Finite Group Databasebeta

← #11922300

Subgroups — #11922300

Order 1152.

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

normal subgroups only

This group has 411 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
1Dic3×#41⋊C3C211yesmaximal, characteristic
2#10593660C211yesmaximal, characteristic
3C3×#5426C211yesmaximal, characteristic
4#10593199C212yesmaximal, complemented
5#10593196C212yesmaximal, complemented
6#85339—31nomaximal
7#78871—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#63869—41nomaximal
10Dic3×SL(2,𝔽3)C2211yescharacteristic
11Dic3×SL(2,𝔽3)C2211yescharacteristic
12C3⋊#859C2212yes—
13C3×#859C2212yes—
14Dic3×#41D311yescharacteristic
15C2×#890—31no—
16C4×#41⋊C3—31no—
17#5426—31no—
18#5426—61no—
19#5426D311yescharacteristic
20#5389—32no—
21#5389—32no—
22C3×#417—31no—
23#5232—31no—
24#5121—31no—
25#5118—31no—
26#4964—31no—
27#4799—32no—
28#4796—32no—
29#4766—32no—
30#4763—32no—
31C3×#41⋊C3Q812yes—
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#3080—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C2×#41⋊C3—21no—
41C2×#41⋊C3C2×D311yescharacteristic
42C2×C3×M16—31no—
43C2×C3×C4⋊C4—31no—
44Q8×Dic3C2×D311yescharacteristic
45Q8×Dic3C2×D311yescharacteristic
46D4×Dic3—31no—
47D4×Dic3—31no—
48#926—31no—
49C2×C4⋊Dic3—31no—
50C2×C4⋊Dic3—61no—
51C2×Dic3⋊C4—61no—
52C2×C4×Dic3—31no—
53C2×#208—31no—
54#890—32no—
55#890—32no—
56#890—61no—
57#890—61no—
58#870—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
80C2×#125—91no—
81C4×#41—31no—
82#479—92no—
83#479—92no—
84#478—92no—
85#478—92no—
86#428—91no—
87#428—91no—
88#423—91no—
89#417—31no—
90#417—91no—
91C3×#41—32no—
92C3×#41Dic612yes—
93C2×C3×Q8C22×D311yescharacteristic
94C2×C3×D4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—61no—
97C22×Dic3—31no—
98C22×Dic3—31no—
99C22×Dic3—61no—
100#41⋊C3—22no—
101#41⋊C3Dic612yes—
102C2×SL(2,𝔽3)—21no—
103C2×SL(2,𝔽3)C22×D311yescharacteristic
104C3×M16—62no—
105C2×C3×C8—32no—
106C3×C4⋊C4—32no—
107C3×C4⋊C4—61no—
108C3×C42—121no—
109#217—61no—
110C4⋊Dic3—31no—
111C4⋊Dic3—31no—
112C4⋊Dic3—32no—
113C4⋊Dic3—41no—
114C4⋊Dic3—62no—
115C4⋊Dic3—61no—
116C4⋊Dic3—62no—
117C4⋊Dic3—121no—
118C4⋊Dic3—241no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—122no—
122Dic3⋊C4—122no—
123C4×Dic3—31no—
124C4×Dic3—31no—
125C4×Dic3—31no—
126C4×Dic3S411yescharacteristic
127#208—62no—
128C2×C3⋊C8—32no—
129C22×C32—41no—
130C32×C4—42no—
131C3⋊Dic3—82no—
132C3×Dic3—81no—
133C3×Dic3—81no—
134C3×Dic3—82no—
135C2×#41D3211yescharacteristic
136C2×M16—31no—
137C2×M16—91no—
138#125—92no—
139#125—92no—
140#125—181no—
141#125—181no—
142C4×Q8—31no—
143C4×Q8—31no—
144C4×D4—91no—
145C4×D4—91no—
146#117—91no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—181no—
150C2×C4⋊C4—181no—
151C2×C42—91no—
152#107—92no—
153#107—92no—
