Finite Group Databasebeta

← #83421

Subgroups — #83421

Order 384.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#537C211yesmaximal, characteristic, complemented
2#5833C211yesmaximal, characteristic, complemented
3C2×#950C211yesmaximal, characteristic, complemented
4C2×#948C211yesmaximal, characteristic, complemented
5#5232C211yesmaximal, characteristic, complemented
6#5051C212yesmaximal, complemented
7#5049C212yesmaximal, complemented
8#5042C212yesmaximal, complemented
9#5038C212yesmaximal, complemented
10#4966C211yesmaximal, characteristic, complemented
11C2×#807C211yesmaximal, characteristic, complemented
12#3061—31nomaximal, Sylow
13C2×C3×#41C2211yescharacteristic
14C2×C3×#41C2211yescharacteristic
15C2×#235C2211yescharacteristic
16C3×C22⋊Q8—21no—
17C3×C22⋊Q8C2212yes—
18C3×#121—21no—
19C3×#121—22no—
20C3×#121C2212yes—
21C2×C3×C4⋊C4C2211yescharacteristic
22#950—24no—
23#948—24no—
24#946—21no—
25C2×#216C2211yescharacteristic
26C2×#215C2211yescharacteristic
27#939—22no—
28#938—21no—
29C2×#214C2211yescharacteristic
30C2×#213C2211yescharacteristic
31#930C2212yes—
32C2×C4⋊Dic3C2211yescharacteristic
33#924C2212yes—
34C2×#208C2211yescharacteristic
35C2×#208C2212yes—
36C22×C3⋊C8C2212yes—
37C22×C3⋊C8C2211yescharacteristic
38#835C2212yes—
39#832C2212yes—
40#810C2212yes—
41#809C2212yes—
42#807C2212yes—
43#807C2212yes—
44C2×#135—31no—
45C2×#131—31no—
46#537—31no—
47#537D311yescharacteristic, complemented
48#468—32no—
49#468—32no—
50#467—32no—
51#466—32no—
52C2×#107—31no—
53#417—31no—
54#417—31no—
55C3×#41—22no—
56C3×#41—22no—
57C3×#41—22no—
58C3×#41—22no—
59C2×C3×Q8D411yescharacteristic
60C2×C3×Q8C2311yescharacteristic
61C2×C3×D4—21no—
62C2×C3×D4—22no—
63C2×C3×D4D411yescharacteristic
64C2×C3×D4D412yes—
65C2×C3×D4C2311yescharacteristic
66C22×C3×C4—21no—
67C22×C3×C4—21no—
68C22×C3×C4C2312yes—
69C22×C3×C4C2311yescharacteristic
70C2×#67—21no—
71C2×#67—22no—
72C22×Dic3—21no—
73#235—22no—
74#235—22no—
75C2×D12C2311yescharacteristic
76C2×C4×D3—21no—
77C2×Dic6C2311yescharacteristic
78C3×C4⋊C4—21no—
79C3×C4⋊C4—22no—
80C3×C4⋊C4C2312yes—
81C3×C22⋊C4—22no—
82C3×C22⋊C4—22no—
83#217—22no—
84#216—22no—
85#215—22no—
86#214—22no—
87#213—22no—
88(C2×D3)⋊C4—22no—
89C4⋊Dic3—21no—
90C4⋊Dic3C2312yes—
91Dic3⋊C4—22no—
92#208—22no—
93#208—24no—
94C2×C3⋊C8—24no—
95C2×C3⋊C8D414yescomplemented
96C2×C3⋊C8C2312yes—
97C2×C3⋊C8C2311yescharacteristic
98C2×C3⋊C8C2311yescharacteristic
99C2×#41—31no—
100C2×#41C2×D311yescharacteristic
101C2×#41C2×D311yescharacteristic
102#135—64no—
103C2×Q16—31no—
104C2×SD16—31no—
105C2×SD16—31no—
106C2×D8—31no—
107#131—64no—
108C2×M16—31no—
109C2×M16—32no—
110C22×C8—31no—
111C22×C8—32no—
112C22⋊Q8—21no—
113C22⋊Q8—32no—
114C22⋊Q8—61no—
115C22⋊Q8C2×D312yes—
116#121—21no—
117#121—22no—
118#121—32no—
119#121—61no—
120#121—62no—
121#121C2×D312yes—
122C2×C4⋊C4—31no—
123C2×C4⋊C4C2×D311yescharacteristic
124#107—32no—
125#107—32no—
126#103—32no—
127#103—32no—
128#102—32no—
129#102—32no—
130C23×C3—21no—
131C23×C3C2×D412yes—
132C23×C3C2×D411yescharacteristic
133C22×D3—21no—
134C3×Q8—22no—
135C3×Q8—21no—
136C3×Q8—21no—
137C3×D4—24no—
138C3×D4—22no—
139C3×D4—21no—
140C3×D4—21no—
141C3×D4—42no—
142C3×D4—82no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—21no—
147C2×C3×C4—42no—
148C2×C3×C4—81no—
149C2×C3×C4C2×D412yes—
