38no—
201Q16—34no—
202Q16—34no—
203C2×C8—32no—
204C2×C8—34no—
205C2×C8—92no—
206C2×C8—182no—
207C4⋊C4—92no—
208C4⋊C4—92no—
209C4⋊C4—184no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C42—92no—
213C42—92no—
214C42—184no—
215C22×C3—41no—
216C22×C3—42no—
217C22×C3—42no—
218C22×C3—42no—
219C22×C3—81no—
220C22×C3—82no—
221C22×C3—82no—
222C22×C3—82no—
223C22×C3C4×S412yes—
224C22×C3#98312yes—
225C22×C3#98412yes—
226C22×C3C22×S411yescharacteristic
227C3×C4—31no—
228C3×C4—31no—
229C3×C4—32no—
230C3×C4—64no—
231C3×C4—242no—
232Dic3—22no—
233Dic3—44no—
234Dic3—62no—
235Dic3—122no—
236Dic3—242no—
237Dic3—244no—
238C32—41noSylow
239C23D3×S411yescharacteristic
240Q8—32no—
241Q8—31no—
242Q8—34no—
243Q8—61no—
244Q8—62no—
245Q8—64no—
246Q8C2×D3×Dic311yescharacteristic
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—32no—
250C2×C4—32no—
251C2×C4—32no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—64no—
255C2×C4—92no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—362no—
259C8—34no—
260C8—182no—
261C2×C3—41no—
262C2×C3—41no—
263C2×C3—41no—
264C2×C3—44no—
265C2×C3—81no—
266C2×C3—81no—
267C2×C3—81no—
268C2×C3—84no—
269C2×C3#538814yescomplemented
270C2×C3C2×C4×S411yescharacteristic
271C2×C3C2×#98311yescharacteristic
272C2×C3C2×#98411yescharacteristic
273C22#6419612yes—
274C22#6420212yes—
275C22Dic3×S412yes—
276C22C2×D3×S411yescharacteristic
277C4—31no—
278C4—31no—
279C4—32no—
280C4—62no—
281C4—64no—
282C4—182no—
283C4—362no—
284C3—41no—
285C3—81no—
286C3C2×#538811yescharacteristic, complemented
287C2#1059319814yesdirect product factor
288C2C2×#6419611yescharacteristic
289C2C2×#6420211yescharacteristic
290C2C2×Dic3×S411yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
prime radicalC22×C3×SL(2,𝔽3)C22
cosocleC2×C3×SL(2,𝔽3)C23
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
4. #10593198C2direct (N × H)
8. C2×C3×#226C4semidirect
32. C3×#226C2×C4semidirect
39. C2×#226Dic3semidirect
103. #226C2×Dic3semidirect
269. C2×C3#5388semidirect
286. C3C2×#5388semidirect
287. C2#10593198direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2262
C2×Dic3×SL(2,𝔽3)2
C2×C3⋊#8592
#105931982
C2×#53883
C2×#51843
C2×Dic3⋊Dic34