Finite Group Databasebeta

← #11922357

Subgroups — #11922357

Order 1152.

419 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 419 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#5827⋊C3C211yesmaximal, characteristic
2#10593660C211yesmaximal, characteristic
3C3×#5424C211yesmaximal, characteristic
4#10593212C212yesmaximal, complemented
5#10593199C212yesmaximal, complemented
6#85361—31nomaximal
7#78824—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#63918—41nomaximal
10Dic3×SL(2,𝔽3)C2212yes—
11C3⋊#859C2212yes—
12C3×#859C2211yescharacteristic
13C3×#859C2211yescharacteristic
14#5827D311yescharacteristic
15#5519—31no—
16#520⋊C3—31no—
17#5426—31no—
18#5426—61no—
19#5424D311yescharacteristic
20#5389—32no—
21#5386—32no—
22C3×#416—31no—
23#5232—31no—
24C2×#817—31no—
25#5102—31no—
26#4995—31no—
27#4799—32no—
28#4791—32no—
29#4763—32no—
30#4761—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#3084—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C2×#41⋊C3—21no—
41C2×#41⋊C3C2×D311yescharacteristic
42C22×C3×C8—31no—
43C3×#117—31no—
44Q8×Dic3C2×D312yes—
45D4×Dic3—32no—
46#926—31no—
47C2×C4⋊Dic3—31no—
48C2×C4⋊Dic3—31no—
49C2×#208—31no—
50#890—32no—
51#888—32no—
52#888—121no—
53#878—62no—
54#870—61no—
55#869—61no—
56C4×SL(2,𝔽3)—32no—
57#859—32no—
58#859—62no—
59#859C2×D311yescharacteristic
60#859C2×D311yescharacteristic
61C3×#103—31no—
62C3×#103—31no—
63C3×#102—31no—
64C3×#102—31no—
65#835—32no—
66#832—32no—
67#817—32no—
68#817—32no—
69Dic3⋊C8—32no—
70Dic3⋊C8—32no—
71#808—32no—
72#807—32no—
73C2×C32×C4—41no—
74C2×C3⋊Dic3—42no—
75C2×C3×Dic3—41no—
76C2×C3×Dic3—41no—
77C2×C3×Dic3—42no—
78C3×SL(2,𝔽3)C2×Q811yescharacteristic
79#627—84no—
80#544—91no—
81#520—31no—
82#479—92no—
83#478—92no—
84#476—92no—
85#475—92no—
86#428—91no—
87C2×#106—91no—
88#424—91no—
89#417—91no—
90#416—31no—
91C3×#41—32no—
92C3×#41Dic612yescomplemented
93C2×C3×Q8C22×D311yescharacteristic
94C2×C3×D4—31no—
95C22×C3×C4—31no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C2×Dic6—62no—
99C2×Dic6—122no—
100#41⋊C3—22no—
101#41⋊C3Dic612yescomplemented
102C2×SL(2,𝔽3)—21no—
103C2×SL(2,𝔽3)C22×D311yescharacteristic
104C2×C3×C8—31no—
105C2×C3×C8—31no—
106C2×C3×C8—62no—
107C3×C4⋊C4—31no—
108C3×C4⋊C4—31no—
109C3×C4⋊C4—121no—
110C3×C22⋊C4—61no—
111C3×C42—61no—
112#217—32no—
113C4⋊Dic3—31no—
114C4⋊Dic3—32no—
115C4⋊Dic3—32no—
116C4⋊Dic3—61no—
117C4⋊Dic3—62no—
118C4⋊Dic3—121no—
119C4⋊Dic3—241no—
120C4⋊Dic3S411yescharacteristic
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—122no—
124C4×Dic3—32no—
125C4×Dic3—41no—
126#208—62no—
127C2×C3⋊C8—32no—
128C22×C32—41no—
129C32×C4—42no—
130C3⋊Dic3—82no—
131C3×Dic3—42no—
132C3×Dic3—42no—
133C3×Dic3—82no—
134C2×#41D3211yescharacteristic
135C2×M16—91no—
136C22×C8—31no—
137C4⋊Q8—92no—
138C4⋊Q8—181no—
139#125—92no—
140#125—181no—
141C22⋊Q8—182no—
142C4×Q8—32no—
143C4×D4—92no—
144#117—31no—
