Finite Group Databasebeta

← #11866766

Subgroups — #11866766

Order 1152.

1042 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×#3787C211yesmaximal, characteristic, complemented
2C2×#64225C211yesmaximal, characteristic, complemented
3#10595081C212yesmaximal, complemented
4#10593520C214yesmaximal, complemented
5#10593423C214yesmaximal, complemented
6#10593396C211yesmaximal, characteristic, complemented
7#10593365C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×#3811—22no—
10C2×#3802C2212yes—
11C22×#622C2212yescomplemented
12C2×#3787—24no—
13C2×#3787C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C2×#3787C2212yescomplemented
16C2×#3774C2214yescomplemented
17#64225—24no—
18C3×#930—22no—
19#63980C2214yescomplemented
20#63921—22no—
21#63916—22no—
22#63912C2214yescomplemented
23#63900C2212yes—
24#63743C2214yescomplemented
25#63739C2218yescomplemented
26D3×#121—62no—
27C23×C3⋊D3D411yescharacteristic
28C22×D32—22no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×C3×#67—24no—
38C2×C3×D12—22no—
39#3811—48no—
40C2×#626—24no—
41C2×#625C2314yes—
42C2×#624—22no—
43#3802—24no—
44#3802—24no—
45C2×#622—24no—
46C2×#622C2312yes—
47C2×#622C2312yes—
48#3787—22no—
49#3787—24no—
50#3787D414yescomplemented
51#3774—28no—
52C3×(C2×D3)⋊C4—24no—
53C3×C4⋊Dic3—22no—
54#3724C2314yes—
55(C2×D3)⋊Dic3—24no—
56C2×#466—91nomaximal, Sylow
57C2×D3×D4—62no—
58C2×D3×D4—64no—
59C22×C4×D3—62no—
60C3×#121—62no—
61#939—64no—
62#938—62no—
63#930—22no—
64#895—62no—
65D3×C4⋊C4—62no—
66#884—64no—
67D3×C22⋊C4—64no—
68C23×C32C2×D411yescharacteristic
69C22×C3⋊D3—22no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3D814yescomplemented
72C22×C3⋊D3C2×D411yescharacteristic
73C22×C3⋊D3C2×D411yescharacteristic
74C22×C3×D3—24no—
75C2×D32—44no—
76C2×D32—44no—
77C2×D32—44no—
78C2×C32×C4—22no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—21no—
89C4×C3⋊D3C2×D412yes—
90C4×C3⋊D3#4112yes—
91C3×#67—48no—
92C2×C3×Dic3—24no—
93C3×D12—44no—
94#626—48no—
95#625—24no—
96#625—24no—
97#624—44no—
98#622—22no—
99#622C2×D414yescomplemented
100C22×D8—91no—
101C23×C8—91no—
102C2×#121—92no—
103#466—94no—
104#466—94no—
105C2×#107—91no—
106C2×#102—92no—
107C23×D3—62no—
108C23×D3—64no—
109C2×C3×D4—62no—
110C2×C3×D4—64no—
111C22×C3×C4—22no—
112C2×#67—24no—
113C2×#67—64no—
114C2×#67—64no—
115C22×Dic3—62no—
116D3×D4—124no—
117D3×D4—124no—
118D3×D4—1216no—
119C2×D12—22no—
120C2×D12—64no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C4×D3—124no—
127C2×C4×D3—124no—
128C3×C4⋊C4—62no—
129C3×C22⋊C4—64no—
130#217—64no—
131(C2×D3)⋊C4—24no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—22no—
134Dic3⋊C4—64no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C2×D812yescomplemented
138C22×C32C22×D411yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—28no—
142C2×C3⋊D3#12112yes—
143C2×C3⋊D3C2×D812yes—
144C2×C3⋊D3C2×D812yescomplemented
145C2×C3⋊D3#13512yes—
146C2×C3×D3—44no—
147C2×C3×D3—44no—
148C2×C3×D3—44no—
149D32—88no—
150C32×C4—21no—
151C32×C4#12112yes—
152C3⋊Dic3—21no—
153C3⋊Dic3C22×D411yescharacteristic
154C3⋊Dic3C2×#4111yescharacteristic
155C3×Dic3—44no—
156C22×D4—92no—
157C22×D4—182no—
158C23×C4—91no—
159C2×D8—94no—
160C2×D8—184no—
161C22×C8—91no—
162C22×C8—91no—
163C22×C8—92no—
164C22×C8—92no—
165C22×C8—184no—
166#121—62no—
167#121—94no—
168#121—94no—
169#121—182no—
170C2×C4⋊C4—92no—
171C2×C22⋊C4—182no—
172#107—94no—
173#102—98no—
174C23×C3—22no—
175C23×C3—64no—
176C22×D3—24no—
177C22×D3—62no—
178C22×D3—68no—
179C22×D3—62no—
