Finite Group Databasebeta

← #11778470

Subgroups — #11778470

Order 1152.

684 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#10596105C211yesmaximal, characteristic
2#10592742C211yesmaximal, characteristic, complemented
3#10592420C211yesmaximal, characteristic, complemented
4#10592373C211yesmaximal, characteristic
5C32×#328C211yesmaximal, characteristic, complemented
6#10589334C211yesmaximal, characteristic
7#10589318C211yesmaximal, characteristic, complemented
8#68320—34nomaximal
9C32×C22⋊Q8C2211yescharacteristic
10#64155—21no—
11C2×#3752—21no—
12C2×#3752C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14#64133C2211yescharacteristic
15#64106—21no—
16#64105—21no—
17#64105—21no—
18C22⋊C4×C3⋊D3—21no—
19#64087—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×#95C2211yescharacteristic
22#63662—21no—
23#63658—21no—
24#63657C2211yescharacteristic
25#63644—21no—
26#63643—21no—
27#63635—21no—
28#5634—34no—
29#5043—34no—
30#4721—34no—
31#4674—34no—
32C3×#328D314yescomplemented
33#4468—34no—
34#4452—34no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×Q8D411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×#634—21no—
44C2×#634D411yescharacteristic
45C2×C32×C8—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C22⋊C4—21no—
49#3757—21no—
50#3752—21no—
51#3752—21no—
52#3752—21no—
53#3752—21no—
54#3752—42no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60#3750—21no—
61#3750—21no—
62C2×C3⋊(C3⋊C8)—21no—
63#1608—91noSylow
64C3×C22⋊Q8C2×D314yes—
65#946—64no—
66C2×(C2×D3)⋊C4—34no—
67C2×(C2×D3)⋊C4—64no—
68C2×C4⋊Dic3—34no—
69#924—34no—
70#897—64no—
71#896—64no—
72#896—64no—
73D3×C22⋊C4—64no—
74#878—64no—
75C3×C22⋊C8C2×D314yes—
76C3×#95C2×D314yes—
77#835—64no—
78C3⋊#95—64no—
79#830—34no—
80#817—64no—
81#816—64no—
82#808—64no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—21no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3—41no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3SD1612yes—
89C32×Q8—41no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C4×C3⋊D3—81no—
106C4×C3⋊D3—81no—
107#634—41no—
108#634—81no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—41no—
111#543—91no—
112#483—91no—
113#483—91no—
114#397—91no—
115#328—91no—
116#328C3⋊D311yescharacteristic, complemented
117#323—91no—
118C23×D3—34no—
119C2×C3×Q8D1214yes—
120C22×C3×C4—24no—
121C22×C3×C4C22×D314yes—
122C22×Dic3—34no—
123C22×Dic3—64no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×Dic6—34no—
127C2×Dic6—64no—
128C2×C3×C8—24no—
129C3×C4⋊C4—24no—
130C3×C4⋊C4D1214yes—
131C3×C22⋊C4—24no—
132#217—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135(C2×D3)⋊C4—64no—
136(C2×D3)⋊C4—64no—
137(C2×D3)⋊C4—128no—
138C4⋊Dic3—34no—
139C4⋊Dic3—64no—
140C4⋊Dic3—64no—
141C4⋊Dic3—64no—
142Dic3⋊C4—64no—
143Dic3⋊C4—64no—
144Dic3⋊C4—64no—
145C2×C3⋊C8—64no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32#12011yescharacteristic
149C22×C32C2×SD1611yescharacteristic
150C22×C32#13711yescharacteristic
151C2×C3⋊D3—22no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3—41no—
154C2×C3⋊D3—42no—
155C2×C3⋊D3—81no—
156C32×C4—21no—
157C32×C4—21no—
158C32×C4—41no—
159C32×C4—41no—
160C32×C4—81no—
161C3⋊Dic3—41no—
162C3⋊Dic3—41no—
163C3⋊Dic3—41no—
164C3⋊Dic3—81no—
165C22⋊Q8—91no—
