Finite Group Databasebeta

← #11895621

Subgroups — #11895621

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2#10596056C211yesmaximal, characteristic
3#10592793C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic
5#10592767C212yesmaximal, complemented
6#10592765C212yesmaximal, complemented
7C4×#3756C211yesmaximal, characteristic, complemented
8#10592727C212yesmaximal, complemented
9#10592726C211yesmaximal, characteristic
10C4×#3755C212yesmaximal, complemented
11Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#83697—34nomaximal
13C32×C4⋊Q8—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#125—22no—
16C32×#125C2212yes—
17C32×C4×Q8—21no—
18C32×C4×Q8C2212yes—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21#64156—21no—
22C2×#3756C2211yescharacteristic
23C2×#3755C2212yes—
24#64103—22no—
25#64102—21no—
26#64084C2212yes—
27#64083C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2212yes—
29C4×#634C2211yescharacteristic
30#63662C2211yescharacteristic
31#63637C2212yes—
32#63637C2211yescharacteristic
33#63636C2212yes—
34#63636C2212yes—
35#63636C2212yes—
36#63635C2212yes—
37#63634C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40C4×C3⋊(C3⋊C8)C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2212yes—
42C3×#557D314yescomplemented
43#5585—34no—
44#5094—34no—
45#5088—34no—
46#5068—38no—
47#5066—38no—
48C4×#216—34no—
49#5028—38no—
50#5027—34no—
51C4×#215—38no—
52Q8×C3⋊C8—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×Q8C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—22no—
60C2×#634C2311yescharacteristic
61C32×C4⋊C4—22no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—22no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4D411yescharacteristic
67C32×C4⋊C4D412yes—
68C32×C4⋊C4C2311yescharacteristic
69C32×C4⋊C4C2312yes—
70C32×C42—22no—
71C32×C42—21no—
72C32×C42C2311yescharacteristic
73C32×C42C2312yes—
74#3756—22no—
75#3755—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)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85#3365—91noSylow
86C3×C4⋊Q8—24no—
87C3×C4⋊Q8C2×D314yes—
88C3×#125—28no—
89C3×#125C2×D318yes—
90C3×C4×Q8—24no—
91C3×C4×Q8C2×D318yes—
92C3×C4×Q8C2×D314yes—
93C3×C4×Q8C2×D314yes—
94#947—64no—
95C2×#216—34no—
96C2×#215—38no—
97#894—68no—
98#893—64no—
99#875—38no—
100#874—34no—
101C4×D12—38no—
102C4×Dic6—34no—
103#835—34no—
104#810—38no—
105#810—34no—
106#809—38no—
107#809—38no—
108#809—38no—
109#808—38no—
110#807—34no—
111C4⋊(C3⋊C8)—34no—
112C4⋊(C3⋊C8)—38no—
113C4×C3⋊C8—38no—
114C4×C3⋊C8—34no—
115C22×C3⋊D3—22no—
116C32×Q8—22no—
117C32×Q8—21no—
118C32×Q8—42no—
119C32×Q8#4112yes—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2×D412yes—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—42no—
133C4⋊(C3⋊D3)—81no—
134C4×C3⋊D3—82no—
135#634—21no—
136#634—21no—
137C3⋊(C3⋊C8)—22no—
138C3⋊(C3⋊C8)—21no—
139C3⋊(C3⋊C8)—21no—
140#559—91no—
141#557C3⋊D311yescharacteristic, complemented
142#488—92no—
143#486—91no—
144#478—92no—
145#475—91no—
146#464—92no—
147#460—91no—
148C8×Q8—91no—
149C4×Q16—91no—
150C4×SD16—92no—
151C2×C3×Q8—24no—
152C2×C3×Q8#6714yes—
153C2×C3×Q8C22×D314yes—
154C2×D12—38no—
155C2×D12—64no—
156C2×D12—64no—
157C2×C4×D3—68no—
158C2×Dic6—34no—
159C3×C4⋊C4—28no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—28no—
162C3×C4⋊C4—24no—
163C3×C4⋊C4—28no—
164C3×C4⋊C4#6714yes—
165C3×C4⋊C4#6718yes—
166C3×C4⋊C4C22×D314yes—
167C3×C4⋊C4C22×D318yes—
168C3×C42—28no—
169C3×C42—24no—
170C3×C42C22×D314yes—
171C3×C42C22×D318yes—
172#216—68no—
173#215—616no—
174(C2×D3)⋊C4—68no—
175(C2×D3)⋊C4—68no—
176(C2×D3)⋊C4—68no—
177C4⋊Dic3—34no—
178Dic3⋊C4—64no—
179C4×Dic3—64no—
180C2×C3⋊C8—34no—
181C2×C3⋊C8—34no—
