Finite Group Databasebeta

← #11870420

Subgroups — #11870420

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4#10592545C212yesmaximal, complemented
5#10592542C212yesmaximal, complemented
6#10592435C212yesmaximal, complemented
7#10592431C212yesmaximal, complemented
8C4×#3745C214yesmaximal, complemented
9#79297—34nomaximal
10C2×#3828—21no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C32×C42C2211yescharacteristic
14#64139—21no—
15#64139C2212yes—
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3745C2214yes—
19#64084—21no—
20#64083C2211yescharacteristic, complemented
21C4×C4⋊(C3⋊D3)—21no—
22C4×C4⋊(C3⋊D3)—21no—
23C4×C4⋊(C3⋊D3)—21no—
24C4×C4⋊(C3⋊D3)C2212yes—
25C4×C4⋊(C3⋊D3)C2212yes—
26C4×C4⋊(C3⋊D3)C2212yescomplemented
27#64078C2211yescharacteristic, complemented
28C32×C4⋊C8C2212yescomplemented
29C32×C22⋊C8C2212yes—
30C32×C4×C8C2212yescomplemented
31#63648C2214yes—
32#63648C2214yescomplemented
33#63645C2214yescomplemented
34#5477—34no—
35C2×C4×D12—34no—
36C3×#431D314yescomplemented
37#4846—38no—
38#4843—38no—
39#4736—38no—
40#4732—38no—
41C4×D24—316no—
42C23×C3⋊D3—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—22no—
47C22×C3⋊Dic3—21no—
48#3828—44no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—24no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)C2312yes—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—44no—
59C2×#634—21no—
60C2×C32×C8C2314yes—
61C32×C42D411yescharacteristic
62C32×C42D411yescharacteristic
63C32×C42C2311yescharacteristic
64C32×C42C2311yescharacteristic
65#3752—22no—
66#3752—22no—
67#3752—22no—
68#3752—22no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72C4⋊(C3⋊Dic3)C2312yes—
73#3745—28no—
74#3100—91noSylow
75C2×#235—64no—
76C22×D12—34no—
77C22×C4×D3—64no—
78C2×C3×C42C2×D314yes—
79#930—38no—
80#930—64no—
81C2×(C2×D3)⋊C4—64no—
82C2×C4⋊Dic3—34no—
83C2×D24—316no—
84#875—64no—
85#874—34no—
86C4×D12—38no—
87C4×D12—38no—
88C4×D12—38no—
89C4×D12—64no—
90C4×D12—64no—
91C4×D12—64no—
92#869—34no—
93C3×C4⋊C8C2×D318yescomplemented
94C3×C22⋊C8C2×D318yes—
95C3×C4×C8C2×D318yescomplemented
96#821—316no—
97#821—316no—
98#818—316no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—24no—
101C22×C3⋊D3—22no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3—42no—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4D814yescomplemented
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2411yescharacteristic
114#638—44no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—42no—
118C4⋊(C3⋊D3)—24no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—24no—
121C4⋊(C3⋊D3)—42no—
122C4⋊(C3⋊D3)—42no—
123C4⋊(C3⋊D3)#4114yescomplemented
124C4×C3⋊D3—44no—
125C4×C3⋊D3—44no—
126C4×C3⋊D3—44no—
127#634—42no—
128C32×C8—24no—
129#532—91no—
130C2×C4×D4—91no—
131#480—92no—
132#474—92no—
133#459—92no—
134#447—92no—
135C4×D8—94no—
136#431C3⋊D311yescharacteristic, complemented
137C23×D3—64no—
138C22×C3×C4D1214yes—
139C22×C3×C4D1214yes—
140C22×C3×C4C22×D314yes—
141C2×#67—68no—
142C22×Dic3—64no—
143#235—1216no—
144C2×D12—38no—
145C2×D12—38no—
146C2×D12—616no—
147C2×D12—64no—
148C2×D12—64no—
149C2×D12—64no—
150C2×C4×D3—68no—
151C2×C4×D3—68no—
152C2×C4×D3—68no—
153C2×C4×D3—1216no—
154C2×Dic6—64no—
155C2×C3×C8C22×D3116yes—
156C3×C42D1214yes—
157C3×C42D1214yes—
158C3×C42C22×D314yes—
159C3×C42C22×D314yes—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163(C2×D3)⋊C4—68no—
164C4⋊Dic3—38no—
165C4⋊Dic3—38no—
166C4⋊Dic3—64no—
167C4⋊Dic3—64no—
168D24—632no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×D812yes—
172C22×C32C22×D411yescharacteristic
173C2×C3⋊D3—24no—
174C2×C3⋊D3—48no—
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C32×C4—21no—
181C32×C4—21no—
182C32×C4—21no—
183C32×C4C2×D812yes—
184C32×C4C2×D812yes—
185C32×C4C2×#4112yes—
186C3⋊Dic3—42no—
187C3⋊Dic3—42no—
188C2×#41—181no—
189C22×D4—91no—
190C23×C4—181no—
191C2×D8—94no—
192C4⋊Q8—91no—
193#127—91no—
194#124—181no—
195#121—92no—
196#121—181no—
197C4×D4—92no—
198C4×D4—92no—
199C4×D4—92no—
200C4×D4—181no—
201C4×D4—181no—
202C4×D4—181no—
203C2×C4⋊C4—91no—
204C2×C22⋊C4—181no—
