Finite Group Databasebeta

← #11897530

Subgroups — #11897530

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2#10596014C211yesmaximal, characteristic, complemented
3C32×#474C211yesmaximal, characteristic, complemented
4#10592779C211yesmaximal, characteristic, complemented
5C4×#3753C211yesmaximal, characteristic
6#10592590C212yesmaximal, complemented
7#10592575C212yesmaximal, complemented
8#10592541C211yesmaximal, characteristic, complemented
9#10592530C211yesmaximal, characteristic, complemented
10#10592484C212yesmaximal
11#10592460C212yesmaximal, complemented
12#80959—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64155—21no—
17D4×C3⋊Dic3C2212yes—
18C2×#3753C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)—21no—
20#64133—21no—
21#64105—22no—
22#64102C2212yes—
23#64099C2212yes—
24#64097C2212yes—
25#64087—22no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64078C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C32×#107C2212yes—
30C32×C4⋊C8C2211yescharacteristic
31C32×#102C2212yes—
32#63659C2211yescharacteristic
33#63648C2212yes—
34#63644C2212yes—
35#63642C2212yes—
36#63641C2212yes—
37#63636C2211yescharacteristic
38#63635C2212yes—
39#63635C2212yes—
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5727—34no—
43#5543—34no—
44C3×#474D314yescomplemented
45#5080—34no—
46C4×#213—34no—
47#4891—38no—
48#4876—38no—
49#4842—34no—
50#4831—34no—
51#4785—38no—
52#4761—38no—
53C2×C32×Q8—21no—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C22×C3⋊Dic3—22no—
57Q8×C3⋊D3—44no—
58C2×C4⋊(C3⋊D3)C2311yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634D411yescharacteristic
64C2×C32×C8C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69C32×C42C2311yescharacteristic
70#3757—22no—
71#3753Q814yescomplemented
72#3752—21no—
73#3752—22no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—22no—
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3384—91noSylow
86C2×D3×Q8—64no—
87C3×C4⋊Q8C2×D314yes—
88C3×C4×D4C2×D314yes—
89#946—64no—
90D4×Dic3—38no—
91C2×#213—34no—
92C2×C4⋊Dic3—64no—
93#924—64no—
94#896—68no—
95#893—38no—
96#890—38no—
97#888—38no—
98#878—68no—
99C4×D12—34no—
100#869—34no—
101C4×Dic6—34no—
102C3×#107C2×D318yes—
103C3×C4⋊C8C2×D314yes—
104C3×#102C2×D318yes—
105#832—34no—
106#821—38no—
107#817—38no—
108#815—38no—
109Dic3⋊C8—38no—
110#809—34no—
111#808—38no—
112#808—38no—
113#807—34no—
114C4×C3⋊C8—34no—
115C23×C32—21no—
116C22×C3⋊D3—21no—
117C32×Q8—42no—
118C32×D4—21no—
119C32×D4C2×Q812yescomplemented
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—42no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—82no—
129C2×C3⋊Dic3C2×D412yes—
130C2×C3⋊Dic3C2×D412yes—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)C2×Q812yes—
133C4×C3⋊D3—44no—
134C4×C3⋊D3—42no—
135#634—22no—
136#634—44no—
137#634—81no—
138C32×C8—22no—
139C3⋊(C3⋊C8)—21no—
140C3⋊(C3⋊C8)C2×Q812yescomplemented
141#554—91no—
142D4×Q8—91no—
143#501—92no—
144#498—91no—
145#478—92no—
146#476—91no—
147#476—92no—
148#474C3⋊D311yescharacteristic, complemented
149#446—91no—
150#442—92no—
151C4×D8—91no—
152C2×C3×Q8—24no—
153C2×C3×D4C22×D314yes—
154C22×C3×C4—24no—
155C22×Dic3—68no—
156D3×Q8—1216no—
157C2×D12—34no—
158C2×C4×D3—68no—
159C2×C4×D3—64no—
160C2×Dic6—34no—
161C2×Dic6—68no—
162C2×Dic6—64no—
163C2×C3×C8C22×D318yes—
164C3×C4⋊C4—24no—
165C3×C4⋊C4C22×D314yes—
166C3×C4⋊C4C22×D318yes—
167C3×C22⋊C4—24no—
168C3×C42C22×D314yes—
169#217—68no—
170#213—316no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—64no—
173C4⋊Dic3—34no—
174C4⋊Dic3—34no—
175C4⋊Dic3—38no—
176C4⋊Dic3—68no—
177C4⋊Dic3—64no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180Dic3⋊C4—68no—
181C4×Dic3—38no—
182C2×C3⋊C8—34no—
183C2×C3⋊C8—34no—
184C22×C32—22no—
185C22×C32—41no—
186C22×C32—41no—
187C22×C32C22×D411yescharacteristic
188C2×C3⋊D3—22no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C32×C4—21no—