145#117—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148#107—92no—
149#106—92no—
150#106—92no—
151#106—92no—
152C4⋊C8—92no—
153C4⋊C8—92no—
154#103—31no—
155#103—31no—
156#103—92no—
157#102—31no—
158#102—31no—
159#102—92no—
160C23×C3—31no—
161C3×Q8—31no—
162C3×Q8C2×Dic611yescharacteristic
163C3×D4—32no—
164C3×D4—61no—
165C2×C3×C4—31no—
166C2×C3×C4—32no—
167C2×C3×C4—32no—
168C2×C3×C4—41no—
169C2×C3×C4—61no—
170C2×C3×C4—61no—
171C2×C3×C4—81no—
172C2×C3×C4—122no—
173C2×C3×C4C2×S411yescharacteristic
174C2×Dic3—32no—
175C2×Dic3—41no—
176C2×Dic3—41no—
177C2×Dic3—62no—
178C2×Dic3—122no—
179C2×Dic3—242no—
180C2×Dic3—241no—
181C2×Dic3—241no—
182C2×Dic3C2×S412yes—
183Dic6—242no—
184Dic6—244no—
185SL(2,𝔽3)—21no—
186SL(2,𝔽3)C2×Dic611yescharacteristic
187C3×C8—61no—
188C3×C8—61no—
189C3⋊C8—62no—
190C2×C32—41no—
191C2×C32—41no—
192C2×C32—41no—
193#41—32no—
194#41#62712yescomplemented
195C2×Q8—182no—
196C2×Q8C2×D3211yescharacteristic
197C2×D4—31no—
198C22×C4—31no—
199C22×C4—181no—
200C22×C4—181no—
201M16—182no—
202C2×C8—31no—
203C2×C8—31no—
204C2×C8—62no—
205C2×C8—92no—
206C4⋊C4—31no—
207C4⋊C4—31no—
208C4⋊C4—31no—
209C4⋊C4—92no—
210C4⋊C4—92no—
211C4⋊C4—91no—
212C4⋊C4—182no—
213C4⋊C4—182no—
214C4⋊C4—182no—
215C4⋊C4—181no—
216C22⋊C4—61no—
217C22⋊C4—92no—
218C42—61no—
219C42—92no—
220C22×C3—32no—
221C22×C3—41no—
222C22×C3—61no—
223C22×C3—61no—
224C22×C3—81no—
225C22×C3C22×S411yescharacteristic
226C3×C4—31no—
227C3×C4—31no—
228C3×C4—42no—
229C3×C4—82no—
230C3×C4—121no—
231C3×C4—121no—
232C3×C4—242no—
233C3×C4A4⋊Q812yes—
234Dic3—22no—
235Dic3—42no—
236Dic3—42no—
237Dic3—62no—
238Dic3—122no—
239Dic3—242no—
240Dic3—482no—
241C32—41noSylow
242C23—31no—
243Q8—31no—
244Q8—722no—
245Q8C2×#62711yescharacteristic
246D4—32no—
247D4—61no—
248C2×C4—31no—
249C2×C4—32no—
250C2×C4—32no—
251C2×C4—32no—
252C2×C4—61no—
253C2×C4—61no—
254C2×C4—92no—
255C2×C4—182no—
256C2×C4—721no—
257C2×C4—721no—
258C2×C4D3×S411yescharacteristic
259C8—61no—
260C8—61no—
261C8—182no—
262C2×C3—41no—
263C2×C3—41no—
264C2×C3—41no—
265C2×C3—62no—
266C2×C3—81no—
267C2×C3—81no—
268C2×C3—81no—
269C2×C3C2×A4⋊Q811yescharacteristic
270C2×C3#592411yescharacteristic
271C2×C3#592611yescharacteristic
272C22—32no—
273C22—61no—
274C22—61no—
275C22C2×D3×S411yescharacteristic
276C4—31no—
277C4—31no—
278C4—62no—
279C4—121no—
280C4—121no—
281C4—182no—
282C4—362no—
283C4#6420412yes—
284C3—41no—
285C3—81no—
286C3#8536111yescharacteristic, complemented
287C2—62no—
288C2#1059644711yescharacteristic
289C2#1059645911yescharacteristic
290C2C2×#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. #10593199C2semidirect
31. C3×#41⋊C3Q8semidirect
92. C3×#41Dic6semidirect
101. #41⋊C3Dic6semidirect
194. #41#627semidirect
286. C3#85361semidirect

Maximal subgroups

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

subgroupindex
#5827⋊C32
#105936602
C3×#54242
#105932122
#105931992
#853613
#788243
#639184