180C22×D3—124no—
181C22×D3—124no—
182C22×D3—128no—
183C22×D3—128no—
184C22×D3—128no—
185C3×D4—124no—
186C3×D4—128no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—44no—
190C2×C3×C4—64no—
191#67—48no—
192#67—124no—
193#67—124no—
194#67—128no—
195C2×Dic3—24no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—122no—
199C2×Dic3—122no—
200D12—44no—
201D12—128no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—122no—
205C4×D3—122no—
206C4×D3—124no—
207C4×D3—124no—
208C4×D3—128no—
209C2×C32—22no—
210C2×C32C2×#12111yescharacteristic
211C2×C32C22×D811yescharacteristic
212C2×C32C2×#13511yescharacteristic
213C3⋊D3—22no—
214C3⋊D3#46614yescomplemented
215C3×D3—84no—
216C24—91no—
217C24—182no—
218C2×D4—64no—
219C2×D4—62no—
220C2×D4—94no—
221C2×D4—184no—
222C2×D4—184no—
223C2×D4—184no—
224C2×D4—368no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—182no—
231C22×C4—182no—
232C22×C4—182no—
233C22×C4GO+(4,𝔽2)11yescharacteristic
234D8—188no—
235C2×C8—92no—
236C2×C8—94no—
237C2×C8—92no—
238C2×C8—184no—
239C2×C8—184no—
240C2×C8—182no—
241C4⋊C4—62no—
242C4⋊C4—94no—
243C22⋊C4—64no—
244C22⋊C4—184no—
245C22×C3—22no—
246C22×C3—24no—
247C22×C3—42no—
248C22×C3—42no—
249C22×C3—124no—
250C22×C3—124no—
251C22×C3—124no—
252C2×D3—44no—
253C2×D3—44no—
254C2×D3—44no—
255C2×D3—64no—
256C2×D3—64no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—1216no—
260C2×D3—122no—
261C2×D3—122no—
262C2×D3—2416no—
263C3×C4—24no—
264C3×C4—42no—
265C3×C4—124no—
266Dic3—44no—
267Dic3—62no—
268Dic3—62no—
269Dic3—122no—
270C32C2×#46611yescharacteristic, complemented, Sylow
271C23—64no—
272C23—91no—
273C23—91no—
274C23—94no—
275C23—182no—
276C23—182no—
277C23—364no—
278C23—364no—
279C23—364no—
280C23C2×GO+(4,𝔽2)11yescharacteristic
281D4—128no—
282D4—124no—
283D4—184no—
284D4—184no—
285D4—368no—
286C2×C4—22no—
287C2×C4—64no—
288C2×C4—91no—
289C2×C4—92no—
290C2×C4—92no—
291C2×C4—91no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—182no—
295C2×C4—181no—
296C2×C4—181no—
297C2×C4—182no—
298C2×C4—364no—
299C2×C4C2×GO+(4,𝔽2)11yescharacteristic
300C2×C4C2×GO+(4,𝔽2)11yescharacteristic
301C8—94no—
302C8—182no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—44no—
307C2×C3—244no—
308D3—68no—
309D3—84no—
310D3—124no—
311C22—21no—
312C22—21no—
313C22—92no—
314C22—92no—
315C22—92no—
316C22—92no—
317C22—124no—
318C22—124no—
319C22—124no—
320C22—188no—
321C22—181no—
322C22—181no—
323C22—728no—
324C22#6422512yescomplemented
325C22C22×GO+(4,𝔽2)11yescharacteristic
326C4—21no—
327C4—91no—
328C4—91no—
329C4—124no—
330C4—181no—
331C4#6424212yes—
332C3—22no—
333C2—22no—
334C2—94no—
335C2—182no—
336C2—244no—
337C2C2×#6422511yescharacteristic
338C2#1059650011yescharacteristic
339C2C2×#6424211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#466
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3787C2semidirect
2. C2×#64225C2semidirect
3. #10595081C2semidirect
4. #10593520C2semidirect
5. #10593423C2semidirect
6. #10593396C2semidirect
7. #10593365C2semidirect
11. C22×#622C22semidirect
15. C2×#3787C22semidirect
16. C2×#3774C22semidirect
19. #63980C22semidirect
22. #63912C22semidirect
24. #63743C22semidirect
25. #63739C22semidirect
50. #3787D4semidirect
71. C22×C3⋊D3D8semidirect
99. #622C2×D4semidirect
137. C22×C32C2×D8semidirect
144. C2×C3⋊D3C2×D8semidirect
214. C3⋊D3#466semidirect
270. C32C2×#466semidirect
324. C22#64225semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#642252
#105950812
#105935202
#105934232
#105933962
#105933652
C2×#4669