Finite Group Databasebeta

← #11866242

Subgroups — #11866242

Order 1152.

1482 conjugacy classes of subgroups; only the 265 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 265 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#10596287C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic
4#10595992C211yesmaximal, characteristic, complemented
5C32×#419C211yesmaximal, characteristic, complemented
6#10592818C211yesmaximal, characteristic, complemented
7#10592701C211yesmaximal, characteristic, complemented
8#10592518C214yesmaximal, complemented
9#10592517C214yesmaximal, complemented
10#78976—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64156C2212yescomplemented
17#64155—22no—
18#64153C2212yescomplemented
19C2×#3755—24no—
20C2×#3755C2214yes—
21#64138—22no—
22#64135C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24#64117—24no—
25C2×#3745C2212yes—
26C2×#3744C2212yes—
27#64102C2214yes—
28C22⋊C4×C3⋊D3—22no—
29C4×C4⋊(C3⋊D3)—22no—
30C32×#103C2214yescomplemented
31#63641C2214yescomplemented
32#63637C2212yescomplemented
33#63636C2212yescomplemented
34#5816—34no—
35C22×#215—34no—
36C2×#908—34no—
37#5521—34no—
38C3×#419D314yescomplemented
39#5119—34no—
40#5002—34no—
41#4819—316no—
42#4818—316no—
43C23×C3⋊D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—22no—
46C2×C32×Q8—22no—
47C2×C32×Q8C2312yes—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51#3828—22no—
52#3828—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)D414yes—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—24no—
60C2×#634C2311yescharacteristic
61C32×M16—22no—
62C2×C32×C8C2312yes—
63C32×C4⋊C4C2312yes—
64C32×C22⋊C4—21no—
65C32×C42—21no—
66#3757D412yes—
67#3755—28no—
68#3752—24no—
69#3752—24no—
70C4⋊(C3⋊Dic3)D412yes—
71#3750—24no—
72C4×C3⋊Dic3C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75#3745—24no—
76#3744—24no—
77#3042—91noSylow
78C22×C3×Q8C2×D314yes—
79C2×#235—34no—
80C22×D12—34no—
81C2×C3×M16C2×D314yes—
82C3×#117C2×D314yes—
83#947—38no—
84#946—68no—
85#944—38no—
86C2×#215—316no—
87C2×#215—616no—
88#929—68no—
89#926—34no—
90C22×C3⋊C8—34no—
91#908—616no—
92C2×D24—38no—
93C2×#204—38no—
94#893—316no—
95D3×C22⋊C4—68no—
96C4×D12—68no—
97C3×#103C2×D3116yescomplemented
98Dic3⋊C8—316no—
99#810—38no—
100#809—38no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—24no—
104C22×C3⋊D3—21no—
105C22×C3⋊D3—82no—
106C32×Q8—22no—
107C32×Q8—22no—
108C32×Q8—42no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—42no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4#4112yes—
115C2×C32×C4C2411yescharacteristic
116#638—42no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3C2×D414yes—
119C4⋊(C3⋊D3)—24no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)C2×D414yes—
124C4×C3⋊D3—42no—
125C4×C3⋊D3—84no—
126#634—21no—
127#634—21no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—22no—
130C2×AGL(1,ℤ/8)—91no—
131C22×SD16—91no—
132#536—91no—
133#518—91no—
134#463—94no—
135#461—94no—
136#424—91no—
137#419C3⋊D311yescharacteristic, complemented
138#416—91no—
139C23×D3—64no—
140C2×C3×Q8—24no—
141C2×C3×Q8—28no—
142C2×C3×Q8—28no—
143C2×C3×Q8C22×D318yes—
144C22×C3×C4—24no—
145C22×C3×C4C22×D314yes—
146C2×#67—64no—
147#235—68no—
148#235—68no—
149C2×D12—316no—
150C2×D12—38no—
151C2×D12—34no—
152C2×D12—68no—
153C2×D12—64no—
154C2×C4×D3—64no—
155C2×C4×D3—616no—
156C2×Dic6—34no—
157C3×M16—28no—
158C2×C3×C8C22×D318yes—
159C3×C4⋊C4C22×D318yes—
160C3×C22⋊C4—24no—
161C3×C42—24no—
162#217—38no—
163#215—632no—
164(C2×D3)⋊C4—616no—
165(C2×D3)⋊C4—616no—
166C4⋊Dic3—38no—
167Dic3⋊C4—616no—
168C4×Dic3—38no—
169C2×C3⋊C8—38no—
170C2×C3⋊C8—68no—
171D24—616no—
172#204—616no—
173C22×C32—22no—
174C22×C32#12112yes—
175C22×C32C22×D411yescharacteristic
176C2×C3⋊D3—24no—
177C2×C3⋊D3—44no—
178C2×C3⋊D3—41no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—84no—
181C32×C4—42no—
182C32×C4—42no—
183C32×C4#12112yes—
