Finite Group Databasebeta

← #11922347

Subgroups — #11922347

Order 1152.

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

normal subgroups only

This group has 617 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
1C2×#1010⋊C3C211yesmaximal, characteristic
2C2×C3×#984C211yesmaximal, characteristic, complemented
3#10593658C211yesmaximal, characteristic, complemented
4#10593210C214yesmaximal, complemented
5#85536—31nomaximal
6#83983—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#1010⋊C3—22no—
9C2×D3×SL(2,𝔽3)C2212yes—
10C3×#984—22no—
11C2×C3×#226C2212yes—
12#63863—41nomaximal
13C3⋊#859C2212yes—
14C2×#1010D311yescharacteristic
15C2×2−1+4⋊C3—31no—
16C2×#984D311yescharacteristic, complemented
17C2×C3×#137—31no—
18#5816—31no—
19C22×#216—31no—
20#5424—31no—
21#5424—61no—
22#5419—34no—
23#5233—31no—
24#5186—34no—
25#5173—34no—
26#5129—31no—
27#5120—31no—
28C2×C3×D12—41no—
29C2×C3×Dic6—41no—
30C3×#41⋊C3D412yes—
31C2×C3×SL(2,𝔽3)C2311yescharacteristic
32D3×SL(2,𝔽3)—22no—
33C3×#226—22no—
34C4×C3⋊Dic3—41no—
35(C2×D3)⋊Dic3—44no—
36#3011—91noSylow
37C2×C3×#41C2×D311yescharacteristic
38C22×C3×Q8—31no—
39#1010—22no—
40#1010—62no—
41C2×D3×Q8C2×D312yes—
42C2×#237—32no—
43C2×#235—31no—
44C22×Dic6—31no—
452−1+4⋊C3—62no—
46C2×#41⋊C3—21no—
47C2×#41⋊C3C2×D311yescharacteristic
48C22×SL(2,𝔽3)—32no—
49#984—22no—
50C2×#226C2×D312yes—
51C3×#137—62no—
52C3×#137—62no—
53C2×C3×Q16—32no—
54C2×C3×SD16—32no—
55C2×C3×M16—31no—
56#947—61no—
57#946—34no—
58#944—61no—
59C2×#216—34no—
60C2×#216—64no—
61#936—121no—
62#929—62no—
63#926—31no—
64C22×C3⋊C8—31no—
65#859—32no—
66#859—62no—
67#835—32no—
68#832—32no—
69(C2×D3)⋊C8—34no—
70#816—34no—
71C22×C3×D3—42no—
72C2×C32×C4—41no—
73C2×C3⋊Dic3—42no—
74C2×C3×Dic3—42no—
75C3×D12—82no—
76C3×Dic6—82no—
77C3×SL(2,𝔽3)C2×D411yescharacteristic
78C2×2−1+4—31no—
79C2×#137—31no—
80C22×Q16—91no—
81#536—91no—
82#452—94no—
83#451—94no—
84#419—91no—
85#416—91no—
86#408—91no—
87C3×#41—32no—
88C3×#41#6712yes—
89C2×C3×Q8—32no—
90C2×C3×Q8—62no—
91C2×C3×Q8—62no—
92C2×C3×Q8—61no—
93C2×C3×Q8C22×D311yescharacteristic
94C2×C3×D4—31no—
95C2×C3×D4—121no—
96C22×C3×C4—31no—
97C22×C3×C4—61no—
98C2×#67—32no—
99C22×Dic3—61no—
100D3×Q8—22no—
101D3×Q8—62no—
102#237—64no—
103#237—64no—
104#235—62no—
105#235—62no—
106C2×D12S411yescharacteristic
107C2×C4×D3—32no—
108C2×Dic6—32no—
109C2×Dic6—34no—
110C2×Dic6—31no—
111C2×Dic6—41no—
112C2×Dic6—62no—
113#41⋊C3—22no—
114#41⋊C3#6712yes—
115C2×SL(2,𝔽3)—21no—
116C2×SL(2,𝔽3)—62no—
117C2×SL(2,𝔽3)C22×D311yescharacteristic
118#226—22no—
119C3×Q16—62no—
120C3×Q16—62no—
121C3×SD16—64no—
122C3×M16—62no—
123C2×C3×C8—32no—
124#217—61no—
125#217—124no—
126#216—68no—
127(C2×D3)⋊C4—64no—
128C4⋊Dic3—32no—
129Dic3⋊C4—64no—
130C4×Dic3—61no—
131C4×Dic3—121no—
132C4×Dic3—241no—
133C2×C3⋊C8—32no—
134C2×C3⋊C8—62no—
135C22×C32—41no—
136C2×C3×D3—82no—
137C2×C3×D3—84no—
138C32×C4—42no—
139C3⋊Dic3—82no—
140C3×Dic3—82no—
1412−1+4—62no—
1422−1+4—182no—
143C2×#41—91no—
144C2×#41—92no—
145C2×#41D3211yescharacteristic
146C22×Q8—31no—
147C22×Q8—32no—
148C22×Q8—91no—
149#137—62no—
150#137—62no—
151C2×Q16—32no—
152C2×Q16—94no—
153C2×Q16—184no—
154C2×SD16—32no—
155C2×M16—31no—
