Finite Group Databasebeta

← #11920693

Subgroups — #11920693

Order 1152.

361 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 361 conjugacy classes of subgroups — too many to draw. Only its 45 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×#64265C211yesmaximal, characteristic
2#5827⋊C3C211yesmaximal, characteristic
3C2×C3×GU(2,𝔽3)C211yesmaximal, characteristic
4#73077—31nomaximal
5#70365—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64265—21no—
8#64265C412yescomplemented
9C2×C3⋊#226—21no—
10Dic3×SL(2,𝔽3)—21no—
11C3×GU(2,𝔽3)—21no—
12#63567—41nomaximal
13C2×#984—31no—
14C2×#984—61no—
15#5827D311yescharacteristic
16C2×#951—31no—
17#520⋊C3—31no—
18C2×GU(2,𝔽3)D311yescharacteristic
19C2×C3×#104—31no—
20#5120—31no—
21#4929—31no—
22#4554—31no—
23#4523—31no—
24C2×#634—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3⋊#226—22no—
29C3×C4⋊Dic3—41no—
30C2×C3×C3⋊C8—41no—
31#1882—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×Dic6—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#984—32no—
37#984—62no—
38#984—62no—
39#984—61no—
40C2×#226—62no—
41C2×#226—61no—
42C2×C3×M16—31no—
43C2×C3×C42—31no—
44#951—32no—
45#951—32no—
46#951—61no—
47#951—61no—
48Q8×Dic3—21no—
49C2×#216—61no—
50D4×Dic3—61no—
51C2×#214—61no—
52#926—31no—
53C2×C4⋊Dic3—31no—
54C2×#208—31no—
55C4×SL(2,𝔽3)—61no—
56GU(2,𝔽3)—21no—
57C3×#104—61no—
58C3×#104—61no—
59C3⋊#95—62no—
60#816—61no—
61#816—61no—
62#810—121no—
63C2×C32×C4—41no—
64C2×C3⋊Dic3—81no—
65#634—42no—
66#634—81no—
67C2×C3×Dic3—81no—
68C3×SL(2,𝔽3)C22⋊C411yescharacteristic
69C3×C3⋊C8—81no—
70C2×#137—91no—
71#520—31no—
72C2×#104—31no—
73#419—91no—
74#391—91no—
75#343—91no—
76#339—91no—
77C3×#41—31no—
78C3×#41—31no—
79C3×#41C4×D311yescharacteristic
80C3×#41D1211yescharacteristic
81C2×C3×Q8#6711yescharacteristic
82C2×C3×D4—31no—
83C22×C3×C4—31no—
84C22×C3×C4—61no—
85C22×Dic3—32no—
86C22×Dic3—61no—
87C2×Dic6—32no—
88C2×Dic6—61no—
89C2×Dic6—61no—
90C2×Dic6—61no—
91C2×Dic6—61no—
92C2×Dic6—61no—
93C2×Dic6—121no—
94C2×Dic6—241no—
95#41⋊C3—21no—
96#41⋊C3—21no—
97#41⋊C3C4×D311yescharacteristic
98#41⋊C3#6711yescharacteristic
99C2×SL(2,𝔽3)—21no—
100C2×SL(2,𝔽3)D1211yescharacteristic
101#226—64no—
102#226—62no—
103C3×M16—61no—
104C3×M16—61no—
105C2×C3×C8—61no—
106C3×C4⋊C4—121no—
107C3×C42—61no—
108C3×C42—61no—
109#217—61no—
110#216—62no—
111#216—62no—
112#214—62no—
113#214—62no—
114C4⋊Dic3—31no—
115C4⋊Dic3—61no—
116C4⋊Dic3S411yescharacteristic
117C4×Dic3—61no—
118#208—32no—
119#208—61no—
120C2×C3⋊C8—41no—
121C2×C3⋊C8—61no—
122C22×C32—41no—
123C32×C4—41no—
124C32×C4—41no—
125C3⋊Dic3—82no—
126C3×Dic3—161no—
127C2×#41D3211yescharacteristic
128C22×Q8—91no—
129#137—92no—
130#137—92no—
131#137—181no—
132#137—181no—
133C2×Q16—181no—
134C2×SD16—181no—
135C2×M16—31no—
136C2×M16—91no—
137C4×Q8—61no—
138C4×D4—181no—
139#117—91no—
140C2×C4⋊C4—91no—
141C2×C42—31no—
142#104—61no—
143#104—61no—
144#103—181no—
145#103—181no—
146#95—182no—
147C23×C3—31no—
148C3×Q8—31no—