182C2×C3⋊C8—38no—
183C22×C32C22×D411yescharacteristic
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4—22no—
190C32×C4—21no—
191C32×C4—42no—
192C32×C4—41no—
193C32×C4#13512yes—
194C32×C4C2×#4111yescharacteristic
195C32×C42−1+411yescharacteristic
196C3⋊Dic3—41no—
197C3⋊Dic3—41no—
198C2×Q16—91no—
199C2×SD16—92no—
200C4⋊Q8—21no—
201C4⋊Q8C2×C3⋊D311yescharacteristic
202#127—91no—
203#125—22no—
204#125C2×C3⋊D312yes—
205#124—92no—
206#124—181no—
207#123—182no—
208C4×Q8—21no—
209C4×Q8—91no—
210C4×Q8C2×C3⋊D312yes—
211C4×Q8C2×C3⋊D311yescharacteristic
212C4×Q8C2×C3⋊D311yescharacteristic
213C4×D4—92no—
214C4×D4—181no—
215#107—91no—
216#106—92no—
217C4⋊C8—91no—
218C4⋊C8—92no—
219#103—91no—
220#103—91no—
221#103—92no—
222#102—92no—
223#102—92no—
224#102—92no—
225C4×C8—92no—
226C4×C8—91no—
227C22×D3—68no—
228C3×Q8—28no—
229C3×Q8—24no—
230C3×Q8—48no—
231C3×Q8#23918yes—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—28no—
235C2×C3×C4C2×#6714yes—
236C2×C3×C4C2×#6718yes—
237C2×C3×C4C2×#6718yes—
238C2×C3×C4C2×#6714yes—
239C2×C3×C4C23×D314yes—
240C2×Dic3—64no—
241C2×Dic3—64no—
242D12—68no—
243D12—68no—
244D12—128no—
245D12—244no—
246C4×D3—248no—
247Dic6—64no—
248Dic6—64no—
249C3⋊C8—68no—
250C3⋊C8—64no—
251C3⋊C8—64no—
252C2×C32#54811yescharacteristic
253C2×C32C2×#13511yescharacteristic
254C2×C32#57711yescharacteristic
255C3⋊D3—82no—
256C2×Q8—21no—
257C2×Q8—91no—
258C2×Q8#63811yescharacteristic
259C2×Q8C22×C3⋊D311yescharacteristic
260C2×D4—92no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—182no—
264Q16—182no—
265SD16—184no—
266C2×C8—91no—
267C2×C8—91no—
268C2×C8—92no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—91no—
275C4⋊C4—181no—
276C4⋊C4#63811yescharacteristic
277C4⋊C4#63812yes—
278C4⋊C4C22×C3⋊D312yes—
279C4⋊C4C22×C3⋊D311yescharacteristic
280C22⋊C4—182no—
281C22⋊C4—182no—
282C22⋊C4—182no—
283C42—22no—
284C42—21no—
285C42—181no—
286C42C22×C3⋊D312yes—
287C42C22×C3⋊D311yescharacteristic
288C22×C3C22×#6714yes—
289C2×D3—128no—
290C2×D3—128no—
291C2×D3—128no—
292C3×C4—28no—
293C3×C4—28no—
294C3×C4—28no—
295C3×C4—24no—
296C3×C4—48no—
297C3×C4—44no—
298C3×C4#95018yes—
299C3×C4C2×#23914yes—
300C3×C4#100714yes—
301Dic3—124no—
302Dic3—124no—
303C32#336511yescharacteristic, complemented, Sylow
304C23—182no—
305Q8—21no—
306Q8—22no—
307Q8—42no—
308Q8—181no—
309Q8—181no—
310Q8#383212yes—
311D4—182no—
312D4—182no—
313D4—362no—
314D4—721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—722no—
321C2×C4C2×#63812yes—
322C2×C4C2×#63812yes—
323C2×C4C2×#63811yescharacteristic
324C2×C4C2×#63811yescharacteristic
325C2×C4C23×C3⋊D311yescharacteristic
326C8—182no—
327C8—181no—
328C8—181no—
329C2×C3#581714yes—
330C2×C3C2×#95014yes—
331C2×C3#583714yes—
332D3—248no—
333C22—362no—
334C22—362no—
335C22—362no—
336C22C22×#63811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—361no—
344C4—361no—
345C4#6415912yes—
346C4C2×#383211yescharacteristic
347C4#6436411yescharacteristic
348C3#8369714yescomplemented
349C2—722no—
350C2#1059628811yescharacteristic
351C2C2×#6415911yescharacteristic
352C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radical#64083C22
hypercenter#557C3⋊D3
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. #10592793C2semidirect
5. #10592767C2semidirect
6. #10592765C2semidirect
7. C4×#3756C2semidirect
8. #10592727C2semidirect
10. C4×#3755C2semidirect
11. Q8×C3⋊(C3⋊C8)C2semidirect
42. C3×#557D3semidirect
141. #557C3⋊D3semidirect
303. C32#3365semidirect
348. C3#83697semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
#105960562
#105927932
#105927872
#105927672
#105927652
C4×#37562
#105927272
#105927262
C4×#37552
Q8×C3⋊(C3⋊C8)2
#836973