192C32×C4—42no—
193C32×C4—41no—
194C32×C4AGL(1,ℤ/8)12yes—
195C32×C4C22×Q811yescharacteristic
196C32×C42−1+411yescharacteristic
197C3⋊Dic3—22no—
198C3⋊Dic3—22no—
199C3⋊Dic3—41no—
200C3⋊Dic3—42no—
201C22×Q8—181no—
202C2×D8—91no—
203C4⋊Q8—92no—
204C4⋊Q8—91no—
205C4⋊Q8C2×C3⋊D311yescharacteristic
206#125—92no—
207C22⋊Q8—182no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C22⋊Q8—181no—
211C4×Q8—91no—
212C4×D4—92no—
213C4×D4—92no—
214C4×D4—91no—
215C4×D4C2×C3⋊D311yescharacteristic
216C2×C4⋊C4—181no—
217#107—91no—
218#107C2×C3⋊D312yes—
219#106—92no—
220#106—92no—
221#106—92no—
222C4⋊C8—92no—
223C4⋊C8C2×C3⋊D311yescharacteristic
224#102—91no—
225#102—92no—
226#102—91no—
227#102C2×C3⋊D312yes—
228#97—92no—
229C4×C8—91no—
230C23×C3—24no—
231C22×D3—64no—
232C3×Q8—48no—
233C3×D4—24no—
234C3×D4D3×Q818yescomplemented
235C2×C3×C4—24no—
236C2×C3×C4—28no—
237C2×C3×C4—48no—
238C2×C3×C4D3×D414yes—
239C2×C3×C4D3×D414yes—
240C2×C3×C4C23×D314yes—
241C2×Dic3—38no—
242C2×Dic3—38no—
243C2×Dic3—64no—
244C2×Dic3—68no—
245C2×Dic3—248no—
246D12—38no—
247D12—64no—
248C4×D3—1216no—
249C4×D3—128no—
250Dic6—68no—
251Dic6—1216no—
252Dic6—244no—
253C3×C8—28no—
254C3⋊C8—38no—
255C3⋊C8—64no—
256C2×C32—42no—
257C2×C32D4×Q811yescharacteristic
258C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
259C2×C32#57711yescharacteristic
260C3⋊D3—42no—
261C2×Q8—21no—
262C2×Q8—91no—
263C2×Q8—182no—
264C2×Q8—181no—
265C2×Q8—364no—
266C2×D4—91no—
267C2×D4C22×C3⋊D311yescharacteristic
268C22×C4—21no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4—181no—
272D8—94no—
273C2×C8—91no—
274C2×C8—91no—
275C2×C8C22×C3⋊D312yes—
276C4⋊C4—21no—
277C4⋊C4—91no—
278C4⋊C4—92no—
279C4⋊C4—92no—
280C4⋊C4—91no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C4⋊C4C22×C3⋊D311yescharacteristic
286C4⋊C4C22×C3⋊D312yes—
287C22⋊C4—21no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—181no—
291C42—92no—
292C42C22×C3⋊D311yescharacteristic
293C22×C3—28no—
294C22×C3—44no—
295C22×C3—44no—
296C22×C3C2×D3×D414yes—
297C2×D3—68no—
298C2×D3—124no—
299C2×D3—124no—
300C3×C4—24no—
301C3×C4—48no—
302C3×C4—44no—
303C3×C4#91118yes—
304C3×C4C2×D3×Q814yes—
305C3×C4#101014yes—
306Dic3—68no—
307Dic3—68no—
308Dic3—124no—
309Dic3—128no—
310C32#338411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—181no—
313Q8—42no—
314Q8—182no—
315Q8—364no—
316Q8—721no—
317D4—21no—
318D4—92no—
319D4—181no—
320D4Q8×C3⋊D312yescomplemented
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—182no—
327C2×C4—181no—
328C2×C4—364no—
329C2×C4—362no—
330C2×C4—722no—
331C2×C4D4×C3⋊D311yescharacteristic
332C2×C4D4×C3⋊D311yescharacteristic
333C2×C4C23×C3⋊D311yescharacteristic
334C8—22no—
335C8—92no—
336C8—181no—
337C2×C3—48no—
338C2×C3#563214yes—
339C2×C3C2×#91114yes—
340C2×C3#577814yes—
341D3—128no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22C2×D4×C3⋊D311yescharacteristic
349C4—21no—
350C4—41no—
351C4—42no—
352C4—182no—
353C4—182no—
354C4—361no—
355C4—362no—
356C4#6412012yes—
357C4C2×Q8×C3⋊D311yescharacteristic
358C4#6436711yescharacteristic
359C3#8095914yescomplemented
360C2—42no—
361C2—362no—
362C2#1059610311yescharacteristic
363C2C2×#6412011yescharacteristic
364C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#474C3⋊D3
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
2. #10596014C2semidirect
3. C32×#474C2semidirect
4. #10592779C2semidirect
6. #10592590C2semidirect
7. #10592575C2semidirect
8. #10592541C2semidirect
9. #10592530C2semidirect
11. #10592460C2semidirect
44. C3×#474D3semidirect
71. #3753Q8semidirect
119. C32×D4C2×Q8semidirect
140. C3⋊(C3⋊C8)C2×Q8semidirect
148. #474C3⋊D3semidirect
234. C3×D4D3×Q8semidirect
310. C32#3384semidirect
320. D4Q8×C3⋊D3semidirect
359. C3#80959semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105960142
C32×#4742
#105927792
C4×#37532
#105925902
#105925752
#105925412
#105925302
#105924842
#105924602
#809593