Finite Group Databasebeta

← #11895722

Subgroups — #11895722

Order 1152.

1188 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
1C32×#554C211yesmaximal, characteristic, complemented
2#10596048C211yesmaximal, characteristic, complemented
3#10592787C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592766C212yesmaximal, complemented
6#10592765C212yesmaximal, complemented
7#10592723C211yesmaximal, characteristic, complemented
8#10592714C211yesmaximal, characteristic, complemented
9#10592714C212yesmaximal, complemented
10#10592713C212yesmaximal, complemented
11C4×#3753C211yesmaximal, characteristic, complemented
12#83638—34nomaximal
13C2×#3832—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#125C2212yes—
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8—22no—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2212yes—
21C2×C32×C4⋊C4—21no—
22C2×#3753C2211yescharacteristic
23C2×#3753C2212yes—
24#64104—21no—
25#64104—22no—
26#64083C2211yescharacteristic
27#64083C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yes—
30#63659C2211yescharacteristic
31#63636C2212yes—
32#63636C2212yes—
33#63636C2212yes—
34#63636C2211yescharacteristic
35#63636C2212yes—
36#63635C2212yes—
37#63634C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40#63630C2212yes—
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×#554D314yescomplemented
43#5577—34no—
44#5088—34no—
45#5084—34no—
46#5067—38no—
47#5066—38no—
48#5024—34no—
49#5015—38no—
50#5015—34no—
51#5014—38no—
52C4×#213—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4—22no—
58#3832—44no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—21no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—22no—
70C32×C4⋊C4D411yescharacteristic
71C32×C4⋊C4D412yes—
72C32×C4⋊C4C2311yescharacteristic
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—21no—
75C32×C22⋊C4—22no—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78#3753—22no—
79#3753—24no—
80#3752—21no—
81#3752—22no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3366—91noSylow
87C2×#239—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×#125C2×D318yes—
90C3×C22⋊Q8—24no—
91C3×C22⋊Q8—28no—
92C3×C4×Q8C2×D314yes—
93C3×C4×D4C2×D314yes—
94C3×C4×D4C2×D318yes—
95C2×C3×C4⋊C4—24no—
96C2×#213—34no—
97C2×#213—38no—
98#895—64no—
99#895—68no—
100#874—38no—
101#874—34no—
102C4×D12—34no—
103C4×D12—38no—
104#832—34no—
105#809—34no—
106#809—38no—
107#809—38no—
108#809—38no—
109#809—38no—
110#808—38no—
111#807—34no—
112C4⋊(C3⋊C8)—38no—
113C4⋊(C3⋊C8)—34no—
114#803—38no—
115C4×C3⋊C8—34no—
116C23×C32—21no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—21no—
119C32×Q8—22no—
120C32×Q8—81no—
121C32×D4—21no—
122C32×D4#4112yescomplemented
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4—42no—
126C2×C32×C4—82no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D412yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2411yescharacteristic
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—44no—
138C4⋊(C3⋊D3)—42no—
139C4⋊(C3⋊D3)—82no—
140C4⋊(C3⋊D3)—81no—
141C4×C3⋊D3—44no—
142C4×C3⋊D3—42no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—22no—
145C3⋊(C3⋊C8)—21no—
146#554C3⋊D311yescharacteristic, complemented
147#550—91no—
148#490—92no—
149#486—91no—
150#478—92no—
151#476—91no—
152#459—92no—
153#459—91no—
154#446—91no—
155#442—92no—
156C4×D8—91no—
157C2×C3×Q8—24no—
158C2×C3×Q8#6714yes—
159C2×C3×D4C22×D314yes—
160C22×C3×C4—24no—
161C22×C3×C4—28no—
162#239—1216no—
163C2×D12—34no—
164C2×D12—38no—
165C2×D12—68no—
166C2×D12—64no—
167C2×D12—64no—
168C2×D12—68no—
169C2×C4×D3—68no—
170C2×C4×D3—64no—
171C3×C4⋊C4—28no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4—28no—
174C3×C4⋊C4#6714yes—
175C3×C4⋊C4#6718yes—
176C3×C4⋊C4C22×D314yes—
177C3×C4⋊C4C22×D318yes—
178C3×C22⋊C4—24no—
179C3×C22⋊C4—28no—
180C3×C42C22×D314yes—
181C3×C42C22×D318yes—
182#213—68no—
183#213—616no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—68no—
186C4⋊Dic3—34no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—38no—
190C22×C32—22no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32C22×D411yescharacteristic
194C2×C3⋊D3—42no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3⋊D3—42no—
200C32×C4—22no—
