Finite Group Databasebeta

← #11794285

Subgroups — #11794285

Order 1152.

509 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C3×#5500C211yesmaximal, characteristic
2C3×#4977C211yesmaximal, characteristic
3#10591139C212yesmaximal
4#10589396C211yesmaximal, characteristic
5#10589161C212yesmaximal
6#71901—31nomaximal
7#69543—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3748C2212yes—
10C3×#926C2212yes—
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924—22no—
13C2×C3×C4×Dic3C2211yescharacteristic
14C3×#890—22no—
15C3×#888—22no—
16C3×C3⋊#95—22no—
17#63576—22no—
18#63574—22no—
19C3×#544—31no—
20#5500D311yescharacteristic
21C3×#382—31no—
22#4995—32no—
23#4977D311yescharacteristic
24#4964—32no—
25#4532—32no—
26#4530—31no—
27#4530—31no—
28#4530—61no—
29#4523—32no—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3×Dic3—21no—
33C22×C3×Dic3—21no—
34C2×C3×Dic6—22no—
35C32×C4⋊C4—22no—
36#3748—22no—
37#3748Q814yescomplemented
38C2×C3⋊(C3⋊C8)—22no—
39C3×#217—22no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3D412yes—
43C3×C4⋊Dic3D412yes—
44C3×Dic3⋊C4—24no—
45C3×C4×Dic3—22no—
46C3×C4×Dic3—21no—
47C3×C4×Dic3Q812yescomplemented
48#2061—91noSylow
49C3×C4⋊Q8—62no—
50C3×#125—62no—
51C3×C22⋊Q8—62no—
52C3×#117—32no—
53C2×C3×C4⋊C4—21no—
54C2×C3×C4⋊C4—31no—
55C2×C3×C4⋊C4C2×D311yescharacteristic
56C2×C3×C4⋊C4C2×D311yescharacteristic
57C2×C3×C42—31no—
58#926C2×D312yes—
59C2×C4⋊Dic3C2×D311yescharacteristic
60#924—22no—
61C2×C4×Dic3C2×D311yescharacteristic
62C2×#208—32no—
63C2×#208—32no—
64C2×#208—62no—
65#890—22no—
66#888—22no—
67C3×#95—62no—
68C3⋊#95—22no—
69#808—62no—
70#808—62no—
71#807—62no—
72#807—62no—
73C23×C32C2×D411yescharacteristic
74C2×C32×C4—22no—
75C2×C32×C4—42no—
76C2×C32×C4C2×D412yes—
77C2×C32×C4C2×Q811yescharacteristic
78C2×C32×C4C2×Q812yes—
79C2×C32×C4#4111yescharacteristic
80C2×C3×Dic3—22no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—41no—
87C3×Dic6—82no—
88C3⋊(C3⋊C8)—24no—
89#544—31no—
90#428—92no—
91#382—31no—
92#343—91no—
93#339—92no—
94C2×C3×Q8—62no—
95C22×C3×C4—22no—
96C22×C3×C4—21no—
97C22×C3×C4—61no—
98C22×C3×C4—61no—
99C22×C3×C4#6712yes—
100C22×C3×C4#6712yes—
101C22×C3×C4C22×D311yescharacteristic
102C22×C3×C4C22×D311yescharacteristic
103C22×Dic3—21no—
104C22×Dic3—21no—
105C2×Dic6—22no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—32no—
109C3×C4⋊C4—32no—
110C3×C4⋊C4—42no—
111C3×C4⋊C4—64no—
112C3×C4⋊C4—62no—
113C3×C4⋊C4—62no—
114C3×C22⋊C4—62no—
115C3×C42—32no—
116C3×C42—62no—
117C3×C42—61no—
118#217—22no—
119C4⋊Dic3—22no—
120C4⋊Dic3—22no—
121C4⋊Dic3#6712yes—
122C4⋊Dic3#6712yes—
123Dic3⋊C4—24no—
124C4×Dic3—21no—
125C4×Dic3—22no—
126C4×Dic3Dic612yescomplemented
127#208—34no—
128#208—34no—
129#208—64no—
130#208—62no—
131#208—62no—
132#208—122no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—122no—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32#12011yescharacteristic
139C22×C32C22⋊Q811yescharacteristic
140C22×C32C4⋊Q811yescharacteristic
141C32×C4—42no—
142C32×C4C22⋊Q812yes—
143C32×C4C4⋊Q812yes—
144C3×Dic3—42no—
145C3×Dic3—42no—
146C3×Dic3—42no—
147C3×Dic3—81no—
148C2×M16—92no—
149C4⋊Q8—62no—
150#125—62no—
151C22⋊Q8—62no—
152#117—32no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4D3211yescharacteristic
155C2×C42—31no—
156#107—182no—
