Finite Group Databasebeta

← #11895310

Subgroups — #11895310

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic, complemented
2#10596056C211yesmaximal, characteristic, complemented
3#10592790C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5#10592767C212yesmaximal, complemented
6#10592765C212yesmaximal, complemented
7Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C4×#3754C211yesmaximal, characteristic, complemented
9#10592715C212yesmaximal, complemented
10#10592714C211yesmaximal, characteristic
11C4×#3753C212yesmaximal, complemented
12#83643—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×#125C2212yes—
15C32×C22⋊Q8—21no—
16C32×C22⋊Q8—22no—
17C32×C4×Q8C2211yescharacteristic
18C32×C4×D4C2212yes—
19C32×C4×D4C2211yescharacteristic
20C2×C32×C4⋊C4—21no—
21#64156—21no—
22C2×#3754C2211yescharacteristic
23C2×#3753C2212yes—
24#64103—22no—
25#64102—21no—
26#64084C2212yes—
27#64083C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2212yes—
29C4×#634C2211yescharacteristic
30#63659C2211yescharacteristic
31#63637C2212yes—
32#63637C2211yescharacteristic
33#63636C2212yes—
34#63636C2212yes—
35#63636C2212yes—
36#63635C2211yescharacteristic
37#63634C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40C4×C3⋊(C3⋊C8)C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2212yes—
42C3×#554D314yescomplemented
43#5585—34no—
44#5091—34no—
45#5088—34no—
46#5068—38no—
47#5066—38no—
48Q8×C3⋊C8—34no—
49C4×#214—34no—
50#5016—38no—
51#5015—34no—
52C4×#213—38no—
53C2×C32×Q8—21no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×#634C2311yescharacteristic
63C32×C4⋊C4—22no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4D411yescharacteristic
67C32×C4⋊C4D412yes—
68C32×C4⋊C4C2312yes—
69C32×C4⋊C4C2311yescharacteristic
70C32×C22⋊C4—21no—
71C32×C22⋊C4—22no—
72C32×C42C2311yescharacteristic
73C32×C42C2312yes—
74#3754—22no—
75#3753—24no—
76#3752—22no—
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3361—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×#125C2×D318yes—
88C3×C22⋊Q8—24no—
89C3×C22⋊Q8—28no—
90C3×C4×Q8C2×D314yes—
91C3×C4×D4C2×D318yes—
92C3×C4×D4C2×D314yes—
93C2×C3×C4⋊C4—24no—
94#947—64no—
95C2×#214—34no—
96C2×#213—38no—
97#894—68no—
98#893—64no—
99#875—38no—
100#874—34no—
101C4×D12—38no—
102C4×Dic6—34no—
103#832—34no—
104#810—38no—
105#810—34no—
106#809—38no—
107#809—38no—
108#809—38no—
109#808—34no—
110#807—38no—
111C4⋊(C3⋊C8)—34no—
112C4⋊(C3⋊C8)—38no—
113C4×C3⋊C8—38no—
114C4×C3⋊C8—34no—
115C23×C32—21no—
116C22×C3⋊D3—22no—
117C32×Q8—22no—
118C32×Q8—81no—
119C32×D4—21no—
120C32×D4#4112yes—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—42no—
124C2×C32×C4—82no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—42no—
135C4⋊(C3⋊D3)—81no—
136C4×C3⋊D3—82no—
137#634—21no—
138#634—21no—
139C3⋊(C3⋊C8)—22no—
140C3⋊(C3⋊C8)—21no—
141C3⋊(C3⋊C8)—21no—
142#559—91no—
143#554C3⋊D311yescharacteristic, complemented
144#488—92no—
145#486—91no—
146#478—92no—
147#477—91no—
148#463—92no—
149#459—91no—
150C8×Q8—91no—
151C4×SD16—91no—
152C4×D8—92no—
153C2×C3×Q8—24no—
154C2×C3×Q8#6714yes—
155C2×C3×D4C22×D314yes—
156C22×C3×C4—24no—
157C22×C3×C4—28no—
158C2×D12—38no—
159C2×D12—64no—
160C2×D12—64no—
161C2×C4×D3—68no—
162C2×Dic6—34no—
163C3×C4⋊C4—28no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—28no—
166C3×C4⋊C4#6714yes—
167C3×C4⋊C4#6718yes—
168C3×C4⋊C4C22×D318yes—
169C3×C4⋊C4C22×D314yes—
170C3×C22⋊C4—24no—
171C3×C22⋊C4—28no—
172C3×C42C22×D314yes—
173C3×C42C22×D318yes—
174#214—68no—
175#213—616no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178(C2×D3)⋊C4—68no—
179C4⋊Dic3—34no—
180Dic3⋊C4—64no—
181C4×Dic3—64no—
182C2×C3⋊C8—34no—
183C2×C3⋊C8—38no—
184C2×C3⋊C8—34no—
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32C22×D411yescharacteristic
189C2×C3⋊D3—42no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C32×C4—22no—
