Finite Group Databasebeta

← #11866317

Subgroups — #11866317

Order 1152.

1470 conjugacy classes of subgroups; only the 265 normal subgroups are shown.

normal subgroups only

This group has 1470 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#10596276C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4#10595987C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6#10592818C211yesmaximal, characteristic, complemented
7#10592701C211yesmaximal, characteristic, complemented
8#10592466C214yesmaximal, complemented
9#10592461C214yesmaximal, complemented
10#78945—34nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64162—22no—
17#64149C2212yes—
18#64147—22no—
19#64145C2212yes—
20C2×#3754—24no—
21C2×#3754C2214yes—
22#64135C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24#64118—24no—
25C2×#3746C2212yescomplemented
26C2×#3744C2212yescomplemented
27#64096C2214yescomplemented
28#64086—22no—
29C4×#634—22no—
30C32×#102C2214yes—
31#63641C2214yescomplemented
32#63637C2212yescomplemented
33#63636C2212yescomplemented
34#5805—34no—
35C22×#214—34no—
36C2×#909—34no—
37#5516—34no—
38C3×#418D314yescomplemented
39#5119—34no—
40#5002—34no—
41#4767—316no—
42#4762—316no—
43C24×C32—21no—
44C2×C32×D4—22no—
45C2×C32×D4—21no—
46C2×C32×D4—22no—
47C2×C32×D4C2312yes—
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C2×#638—24no—
51C22×C3⋊Dic3—21no—
52#3828—22no—
53#3828—22no—
54C2×C4⋊(C3⋊D3)C2311yescharacteristic
55C2×C4×C3⋊D3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634D414yescomplemented
59C2×#634C2311yescharacteristic
60C2×#634C2312yes—
61C32×M16—22no—
62C2×C32×C8C2312yes—
63C32×C4⋊C4C2312yes—
64C32×C22⋊C4—21no—
65C32×C42—21no—
66#3757—24no—
67#3757D412yes—
68#3754—28no—
69C4⋊(C3⋊Dic3)D412yes—
70#3750—24no—
71C4×C3⋊Dic3—24no—
72C4×C3⋊Dic3C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75#3746—24no—
76#3744—24no—
77#3043—91noSylow
78C22×C3×D4C2×D314yes—
79C2×#235—34no—
80C22×Dic6—34no—
81C2×C3×M16C2×D314yes—
82C3×#117C2×D314yes—
83#953—68no—
84#940—38no—
85#938—68no—
86#936—38no—
87C2×#214—316no—
88C2×#214—616no—
89#926—34no—
90C22×C3⋊C8—34no—
91#909—616no—
92C2×Dic12—38no—
93C2×#204—38no—
94#887—316no—
95#877—68no—
96C4×Dic6—68no—
97C3×#102C2×D3116yes—
98Dic3⋊C8—316no—
99#810—38no—
100#809—38no—
101C23×C32—22no—
102C23×C32—42no—
103C23×C32—82no—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3—21no—
106C32×D4—22no—
107C32×D4—22no—
108C32×D4—42no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D412yes—
112C2×C32×C4#4112yes—
113C2×C32×C4C2411yescharacteristic
114#638—42no—
115#638—84no—
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3C2×D414yes—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—21no—
122C4×C3⋊D3—42no—
123#634—24no—
124#634—22no—
125#634—21no—
126#634—21no—
127#634C2×D414yes—
128C32×C8—22no—
129C3⋊(C3⋊C8)—22no—
130C2×#137—91no—
131C22×SD16—91no—
132#535—91no—
133#519—91no—
134#464—94no—
135#460—94no—
136#424—91no—
137#418C3⋊D311yescharacteristic, complemented
138#416—91no—
139C24×C3—24no—
140C2×C3×D4—28no—
141C2×C3×D4—28no—
142C2×C3×D4—24no—
143C2×C3×D4C22×D318yes—
144C22×C3×C4C22×D314yes—
145C2×#67—616no—
146C2×#67—64no—
147C22×Dic3—64no—
148#235—68no—
149#235—68no—
150C2×D12—34no—
151C2×C4×D3—64no—
152C2×Dic6—316no—
153C2×Dic6—38no—
154C2×Dic6—34no—
155C2×Dic6—68no—
156C2×Dic6—64no—
157C3×M16—28no—
158C2×C3×C8C22×D318yes—
159C3×C4⋊C4C22×D318yes—
160C3×C22⋊C4—24no—
161C3×C42—24no—
162#217—38no—
163#217—616no—
164#214—632no—
165C4⋊Dic3—38no—
166Dic3⋊C4—616no—
167C4×Dic3—38no—
168C4×Dic3—616no—
169C2×C3⋊C8—38no—
170C2×C3⋊C8—68no—
171Dic12—616no—
172#204—616no—
173C22×C32—22no—
174C22×C32—42no—
175C22×C32—44no—
176C22×C32—84no—
177C22×C32#12112yes—
178C22×C32C22×D411yescharacteristic
179C2×C3⋊D3—41no—