201C32×C4—22no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4—42no—
205C32×C4AGL(1,ℤ/8)12yes—
206C32×C4C2×#4111yescharacteristic
207C32×C42−1+411yescharacteristic
208C3⋊Dic3—41no—
209C2×#41—181no—
210C2×D8—91no—
211C2×D8—92no—
212C4⋊Q8C2×C3⋊D311yescharacteristic
213#127—91no—
214#127—92no—
215#125C2×C3⋊D312yes—
216C22⋊Q8—21no—
217C22⋊Q8—22no—
218#121—181no—
219#121—182no—
220C4×Q8C2×C3⋊D311yescharacteristic
221C4×D4—91no—
222C4×D4—92no—
223C4×D4C2×C3⋊D311yescharacteristic
224C4×D4C2×C3⋊D312yes—
225C2×C4⋊C4—21no—
226#107—91no—
227#106—92no—
228C4⋊C8—91no—
229C4⋊C8—92no—
230#102—91no—
231#102—91no—
232#102—92no—
233#102—92no—
234#102—92no—
235#102—92no—
236#97—92no—
237C4×C8—91no—
238C23×C3—24no—
239C22×D3—68no—
240C22×D3—64no—
241C3×Q8—28no—
242C3×Q8—84no—
243C3×D4—24no—
244C3×D4#23918yescomplemented
245C2×C3×C4—24no—
246C2×C3×C4—28no—
247C2×C3×C4—48no—
248C2×C3×C4—88no—
249C2×C3×C4C2×#6714yes—
250C2×C3×C4C2×#6718yes—
251C2×C3×C4C2×#6718yes—
252C2×C3×C4C2×#6714yes—
253C2×C3×C4C23×D314yes—
254C2×Dic3—64no—
255D12—64no—
256D12—68no—
257D12—64no—
258D12—68no—
259D12—1216no—
260D12—128no—
261D12—248no—
262D12—244no—
263C4×D3—1216no—
264C4×D3—128no—
265C3⋊C8—64no—
266C3⋊C8—68no—
267C3⋊C8—64no—
268C2×C32—42no—
269C2×C32#54811yescharacteristic
270C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
271C2×C32#57611yescharacteristic
272C3⋊D3—82no—
273C3⋊D3—81no—
274#41—364no—
275C2×Q8—21no—
276C2×Q8#63811yescharacteristic
277C2×D4—91no—
278C2×D4—92no—
279C2×D4—182no—
280C2×D4—181no—
281C2×D4—181no—
282C2×D4—182no—
283C2×D4C22×C3⋊D311yescharacteristic
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—182no—
287C22×C4—181no—
288D8—182no—
289D8—184no—
290C2×C8—91no—
291C2×C8—91no—
292C2×C8—92no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—91no—
297C4⋊C4#63811yescharacteristic
298C4⋊C4#63812yes—
299C4⋊C4C22×C3⋊D312yes—
300C4⋊C4C22×C3⋊D311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—22no—
303C22⋊C4—181no—
304C22⋊C4—182no—
305C42C22×C3⋊D311yescharacteristic
306C42C22×C3⋊D312yes—
307C22×C3—28no—
308C22×C3—44no—
309C22×C3—44no—
310C22×C3C22×#6714yes—
311C2×D3—128no—
312C2×D3—124no—
313C2×D3—128no—
314C2×D3—124no—
315C2×D3—124no—
316C2×D3—128no—
317C3×C4—28no—
318C3×C4—28no—
319C3×C4—24no—
320C3×C4—44no—
321C3×C4—48no—
322C3×C4#94918yes—
323C3×C4C2×#23914yes—
324C3×C4#100714yes—
325Dic3—124no—
326C32#336611yescharacteristic, complemented, Sylow
327C23—21no—
328C23—182no—
329C23—181no—
330Q8—22no—
331Q8—81no—
332D4—21no—
333D4—181no—
334D4—182no—
335D4—181no—
336D4—182no—
337D4—364no—
338D4—362no—
339D4—722no—
340D4—721no—
341D4#383212yescomplemented
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—181no—
347C2×C4—364no—
348C2×C4—362no—
349C2×C4C2×#63811yescharacteristic
350C2×C4C2×#63812yes—
351C2×C4C2×#63812yes—
352C2×C4C2×#63811yescharacteristic
353C2×C4C23×C3⋊D311yescharacteristic
354C8—181no—
355C8—182no—
356C8—181no—
357C2×C3—48no—
358C2×C3#581714yes—
359C2×C3C2×#94914yes—
360C2×C3#583514yes—
361D3—248no—
362D3—244no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—362no—
367C22—361no—
368C22—362no—
369C22—361no—
370C22—361no—
371C22—362no—
372C22C22×#63811yescharacteristic
373C4—22no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—42no—
378C4—361no—
379C4#6415812yes—
380C4C2×#383211yescharacteristic
381C4#6436411yescharacteristic
382C3#8363814yescomplemented
383C2—42no—
384C2—722no—
385C2—721no—
386C2#1059628811yescharacteristic
387C2C2×#6415811yescharacteristic
388C2#1059630611yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#554C2
socleC22×C32C22×D4
hypercenter#554C3⋊D3
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
2. #10596048C2semidirect
3. #10592787C2semidirect
4. #10592783C2semidirect
5. #10592766C2semidirect
6. #10592765C2semidirect
7. #10592723C2semidirect
8. #10592714C2semidirect
9. #10592714C2semidirect
10. #10592713C2semidirect
11. C4×#3753C2semidirect
42. C3×#554D3semidirect
122. C32×D4#41semidirect
146. #554C3⋊D3semidirect
244. C3×D4#239semidirect
326. C32#3366semidirect
341. D4#3832semidirect
382. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
#105960482
#105927872
#105927832
#105927662
#105927652
#105927232
#105927142
#105927132
C4×#37532
#836383