149C3×Q8(C2×D3)⋊C411yescharacteristic
150C3×D4—31no—
151C3×D4—31no—
152C3×D4—61no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—41no—
159C2×C3×C4—62no—
160C2×C3×C4—81no—
161C2×C3×C4—121no—
162C2×C3×C4—121no—
163C2×C3×C4—241no—
164C2×C3×C4C2×S411yescharacteristic
165C2×Dic3—21no—
166C2×Dic3—62no—
167C2×Dic3—61no—
168C2×Dic3—121no—
169C2×Dic3—121no—
170C2×Dic3—122no—
171C2×Dic3—241no—
172C2×Dic3—242no—
173Dic6—62no—
174Dic6—62no—
175Dic6—122no—
176Dic6—121no—
177Dic6—121no—
178Dic6—242no—
179Dic6—241no—
180Dic6—242no—
181SL(2,𝔽3)—21no—
182SL(2,𝔽3)(C2×D3)⋊C411yescharacteristic
183C3×C8—121no—
184C3⋊C8—62no—
185C3⋊C8—81no—
186C2×C32—41no—
187C2×C32—41no—
188C2×C32—41no—
189#41—31no—
190#41—31no—
191#41#62411yescharacteristic
192#41#62611yescharacteristic
193C2×Q8—92no—
194C2×Q8—181no—
195C2×Q8—181no—
196C2×Q8—181no—
197C2×Q8—181no—
198C2×Q8—181no—
199C2×Q8#62611yescharacteristic
200C2×D4—31no—
201C22×C4—31no—
202C22×C4—61no—
203C22×C4—92no—
204C22×C4—181no—
205Q16—182no—
206Q16—182no—
207SD16—182no—
208SD16—182no—
209M16—61no—
210M16—61no—
211M16—92no—
212M16—181no—
213C2×C8—61no—
214C2×C8—181no—
215C4⋊C4—31no—
216C4⋊C4—91no—
217C4⋊C4—181no—
218C22⋊C4—181no—
219C42—61no—
220C42—61no—
221C42—181no—
222C22×C3—31no—
223C22×C3—31no—
224C22×C3—41no—
225C22×C3—61no—
226C22×C3—61no—
227C22×C3—81no—
228C22×C3GL(2,ℤ/4)11yescharacteristic
229C3×C4—31no—
230C3×C4—31no—
231C3×C4—41no—
232C3×C4—41no—
233C3×C4—81no—
234C3×C4—81no—
235C3×C4—122no—
236C3×C4—481no—
237C3×C4C4×S411yescharacteristic
238C3×C4C4⋊S411yescharacteristic
239Dic3—41no—
240Dic3—122no—
241Dic3—121no—
242Dic3—242no—
243Dic3—244no—
244C32—41noSylow
245C23—31no—
246Q8—31no—
247Q8—182no—
248Q8—182no—
249Q8—361no—
250Q8—361no—
251Q8#372211yescharacteristic
252D4—31no—
253D4—31no—
254D4—61no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—31no—
259C2×C4—31no—
260C2×C4—62no—
261C2×C4—61no—
262C2×C4—121no—
263C2×C4—121no—
264C2×C4—182no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4—362no—
269C2×C4D3×S411yescharacteristic
270C8—121no—
271C8—182no—
272C2×C3—41no—
273C2×C3—41no—
274C2×C3—41no—
275C2×C3—61no—
276C2×C3—61no—
277C2×C3—81no—
278C2×C3—81no—
279C2×C3—81no—
280C2×C3(C2×S4)⋊C411yescharacteristic
281C2×C3#542811yescharacteristic
282C2×C3#543011yescharacteristic
283C22—31no—
284C22—31no—
285C22—61no—
286C22—61no—
287C22#6421011yescharacteristic
288C4—31no—
289C4—31no—
290C4—122no—
291C4—121no—
292C4—361no—
293C4—362no—
294C4(C3⋊S4)⋊C411yescharacteristic
295C4#6420711yescharacteristic
296C3—41no—
297C3—81no—
298C3#7307711yescharacteristic, complemented
299C2—61no—
300C2—61no—
301C2#1059323211yescharacteristic
302C2#1059323611yescharacteristic
303C2#1059324211yescharacteristic
subgroupG/H
centerC22#64210
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3GL(2,ℤ/4)
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. #64265C4semidirect
298. C3#73077semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
#5827⋊C32
C2×C3×GU(2,𝔽3)2
#730773
#703653
#635674