Finite Group Databasebeta

← #11870417

Subgroups — #11870417

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
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic, complemented
3#10592916C212yesmaximal, complemented
4#10592714C212yesmaximal, complemented
5C4×#3753C214yesmaximal, complemented
6#10592706C212yesmaximal, complemented
7#10592666C212yesmaximal, complemented
8#10592624C211yesmaximal, characteristic, complemented
9#82308—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4—21no—
12C2×#3828—21no—
13C32×C4×D4—21no—
14C32×C4×D4—21no—
15C32×C4×D4C2212yes—
16C32×C4×D4C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4—21no—
19C2×C32×C42C2211yescharacteristic
20C2×#3753C2214yes—
21#64139—21no—
22#64139C2212yes—
23#64084—21no—
24#64083C2211yescharacteristic, complemented
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2212yescomplemented
27#64078C2211yescharacteristic, complemented
28#63659C2214yes—
29#63657C2212yes—
30#63636C2214yescomplemented
31#63634C2214yescomplemented
32C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
33C4×C3⋊(C3⋊C8)C2212yescomplemented
34C2×C3×C4×D4D314yescomplemented
35#5477—34no—
36#5217—38no—
37#5015—38no—
38C4×#213—316no—
39#5007—38no—
40#4967—38no—
41#4925—34no—
42C24×C32—21no—
43C2×C32×D4—24no—
44C2×C32×D4—21no—
45C2×C32×D4C2312yes—
46C22×C32×C4—21no—
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—44no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×#638—22no—
54#3828—44no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—22no—
59C2×#634—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C22⋊C4—22no—
63C32×C22⋊C4—22no—
64C32×C42D411yescharacteristic
65C32×C42D411yescharacteristic
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68#3753—28no—
69#3752—22no—
70#3752—22no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊C8)C2314yes—
74#3100—91noSylow
75C22×C3×D4C2×D314yes—
76C23×C3×C4—24no—
77C2×#235—64no—
78C3×C4×D4—24no—
79C3×C4×D4—24no—
80C3×C4×D4C2×D318yes—
81C3×C4×D4C2×D318yes—
82C2×C3×C4⋊C4C2×D314yes—
83C2×C3×C22⋊C4—24no—
84C2×C3×C42C2×D314yes—
85C2×#213—316no—
86#930—38no—
87#930—64no—
88#875—64no—
89#874—34no—
90C4×D12—38no—
91C4×D12—64no—
92#869—34no—
93#832—316no—
94#830—38no—
95#809—316no—
96#807—316no—
97C4⋊(C3⋊C8)—38no—
98C4×C3⋊C8—38no—
99C23×C32—24no—
100C23×C32—22no—
101C23×C32—42no—
102C23×C32—42no—
103C23×C32C2×D411yescharacteristic
104C22×C3⋊D3—22no—
105C32×D4—24no—
106C32×D4—22no—
107C32×D4#4114yescomplemented
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—41no—
111C2×C32×C4—42no—
112C2×C32×C4—44no—
113C2×C32×C4—44no—
114C2×C32×C4D814yescomplemented
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2411yescharacteristic
121#638—44no—
122C2×C3⋊Dic3—22no—
123C4⋊(C3⋊D3)—24no—
124C4⋊(C3⋊D3)—42no—
125C4⋊(C3⋊D3)—42no—
126C4×C3⋊D3—44no—
127#634—42no—
128C3⋊(C3⋊C8)—24no—
129#532—91no—
130C2×C4×D4C3⋊D311yescharacteristic, complemented
131#480—92no—
132#474—92no—
133#459—92no—
134#447—92no—
135C4×D8—94no—
136#431—91no—
137C24×C3—24no—
138C2×C3×D4—216no—
139C2×C3×D4—24no—
140C2×C3×D4C22×D318yes—
141C22×C3×C4—24no—
142C22×C3×C4—28no—
143C22×C3×C4—28no—
144C22×C3×C4—416no—
145C22×C3×C4#6714yes—
146C22×C3×C4#6714yes—
147C22×C3×C4C22×D314yes—
148C2×#67—68no—
149#235—1216no—
150C2×D12—38no—
151C2×D12—64no—
152C2×D12—64no—
153C2×C4×D3—68no—
154C2×Dic6—64no—
155C3×C4⋊C4—24no—
156C3×C4⋊C4C22×D318yes—
157C3×C22⋊C4—28no—
158C3×C22⋊C4—28no—
159C3×C42#6714yes—
160C3×C42#6714yes—
161C3×C42C22×D314yes—
162C3×C42C22×D314yes—
163#213—632no—
164(C2×D3)⋊C4—68no—
165(C2×D3)⋊C4—68no—
166C4⋊Dic3—38no—
167C4⋊Dic3—64no—
168C2×C3⋊C8—316no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—24no—
172C22×C32—48no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32C2×D812yes—
176C22×C32C22×D411yescharacteristic
177C2×C3⋊D3—42no—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C32×C4—21no—
181C32×C4—21no—
182C32×C4—21no—
183C32×C4—42no—
184C32×C4C2×D812yes—
185C32×C4C2×D812yes—
186C32×C4C2×#4112yes—
187C3⋊Dic3—42no—
188C2×#41—181no—
189C22×D4C2×C3⋊D311yescharacteristic
190C23×C4—21no—