193C32×C4—22no—
194C32×C4—21no—
195C32×C4—41no—
196C32×C4—42no—
197C32×C4#13512yes—
198C32×C4C2×#4111yescharacteristic
199C32×C42−1+411yescharacteristic
200C3⋊Dic3—41no—
201C3⋊Dic3—41no—
202C2×SD16—91no—
203C2×D8—92no—
204C4⋊Q8C2×C3⋊D311yescharacteristic
205#127—91no—
206#125C2×C3⋊D312yes—
207#124—92no—
208#124—181no—
209#123—182no—
210C22⋊Q8—21no—
211C22⋊Q8—22no—
212C4×Q8—91no—
213C4×Q8C2×C3⋊D311yescharacteristic
214C4×D4—92no—
215C4×D4—181no—
216C4×D4C2×C3⋊D312yes—
217C4×D4C2×C3⋊D311yescharacteristic
218C2×C4⋊C4—21no—
219#107—92no—
220#106—91no—
221C4⋊C8—91no—
222C4⋊C8—92no—
223#103—91no—
224#103—92no—
225#102—91no—
226#102—92no—
227#102—92no—
228#102—92no—
229C4×C8—92no—
230C4×C8—91no—
231C23×C3—24no—
232C22×D3—68no—
233C3×Q8—28no—
234C3×Q8—84no—
235C3×D4—24no—
236C3×D4#23918yes—
237C2×C3×C4—24no—
238C2×C3×C4—28no—
239C2×C3×C4—48no—
240C2×C3×C4—88no—
241C2×C3×C4C2×#6714yes—
242C2×C3×C4C2×#6718yes—
243C2×C3×C4C2×#6718yes—
244C2×C3×C4C2×#6714yes—
245C2×C3×C4C23×D314yes—
246C2×Dic3—64no—
247C2×Dic3—64no—
248D12—68no—
249D12—68no—
250D12—128no—
251D12—244no—
252C4×D3—248no—
253Dic6—64no—
254Dic6—64no—
255C3⋊C8—68no—
256C3⋊C8—64no—
257C3⋊C8—64no—
258C2×C32—42no—
259C2×C32#54811yescharacteristic
260C2×C32C2×#13511yescharacteristic
261C2×C32#57611yescharacteristic
262C3⋊D3—82no—
263C2×Q8—21no—
264C2×Q8—91no—
265C2×Q8#63811yescharacteristic
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—182no—
273SD16—182no—
274D8—184no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8—92no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—91no—
282C4⋊C4—181no—
283C4⋊C4#63811yescharacteristic
284C4⋊C4#63812yes—
285C4⋊C4C22×C3⋊D311yescharacteristic
286C4⋊C4C22×C3⋊D312yes—
287C22⋊C4—21no—
288C22⋊C4—22no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C42—181no—
293C42C22×C3⋊D312yes—
294C42C22×C3⋊D311yescharacteristic
295C22×C3—28no—
296C22×C3—44no—
297C22×C3—44no—
298C22×C3C22×#6714yes—
299C2×D3—128no—
300C2×D3—128no—
301C2×D3—128no—
302C3×C4—28no—
303C3×C4—28no—
304C3×C4—24no—
305C3×C4—44no—
306C3×C4—48no—
307C3×C4#95018yes—
308C3×C4C2×#23914yes—
309C3×C4#100714yes—
310Dic3—124no—
311Dic3—124no—
312C32#336111yescharacteristic, complemented, Sylow
313C23—21no—
314C23—182no—
315Q8—22no—
316Q8—81no—
317Q8—181no—
318Q8—181no—
319D4—21no—
320D4—182no—
321D4—182no—
322D4—362no—
323D4—721no—
324D4#383212yes—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—722no—
332C2×C4C2×#63812yes—
333C2×C4C2×#63811yescharacteristic
334C2×C4C2×#63812yes—
335C2×C4C2×#63811yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—182no—
338C8—181no—
339C8—181no—
340C2×C3—48no—
341C2×C3#581714yes—
342C2×C3C2×#95014yes—
343C2×C3#583514yes—
344D3—248no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—362no—
349C22—362no—
350C22—362no—
351C22C22×#63811yescharacteristic
352C4—22no—
353C4—22no—
354C4—21no—
355C4—41no—
356C4—42no—
357C4—361no—
358C4—361no—
359C4#6415912yes—
360C4C2×#383211yescharacteristic
361C4#6436411yescharacteristic
362C3#8364314yescomplemented
363C2—42no—
364C2—722no—
365C2#1059628811yescharacteristic
366C2C2×#6415911yescharacteristic
367C2#1059630611yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#554C2
socleC22×C32C22×D4
prime radical#10592714C2
hypercenter#554C3⋊D3
hypocenterC32#3361
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. #10596056C2semidirect
3. #10592790C2semidirect
4. #10592787C2semidirect
5. #10592767C2semidirect
6. #10592765C2semidirect
7. Q8×C3⋊(C3⋊C8)C2semidirect
8. C4×#3754C2semidirect
9. #10592715C2semidirect
11. C4×#3753C2semidirect
42. C3×#554D3semidirect
143. #554C3⋊D3semidirect
312. C32#3361semidirect
362. C3#83643semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
#105960562
#105927902
#105927872
#105927672
#105927652
Q8×C3⋊(C3⋊C8)2
C4×#37542
#105927152
#105927142
C4×#37532
#836433