Finite Group Databasebeta

← #11922308

Subgroups — #11922308

Order 1152.

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

normal subgroups only

This group has 407 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#10593202C212yesmaximal, complemented
5#10593196C212yesmaximal, complemented
6#85363—31nomaximal
7#78823—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#63869—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#5391—32no—
21#5389—32no—
22C3×#416—31no—
23#5232—31no—
24C2×#818—31no—
25#5102—31no—
26#4995—31no—
27#4796—32no—
28#4793—32no—
29#4766—32no—
30#4759—32no—
31C3×#41⋊C3Q812yescomplemented
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C4⋊(C3⋊Dic3)—41no—
34C3×C4⋊Dic3—41no—
35C3×C4×Dic3—41no—
36#3724—42no—
37Dic3⋊Dic3—42no—
38#3083—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#890—121no—
52#888—32no—
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#818—32no—
68#818—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#544—91no—
80#520—31no—
81#479—92no—
82#478—92no—
83#477—92no—
84#474—92no—
85#428—91no—
86C2×#107—91no—
87#424—91no—
88#417—91no—
89#416—31no—
90C3×#41—32no—
91C3×#41Dic612yes—
92C2×C3×Q8C22×D311yescharacteristic
93C2×C3×D4—31no—
94C22×C3×C4—31no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C2×Dic6—62no—
98#41⋊C3—22no—
99#41⋊C3Dic612yescomplemented
100C2×SL(2,𝔽3)—21no—
101C2×SL(2,𝔽3)C22×D311yescharacteristic
102C2×C3×C8—31no—
103C2×C3×C8—31no—
104C2×C3×C8—62no—
105C3×C4⋊C4—31no—
106C3×C4⋊C4—31no—
107C3×C4⋊C4—121no—
108C3×C22⋊C4—61no—
109C3×C42—61no—
110#217—32no—
111C4⋊Dic3—31no—
112C4⋊Dic3—32no—
113C4⋊Dic3—32no—
114C4⋊Dic3—62no—
115C4⋊Dic3—61no—
116C4⋊Dic3—122no—
117C4⋊Dic3—121no—
118C4⋊Dic3—241no—
119C4⋊Dic3S411yescharacteristic
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—122no—
123C4×Dic3—32no—
124C4×Dic3—41no—
125#208—62no—
126C2×C3⋊C8—32no—
127C22×C32—41no—
128C32×C4—42no—
129C3⋊Dic3—82no—
130C3×Dic3—82no—
131C3×Dic3—81no—
132C3×Dic3—81no—
133C2×#41D3211yescharacteristic
134C2×M16—91no—
135C22×C8—31no—
136C4⋊Q8—92no—
137C4⋊Q8—181no—
138#125—92no—
139#125—181no—
140C22⋊Q8—182no—
141C4×Q8—32no—
142C4×D4—92no—
143#117—31no—
144#117—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—91no—
147#107—92no—
148#107—92no—
149#107—92no—
150#106—92no—
151C4⋊C8—92no—
152C4⋊C8—92no—
153#103—31no—
154#103—31no—
155#103—92no—
156#102—31no—
157#102—31no—
158#102—92no—
159C23×C3—31no—
160C3×Q8—31no—
161C3×Q8C2×Dic611yescharacteristic
162C3×D4—32no—
163C3×D4—61no—
164C2×C3×C4—31no—
165C2×C3×C4—32no—
166C2×C3×C4—32no—
167C2×C3×C4—41no—
168C2×C3×C4—61no—
169C2×C3×C4—61no—
170C2×C3×C4—81no—
171C2×C3×C4—122no—
172C2×C3×C4C2×S411yescharacteristic
173C2×Dic3—32no—
174C2×Dic3—41no—
175C2×Dic3—41no—
176C2×Dic3—62no—
177C2×Dic3—122no—
178C2×Dic3—242no—
179C2×Dic3—241no—
180C2×Dic3—241no—
181C2×Dic3C2×S412yes—
182Dic6—242no—
183SL(2,𝔽3)—21no—
184SL(2,𝔽3)C2×Dic611yescharacteristic
185C3×C8—61no—
186C3×C8—61no—
187C3⋊C8—62no—
188C2×C32—41no—
189C2×C32—41no—
190C2×C32—41no—
191#41—32no—
192#41#62712yes—
193C2×Q8—182no—
194C2×Q8C2×D3211yescharacteristic
195C2×D4—31no—
196C22×C4—31no—
197C22×C4—181no—
198C22×C4—181no—
199M16—182no—
200C2×C8—31no—
201C2×C8—31no—
202C2×C8—62no—
203C2×C8—92no—
204C4⋊C4—31no—
205C4⋊C4—31no—
206C4⋊C4—31no—
207C4⋊C4—92no—
208C4⋊C4—92no—
209C4⋊C4—91no—
210C4⋊C4—182no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C4⋊C4—181no—
214C22⋊C4—61no—
215C22⋊C4—92no—
216C42—61no—
217C42—92no—
218C22×C3—32no—
219C22×C3—41no—
220C22×C3—61no—
221C22×C3—61no—
222C22×C3—81no—
223C22×C3C22×S411yescharacteristic
224C3×C4—31no—
225C3×C4—31no—
226C3×C4—42no—
227C3×C4—82no—
228C3×C4—121no—
229C3×C4—121no—
230C3×C4—242no—
231C3×C4A4⋊Q812yes—
232Dic3—22no—
233Dic3—62no—
234Dic3—81no—
235Dic3—81no—
236Dic3—122no—
237Dic3—242no—
238Dic3—482no—
239C32—41noSylow
240C23—31no—
241Q8—31no—
242Q8—722no—
243Q8C2×#62711yescharacteristic
244D4—32no—
245D4—61no—
246C2×C4—31no—
247C2×C4—32no—
248C2×C4—32no—
249C2×C4—32no—
250C2×C4—61no—
251C2×C4—61no—
252C2×C4—92no—
253C2×C4—182no—
254C2×C4—721no—
255C2×C4—721no—
256C2×C4D3×S411yescharacteristic
257C8—61no—
258C8—61no—
259C8—182no—
260C2×C3—41no—
261C2×C3—41no—
262C2×C3—41no—
263C2×C3—62no—
264C2×C3—81no—
265C2×C3—81no—
266C2×C3—81no—
267C2×C3C2×A4⋊Q811yescharacteristic
268C2×C3#592511yescharacteristic
269C2×C3#592711yescharacteristic
270C22—32no—
271C22—61no—
272C22—61no—
273C22C2×D3×S411yescharacteristic
274C4—31no—
275C4—31no—
276C4—62no—
277C4—121no—
278C4—121no—
279C4—182no—
280C4—362no—
281C4#6420412yes—
282C3—41no—
283C3—81no—
284C3#8536311yescharacteristic, complemented
285C2—62no—
286C2#1059644911yescharacteristic
287C2#1059645211yescharacteristic
288C2C2×#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. #10593202C2semidirect
5. #10593196C2semidirect
31. C3×#41⋊C3Q8semidirect
99. #41⋊C3Dic6semidirect
284. C3#85363semidirect

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
#105932022
#105931962
#853633
#788233
#638694