Finite Group Databasebeta

← #11895145

Subgroups — #11895145

Order 1152.

1110 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic
2#10596192C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4#10592793C211yesmaximal, characteristic, complemented
5#10592782C211yesmaximal, characteristic
6#10592517C212yesmaximal
7#10592491C212yesmaximal, complemented
8#10592490C212yesmaximal, complemented
9#10592487C212yesmaximal
10C4×#3744C211yesmaximal, characteristic
11C8×#634C211yesmaximal, characteristic, complemented
12#81620—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16#64155—21no—
17Q8×C3⋊Dic3C2212yes—
18#64153C2212yes—
19C2×#3755C2212yes—
20C2×#3744C2211yescharacteristic
21#64105—22no—
22#64102C2212yes—
23#64099—21no—
24#64098—22no—
25#64097C2212yes—
26#64096—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#103C2212yes—
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63662C2212yes—
34#63648C2211yescharacteristic
35#63644C2211yescharacteristic
36#63643C2211yescharacteristic
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63637C2212yes—
40#63635C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5727—34no—
43#5721—34no—
44C3×#487D314yescomplemented
45#5094—34no—
46#5083—34no—
47#4818—38no—
48#4792—38no—
49#4791—38no—
50#4788—38no—
51C4×#204—34no—
52C8×Dic6—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55Q8×C3⋊D3—44no—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—22no—
59C2×#634—22no—
60C2×#634D411yescharacteristic
61C2×#634C2311yescharacteristic
62C2×C32×C8C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C32×C42C2311yescharacteristic
69#3755—24no—
70#3752—21no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—22no—
73C4⋊(C3⋊Dic3)D411yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76#3750—21no—
77#3750—22no—
78#3750—22no—
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85#3744—22no—
86#3359—91noSylow
87C2×D3×Q8—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×C4⋊Q8C2×D314yes—
90#946—64no—
91Q8×Dic3—38no—
92#944—38no—
93C2×#215—38no—
94C2×#204—34no—
95#896—68no—
96#893—38no—
97#890—64no—
98#889—68no—
99#888—38no—
100#887—64no—
101C4×D12—34no—
102C4×Dic6—34no—
103C4×Dic6—34no—
104C3×#103C2×D318yes—
105C3×#103C2×D318yes—
106C3×C4×C8C2×D314yes—
107#835—38no—
108#821—34no—
109#817—34no—
110#816—34no—
111Dic3⋊C8—38no—
112C8×Dic3—38no—
113#810—38no—
114#808—38no—
115C4⋊(C3⋊C8)—34no—
116C22×C3⋊D3—21no—
117C32×Q8—22no—
118C32×Q8—22no—
119C32×Q8—42no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3C2×D412yes—
129C2×C3⋊Dic3C2×D412yes—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)#4112yes—
132C4×C3⋊D3—42no—
133C4×C3⋊D3—44no—
134#634—21no—
135#634—21no—
136#634—44no—
137#634SD1614yescomplemented
138C32×C8—21no—
139C32×C8—21no—
140C3⋊(C3⋊C8)—22no—
141#557—91no—
142D4×Q8—91no—
143#487—92no—
144#487C3⋊D311yescharacteristic, complemented
145#475—91no—
146#475—92no—
147#461—91no—
148#461—92no—
149C8×Q8—91no—
150C4×SD16—92no—
151C4×SD16—91no—
152C2×C3×Q8—24no—
153C2×C3×Q8C22×D318yes—
154D3×Q8—1216no—
155C2×D12—34no—
156C2×C4×D3—68no—
157C2×C4×D3—64no—
158C2×Dic6—34no—
159C2×Dic6—34no—
160C2×Dic6—68no—
161C2×C3×C8C22×D314yes—
162C2×C3×C8C22×D314yes—
163C3×C4⋊C4—24no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—24no—
166C3×C4⋊C4C22×D318yes—
167C3×C42C22×D314yes—
168#215—616no—
169(C2×D3)⋊C4—68no—
170(C2×D3)⋊C4—64no—
171C4⋊Dic3—34no—
172C4⋊Dic3—34no—
173C4⋊Dic3—34no—
174C4⋊Dic3—68no—
175Dic3⋊C4—38no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178Dic3⋊C4—68no—
179Dic3⋊C4—64no—
180C4×Dic3—38no—
181C4×Dic3—68no—
182C4×Dic3—64no—
183C2×C3⋊C8—38no—
