Finite Group Databasebeta

← C2×#10593199 #11922096

Subgroups — C2×#10593199 #11922096

Order 1152.

473 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×Dic3×SL(2,𝔽3)C211yesmaximal, characteristic
2C2×C3⋊#859C211yesmaximal, characteristic
3C2×C3×#859C211yesmaximal, characteristic
4#10593199C214yesmaximal, direct product factor
5C2×#5389—31nomaximal
6C2×#4799—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×Dic3⋊Dic3—41nomaximal
9Dic3×SL(2,𝔽3)C2212yes—
10C3⋊#859C2212yes—
11C3×#859C2212yes—
12C2×Q8×Dic3D311yescharacteristic
13C2×#890—31no—
14C2×C4×SL(2,𝔽3)—31no—
15C2×#859—31no—
16C2×#859—61no—
17C2×#859D311yescharacteristic
18#5389—34no—
19C2×C3×#103—31no—
20C2×#835—31no—
21C2×#817—31no—
22C2×Dic3⋊C8—31no—
23C2×#807—31no—
24#4799—34no—
25#4799—34no—
26C22×C3⋊Dic3—41no—
27C22×C3×Dic3—41no—
28C22×C3×Dic3—41no—
29C2×C3×SL(2,𝔽3)Q812yes—
30C2×C3×SL(2,𝔽3)C2311yescharacteristic
31Dic3⋊Dic3—44no—
32C2×#479—91noSylow
33C22×C3×Q8C2×D311yescharacteristic
34C22×SL(2,𝔽3)—21no—
35C22×SL(2,𝔽3)C2×D311yescharacteristic
36C22×C3×C8—31no—
37C2×C3×C4⋊C4—31no—
38Q8×Dic3—32no—
39Q8×Dic3C2×D312yes—
40C2×C4⋊Dic3—31no—
41C2×C4⋊Dic3—31no—
42C2×C4⋊Dic3—61no—
43C2×Dic3⋊C4—61no—
44C2×Dic3⋊C4—121no—
45C2×C4×Dic3—31no—
46C22×C3⋊C8—31no—
47#890—34no—
48#890—62no—
49C4×SL(2,𝔽3)—32no—
50#859—32no—
51#859—62no—
52#859C2×D312yes—
53C3×#103—32no—
54C3×#103—32no—
55#835—32no—
56#835—32no—
57#817—34no—
58Dic3⋊C8—34no—
59#807—34no—
60C23×C32—41no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3—82no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—44no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—82no—
67C3×SL(2,𝔽3)C2×Q811yescharacteristic
68C2×#125—91no—
69C2×C4×Q8—31no—
70#479—94no—
71#479—94no—
72C2×#107—91no—
73C2×#106—91no—
74C2×C4⋊C8—91no—
75C2×#103—31no—
76C2×#103—91no—
77C2×C3×Q8—31no—
78C2×C3×Q8—32no—
79C2×C3×Q8Dic612yes—
80C2×C3×Q8C22×D311yescharacteristic
81C22×C3×C4—31no—
82C22×C3×C4—61no—
83C22×C3×C4—121no—
84C22×Dic3—31no—
85C22×Dic3—41no—
86C22×Dic3—61no—
87C22×Dic3—121no—
88C22×Dic3—241no—
89C22×Dic3S411yescharacteristic
90C2×SL(2,𝔽3)—22no—
91C2×SL(2,𝔽3)—21no—
92C2×SL(2,𝔽3)Dic612yes—
93C2×SL(2,𝔽3)C22×D311yescharacteristic
94C2×C3×C8—32no—
95C2×C3×C8—62no—
96C3×C4⋊C4—32no—
97C3×C4⋊C4—61no—
98C4⋊Dic3—32no—
99C4⋊Dic3—32no—
100C4⋊Dic3—61no—
101C4⋊Dic3—61no—
102C4⋊Dic3—64no—
103Dic3⋊C4—64no—
104Dic3⋊C4—124no—
105C4×Dic3—32no—
106C4×Dic3—32no—
107C2×C3⋊C8—32no—
108C2×C3⋊C8—62no—
109C22×C32—42no—
110C22×C32—42no—
111C22×C32—42no—
112C22×C32—41no—
113C3⋊Dic3—82no—
114C3×Dic3—44no—
115C3×Dic3—82no—
116C22×Q8D3211yescharacteristic
117C22×C8—31no—
118C22×C8—91no—
119#125—94no—
120#125—182no—
121C4×Q8—32no—
122C4×Q8—92no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—91no—
125C2×C4⋊C4—91no—
126C2×C4⋊C4—181no—
127C2×C4⋊C4—181no—
128C2×C42—91no—
129#107—94no—
130#106—94no—
131C4⋊C8—94no—
132#103—32no—
