Finite Group Databasebeta

← C2×#10593212 #11922122

Subgroups — C2×#10593212 #11922122

Order 1152.

569 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 569 conjugacy classes of subgroups — too many to draw. Only its 83 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#10593212C214yesmaximal, direct product factor
5C2×#5386—31nomaximal
6C2×#4791—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C22×#627—41nomaximal
9Dic3×SL(2,𝔽3)C2212yes—
10C3⋊#859C2212yes—
11C3×#859C2212yes—
12C2×Q8×Dic3D311yescharacteristic
13C2×#888—31no—
14C2×C4×SL(2,𝔽3)—31no—
15C2×#859—31no—
16C2×#859—61no—
17C2×#859D311yescharacteristic
18#5386—34no—
19C2×C3×#103—31no—
20C2×#835—31no—
21C2×#817—31no—
22C2×Dic3⋊C8—31no—
23C2×#808—31no—
24#4791—34no—
25#4791—34no—
26C22×C3⋊Dic3—41no—
27C22×C3×Dic3—41no—
28C22×C3×Dic3—41no—
29C2×C3×SL(2,𝔽3)Q812yescomplemented
30C2×C3×SL(2,𝔽3)C2311yescharacteristic
31C2×#627—44no—
32C2×#627—48no—
33C2×#475—91noSylow
34C22×C3×Q8C2×D311yescharacteristic
35C22×Dic6—61no—
36C22×Dic6—121no—
37C22×SL(2,𝔽3)—21no—
38C22×SL(2,𝔽3)C2×D311yescharacteristic
39C22×C3×C8—31no—
40C2×C3×C4⋊C4—31no—
41Q8×Dic3—32no—
42Q8×Dic3C2×D312yes—
43C2×C4⋊Dic3—31no—
44C2×C4⋊Dic3—31no—
45C2×Dic3⋊C4—61no—
46C2×C4×Dic3—31no—
47C22×C3⋊C8—31no—
48#888—34no—
49#888—62no—
50C4×SL(2,𝔽3)—32no—
51#859—32no—
52#859—62no—
53#859C2×D312yes—
54C3×#103—32no—
55C3×#103—32no—
56#835—32no—
57#835—32no—
58#817—34no—
59Dic3⋊C8—34no—
60#808—34no—
61C23×C32—41no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3—44no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—44no—
66C2×C3×Dic3—44no—
67C2×C3×Dic3—42no—
68C3×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
69#627—416no—
70C2×C4⋊Q8—91no—
71C2×C4×Q8—31no—
72#475—94no—
73#475—94no—
74C2×#106—91no—
75C2×#106—91no—
76C2×C4⋊C8—91no—
77C2×#103—31no—
78C2×#103—91no—
79C2×C3×Q8—31no—
80C2×C3×Q8—32no—
81C2×C3×Q8Dic612yescomplemented
82C2×C3×Q8C22×D311yescharacteristic
83C22×C3×C4—31no—
84C22×C3×C4—61no—
85C22×C3×C4—121no—
86C22×Dic3—31no—
87C22×Dic3—41no—
88C22×Dic3—61no—
89C22×Dic3—121no—
90C22×Dic3—241no—
91C22×Dic3S411yescharacteristic
92C2×Dic6—64no—
93C2×Dic6—124no—
94C2×Dic6—128no—
95C2×Dic6—124no—
96C2×SL(2,𝔽3)—22no—
97C2×SL(2,𝔽3)—21no—
98C2×SL(2,𝔽3)Dic612yescomplemented
99C2×SL(2,𝔽3)C22×D311yescharacteristic
100C2×C3×C8—32no—
101C2×C3×C8—62no—
102C3×C4⋊C4—32no—
103C3×C4⋊C4—61no—
104C4⋊Dic3—32no—
105C4⋊Dic3—32no—
106C4⋊Dic3—61no—
107C4⋊Dic3—61no—
108Dic3⋊C4—64no—
109C4×Dic3—32no—
110C4×Dic3—32no—
111C2×C3⋊C8—32no—
112C2×C3⋊C8—62no—
113C22×C32—42no—
114C22×C32—42no—
115C22×C32—42no—
116C22×C32—41no—
117C3⋊Dic3—44no—
118C3×Dic3—44no—
119C3×Dic3—44no—
120C22×Q8—181no—
121C22×Q8D3211yescharacteristic
122C22×C8—31no—
123C22×C8—91no—
124C4⋊Q8—94no—
125C4⋊Q8—182no—
126C4×Q8—32no—
127C4×Q8—92no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—91no—
131C2×C4⋊C4—181no—
132C2×C42—91no—
133#106—94no—
134#106—94no—
135C4⋊C8—94no—
136#103—32no—
137#103—32no—
138#103—92no—
139#103—92no—
140C23×C3—41no—
141C23×C3—81no—
