Finite Group Databasebeta

← C2×#10593195 #11922090

Subgroups — C2×#10593195 #11922090

Order 1152.

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

normal subgroups only

This group has 593 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
1C22×C3⋊#226C211yesmaximal, characteristic
2C2×Dic3×SL(2,𝔽3)C211yesmaximal, characteristic
3C2×C3×#859C211yesmaximal, characteristic
4#10593195C214yesmaximal, direct product factor
5C2×#5388—31nomaximal
6C2×#4789—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3⋊#226C414yescomplemented
9C2×C3⋊#226C2212yes—
10C2×#3724—41nomaximal
11Dic3×SL(2,𝔽3)C2212yes—
12C3×#859C2212yes—
13C22×#226—31no—
14C22×#226—61no—
15C2×Q8×Dic3D311yescharacteristic
16C22×#216—31no—
17C2×#887—31no—
18C2×C4×SL(2,𝔽3)—31no—
19C2×#859D311yescharacteristic
20#5388—34no—
21C2×C3×#103—31no—
22C2×#816—31no—
23C2×#815—31no—
24C2×#808—31no—
25#4789—34no—
26#4789—34no—
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
33#3724—44no—
34C2×#441—91noSylow
35C22×C3×Q8C2×D311yescharacteristic
36C22×Dic6—31no—
37C22×SL(2,𝔽3)—21no—
38C22×SL(2,𝔽3)C2×D311yescharacteristic
39C2×#226—34no—
40C2×#226—32no—
41C2×#226—64no—
42C2×#226—62no—
43C22×C3×C8—31no—
44C2×C3×C4⋊C4—31no—
45Q8×Dic3—32no—
46Q8×Dic3C2×D312yes—
47C2×#216—34no—
48C2×#216—32no—
49C2×#216—34no—
50C2×#216—32no—
51C2×C4⋊Dic3—31no—
52C2×Dic3⋊C4—61no—
53C2×Dic3⋊C4—121no—
54C2×C4×Dic3—31no—
55C2×C4×Dic3—61no—
56C22×C3⋊C8—31no—
57#887—34no—
58#887—62no—
59C4×SL(2,𝔽3)—32no—
60#859C2×D312yes—
61C3×#103—32no—
62C3×#103—32no—
63#816—34no—
64#815—34no—
65#808—34no—
66C23×C32—41no—
67C2×C3⋊Dic3—44no—
68C2×C3⋊Dic3—42no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—42no—
71C2×C3×Dic3—82no—
72C2×C3×Dic3—82no—
73C3×SL(2,𝔽3)C22×C411yescharacteristic
74C22×Q16—91no—
75C2×C4×Q8—31no—
76C2×C4×Q8—91no—
77#441—94no—
78#441—94no—
79C2×#106—91no—
80C2×#103—31no—
81C2×#103—91no—
82C2×#97—91no—
83C2×C3×Q8—31no—
84C2×C3×Q8—32no—
85C2×C3×Q8C4×D312yes—
86C2×C3×Q8C22×D311yescharacteristic
87C22×C3×C4—31no—
88C22×C3×C4—61no—
89C22×C3×C4—121no—
90C22×Dic3—31no—
91C22×Dic3—41no—
92C22×Dic3—61no—
93C22×Dic3—121no—
94C22×Dic3—241no—
95C22×Dic3S411yescharacteristic
96C2×Dic6—32no—
97C2×Dic6—34no—
98C2×Dic6—61no—
99C2×Dic6—62no—
100C2×SL(2,𝔽3)—22no—
101C2×SL(2,𝔽3)—21no—
102C2×SL(2,𝔽3)C4×D312yes—
103C2×SL(2,𝔽3)C22×D311yescharacteristic
104#226—34no—
105#226—64no—
106C2×C3×C8—32no—
107C2×C3×C8—62no—
108C3×C4⋊C4—32no—
109C3×C4⋊C4—61no—
110#216—38no—
111#216—34no—
112#216—34no—
113C4⋊Dic3—32no—
114C4⋊Dic3—61no—
115Dic3⋊C4—64no—
116Dic3⋊C4—124no—
117C4×Dic3—32no—
118C4×Dic3—32no—
119C4×Dic3—64no—
120C2×C3⋊C8—32no—
121C2×C3⋊C8—34no—
122C22×C32—42no—
123C22×C32—42no—
124C22×C32—42no—
125C22×C32—41no—
126C3⋊Dic3—44no—
127C3×Dic3—82no—
128C3×Dic3—82no—
129C22×Q8—91no—
130C22×Q8D3211yescharacteristic
131C2×Q16—94no—
132C2×Q16—92no—
133C2×Q16—94no—
134C2×Q16—92no—
135C22×C8—31no—
136C22×C8—91no—
137C4×Q8—32no—
138C4×Q8—92no—
139C4×Q8—94no—
140C4×Q8—182no—
141C2×C4⋊C4—31no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—181no—