157#106—182no—
158#95—62no—
159C23×C3—21no—
160C23×C3C2×#6711yescharacteristic
161C23×C3C2×#6711yescharacteristic
162C3×Q8—242no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—21no—
166C2×C3×C4—22no—
167C2×C3×C4—21no—
168C2×C3×C4—22no—
169C2×C3×C4—42no—
170C2×C3×C4—42no—
171C2×C3×C4—42no—
172C2×C3×C4—62no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4—82no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4—122no—
179C2×C3×C4—121no—
180C2×C3×C4C2×Dic611yescharacteristic
181C2×C3×C4#23511yescharacteristic
182C2×C3×C4D3×D412yes—
183C2×C3×C4D3×Q811yescharacteristic
184C2×C3×C4D3×Q812yes—
185C2×C3×C4D3×Q812yes—
186C2×C3×C4#23911yescharacteristic
187C2×C3×C4C2×#6712yes—
188C2×Dic3—22no—
189C2×Dic3—22no—
190C2×Dic3—22no—
191C2×Dic3—41no—
192C2×Dic3—41no—
193C2×Dic3—42no—
194C2×Dic3—41no—
195Dic6—82no—
196C3⋊C8—64no—
197C3⋊C8—64no—
198C3⋊C8—124no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32#39511yescharacteristic
202C2×C32#45411yescharacteristic
203C2×C32#45511yescharacteristic
204C2×Q8—62no—
205C22×C4—61no—
206C22×C4—61no—
207C22×C4#62512yes—
208C22×C4C2×D3211yescharacteristic
209M16—94no—
210M16—182no—
211C2×C8—182no—
212C4⋊C4—22no—
213C4⋊C4—32no—
214C4⋊C4—32no—
215C4⋊C4—62no—
216C4⋊C4—64no—
217C4⋊C4—62no—
218C22⋊C4—62no—
219C42—32no—
220C42—61no—
221C42—62no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3#92411yescharacteristic
232C22×C3#93711yescharacteristic
233C22×C3#94411yescharacteristic
234C22×C3#94411yescharacteristic
235C22×C3#94611yescharacteristic
236C22×C3#95311yescharacteristic
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—42no—
240C3×C4—42no—
241C3×C4—82no—
242C3×C4—122no—
243C3×C4—122no—
244C3×C4—122no—
245C3×C4—241no—
246C3×C4#88812yes—
247C3×C4#89612yes—
248C3×C4#94412yes—
249C3×C4#94612yes—
250Dic3—42no—
251Dic3—42no—
252Dic3—42no—
253Dic3—81no—
254C32#206111yescharacteristic, complemented, Sylow
255C23C2×#62511yescharacteristic
256Q8—242no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—62no—
260C2×C4—62no—
261C2×C4—62no—
262C2×C4—121no—
263C2×C4—121no—
264C2×C4—122no—
265C2×C4—121no—
266C2×C4D3×Dic611yescharacteristic
267C2×C4#379712yes—
268C2×C4#379911yescharacteristic
269C2×C4D3×#6712yes—
270C8—184no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—41no—
279C2×C3—41no—
280C2×C3#497911yescharacteristic
281C2×C3#506111yescharacteristic
282C2×C3#506211yescharacteristic
283C2×C3#523011yescharacteristic
284C2×C3#524211yescharacteristic
285C2×C3#524511yescharacteristic
286C22—21no—
287C22—21no—
288C22#6385611yescharacteristic
289C22#6387311yescharacteristic
290C22#6397611yescharacteristic
291C4—42no—
292C4—122no—
293C4—122no—
294C4—122no—
295C4—241no—
296C4#6383912yes—
297C4#6388812yes—
298C3—21no—
299C3#6954311yescharacteristic, complemented
300C3#7190111yescharacteristic, complemented
301C2—21no—
302C2—21no—
303C2#1059134411yescharacteristic
304C2#1059151211yescharacteristic
305C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2061
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. #3748Q8semidirect
47. C3×C4×Dic3Q8semidirect
126. C4×Dic3Dic6semidirect
254. C32#2061semidirect
299. C3#69543semidirect
300. C3#71901semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
C3×#49772
#105911392
#105893962
#105891612
#719013
#695433