142C23×C3C2×S411yescharacteristic
143C3×Q8—32no—
144C3×Q8—31no—
145C3×Q8—61no—
146C3×Q8C2×Dic611yescharacteristic, complemented
147C2×C3×C4—32no—
148C2×C3×C4—32no—
149C2×C3×C4—31no—
150C2×C3×C4—31no—
151C2×C3×C4—62no—
152C2×C3×C4—122no—
153C2×C3×C4—124no—
154C2×C3×C4—122no—
155C2×Dic3—32no—
156C2×Dic3—42no—
157C2×Dic3—44no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—122no—
161C2×Dic3—124no—
162C2×Dic3—122no—
163C2×Dic3—242no—
164C2×Dic3—244no—
165C2×Dic3GL(2,𝔽3)14yes—
166C2×Dic3C2×S412yes—
167Dic6—1216no—
168Dic6—128no—
169SL(2,𝔽3)—21no—
170SL(2,𝔽3)C2×Dic611yescharacteristic, complemented
171C3×C8—62no—
172C3⋊C8—62no—
173C2×C32—44no—
174C2×C32—41no—
175C2×C32—41no—
176C2×C32—41no—
177C2×Q8—31no—
178C2×Q8—32no—
179C2×Q8—184no—
180C2×Q8—364no—
181C2×Q8#62712yescomplemented
182C2×Q8C2×D3211yescharacteristic
183C22×C4—31no—
184C22×C4—31no—
185C22×C4—61no—
186C22×C4—91no—
187C22×C4—181no—
188C2×C8—32no—
189C2×C8—62no—
190C2×C8—92no—
191C2×C8—182no—
192C4⋊C4—32no—
193C4⋊C4—61no—
194C4⋊C4—92no—
195C4⋊C4—92no—
196C4⋊C4—181no—
197C4⋊C4—181no—
198C4⋊C4—184no—
199C42—92no—
200C42—92no—
201C22×C3—41no—
202C22×C3—42no—
203C22×C3—42no—
204C22×C3—42no—
205C22×C3—81no—
206C22×C3—82no—
207C22×C3—82no—
208C22×C3—82no—
209C22×C3A4⋊Q812yes—
210C22×C3C2×GL(2,𝔽3)12yes—
211C22×C3#98412yes—
212C22×C3C22×S411yescharacteristic
213C3×C4—31no—
214C3×C4—31no—
215C3×C4—32no—
216C3×C4—124no—
217C3×C4—122no—
218Dic3—44no—
219Dic3—62no—
220Dic3—124no—
221Dic3—122no—
222Dic3—244no—
223Dic3C2×GL(2,𝔽3)14yes—
224C32—41noSylow
225C23D3×S411yescharacteristic
226Q8—32no—
227Q8—31no—
228Q8—61no—
229Q8—368no—
230Q8C2×#62711yescharacteristic, complemented
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—32no—
234C2×C4—34no—
235C2×C4—32no—
236C2×C4—32no—
237C2×C4—62no—
238C2×C4—92no—
239C2×C4—122no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4—362no—
243C8—62no—
244C8—182no—
245C2×C3—41no—
246C2×C3—41no—
247C2×C3—41no—
248C2×C3—44no—
249C2×C3—81no—
250C2×C3—81no—
251C2×C3—81no—
252C2×C3—84no—
253C2×C3#538614yescomplemented
254C2×C3C2×A4⋊Q811yescharacteristic
255C2×C3C22×GL(2,𝔽3)11yescharacteristic
256C2×C3C2×#98411yescharacteristic
257C22#6419612yes—
258C22D3×GL(2,𝔽3)12yes—
259C22#6420412yes—
260C22C2×D3×S411yescharacteristic
261C4—34no—
262C4—31no—
263C4—31no—
264C4—32no—
265C4—122no—
266C4—182no—
267C4—362no—
268C3—41no—
269C3—81no—
270C3C2×#538611yescharacteristic, complemented
271C2#1059321214yesdirect product factor
272C2C2×#6419611yescharacteristic
273C2C2×D3×GL(2,𝔽3)11yescharacteristic
274C2C2×#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. #10593212C2direct (N × H)
29. C2×C3×SL(2,𝔽3)Q8semidirect
68. C3×SL(2,𝔽3)C2×Q8semidirect
81. C2×C3×Q8Dic6semidirect
98. C2×SL(2,𝔽3)Dic6semidirect
146. C3×Q8C2×Dic6semidirect
170. SL(2,𝔽3)C2×Dic6semidirect
181. C2×Q8#627semidirect
230. Q8C2×#627semidirect
253. C2×C3#5386semidirect
270. C3C2×#5386semidirect
271. C2#10593212direct (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
#105932122
C2×#53863
C2×#47913
C22×#6274