Finite Group Databasebeta

← #11922354

Subgroups — #11922354

Order 1152.

455 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 455 conjugacy classes of subgroups — too many to draw. Only its 63 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
1Dic3×#41⋊C3C211yesmaximal, characteristic
2#10593660C211yesmaximal, characteristic
3C3×#5426C211yesmaximal, characteristic
4#10593212C212yesmaximal, complemented
5#10593202C212yesmaximal, complemented
6#85337—31nomaximal
7#78870—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#63918—41nomaximal
10Dic3×SL(2,𝔽3)C2211yescharacteristic
11Dic3×SL(2,𝔽3)C2211yescharacteristic
12C3⋊#859C2212yes—
13C3×#859C2212yes—
14Dic3×#41D311yescharacteristic
15C2×#888—31no—
16C4×#41⋊C3—31no—
17#5426—31no—
18#5426—61no—
19#5426D311yescharacteristic
20#5391—32no—
21#5386—32no—
22C3×#417—31no—
23#5232—31no—
24#5121—31no—
25#5118—31no—
26#4964—31no—
27#4793—32no—
28#4791—32no—
29#4761—32no—
30#4759—32no—
31C3×#41⋊C3Q812yescomplemented
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C2×#627—42no—
34C4⋊(C3⋊Dic3)—41no—
35C3×C4⋊Dic3—41no—
36C3×C4×Dic3—41no—
37Dic3⋊Dic3—42no—
38#3079—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C22×Dic6—61no—
41C2×#41⋊C3—21no—
42C2×#41⋊C3C2×D311yescharacteristic
43C2×C3×M16—31no—
44C2×C3×C4⋊C4—31no—
45Q8×Dic3C2×D311yescharacteristic
46Q8×Dic3C2×D311yescharacteristic
47D4×Dic3—31no—
48D4×Dic3—31no—
49#926—31no—
50C2×C4⋊Dic3—31no—
51C2×Dic3⋊C4—61no—
52C2×C4×Dic3—31no—
53C2×#208—31no—
54#888—32no—
55#888—32no—
56#888—61no—
57#888—61no—
58#869—121no—
59C4×SL(2,𝔽3)—31no—
60C4×SL(2,𝔽3)—31no—
61#859—32no—
62#859—62no—
63#859C2×D312yes—
64C3×#103—32no—
65C3×#102—32no—
66#835—32no—
67#832—32no—
68#818—32no—
69#817—32no—
70Dic3⋊C8—32no—
71Dic3⋊C8—32no—
72#808—32no—
73#807—32no—
74C2×C32×C4—41no—
75C2×C3⋊Dic3—42no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—41no—
78C2×C3×Dic3—41no—
79C3×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
80#627—84no—
81C2×C4⋊Q8—91no—
82C4×#41—31no—
83#477—92no—
84#476—92no—
85#475—92no—
86#474—92no—
87#428—91no—
88#428—91no—
89#423—91no—
90#417—31no—
91#417—91no—
92C3×#41—32no—
93C3×#41Dic612yescomplemented
94C2×C3×Q8C22×D311yescharacteristic
95C2×C3×D4—31no—
96C22×C3×C4—31no—
97C22×C3×C4—61no—
98C22×Dic3—31no—
99C22×Dic3—31no—
100C22×Dic3—61no—
101C2×Dic6—62no—
102C2×Dic6—62no—
103C2×Dic6—122no—
104C2×Dic6—124no—
105#41⋊C3—22no—
106#41⋊C3Dic612yescomplemented
107C2×SL(2,𝔽3)—21no—
108C2×SL(2,𝔽3)C22×D311yescharacteristic
109C3×M16—62no—
110C2×C3×C8—32no—
111C3×C4⋊C4—32no—
112C3×C4⋊C4—61no—
113C3×C42—121no—
114#217—61no—
115C4⋊Dic3—31no—
116C4⋊Dic3—31no—
117C4⋊Dic3—32no—
118C4⋊Dic3—41no—
119C4⋊Dic3—61no—
120C4⋊Dic3—122no—
121C4⋊Dic3—121no—
122C4⋊Dic3—241no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125C4×Dic3—31no—
126C4×Dic3—31no—
127C4×Dic3—31no—
128C4×Dic3S411yescharacteristic
129#208—62no—
130C2×C3⋊C8—32no—
131C22×C32—41no—
132C32×C4—42no—
133C3⋊Dic3—82no—
134C3×Dic3—42no—
135C3×Dic3—42no—
136C3×Dic3—82no—
137C2×#41D3211yescharacteristic
138C22×Q8—181no—
139C2×M16—31no—
140C2×M16—91no—
141C4⋊Q8—92no—
142C4⋊Q8—92no—
143C4⋊Q8—181no—
144C4⋊Q8—181no—
145C4×Q8—31no—
146C4×Q8—31no—
147C4×D4—91no—
148C4×D4—91no—