150C2×C3×C4C2×D412yes—
151C2×C3×C4C2×D411yescharacteristic
152C2×C3×C4#4112yes—
153C2×C3×C4C2411yescharacteristic
154#67—42no—
155#67—82no—
156C2×Dic3—21no—
157C2×Dic3—22no—
158C2×Dic3—81no—
159D12—21no—
160D12—21no—
161C4×D3—42no—
162Dic6—21no—
163Dic6—21no—
164C3⋊C8—22no—
165C3⋊C8C2×D412yes—
166C3⋊C8C2×D412yes—
167#41—22no—
168#41—22no—
169#41—22no—
170#41—22no—
171#41—62no—
172#41—62no—
173C2×Q8—31no—
174C2×Q8#6711yescharacteristic
175C2×Q8C22×D311yescharacteristic
176C2×D4—21no—
177C2×D4—22no—
178C2×D4—31no—
179C2×D4—61no—
180C2×D4—62no—
181C2×D4#6712yes—
182C2×D4#6711yescharacteristic
183C2×D4C22×D311yescharacteristic
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—61no—
187C22×C4—61no—
188C22×C4C22×D312yes—
189C22×C4C22×D311yescharacteristic
190Q16—62no—
191SD16—62no—
192SD16—62no—
193D8—62no—
194M16—64no—
195M16—62no—
196C2×C8—34no—
197C2×C8—31no—
198C2×C8—31no—
199C2×C8—32no—
200C2×C8—64no—
201C4⋊C4—21no—
202C4⋊C4—22no—
203C4⋊C4—32no—
204C4⋊C4—61no—
205C4⋊C4—62no—
206C4⋊C4C22×D312yes—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—62no—
210C22⋊C4—62no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—41no—
217C22×C3—41no—
218C22×C3—41no—
219C22×C3#12112yes—
220C22×C3C22×D411yescharacteristic
221C2×D3—41no—
222C2×D3—41no—
223C2×D3—41no—
224C3×C4—22no—
225C3×C4—41no—
226C3×C4—42no—
227C3×C4#12112yes—
228C3×C4C22×D411yescharacteristic
229C3×C4C2×#4111yescharacteristic
230Dic3—41no—
231Dic3—42no—
232C23—21no—
233C23—61no—
234C23C2×#6712yes—
235C23C2×#6711yescharacteristic
236Q8—22no—
237Q8—21no—
238Q8—21no—
239Q8—61no—
240Q8—61no—
241D4—24no—
242D4—22no—
243D4—21no—
244D4—21no—
245D4—42no—
246D4—61no—
247D4—61no—
248D4—82no—
249D4—122no—
250D4—242no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—62no—
257C2×C4—61no—
258C2×C4—81no—
259C2×C4—122no—
260C2×C4—241no—
261C2×C4D3×D412yes—
262C2×C4#23712yes—
263C2×C4C2×#6712yes—
264C2×C4C2×#6711yescharacteristic
265C2×C4C23×D311yescharacteristic
266C8—32no—
267C8—32no—
268C8—62no—
269C2×C3—22no—
270C2×C3—42no—
271C2×C3—81no—
272C2×C3C2×#12111yescharacteristic
273C2×C3#57611yescharacteristic
274C2×C3#57811yescharacteristic
275D3—81no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—121no—
285C22—121no—
286C22—121no—
287C22#93912yes—
288C22C22×#6711yescharacteristic
289C4—22no—
290C4—41no—
291C4—42no—
292C4—121no—
293C4—122no—
294C4#93912yes—
295C4C2×D3×D411yescharacteristic
296C4C2×#23711yescharacteristic
297C3#306111yescharacteristic, complemented, Sylow
298C2—22no—
299C2—42no—
300C2—81no—
301C2—241no—
302C2C2×#93911yescharacteristic
303C2#583511yescharacteristic
304C2#583811yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#537C2
socleC22×C3C22×D4
hypercenter#537D3
hypocenterC3#3061
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C3×#537C2semidirect
2. #5833C2semidirect
3. C2×#950C2semidirect
4. C2×#948C2semidirect
5. #5232C2semidirect
6. #5051C2semidirect
7. #5049C2semidirect
8. #5042C2semidirect
9. #5038C2semidirect
10. #4966C2semidirect
11. C2×#807C2semidirect
47. #537D3semidirect
95. C2×C3⋊C8D4semidirect
297. C3#3061semidirect

Maximal subgroups

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

subgroupindex
C3×#5372
#58332
C2×#9502
C2×#9482
#52322
#50512
#50492
#50422
#50382
#49662
C2×#8072
#30613