156C22×C8—91no—
157C4⋊Q8—181no—
158#124—181no—
159#123—182no—
160C22⋊Q8—94no—
161#117—91no—
162#103—94no—
163#103—92no—
164#102—92no—
165C22⋊C8—94no—
166C23×C3—31no—
167C23×C3—122no—
168C22×D3C2×S412yes—
169C3×Q8—31no—
170C3×Q8—62no—
171C3×Q8—62no—
172C3×Q8—122no—
173C3×Q8C2×#6711yescharacteristic
174C3×D4—32no—
175C3×D4—61no—
176C3×D4—242no—
177C2×C3×C4—31no—
178C2×C3×C4—32no—
179C2×C3×C4—32no—
180C2×C3×C4—41no—
181C2×C3×C4—62no—
182C2×C3×C4—81no—
183C2×C3×C4—122no—
184C2×C3×C4C2×S411yescharacteristic
185#67—64no—
186C2×Dic3—32no—
187C2×Dic3—42no—
188C2×Dic3—64no—
189C2×Dic3—62no—
190C2×Dic3—122no—
191C2×Dic3—242no—
192D12—22no—
193C4×D3—62no—
194C4×D3—62no—
195Dic6—34no—
196Dic6—62no—
197Dic6—62no—
198Dic6—82no—
199SL(2,𝔽3)—21no—
200SL(2,𝔽3)C2×#6711yescharacteristic
201C3×C8—62no—
202C3⋊C8—62no—
203C2×C32—42no—
204C2×C32—41no—
205C3×D3—162no—
206#41—32no—
207#41—182no—
208#41—182no—
209#41—184no—
210#41—184no—
211#41#62512yes—
212C2×Q8—32no—
213C2×Q8—62no—
214C2×Q8—62no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8—92no—
218C2×Q8—94no—
219C2×Q8—91no—
220C2×Q8—182no—
221C2×Q8—182no—
222C2×Q8C2×D3211yescharacteristic
223C2×D4—31no—
224C2×D4—31no—
225C2×D4—92no—
226C22×C4—31no—
227C22×C4—61no—
228C22×C4—92no—
229C22×C4—181no—
230Q16—62no—
231Q16—62no—
232Q16—188no—
233SD16—64no—
234M16—62no—
235C2×C8—32no—
236C2×C8—92no—
237C2×C8—182no—
238C4⋊C4—92no—
239C4⋊C4—184no—
240C22⋊C4—184no—
241C22⋊C4—181no—
242C42—181no—
243C22×C3—32no—
244C22×C3—41no—
245C22×C3—62no—
246C22×C3—81no—
247C22×C3—242no—
248C22×C3—244no—
249C22×C3C22×S411yescharacteristic
250C2×D3—24no—
251C2×D3—22no—
252C3×C4—31no—
253C3×C4—31no—
254C3×C4—42no—
255C3×C4—82no—
256C3×C4—122no—
257C3×C4GL(2,ℤ/4)12yes—
258Dic3—62no—
259Dic3—82no—
260Dic3—122no—
261Dic3—242no—
262Dic3—244no—
263C32—41noSylow
264C23—31no—
265C23—32no—
266Q8—31no—
267Q8—62no—
268Q8—62no—
269Q8—94no—
270Q8—122no—
271Q8—182no—
272Q8—182no—
273Q8C2×#62511yescharacteristic
274D4—32no—
275D4—61no—
276D4—62no—
277D4—184no—
278C2×C4—31no—
279C2×C4—32no—
280C2×C4—32no—
281C2×C4—62no—
282C2×C4—92no—
283C2×C4—122no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4—184no—
287C2×C4—182no—
288C2×C4D3×S411yescharacteristic
289C8—62no—
290C8—182no—
291C2×C3—42no—
292C2×C3—41no—
293C2×C3—62no—
294C2×C3—82no—
295C2×C3—81no—
296C2×C3—482no—
297C2×C3#592712yes—
298C2×C3C2×GL(2,ℤ/4)11yescharacteristic
299D3—42no—
300C22—32no—
301C22—62no—
302C22—64no—
303C22—62no—
304C22C2×D3×S411yescharacteristic
305C4—31no—
306C4—31no—
307C4—122no—
308C4—182no—
309C4—362no—
310C4#6420912yes—
311C3—41no—
312C3—81no—
313C3#8553611yescharacteristic, complemented
314C2—62no—
315C2—122no—
316C2#1059645312yes—
317C2C2×#6420911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×#1010⋊C3C2
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
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
2. C2×C3×#984C2semidirect
3. #10593658C2semidirect
4. #10593210C2semidirect
16. C2×#984D3semidirect
313. C3#85536semidirect

Maximal subgroups

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

subgroupindex
C2×#1010⋊C32
C2×C3×#9842
#105936582
#105932102
#855363
#839833
#638634