205C2×C42C2×C3⋊D311yescharacteristic
206#107—94no—
207C4⋊C8C2×C3⋊D312yescomplemented
208#102—94no—
209#102—94no—
210C22⋊C8C2×C3⋊D312yes—
211C4×C8C2×C3⋊D312yescomplemented
212C23×C3C2×D1214yes—
213C22×D3—616no—
214C22×D3—68no—
215C22×D3—68no—
216C22×D3—128no—
217C22×D3—128no—
218C2×C3×C4—28no—
219C2×C3×C4—44no—
220C2×C3×C4D24116yescomplemented
221C2×C3×C4C2×D1214yes—
222C2×C3×C4C2×D1214yes—
223C2×C3×C4C2×D1214yes—
224C2×C3×C4C2×D1214yes—
225C2×C3×C4C2×D1214yes—
226C2×C3×C4C23×D314yes—
227#67—1216no—
228C2×Dic3—68no—
229C2×Dic3—68no—
230C2×Dic3—128no—
231D12—316no—
232D12—616no—
233D12—68no—
234D12—616no—
235D12—128no—
236D12—128no—
237C4×D3—1216no—
238C4×D3—1216no—
239C4×D3—1216no—
240Dic6—128no—
241C3×C8—216no—
242C2×C32—22no—
243C2×C32#52511yescharacteristic
244C2×C32C22×D811yescharacteristic
245C2×C32#57511yescharacteristic
246C3⋊D3—44no—
247C3⋊D3—82no—
248C24—181no—
249#41—364no—
250C2×Q8—181no—
251C2×D4—92no—
252C2×D4—92no—
253C2×D4—184no—
254C2×D4—182no—
255C2×D4—181no—
256C2×D4—181no—
257C2×D4—181no—
258C22×C4—181no—
259C22×C4—182no—
260C22×C4—182no—
261C22×C4—182no—
262C22×C4—364no—
263C22×C4C4⋊(C3⋊D3)11yescharacteristic
264C22×C4C4⋊(C3⋊D3)11yescharacteristic
265C22×C4C22×C3⋊D311yescharacteristic
266D8—188no—
267C2×C8C22×C3⋊D314yes—
268C4⋊C4—92no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C4⋊C4—181no—
272C22⋊C4—182no—
273C22⋊C4—182no—
274C22⋊C4—182no—
275C22⋊C4—182no—
276C42C4⋊(C3⋊D3)11yescharacteristic
277C42C4⋊(C3⋊D3)11yescharacteristic
278C42C22×C3⋊D311yescharacteristic
279C42C22×C3⋊D311yescharacteristic
280C22×C3—24no—
281C22×C3—24no—
282C22×C3C2×D2418yes—
283C22×C3C22×D1214yes—
284C2×D3—616no—
285C2×D3—1232no—
286C2×D3—128no—
287C2×D3—128no—
288C2×D3—128no—
289C2×D3—128no—
290C2×D3—128no—
291C3×C4—24no—
292C3×C4—24no—
293C3×C4—24no—
294C3×C4C2×D2418yes—
295C3×C4C2×D2418yes—
296C3×C4D3×#4118yes—
297Dic3—128no—
298Dic3—128no—
299C32#310011yescharacteristic, complemented, Sylow
300C23—184no—
301C23—182no—
302C23—182no—
303C23—362no—
304C23—362no—
305C23C2×C4⋊(C3⋊D3)11yescharacteristic
306Q8—362no—
307D4—94no—
308D4—184no—
309D4—182no—
310D4—184no—
311D4—362no—
312D4—364no—
313D4—362no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—362no—
319C2×C4—364no—
320C2×C4—364no—
321C2×C4—364no—
322C2×C4#374514yescomplemented
323C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
324C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
325C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
326C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
327C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—24no—
330C2×C3—28no—
331C2×C3#552414yes—
332C2×C3C22×D2414yes—
333C2×C3#574814yes—
334D3—1216no—
335D3—248no—
336C22—21no—
337C22—21no—
338C22—184no—
339C22—368no—
340C22—362no—
341C22—362no—
342C22—362no—
343C22—362no—
344C22—362no—
345C22C2×#374512yes—
346C22C22×C4⋊(C3⋊D3)11yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—362no—
351C4—362no—
352C4C2×#374512yes—
353C4C2×#374512yes—
354C4#41×C3⋊D312yes—
355C3#7929714yescomplemented
356C2—22no—
357C2—364no—
358C2—722no—
359C2#1059599511yescharacteristic
360C2C22×#374511yescharacteristic
361C2#1059621911yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#431C2
socleC22×C32C22×D4
hypercenter#431C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C32×#431C2semidirect
4. #10592545C2semidirect
5. #10592542C2semidirect
6. #10592435C2semidirect
7. #10592431C2semidirect
8. C4×#3745C2semidirect
20. #64083C22semidirect
26. C4×C4⋊(C3⋊D3)C22semidirect
27. #64078C22semidirect
28. C32×C4⋊C8C22semidirect
30. C32×C4×C8C22semidirect
32. #63648C22semidirect
33. #63645C22semidirect
36. C3×#431D3semidirect
93. C3×C4⋊C8C2×D3semidirect
95. C3×C4×C8C2×D3semidirect
107. C2×C32×C4D8semidirect
123. C4⋊(C3⋊D3)#41semidirect
136. #431C3⋊D3semidirect
207. C4⋊C8C2×C3⋊D3semidirect
211. C4×C8C2×C3⋊D3semidirect
220. C2×C3×C4D24semidirect
299. C32#3100semidirect
322. C2×C4#3745semidirect
355. C3#79297semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C4×C4⋊(C3⋊D3)2
C32×#4312
#105925452
#105925422
#105924352
#105924312
C4×#37452
#792973