184C32×C4C22×D411yescharacteristic
185C32×C4C2×#4111yescharacteristic
186C3⋊Dic3—24no—
187C3⋊Dic3—41no—
188C2×#41—91no—
189C22×Q8C2×C3⋊D311yescharacteristic
190C22×D4—91no—
191AGL(1,ℤ/8)—184no—
192C2×SD16—94no—
193C2×SD16—92no—
194C2×SD16—184no—
195C2×D8—92no—
196C2×M16C2×C3⋊D311yescharacteristic
197C22×C8—91no—
198C4⋊Q8—92no—
199#124—92no—
200#123—182no—
201C22⋊Q8—182no—
202C4×D4—94no—
203C4×D4—182no—
204#117—91no—
205#117C2×C3⋊D311yescharacteristic
206C2×C22⋊C4—182no—
207C4⋊C8—94no—
208#103—92no—
209#103C2×C3⋊D314yescomplemented
210#102—92no—
211C23×C3D3×D414yes—
212C22×D3—68no—
213C22×D3—616no—
214C22×D3—64no—
215C22×D3—248no—
216C3×Q8—28no—
217C3×Q8—28no—
218C3×Q8—48no—
219C2×C3×C4—28no—
220C2×C3×C4—28no—
221C2×C3×C4—48no—
222C2×C3×C4#23518yes—
223C2×C3×C4D3×D414yes—
224C2×C3×C4D3×D418yes—
225C2×C3×C4C23×D314yes—
226#67—128no—
227C2×Dic3—316no—
228C2×Dic3—64no—
229D12—316no—
230D12—616no—
231D12—68no—
232D12—64no—
233D12—64no—
234C4×D3—128no—
235C4×D3—2416no—
236Dic6—64no—
237Dic6—64no—
238C3×C8—28no—
239C3⋊C8—68no—
240C2×C32—22no—
241C2×C32C2×#12111yescharacteristic
242C2×C32#57712yes—
243C3⋊D3—44no—
244C3⋊D3—81no—
245C24—181no—
246#41—182no—
247#41—182no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—91no—
252C2×Q8C22×C3⋊D312yes—
253C2×D4—92no—
254C2×D4—91no—
255C2×D4—94no—
256C2×D4—181no—
257C2×D4—182no—
258C2×D4—181no—
259C22×C4—21no—
260C22×C4—184no—
261C22×C4—181no—
262C22×C4C22×C3⋊D311yescharacteristic
263SD16—184no—
264SD16—188no—
265D8—184no—
266M16—22no—
267C2×C8—92no—
268C2×C8—182no—
269C2×C8C22×C3⋊D312yes—
270C4⋊C4—92no—
271C4⋊C4—184no—
272C4⋊C4C22×C3⋊D312yes—
273C22⋊C4—21no—
274C22⋊C4—92no—
275C22⋊C4—184no—
276C22⋊C4—184no—
277C42—21no—
278C42—92no—
279C22×C3—28no—
280C22×C3#88418yes—
281C22×C3C2×D3×D414yes—
282C2×D3—616no—
283C2×D3—1216no—
284C2×D3—124no—
285C2×D3—128no—
286C2×D3—2416no—
287C3×C4—48no—
288C3×C4—48no—
289C3×C4#88418yes—
290C3×C4C2×#23514yes—
291C3×C4C2×D3×D414yes—
292Dic3—616no—
293Dic3—124no—
294C32#304211yescharacteristic, complemented, Sylow
295C23—182no—
296C23—184no—
297C23—181no—
298C23—722no—
299C23D4×C3⋊D311yescharacteristic
300Q8—22no—
301Q8—22no—
302Q8—42no—
303Q8—181no—
304Q8—181no—
305D4—94no—
306D4—184no—
307D4—182no—
308D4—181no—
309D4—181no—
310D4—362no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—42no—
314C2×C4—94no—
315C2×C4—181no—
316C2×C4—362no—
317C2×C4—724no—
318C2×C4#382812yes—
319C2×C4D4×C3⋊D311yescharacteristic
320C2×C4D4×C3⋊D312yes—
321C2×C4C23×C3⋊D311yescharacteristic
322C8—22no—
323C8—182no—
324C2×C3—28no—
325C2×C3C2×#88414yes—
326C2×C3#577818yes—
327D3—1216no—
328D3—244no—
329C22—22no—
330C22—184no—
331C22—364no—
332C22—361no—
333C22—362no—
334C22—724no—
335C22#6409312yes—
336C22C2×D4×C3⋊D311yescharacteristic
337C4—42no—
338C4—42no—
339C4—184no—
340C4—361no—
341C4#6409312yes—
342C4C2×#382811yescharacteristic
343C4C2×D4×C3⋊D311yescharacteristic
344C3#7897614yescomplemented
345C2—22no—
346C2—364no—
347C2—721no—
348C2C2×#6409311yescharacteristic
349C2#1059624912yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#419C2
socleC22×C32C22×D4
prime radicalC2×#64117C2
hypercenter#419C3⋊D3
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #10596287C2semidirect
2. C22×#3755C2semidirect
4. #10595992C2semidirect
5. C32×#419C2semidirect
6. #10592818C2semidirect
7. #10592701C2semidirect
8. #10592518C2semidirect
9. #10592517C2semidirect
16. #64156C22semidirect
18. #64153C22semidirect
30. C32×#103C22semidirect
31. #63641C22semidirect
32. #63637C22semidirect
33. #63636C22semidirect
38. C3×#419D3semidirect
97. C3×#103C2×D3semidirect
137. #419C3⋊D3semidirect
209. #103C2×C3⋊D3semidirect
294. C32#3042semidirect
344. C3#78976semidirect

Maximal subgroups

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

subgroupindex
#105962872
C22×#37552
C2×#641172
#105959922
C32×#4192
#105928182
#105927012
#105925182
#105925172
#789763