Finite Group Databasebeta

← #11786619

Subgroups — #11786619

Order 1152.

637 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic
2#10592928C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic
4#10591131C212yesmaximal
5#10589160C212yesmaximal
6#71658—31nomaximal
7#70102—31nomaximal
8C22×C32×Q8C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C3×Q8×Dic3—22no—
12C3×Q8×Dic3—22no—
13C3×#926—22no—
14C3×#926C2212yes—
15C2×C3×#208C2212yes—
16#63658—22no—
17C3×#836C414yescomplemented
18#63575—22no—
19#63573—22no—
20C3×#519—31no—
21#5812D311yescharacteristic
22C2×C3×#101—31no—
23#5229—31no—
24#5229—31no—
25#5229—61no—
26C2×#836D311yescharacteristic
27#5121—32no—
28#4995—32no—
29#4555—32no—
30#4532—32no—
31C2×C32×Q8—22no—
32C2×C32×Q8—22no—
33C2×C32×Q8C2×C412yes—
34C2×C32×Q8Q812yes—
35C22×C32×C4D412yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—21no—
39C4⋊(C3⋊Dic3)—22no—
40C4×C3⋊Dic3—22no—
41C3×#217—22no—
42C3×C4⋊Dic3—22no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3D412yes—
45C3×C4⋊Dic3D412yes—
46C3×C4×Dic3—24no—
47C3×C4×Dic3—22no—
48C3×#208—22no—
49C3×#208C2×C414yes—
50C2×C3×C3⋊C8—22no—
51#1857—91noSylow
52C22×C3×Q8—21no—
53C22×C3×Q8C2×D311yescharacteristic
54C22×C3×Q8C2×D311yescharacteristic
55C2×C3×M16—32no—
56C3×C4×Q8—62no—
57C3×C4×Q8—62no—
58C3×#117—32no—
59C3×#117—62no—
60Q8×Dic3—22no—
61Q8×Dic3—22no—
62#926—22no—
63#926C2×D312yes—
64C2×C4⋊Dic3—31no—
65C2×C4⋊Dic3—31no—
66C2×C4⋊Dic3—61no—
67C2×C4×Dic3—31no—
68C2×C4×Dic3—31no—
69C2×C4×Dic3—61no—
70C2×#208C2×D312yes—
71C3×#101—34no—
72#836Dic314yescomplemented
73C3⋊#95—64no—
74C3⋊#95—62no—
75C3⋊#95—62no—
76#818—62no—
77#817—62no—
78#808—62no—
79#807—62no—
80C23×C32C2×D411yescharacteristic
81C32×Q8—24no—
82C32×Q8—24no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C4⋊C414yes—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D412yes—
88C2×C32×C4C2×Q811yescharacteristic
89C2×C32×C4#4112yes—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—42no—
94C2×C3⋊Dic3—41no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C3×C3⋊C8—24no—
98#519—31no—
99#428—92no—
100C2×#101—31no—
101#391—91no—
102#339—92no—
103C2×C3×Q8—22no—
104C2×C3×Q8—22no—
105C2×C3×Q8—22no—
106C2×C3×Q8—22no—
107C2×C3×Q8—22no—
108C2×C3×Q8—22no—
109C2×C3×Q8—42no—
110C2×C3×Q8—42no—
111C2×C3×Q8Dic612yes—
112C2×C3×Q8Dic612yes—
113C2×C3×Q8C4×D312yes—
114C2×C3×Q8C2×Dic312yes—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4D1212yes—
118C22×C3×C4#6712yes—
119C22×C3×C4C22×D311yescharacteristic
120C22×C3×C4C22×D311yescharacteristic
121C22×Dic3—62no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—62no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C3×M16—34no—
128C3×M16—62no—
129C2×C3×C8—62no—
130C3×C4⋊C4—32no—
131C3×C4⋊C4—32no—
132C3×C4⋊C4—62no—
133C3×C4⋊C4—62no—
134C3×C22⋊C4—62no—
135C3×C42—64no—
136C3×C42—62no—
137#217—22no—
138C4⋊Dic3—22no—
139C4⋊Dic3—22no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142C4⋊Dic3—122no—
143C4⋊Dic3#6712yes—
144C4⋊Dic3#6712yes—
145C4×Dic3—24no—
146C4×Dic3—22no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C4×Dic3—122no—
150#208—22no—
151#208C2×Dic314yes—
152C2×C3⋊C8—22no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32C2×C4⋊C411yescharacteristic
156C22×C32#12011yescharacteristic
157C22×C32#12311yescharacteristic
158C32×C4—24no—
159C32×C4C4×D412yes—
160C32×C4C22⋊Q812yes—
161C3⋊Dic3—42no—
162C3⋊Dic3—81no—
163C3×Dic3—42no—
164C3×Dic3—42no—
165C22×Q8D3211yescharacteristic
166C2×M16—32no—
167C4×Q8—62no—
168C4×Q8—62no—
169#117—32no—
170#117—62no—
171C2×C4⋊C4—91no—
172C2×C42—91no—
173#107—182no—