133#103—32no—
134#103—92no—
135#103—92no—
136C23×C3—41no—
137C23×C3—81no—
138C23×C3C2×S411yescharacteristic
139C3×Q8—32no—
140C3×Q8—31no—
141C3×Q8—61no—
142C3×Q8C2×Dic611yescharacteristic
143C2×C3×C4—32no—
144C2×C3×C4—32no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—62no—
148C2×C3×C4—122no—
149C2×C3×C4—122no—
150C2×C3×C4—242no—
151C2×Dic3—22no—
152C2×Dic3—32no—
153C2×Dic3—42no—
154C2×Dic3—44no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—122no—
158C2×Dic3—122no—
159C2×Dic3—242no—
160C2×Dic3—242no—
161C2×Dic3—244no—
162C2×Dic3C2×S412yes—
163SL(2,𝔽3)—21no—
164SL(2,𝔽3)C2×Dic611yescharacteristic
165C3×C8—62no—
166C3⋊C8—62no—
167C2×C32—44no—
168C2×C32—41no—
169C2×C32—41no—
170C2×C32—41no—
171C2×Q8—31no—
172C2×Q8—32no—
173C2×Q8#62712yes—
174C2×Q8C2×D3211yescharacteristic
175C22×C4—31no—
176C22×C4—31no—
177C22×C4—61no—
178C22×C4—91no—
179C22×C4—181no—
180C2×C8—32no—
181C2×C8—62no—
182C2×C8—92no—
183C2×C8—182no—
184C4⋊C4—32no—
185C4⋊C4—61no—
186C4⋊C4—92no—
187C4⋊C4—92no—
188C4⋊C4—184no—
189C4⋊C4—181no—
190C4⋊C4—181no—
191C4⋊C4—184no—
192C42—92no—
193C42—92no—
194C22×C3—41no—
195C22×C3—42no—
196C22×C3—42no—
197C22×C3—42no—
198C22×C3—81no—
199C22×C3—82no—
200C22×C3—82no—
201C22×C3—82no—
202C22×C3A4⋊Q812yes—
203C22×C3#98312yes—
204C22×C3#98512yes—
205C22×C3C22×S411yescharacteristic
206C3×C4—31no—
207C3×C4—31no—
208C3×C4—32no—
209C3×C4—122no—
210C3×C4—242no—
211Dic3—22no—
212Dic3—44no—
213Dic3—62no—
214Dic3—122no—
215Dic3—242no—
216Dic3—244no—
217C32—41noSylow
218C23D3×S411yescharacteristic
219Q8—32no—
220Q8—31no—
221Q8—61no—
222Q8C2×#62711yescharacteristic
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—32no—
226C2×C4—32no—
227C2×C4—32no—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—92no—
231C2×C4—122no—
232C2×C4—182no—
233C2×C4—182no—
234C2×C4—362no—
235C8—62no—
236C8—182no—
237C2×C3—41no—
238C2×C3—41no—
239C2×C3—41no—
240C2×C3—44no—
241C2×C3—81no—
242C2×C3—81no—
243C2×C3—81no—
244C2×C3—84no—
245C2×C3#538914yescomplemented
246C2×C3C2×A4⋊Q811yescharacteristic
247C2×C3C2×#98311yescharacteristic
248C2×C3C2×#98511yescharacteristic
249C22#6419712yes—
250C22#6420212yes—
251C22#6420412yes—
252C22C2×D3×S411yescharacteristic
253C4—31no—
254C4—31no—
255C4—32no—
256C4—62no—
257C4—122no—
258C4—182no—
259C4—362no—
260C3—41no—
261C3—81no—
262C3C2×#538911yescharacteristic, complemented
263C2#1059319914yesdirect product factor
264C2C2×#6419711yescharacteristic
265C2C2×#6420211yescharacteristic
266C2C2×#6420411yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
prime radicalC22×C3×SL(2,𝔽3)C22
hypocenterC3×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
4. #10593199C2direct (N × H)
245. C2×C3#5389semidirect
262. C3C2×#5389semidirect
263. C2#10593199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Dic3×SL(2,𝔽3)2
C2×C3⋊#8592
C2×C3×#8592
#105931992
C2×#53893
C2×#47993
C2×Dic3⋊Dic34