166C22⋊Q8—181no—
167C22⋊Q8—181no—
168C22⋊Q8—181no—
169C22⋊Q8—181no—
170C22⋊Q8—181no—
171C22⋊Q8C2×C3⋊D311yescharacteristic
172C2×C4⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C22⋊C4—181no—
175C2×C22⋊C4—181no—
176#106—181no—
177#106—181no—
178#103—181no—
179#103—181no—
180C22⋊C8—91no—
181C22⋊C8C2×C3⋊D311yescharacteristic
182#95—181no—
183#95C2×C3⋊D311yescharacteristic
184C23×C3D3×D414yes—
185C22×D3—38no—
186C22×D3—64no—
187C22×D3—64no—
188C22×D3—124no—
189C22×D3—124no—
190C3×Q8—44no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4—44no—
197C2×C3×C4C2×D1214yes—
198C2×C3×C4D3×D414yes—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—124no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C4×D3—244no—
207C4×D3—244no—
208Dic6—124no—
209Dic6—244no—
210C3×C8—44no—
211C3⋊C8—124no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#44811yescharacteristic
215C2×C32#45511yescharacteristic
216C2×C32#45811yescharacteristic
217C3⋊D3—42no—
218C24—91no—
219C2×Q8—91no—
220C2×Q8—181no—
221C2×Q8C4⋊(C3⋊D3)11yescharacteristic
222C22×C4—21no—
223C22×C4—91no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4—181no—
227C22×C4C22×C3⋊D311yescharacteristic
228C2×C8—21no—
229C2×C8—181no—
230C4⋊C4—21no—
231C4⋊C4—91no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—181no—
241C22⋊C4—181no—
242C22⋊C4—181no—
243C22⋊C4—181no—
244C22⋊C4—181no—
245C22⋊C4—362no—
246C22×C3—24no—
247C22×C3—24no—
248C22×C3#88214yes—
249C22×C3D3×SD1614yes—
250C22×C3#91814yes—
251C2×D3—68no—
252C2×D3—124no—
253C2×D3—124no—
254C2×D3—128no—
255C2×D3—244no—
256C3×C4—24no—
257C3×C4—24no—
258C3×C4—44no—
259C3×C4—44no—
260C3×C4—84no—
261Dic3—124no—
262Dic3—124no—
263Dic3—124no—
264Dic3—244no—
265C32#160811yescharacteristic, complemented, Sylow
266C23—92no—
267C23—181no—
268C23—181no—
269C23—361no—
270C23—361no—
271C23D4×C3⋊D311yescharacteristic
272Q8—41no—
273Q8—361no—
274Q8—721no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4—361no—
285C2×C4—361no—
286C2×C4—361no—
287C2×C4—361no—
288C2×C4—721no—
289C2×C4—721no—
290C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
291C2×C4D4×C3⋊D311yescharacteristic
292C8—41no—
293C8—361no—
294C2×C3—24no—
295C2×C3—24no—
296C2×C3#474214yes—
297C2×C3#480614yes—
298C2×C3#482514yes—
299D3—128no—
300C22—21no—
301C22—21no—
302C22—182no—
303C22—362no—
304C22—361no—
305C22—361no—
306C22—721no—
307C22#6409111yescharacteristic
308C22SD16×C3⋊D311yescharacteristic
309C22#6412711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—361no—
316C4—361no—
317C4—361no—
318C4—721no—
319C3#6832014yescomplemented
320C2—21no—
321C2—21no—
322C2—362no—
323C2#1059244111yescharacteristic
324C2#1059250511yescharacteristic
325C2#1059252411yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32#120
prime radicalC23×C3⋊D3D4
hypercenter#328C3⋊D3
hypocenterC32#1608
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #10592742C2semidirect
3. #10592420C2semidirect
5. C32×#328C2semidirect
7. #10589318C2semidirect
32. C3×#328D3semidirect
116. #328C3⋊D3semidirect
265. C32#1608semidirect
319. C3#68320semidirect

Maximal subgroups

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

subgroupindex
#105961052
#105927422
#105924202
#105923732
C32×#3282
#105893342
#105893182
#683203