149#117—91no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—91no—
152C2×C4⋊C4—181no—
153C2×C42—91no—
154#107—92no—
155#107—92no—
156#106—92no—
157#106—92no—
158C4⋊C8—92no—
159C4⋊C8—92no—
160#103—32no—
161#103—92no—
162#102—32no—
163#102—92no—
164C23×C3—31no—
165C3×Q8—31no—
166C3×Q8C2×Dic611yescharacteristic
167C3×D4—32no—
168C3×D4—61no—
169C2×C3×C4—31no—
170C2×C3×C4—32no—
171C2×C3×C4—32no—
172C2×C3×C4—41no—
173C2×C3×C4—62no—
174C2×C3×C4—81no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4—122no—
178C2×C3×C4C2×S411yescharacteristic
179C2×Dic3—31no—
180C2×Dic3—31no—
181C2×Dic3—42no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—242no—
188C2×Dic3C2×S411yescharacteristic
189C2×Dic3C2×S411yescharacteristic
190Dic6—124no—
191Dic6—124no—
192Dic6—244no—
193SL(2,𝔽3)—21no—
194SL(2,𝔽3)C2×Dic611yescharacteristic, complemented
195C3×C8—62no—
196C3⋊C8—62no—
197C2×C32—41no—
198C2×C32—41no—
199C2×C32—41no—
200#41—32no—
201#41#62712yescomplemented
202C2×Q8—182no—
203C2×Q8—182no—
204C2×Q8—364no—
205C2×Q8C2×D3211yescharacteristic
206C2×D4—31no—
207C22×C4—31no—
208C22×C4—61no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—181no—
212M16—62no—
213M16—182no—
214C2×C8—32no—
215C2×C8—92no—
216C4⋊C4—32no—
217C4⋊C4—61no—
218C4⋊C4—91no—
219C4⋊C4—91no—
220C4⋊C4—92no—
221C4⋊C4—182no—
222C4⋊C4—182no—
223C4⋊C4—181no—
224C22⋊C4—181no—
225C42—31no—
226C42—91no—
227C42—91no—
228C42—91no—
229C22×C3—32no—
230C22×C3—41no—
231C22×C3—61no—
232C22×C3—61no—
233C22×C3—81no—
234C22×C3C22×S411yescharacteristic
235C3×C4—31no—
236C3×C4—31no—
237C3×C4—42no—
238C3×C4—82no—
239C3×C4—122no—
240C3×C4—122no—
241C3×C4—122no—
242C3×C4A4⋊Q812yes—
243Dic3—61no—
244Dic3—61no—
245Dic3—82no—
246Dic3—122no—
247Dic3—242no—
248Dic3—482no—
249Dic3#98412yes—
250Dic3#98612yes—
251C32—41noSylow
252C23—31no—
253Q8—31no—
254Q8—364no—
255Q8—364no—
256Q8C2×#62711yescharacteristic
257D4—32no—
258D4—61no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—31no—
262C2×C4—32no—
263C2×C4—32no—
264C2×C4—62no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—122no—
268C2×C4—182no—
269C2×C4—182no—
270C2×C4—182no—
271C2×C4—362no—
272C2×C4D3×S411yescharacteristic
273C8—62no—
274C8—182no—
275C2×C3—41no—
276C2×C3—41no—
277C2×C3—41no—
278C2×C3—62no—
279C2×C3—81no—
280C2×C3—81no—
281C2×C3—81no—
282C2×C3C2×A4⋊Q811yescharacteristic
283C2×C3C2×#98411yescharacteristic
284C2×C3C2×#98611yescharacteristic
285C22—32no—
286C22—61no—
287C22—61no—
288C22C2×D3×S411yescharacteristic
289C4—32no—
290C4—32no—
291C4—31no—
292C4—31no—
293C4—122no—
294C4—181no—
295C4—181no—
296C4—362no—
297C4#6420412yes—
298C3—41no—
299C3—81no—
300C3#8533711yescharacteristic, complemented
301C2—62no—
302C2D3×#98411yescharacteristic
303C2D3×#98611yescharacteristic
304C2C2×#6420411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593212C2semidirect
5. #10593202C2semidirect
31. C3×#41⋊C3Q8semidirect
79. C3×SL(2,𝔽3)C2×Q8semidirect
93. C3×#41Dic6semidirect
106. #41⋊C3Dic6semidirect
194. SL(2,𝔽3)C2×Dic6semidirect
201. #41#627semidirect
300. C3#85337semidirect

Maximal subgroups

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

subgroupindex
Dic3×#41⋊C32
#105936602
C3×#54262
#105932122
#105932022
#853373
#788703
#639184