Finite Group Databasebeta

← #11865844

Subgroups — #11865844

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64141C212yesmaximal, complemented
3#10595948C211yesmaximal, characteristic, complemented
4#10592718C212yesmaximal, complemented
5#10592715C214yesmaximal, complemented
6#10592714C212yesmaximal, complemented
7#10592665C212yesmaximal, complemented
8#10592623C211yesmaximal, characteristic, complemented
9#82307—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4—21no—
12C2×#3828C2212yes—
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×#3754C2214yes—
21#64141—28no—
22C2×#3753C2214yes—
23#64139—21no—
24#64139—21no—
25C2×#3748C2212yes—
26#64084C2212yescomplemented
27#64083C2211yescharacteristic, complemented
28C4×C4⋊(C3⋊D3)—21no—
29C4×C4⋊(C3⋊D3)—21no—
30#64078C2211yescharacteristic, complemented
31#63637C2214yescomplemented
32#63636C2214yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
34C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
35C2×C3×C4×D4D314yescomplemented
36C2×#932—38no—
37#5477—34no—
38#5019—38no—
39#5016—316no—
40#5015—38no—
41#4966—38no—
42#4924—34no—
43C24×C32—21no—
44C2×C32×D4—21no—
45C2×C32×D4—22no—
46C2×C32×D4D414yescomplemented
47C2×C32×D4C2312yes—
48C22×C32×C4—21no—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4—44no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C2×#638—22no—
56#3828—24no—
57#3828—24no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×#634C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C22⋊C4—22no—
66C32×C22⋊C4—22no—
67C32×C42D411yescharacteristic
68C32×C42D411yescharacteristic
69C32×C42C2311yescharacteristic
70C32×C42C2311yescharacteristic
71#3754—28no—
72#3753—28no—
73#3752—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77#3748—24no—
78C2×C3⋊(C3⋊C8)C2314yes—
79#3036—91noSylow
80C22×C3×D4C2×D314yes—
81C23×C3×C4—24no—
82C2×#235—38no—
83C3×C4×D4—24no—
84C3×C4×D4—24no—
85C3×C4×D4C2×D318yes—
86C3×C4×D4C2×D318yes—
87C2×C3×C4⋊C4C2×D314yes—
88C2×C3×C22⋊C4—24no—
89C2×C3×C42C2×D314yes—
90C2×#214—316no—
91#932—632no—
92C2×#213—316no—
93#930—64no—
94#930—64no—
95C2×#208—38no—
96#875—38no—
97#874—34no—
98C4×D12—64no—
99C4×D12—64no—
100#869—34no—
101#810—316no—
102#809—316no—
103C4⋊(C3⋊C8)—38no—
104C4⋊(C3⋊C8)—38no—
105C23×C32—24no—
106C23×C32—22no—
107C23×C32—42no—
108C23×C32—42no—
109C23×C32C2×D411yescharacteristic
110C22×C3⋊D3—22no—
111C32×D4—24no—
112C32×D4—22no—
113C32×D4C2×D414yes—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—44no—
118C2×C32×C4—42no—
119C2×C32×C4—44no—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4112yes—
127C2×C32×C4C2411yescharacteristic
128#638—44no—
129C2×C3⋊Dic3—22no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—42no—
133C4⋊(C3⋊D3)—42no—
134C4×C3⋊D3—44no—
135#634—22no—
136#634—22no—
137C3⋊(C3⋊C8)—24no—
138C2×AGL(1,ℤ/8)—92no—
139#532—91no—
140C2×C4×D4C3⋊D311yescharacteristic, complemented
141#463—94no—
142#461—92no—
143#459—92no—
144#423—91no—
145#417—92no—
146C24×C3—24no—
147C2×C3×D4—28no—
148C2×C3×D4—24no—
149C2×C3×D4D12116yescomplemented
150C2×C3×D4C22×D318yes—
151C22×C3×C4—24no—
152C22×C3×C4—28no—
153C22×C3×C4—28no—
154C22×C3×C4—416no—
155C22×C3×C4#6714yes—
156C22×C3×C4#6714yes—
157C22×C3×C4C22×D314yes—
158C2×#67—68no—
159#235—616no—
160#235—616no—
161C2×D12—38no—
162C2×D12—64no—
163C2×D12—64no—
164C2×C4×D3—68no—
165C2×Dic6—38no—
166C3×C4⋊C4—24no—
167C3×C4⋊C4C22×D318yes—
168C3×C22⋊C4—28no—
169C3×C22⋊C4—28no—
170C3×C42#6714yes—
171C3×C42#6714yes—
172C3×C42C22×D314yes—
173C3×C42C22×D314yes—
174#214—632no—
175#213—632no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178C4⋊Dic3—64no—
179C4⋊Dic3—64no—
180#208—616no—
181C2×C3⋊C8—316no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—24no—
185C22×C32—48no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32#12112yes—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—42no—
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—42no—
197C32×C4#12112yes—
198C32×C4AGL(1,ℤ/8)12yescomplemented
199C32×C4C22×D411yescharacteristic
200C32×C4C2×#4111yescharacteristic
201C3⋊Dic3—42no—
202C2×#41—92no—
203C22×D4C2×C3⋊D311yescharacteristic
204C23×C4—21no—
205AGL(1,ℤ/8)—188no—
206C2×SD16—94no—
207C2×D8—94no—
208C2×M16—92no—
209C4⋊Q8—91no—
210#127—91no—
211#124—92no—
212#121—181no—