180C2×C3⋊D3—42no—
181C32×C4—42no—
182C32×C4#12112yes—
183C32×C4C22×D411yescharacteristic
184C32×C4C2×#4111yescharacteristic
185C3⋊Dic3—24no—
186C3⋊Dic3—24no—
187C3⋊Dic3—41no—
188C2×#41—91no—
189C22×Q8—91no—
190C22×D4C2×C3⋊D311yescharacteristic
191#137—184no—
192C2×Q16—92no—
193C2×SD16—94no—
194C2×SD16—92no—
195C2×SD16—184no—
196C2×M16C2×C3⋊D311yescharacteristic
197C22×C8—91no—
198#127—92no—
199#124—92no—
200#121—182no—
201#120—182no—
202C4×Q8—94no—
203C4×Q8—182no—
204#117—91no—
205#117—182no—
206#117C2×C3⋊D311yescharacteristic
207C4⋊C8—94no—
208#103—92no—
209#102—92no—
210#102C2×C3⋊D314yes—
211C23×C3—28no—
212C23×C3—48no—
213C23×C3—88no—
214C23×C3D3×D414yes—
215C22×D3—64no—
216C3×D4—28no—
217C3×D4—28no—
218C3×D4—48no—
219C2×C3×C4—28no—
220C2×C3×C4#23518yes—
221C2×C3×C4D3×D414yes—
222C2×C3×C4D3×D418yes—
223C2×C3×C4C23×D314yes—
224#67—128no—
225#67—2416no—
226C2×Dic3—316no—
227C2×Dic3—616no—
228C2×Dic3—68no—
229C2×Dic3—64no—
230D12—64no—
231D12—64no—
232C4×D3—128no—
233Dic6—316no—
234Dic6—616no—
235Dic6—68no—
236Dic6—64no—
237Dic6—64no—
238C3×C8—28no—
239C3⋊C8—68no—
240C2×C32—22no—
241C2×C32—82no—
242C2×C32C2×#12111yescharacteristic
243C2×C32#57712yes—
244C3⋊D3—81no—
245C24—21no—
246#41—182no—
247#41—182no—
248C2×Q8—92no—
249C2×Q8—91no—
250C2×Q8—94no—
251C2×Q8—182no—
252C2×Q8—181no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—91no—
257C2×D4—184no—
258C2×D4—181no—
259C2×D4C22×C3⋊D312yes—
260C22×C4—181no—
261C22×C4—181no—
262C22×C4C22×C3⋊D311yescharacteristic
263Q16—184no—
264SD16—184no—
265SD16—188no—
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—
276C42—21no—
277C42—92no—
278C42—184no—
279C22×C3—28no—
280C22×C3—48no—
281C22×C3—416no—
282C22×C3—816no—
283C22×C3#88418yes—
284C22×C3C2×D3×D414yes—
285C2×D3—124no—
286C2×D3—128no—
287C3×C4—48no—
288C3×C4#88418yes—
289C3×C4C2×#23514yes—
290C3×C4C2×D3×D414yes—
291Dic3—616no—
292Dic3—616no—
293Dic3—124no—
294C32#304311yescharacteristic, complemented, Sylow
295C23—22no—
296C23—42no—
297C23—82no—
298C23—181no—
299C23D4×C3⋊D311yescharacteristic
300Q8—94no—
301Q8—184no—
302Q8—182no—
303Q8—181no—
304Q8—181no—
305D4—22no—
306D4—22no—
307D4—42no—
308D4—181no—
309D4—181no—
310D4—362no—
311D4—724no—
312C2×C4—22no—
313C2×C4—94no—
314C2×C4—184no—
315C2×C4—182no—
316C2×C4—181no—
317C2×C4—362no—
318C2×C4#382812yes—
319C2×C4D4×C3⋊D311yescharacteristic
320C2×C4D4×C3⋊D312yes—
321C2×C4C23×C3⋊D311yescharacteristic
322C8—22no—
323C8—182no—
324C2×C3—28no—
325C2×C3—88no—
326C2×C3C2×#88414yes—
327C2×C3#577518yes—
328D3—244no—
329C22—22no—
330C22—42no—
331C22—44no—
332C22—84no—
333C22—361no—
334C22—362no—
335C22#6409312yes—
336C22C2×D4×C3⋊D311yescharacteristic
337C4—42no—
338C4—184no—
339C4—184no—
340C4—361no—
341C4#6409312yes—
342C4C2×#382811yescharacteristic
343C4C2×D4×C3⋊D311yescharacteristic
344C3#7894514yescomplemented
345C2—22no—
346C2—82no—
347C2—721no—
348C2C2×#6409311yescharacteristic
349C2#1059624612yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radical#10596276C2
hypercenter#418C3⋊D3
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C22×#3754C2semidirect
3. C2×#64118C2semidirect
4. #10595987C2semidirect
5. C32×#418C2semidirect
6. #10592818C2semidirect
7. #10592701C2semidirect
8. #10592466C2semidirect
9. #10592461C2semidirect
25. C2×#3746C22semidirect
26. C2×#3744C22semidirect
27. #64096C22semidirect
31. #63641C22semidirect
32. #63637C22semidirect
33. #63636C22semidirect
38. C3×#418D3semidirect
58. C2×#634D4semidirect
137. #418C3⋊D3semidirect
294. C32#3043semidirect
344. C3#78945semidirect

Maximal subgroups

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

subgroupindex
#105962762
C22×#37542
C2×#641182
#105959872
C32×#4182
#105928182
#105927012
#105924662
#105924612
#789453