154#106—92no—
155#106—92no—
156C4⋊C8—92no—
157C4⋊C8—92no—
158#103—32no—
159#103—92no—
160#102—32no—
161#102—92no—
162C23×C3—31no—
163C3×Q8—31no—
164C3×Q8C2×Dic611yescharacteristic
165C3×D4—32no—
166C3×D4—61no—
167C2×C3×C4—31no—
168C2×C3×C4—32no—
169C2×C3×C4—32no—
170C2×C3×C4—41no—
171C2×C3×C4—62no—
172C2×C3×C4—81no—
173C2×C3×C4—121no—
174C2×C3×C4—121no—
175C2×C3×C4—122no—
176C2×C3×C4C2×S411yescharacteristic
177C2×Dic3—31no—
178C2×Dic3—31no—
179C2×Dic3—42no—
180C2×Dic3—62no—
181C2×Dic3—122no—
182C2×Dic3—121no—
183C2×Dic3—121no—
184C2×Dic3—122no—
185C2×Dic3—242no—
186C2×Dic3C2×S411yescharacteristic
187C2×Dic3C2×S411yescharacteristic
188SL(2,𝔽3)—21no—
189SL(2,𝔽3)C2×Dic611yescharacteristic
190C3×C8—62no—
191C3⋊C8—62no—
192C2×C32—41no—
193C2×C32—41no—
194C2×C32—41no—
195#41—32no—
196#41#62712yes—
197C2×Q8C2×D3211yescharacteristic
198C2×D4—31no—
199C22×C4—31no—
200C22×C4—61no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—181no—
204M16—62no—
205M16—182no—
206C2×C8—32no—
207C2×C8—92no—
208C4⋊C4—32no—
209C4⋊C4—61no—
210C4⋊C4—91no—
211C4⋊C4—91no—
212C4⋊C4—92no—
213C4⋊C4—182no—
214C4⋊C4—182no—
215C4⋊C4—182no—
216C4⋊C4—182no—
217C4⋊C4—181no—
218C22⋊C4—181no—
219C42—31no—
220C42—91no—
221C42—91no—
222C42—91no—
223C22×C3—32no—
224C22×C3—41no—
225C22×C3—61no—
226C22×C3—61no—
227C22×C3—81no—
228C22×C3C22×S411yescharacteristic
229C3×C4—31no—
230C3×C4—31no—
231C3×C4—42no—
232C3×C4—82no—
233C3×C4—122no—
234C3×C4—241no—
235C3×C4—241no—
236C3×C4A4⋊Q812yes—
237Dic3—21no—
238Dic3—21no—
239Dic3—61no—
240Dic3—61no—
241Dic3—82no—
242Dic3—122no—
243Dic3—242no—
244Dic3—482no—
245C32—41noSylow
246C23—31no—
247Q8—31no—
248Q8C2×#62711yescharacteristic
249D4—32no—
250D4—61no—
251C2×C4—31no—
252C2×C4—32no—
253C2×C4—32no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—62no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—122no—
260C2×C4—182no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4—362no—
264C2×C4D3×S411yescharacteristic
265C8—62no—
266C8—182no—
267C2×C3—41no—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3—62no—
271C2×C3—81no—
272C2×C3—81no—
273C2×C3—81no—
274C2×C3C2×A4⋊Q811yescharacteristic
275C2×C3#592311yescharacteristic
276C2×C3#592311yescharacteristic
277C22—32no—
278C22—61no—
279C22—61no—
280C22C2×D3×S411yescharacteristic
281C4—31no—
282C4—31no—
283C4—61no—
284C4—61no—
285C4—122no—
286C4—181no—
287C4—181no—
288C4—362no—
289C4#6420412yes—
290C3—41no—
291C3—81no—
292C3#8533911yescharacteristic, complemented
293C2—62no—
294C2#1059645511yescharacteristic
295C2#1059645611yescharacteristic
296C2C2×#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. #10593199C2semidirect
5. #10593196C2semidirect
292. C3#85339semidirect

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
#105931992
#105931962
#853393
#788713
#638694