144C2×C42—91no—
145C2×C42—181no—
146#106—94no—
147#103—32no—
148#103—32no—
149#103—94no—
150#97—94no—
151C23×C3—41no—
152C23×C3—81no—
153C23×C3C2×S411yescharacteristic
154C3×Q8—32no—
155C3×Q8—31no—
156C3×Q8—61no—
157C3×Q8C2×C4×D311yescharacteristic
158C2×C3×C4—32no—
159C2×C3×C4—32no—
160C2×C3×C4—31no—
161C2×C3×C4—31no—
162C2×C3×C4—62no—
163C2×C3×C4—122no—
164C2×C3×C4—122no—
165C2×C3×C4—242no—
166C2×Dic3—22no—
167C2×Dic3—32no—
168C2×Dic3—42no—
169C2×Dic3—64no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—82no—
173C2×Dic3—122no—
174C2×Dic3—124no—
175C2×Dic3—242no—
176C2×Dic3—244no—
177C2×Dic3C2×S412yes—
178Dic6—34no—
179Dic6—62no—
180Dic6—64no—
181SL(2,𝔽3)—21no—
182SL(2,𝔽3)C2×C4×D311yescharacteristic
183C3×C8—62no—
184C3⋊C8—34no—
185C2×C32—44no—
186C2×C32—41no—
187C2×C32—41no—
188C2×C32—41no—
189C2×Q8—31no—
190C2×Q8—32no—
191C2×Q8—92no—
192C2×Q8—94no—
193C2×Q8—181no—
194C2×Q8—182no—
195C2×Q8#62412yes—
196C2×Q8C2×D3211yescharacteristic
197C22×C4—31no—
198C22×C4—31no—
199C22×C4—61no—
200C22×C4—91no—
201C22×C4—181no—
202Q16—98no—
203Q16—94no—
204Q16—94no—
205C2×C8—32no—
206C2×C8—62no—
207C2×C8—92no—
208C2×C8—94no—
209C4⋊C4—32no—
210C4⋊C4—61no—
211C4⋊C4—92no—
212C4⋊C4—184no—
213C4⋊C4—181no—
214C42—92no—
215C42—92no—
216C42—184no—
217C22×C3—41no—
218C22×C3—42no—
219C22×C3—42no—
220C22×C3—42no—
221C22×C3—81no—
222C22×C3—82no—
223C22×C3—82no—
224C22×C3—82no—
225C22×C3C4×S412yes—
226C22×C3#98312yes—
227C22×C3#98412yes—
228C22×C3C22×S411yescharacteristic
229C3×C4—31no—
230C3×C4—31no—
231C3×C4—32no—
232C3×C4—122no—
233C3×C4—242no—
234Dic3—22no—
235Dic3—64no—
236Dic3—62no—
237Dic3—82no—
238Dic3—124no—
239Dic3—244no—
240C32—41noSylow
241C23D3×S411yescharacteristic
242Q8—32no—
243Q8—31no—
244Q8—61no—
245Q8—94no—
246Q8—182no—
247Q8—184no—
248Q8C2×#62411yescharacteristic
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—32no—
252C2×C4—32no—
253C2×C4—32no—
254C2×C4—62no—
255C2×C4—62no—
256C2×C4—92no—
257C2×C4—122no—
258C2×C4—182no—
259C2×C4—182no—
260C2×C4—184no—
261C8—62no—
262C8—94no—
263C2×C3—41no—
264C2×C3—41no—
265C2×C3—41no—
266C2×C3—44no—
267C2×C3—81no—
268C2×C3—81no—
269C2×C3—81no—
270C2×C3—84no—
271C2×C3#538814yescomplemented
272C2×C3C2×C4×S411yescharacteristic
273C2×C3C2×#98311yescharacteristic
274C2×C3C2×#98411yescharacteristic
275C22#6419612yes—
276C22#6420112yes—
277C22(C3⋊S4)⋊C412yes—
278C22C2×D3×S411yescharacteristic
279C4—31no—
280C4—31no—
281C4—32no—
282C4—62no—
283C4—122no—
284C4—182no—
285C4—184no—
286C3—41no—
287C3—81no—
288C3C2×#538811yescharacteristic, complemented
289C2#1059319514yesdirect product factor
290C2C2×#6419611yescharacteristic
291C2C2×#6420111yescharacteristic
292C2C2×(C3⋊S4)⋊C411yescharacteristic
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. #10593195C2direct (N × H)
8. C2×C3⋊#226C4semidirect
32. C3⋊#226C2×C4semidirect
271. C2×C3#5388semidirect
288. C3C2×#5388semidirect
289. C2#10593195direct (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
#105931952
C2×#53883
C2×#47893
C2×#37244