191C2×D8—94no—
192C4⋊Q8—91no—
193#127—91no—
194#124—181no—
195#121—92no—
196#121—181no—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—92no—
200C4×D4—181no—
201C4×D4C2×C3⋊D312yes—
202C4×D4C2×C3⋊D312yes—
203C2×C4⋊C4C2×C3⋊D311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C42C2×C3⋊D311yescharacteristic
206#107—94no—
207C4⋊C8—92no—
208#102—94no—
209#102—94no—
210C22⋊C8—92no—
211C4×C8—92no—
212C23×C3—216no—
213C23×C3—28no—
214C23×C3—48no—
215C23×C3—48no—
216C23×C3C2×#6714yes—
217C22×D3—68no—
218C3×D4—216no—
219C3×D4—28no—
220C3×D4#235116yescomplemented
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—44no—
224C2×C3×C4—48no—
225C2×C3×C4—416no—
226C2×C3×C4—416no—
227C2×C3×C4#213116yescomplemented
228C2×C3×C4C2×#6714yes—
229C2×C3×C4C2×#6714yes—
230C2×C3×C4C2×#6714yes—
231C2×C3×C4C2×#6714yes—
232C2×C3×C4C2×#6714yes—
233C2×C3×C4C23×D314yes—
234#67—1216no—
235C2×Dic3—68no—
236D12—616no—
237D12—128no—
238D12—128no—
239C4×D3—1216no—
240Dic6—128no—
241C3⋊C8—616no—
242C2×C32—22no—
243C2×C32—44no—
244C2×C32#52511yescharacteristic
245C2×C32C22×D811yescharacteristic
246C2×C32#57511yescharacteristic
247C3⋊D3—82no—
248C24—21no—
249#41—364no—
250C2×Q8—181no—
251C2×D4—24no—
252C2×D4—21no—
253C2×D4—92no—
254C2×D4—182no—
255C2×D4—181no—
256C2×D4—181no—
257C2×D4C22×C3⋊D312yes—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—44no—
262C22×C4—182no—
263C22×C4#63811yescharacteristic
264C22×C4#63811yescharacteristic
265C22×C4C22×C3⋊D311yescharacteristic
266D8—188no—
267C2×C8—94no—
268C4⋊C4—21no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C4⋊C4C22×C3⋊D312yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—182no—
275C22⋊C4—182no—
276C42#63811yescharacteristic
277C42#63811yescharacteristic
278C42C22×C3⋊D311yescharacteristic
279C42C22×C3⋊D311yescharacteristic
280C22×C3—24no—
281C22×C3—24no—
282C22×C3—216no—
283C22×C3—432no—
284C22×C3—48no—
285C22×C3—48no—
286C22×C3C2×#21318yes—
287C22×C3C22×#6714yes—
288C2×D3—128no—
289C2×D3—128no—
290C2×D3—128no—
291C3×C4—24no—
292C3×C4—24no—
293C3×C4—24no—
294C3×C4—48no—
295C3×C4C2×#21318yes—
296C3×C4C2×#21318yes—
297C3×C4C2×#23518yes—
298Dic3—128no—
299C32#310011yescharacteristic, complemented, Sylow
300C23—24no—
301C23—22no—
302C23—42no—
303C23—42no—
304C23—182no—
305C23C2×#63811yescharacteristic
306Q8—362no—
307D4—24no—
308D4—22no—
309D4—184no—
310D4—362no—
311D4—364no—
312D4—362no—
313D4#382814yescomplemented
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—182no—
321C2×C4—364no—
322C2×C4#375314yescomplemented
323C2×C4C2×#63811yescharacteristic
324C2×C4C2×#63811yescharacteristic
325C2×C4C2×#63811yescharacteristic
326C2×C4C2×#63811yescharacteristic
327C2×C4C2×#63811yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—184no—
330C2×C3—28no—
331C2×C3—416no—
332C2×C3#579114yes—
333C2×C3C22×#21314yes—
334C2×C3#582214yes—
335D3—248no—
336C22—21no—
337C22—21no—
338C22—24no—
339C22—48no—
340C22—42no—
341C22—42no—
342C22—362no—
343C22—362no—
344C22—362no—
345C22C2×#375312yes—
346C22C22×#63811yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—362no—
352C4C2×#375312yes—
353C4C2×#375312yes—
354C4C2×#382812yes—
355C3#8230814yescomplemented
356C2—22no—
357C2—44no—
358C2—722no—
359C2#1059626211yescharacteristic
360C2C22×#375311yescharacteristic
361C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. #10595948C2semidirect
3. #10592916C2semidirect
4. #10592714C2semidirect
5. C4×#3753C2semidirect
6. #10592706C2semidirect
7. #10592666C2semidirect
8. #10592624C2semidirect
24. #64083C22semidirect
26. C4×C4⋊(C3⋊D3)C22semidirect
27. #64078C22semidirect
30. #63636C22semidirect
31. #63634C22semidirect
32. C4⋊(C3⋊(C3⋊C8))C22semidirect
33. C4×C3⋊(C3⋊C8)C22semidirect
34. C2×C3×C4×D4D3semidirect
107. C32×D4#41semidirect
114. C2×C32×C4D8semidirect
130. C2×C4×D4C3⋊D3semidirect
220. C3×D4#235semidirect
227. C2×C3×C4#213semidirect
299. C32#3100semidirect
313. D4#3828semidirect
322. C2×C4#3753semidirect
355. C3#82308semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
#105959482
#105929162
#105927142
C4×#37532
#105927062
#105926662
#105926242
#823083