184#204—68no—
185C22×C32C22×D411yescharacteristic
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C32×C4—21no—
190C32×C4—42no—
191C32×C4—42no—
192C32×C4C2×SD1612yes—
193C32×C4C2×#4111yescharacteristic
194C32×C42−1+411yescharacteristic
195C3⋊Dic3—22no—
196C3⋊Dic3—41no—
197C3⋊Dic3—41no—
198C3⋊Dic3—41no—
199C3⋊Dic3C2×SD1614yes—
200C22×Q8—181no—
201C2×SD16—92no—
202C2×SD16—91no—
203C4⋊Q8—92no—
204C4⋊Q8—92no—
205C4⋊Q8C2×C3⋊D311yescharacteristic
206C4⋊Q8C2×C3⋊D311yescharacteristic
207#125—182no—
208#125—181no—
209C22⋊Q8—182no—
210C22⋊Q8—181no—
211C4×Q8—91no—
212C4×Q8—92no—
213C4×Q8—91no—
214C4×Q8—181no—
215C4×D4—92no—
216C4×D4—91no—
217#106—91no—
218#106—92no—
219C4⋊C8—92no—
220C4⋊C8—91no—
221#103—92no—
222#103—91no—
223#103—92no—
224#103C2×C3⋊D312yes—
225#103C2×C3⋊D312yes—
226#102—91no—
227C4×C8—92no—
228C4×C8C2×C3⋊D311yescharacteristic
229C22×D3—64no—
230C3×Q8—28no—
231C3×Q8—28no—
232C3×Q8—48no—
233C2×C3×C4—28no—
234C2×C3×C4—28no—
235C2×C3×C4D3×D414yes—
236C2×C3×C4D3×D414yes—
237C2×C3×C4C23×D314yes—
238C2×Dic3—38no—
239C2×Dic3—38no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243D12—38no—
244D12—64no—
245C4×D3—1216no—
246C4×D3—128no—
247Dic6—316no—
248Dic6—64no—
249Dic6—64no—
250Dic6—1216no—
251C3×C8—24no—
252C3×C8—24no—
253C3⋊C8—68no—
254C2×C32#54811yescharacteristic
255C2×C32C22×SD1611yescharacteristic
256C2×C32#57811yescharacteristic
257C3⋊D3—42no—
258C2×Q8—21no—
259C2×Q8—91no—
260C2×Q8—91no—
261C2×Q8—182no—
262C2×Q8—364no—
263C2×Q8C22×C3⋊D312yes—
264C2×D4—91no—
265C22×C4—182no—
266C22×C4—181no—
267SD16—182no—
268SD16—184no—
269C2×C8—92no—
270C2×C8C22×C3⋊D311yescharacteristic
271C2×C8C22×C3⋊D311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—92no—
276C4⋊C4—91no—
277C4⋊C4—91no—
278C4⋊C4—91no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4C22×C3⋊D312yes—
285C22⋊C4—182no—
286C22⋊C4—181no—
287C42—92no—
288C42—182no—
289C42—181no—
290C42C22×C3⋊D311yescharacteristic
291C22×C3C2×D3×D414yes—
292C2×D3—68no—
293C2×D3—124no—
294C2×D3—124no—
295C3×C4—24no—
296C3×C4—48no—
297C3×C4—48no—
298C3×C4D3×SD1618yes—
299C3×C4D3×#4114yes—
300C3×C4#101014yes—
301Dic3—316no—
302Dic3—68no—
303Dic3—124no—
304Dic3—124no—
305Dic3—124no—
306C32#335911yescharacteristic, complemented, Sylow
307C23—181no—
308Q8—22no—
309Q8—22no—
310Q8—42no—
311Q8—94no—
312Q8—181no—
313Q8—181no—
314Q8—364no—
315D4—92no—
316D4—181no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4—181no—
324C2×C4—364no—
325C2×C4—362no—
326C2×C4D4×C3⋊D311yescharacteristic
327C2×C4D4×C3⋊D311yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—21no—
330C8—21no—
331C8—182no—
332C2×C3#567714yes—
333C2×C3C2×D3×SD1614yes—
334C2×C3#576614yes—
335D3—128no—
336C22—182no—
337C22—361no—
338C22—361no—
339C22C2×D4×C3⋊D311yescharacteristic
340C4—21no—
341C4—42no—
342C4—42no—
343C4—94no—
344C4—182no—
345C4—361no—
346C4—361no—
347C4—361no—
348C4SD16×C3⋊D312yes—
349C4#41×C3⋊D311yescharacteristic
350C4#6436711yescharacteristic
351C3#8162014yescomplemented
352C2—362no—
353C2#1059614811yescharacteristic
354C2C2×SD16×C3⋊D311yescharacteristic
355C2#1059623711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#487C3⋊D3
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #10596192C2semidirect
3. C32×#487C2semidirect
4. #10592793C2semidirect
7. #10592491C2semidirect
8. #10592490C2semidirect
11. C8×#634C2semidirect
44. C3×#487D3semidirect
137. #634SD16semidirect
144. #487C3⋊D3semidirect
306. C32#3359semidirect
351. C3#81620semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105961922
C32×#4872
#105927932
#105927822
#105925172
#105924912
#105924902
#105924872
C4×#37442
C8×#6342
#816203