213#121—181no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4—181no—
217C4×D4—181no—
218C4×D4C2×C3⋊D312yes—
219C4×D4C2×C3⋊D312yes—
220C2×C4⋊C4C2×C3⋊D311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C2×C3⋊D311yescharacteristic
223C4⋊C8—92no—
224C4⋊C8—92no—
225#103—94no—
226#102—94no—
227C23×C3—216no—
228C23×C3—28no—
229C23×C3—48no—
230C23×C3—48no—
231C23×C3C2×#6714yes—
232C22×D3—68no—
233C3×D4—216no—
234C3×D4—28no—
235C3×D4C2×D12116yes—
236C2×C3×C4—28no—
237C2×C3×C4—28no—
238C2×C3×C4—44no—
239C2×C3×C4—416no—
240C2×C3×C4—48no—
241C2×C3×C4—416no—
242C2×C3×C4C2×D1218yes—
243C2×C3×C4#23518yes—
244C2×C3×C4C2×#6714yes—
245C2×C3×C4C2×#6714yes—
246C2×C3×C4C2×#6714yes—
247C2×C3×C4C2×#6714yes—
248C2×C3×C4C2×#6714yes—
249C2×C3×C4C23×D314yes—
250#67—1216no—
251C2×Dic3—68no—
252D12—68no—
253D12—68no—
254D12—128no—
255D12—128no—
256C4×D3—1216no—
257Dic6—68no—
258Dic6—68no—
259C3⋊C8—616no—
260C2×C32—22no—
261C2×C32—44no—
262C2×C32C2×#12111yescharacteristic
263C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
264C2×C32#57511yescharacteristic
265C3⋊D3—82no—
266C24—21no—
267#41—184no—
268#41—184no—
269C2×Q8—92no—
270C2×D4—22no—
271C2×D4—21no—
272C2×D4—92no—
273C2×D4—182no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4C4⋊(C3⋊D3)14yescomplemented
277C2×D4C22×C3⋊D312yes—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—44no—
282C22×C4—182no—
283C22×C4#63811yescharacteristic
284C22×C4#63811yescharacteristic
285C22×C4C22×C3⋊D311yescharacteristic
286SD16—188no—
287D8—188no—
288M16—184no—
289C2×C8—94no—
290C4⋊C4—21no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4C22×C3⋊D312yes—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C42#63811yescharacteristic
299C42#63811yescharacteristic
300C42C22×C3⋊D311yescharacteristic
301C42C22×C3⋊D311yescharacteristic
302C22×C3—24no—
303C22×C3—24no—
304C22×C3—216no—
305C22×C3—432no—
306C22×C3—48no—
307C22×C3—48no—
308C22×C3#93018yes—
309C22×C3C22×#6714yes—
310C2×D3—128no—
311C2×D3—128no—
312C2×D3—128no—
313C3×C4—24no—
314C3×C4—24no—
315C3×C4—24no—
316C3×C4—48no—
317C3×C4#93018yes—
318C3×C4#93218yescomplemented
319C3×C4C22×D1214yes—
320C3×C4C2×#23514yes—
321Dic3—128no—
322C32#303611yescharacteristic, complemented, Sylow
323C23—22no—
324C23—24no—
325C23—42no—
326C23—42no—
327C23—182no—
328C23C2×#63811yescharacteristic
329Q8—182no—
330Q8—182no—
331D4—22no—
332D4—24no—
333D4—182no—
334D4—182no—
335D4—362no—
336D4—364no—
337D4—362no—
338D4C2×C4⋊(C3⋊D3)14yes—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—182no—
346C2×C4—364no—
347C2×C4C2×C4⋊(C3⋊D3)12yes—
348C2×C4#382812yes—
349C2×C4C2×#63811yescharacteristic
350C2×C4C2×#63811yescharacteristic
351C2×C4C2×#63811yescharacteristic
352C2×C4C2×#63811yescharacteristic
353C2×C4C2×#63811yescharacteristic
354C2×C4C23×C3⋊D311yescharacteristic
355C8—184no—
356C2×C3—28no—
357C2×C3—416no—
358C2×C3C2×#93014yes—
359C2×C3C2×#93214yes—
360C2×C3#582214yes—
361D3—248no—
362C22—21no—
363C22—21no—
364C22—24no—
365C22—48no—
366C22—42no—
367C22—42no—
368C22—362no—
369C22—362no—
370C22—362no—
371C22#6413912yes—
372C22C22×#63811yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—362no—
378C4#6413912yes—
379C4#6414112yescomplemented
380C4C22×C4⋊(C3⋊D3)11yescharacteristic
381C4C2×#382811yescharacteristic
382C3#8230714yescomplemented
383C2—22no—
384C2—44no—
385C2—722no—
386C2C2×#6413911yescharacteristic
387C2C2×#6414111yescharacteristic
388C2#1059629311yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ 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. C2×#64141C2semidirect
3. #10595948C2semidirect
4. #10592718C2semidirect
5. #10592715C2semidirect
6. #10592714C2semidirect
7. #10592665C2semidirect
8. #10592623C2semidirect
26. #64084C22semidirect
27. #64083C22semidirect
30. #64078C22semidirect
31. #63637C22semidirect
32. #63636C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C4⋊(C3⋊(C3⋊C8))C22semidirect
35. C2×C3×C4×D4D3semidirect
46. C2×C32×D4D4semidirect
140. C2×C4×D4C3⋊D3semidirect
149. C2×C3×D4D12semidirect
198. C32×C4AGL(1,ℤ/8)semidirect
276. C2×D4C4⋊(C3⋊D3)semidirect
318. C3×C4#932semidirect
322. C32#3036semidirect
379. C4#64141semidirect
382. C3#82307semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641412
#105959482
#105927182
#105927152
#105927142
#105926652
#105926232
#823073