174#106—182no—
175#101—34no—
176#95—182no—
177C23×C3—21no—
178C23×C3C2×D1211yescharacteristic
179C23×C3C2×#6711yescharacteristic
180C3×Q8—24no—
181C3×Q8—24no—
182C3×Q8—24no—
183C3×Q8—24no—
184C3×Q8—44no—
185C3×Q8—44no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—24no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4—22no—
195C2×C3×C4—42no—
196C2×C3×C4—42no—
197C2×C3×C4—62no—
198C2×C3×C4—62no—
199C2×C3×C4Dic3⋊C414yes—
200C2×C3×C4C4⋊Dic314yes—
201C2×C3×C4C2×Dic611yescharacteristic
202C2×C3×C4C2×Dic611yescharacteristic
203C2×C3×C4C2×C4×D311yescharacteristic
204C2×C3×C4#23512yes—
205C2×C3×C4D3×D412yes—
206C2×C3×C4#23712yes—
207C2×C3×C4C22×Dic311yescharacteristic
208C2×C3×C4C2×#6712yes—
209C2×Dic3—22no—
210C2×Dic3—22no—
211C2×Dic3—64no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—122no—
215C2×Dic3—122no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219C2×Dic3—121no—
220C2×Dic3—122no—
221C2×Dic3—124no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226C3×C8—64no—
227C3⋊C8—24no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32#38511yescharacteristic
231C2×C32#45411yescharacteristic
232C2×C32#45611yescharacteristic
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8D3×Dic312yes—
236C2×Q8#62712yes—
237C22×C4—181no—
238C22×C4—181no—
239C22×C4#62612yes—
240C22×C4C2×D3211yescharacteristic
241M16—34no—
242M16—62no—
243C2×C8—62no—
244C4⋊C4—32no—
245C4⋊C4—32no—
246C4⋊C4—62no—
247C4⋊C4—62no—
248C4⋊C4—182no—
249C22⋊C4—62no—
250C42—64no—
251C42—62no—
252C42—182no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3#88211yescharacteristic
263C22×C3#88611yescharacteristic
264C22×C3C2×Dic3⋊C411yescharacteristic
265C22×C3C2×C4⋊Dic311yescharacteristic
266C22×C3#92911yescharacteristic
267C22×C3#95311yescharacteristic
268C3×C4—24no—
269C3×C4—24no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—44no—
273C3×C4—122no—
274C3×C4—122no—
275C3×C4#87812yes—
276C3×C4#92412yes—
277C3×C4C4×#6712yes—
278C3×C4D4×Dic312yes—
279Dic3—42no—
280Dic3—42no—
281Dic3—124no—
282Dic3—122no—
283Dic3—122no—
284Dic3—242no—
285Dic3—241no—
286Dic3—241no—
287C32#185711yescharacteristic, complemented, Sylow
288C23C2×#62611yescharacteristic
289Q8—24no—
290Q8—24no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—62no—
294C2×C4—62no—
295C2×C4—182no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4—362no—
299C2×C4—361no—
300C2×C4Dic3⋊Dic314yes—
301C2×C4C2×D3×Dic311yescharacteristic
302C2×C4#380412yes—
303C2×C4C2×#62711yescharacteristic
304C2×C4D3×#6712yes—
305C8—64no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3#475211yescharacteristic
316C2×C3#475311yescharacteristic
317C2×C3#495011yescharacteristic
318C2×C3#521011yescharacteristic
319C2×C3#524511yescharacteristic
320C2×C3#524611yescharacteristic
321C22—21no—
322C22—21no—
323C22C2×Dic3⋊Dic311yescharacteristic
324C22#6396611yescharacteristic
325C22#6397711yescharacteristic
326C4—24no—
327C4—122no—
328C4—122no—
329C4—362no—
330C4—721no—
331C4#6396412yes—
332C4Dic3×#6712yes—
333C3—21no—
334C3#7010211yescharacteristic, complemented
335C3#7165811yescharacteristic, complemented
336C2—21no—
337C2—21no—
338C2#1059164611yescharacteristic
339C2#1059164911yescharacteristic
340C2#1059171811yescharacteristic
subgroupG/H
centerC22#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1857
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
17. C3×#836C4semidirect
72. #836Dic3semidirect
287. C32#1857semidirect
334. C3#70102semidirect
335. C3#71658semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
#105929282
C2×C3×#8362
#105911312
#105891602
#716583
#701023