Finite Group Databasebeta

← #11895838

Subgroups — #11895838

Order 1152.

1116 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
1#10596203C211yesmaximal, characteristic, complemented
2#10596198C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592782C211yesmaximal, characteristic, complemented
6#10592518C212yesmaximal
7#10592516C212yesmaximal, complemented
8#10592493C212yesmaximal, complemented
9#10592492C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic
11#10592378C211yesmaximal, characteristic, complemented
12#81622—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16#64156C2212yes—
17#64155—21no—
18Q8×C3⋊Dic3C2212yes—
19C2×#3755C2212yes—
20C2×#3745C2211yescharacteristic
21#64107—22no—
22#64106—21no—
23#64105—22no—
24#64102C2212yes—
25#64101—21no—
26#64097C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#103C2212yes—
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63662C2212yes—
34#63648C2211yescharacteristic
35#63648C2211yescharacteristic
36#63645C2211yescharacteristic
37#63642C2212yes—
38#63641C2212yes—
39#63636C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5732—34no—
43#5727—34no—
44C3×#487D314yescomplemented
45#5087—34no—
46#5083—34no—
47#4819—38no—
48#4817—38no—
49#4794—38no—
50#4793—38no—
51C4×D24—34no—
52#4679—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55Q8×C3⋊D3—44no—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×#634—22no—
62C2×#634D411yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2312yes—
69C32×C42C2311yescharacteristic
70#3755—24no—
71#3752—21no—
72#3752—21no—
73#3752—22no—
74#3752—22no—
75#3752—22no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)D411yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85#3745—22no—
86#3367—91noSylow
87C2×D3×Q8—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×C4⋊Q8C2×D314yes—
90#947—38no—
91#946—64no—
92Q8×Dic3—38no—
93C2×#215—38no—
94C2×D24—34no—
95#898—68no—
96#897—64no—
97#896—68no—
98#893—38no—
99#892—64no—
100#888—38no—
101C4×D12—34no—
102C4×D12—34no—
103C4×Dic6—34no—
104C3×#103C2×D318yes—
105C3×#103C2×D318yes—
106C3×C4×C8C2×D314yes—
107#835—38no—
108#821—34no—
109#821—34no—
110#818—34no—
111#815—38no—
112Dic3⋊C8—38no—
113#809—38no—
114#807—38no—
115C4⋊(C3⋊C8)—34no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C32×Q8—22no—
119C32×Q8—22no—
120C32×Q8—42no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3C2×D412yes—
129C2×C3⋊Dic3C2×D412yes—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)—21no—
133C4⋊(C3⋊D3)#4112yes—
134C4×C3⋊D3—44no—
135C4×C3⋊D3—42no—
136C4×C3⋊D3—42no—
137#634—22no—
138#634—44no—
139C32×C8—21no—
140C32×C8—21no—
141C3⋊(C3⋊C8)—22no—
142#556—91no—
143D4×Q8—91no—
144#489—92no—
145#487C3⋊D311yescharacteristic, complemented
146#477—92no—
147#474—91no—
148#463—92no—
149#461—91no—
150#446—91no—
151#440—92no—
152C4×D8—91no—
153C2×C3×Q8—24no—
154C2×C3×Q8C22×D318yes—
155D3×Q8—1216no—
156C2×D12—34no—
157C2×D12—34no—
158C2×C4×D3—68no—
159C2×C4×D3—64no—
160C2×C4×D3—64no—
161C2×Dic6—34no—
162C2×Dic6—68no—
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—24no—
167C3×C4⋊C4—24no—
168C3×C4⋊C4C22×D318yes—
169C3×C42C22×D314yes—
170#215—616no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—64no—
175(C2×D3)⋊C4—64no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—34no—
179C4⋊Dic3—68no—
180Dic3⋊C4—38no—
181Dic3⋊C4—68no—
182C4×Dic3—38no—
183C4×Dic3—68no—
184C2×C3⋊C8—38no—
185D24—68no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C32×C4—21no—
194C32×C4—42no—
195C32×C4—42no—
196C32×C4AGL(1,ℤ/8)12yes—
197C32×C4C2×#4111yescharacteristic
198C32×C42−1+411yescharacteristic
199C3⋊Dic3—22no—
200C3⋊Dic3—22no—
201C3⋊Dic3—41no—
202C3⋊Dic3—41no—
203C22×Q8—181no—
204C2×SD16—92no—
205C2×D8—91no—
206C4⋊Q8—92no—
207C4⋊Q8C2×C3⋊D311yescharacteristic
208C4⋊Q8C2×C3⋊D311yescharacteristic
209#126—182no—
210#124—92no—
211C22⋊Q8—182no—
212C22⋊Q8—181no—
213C22⋊Q8—181no—
214C4×Q8—91no—
215C4×Q8—92no—
216C4×D4—92no—
217C4×D4—91no—
218C4×D4—91no—
219#117—181no—
220#107—91no—
221#107—92no—
222C4⋊C8—92no—
223C4⋊C8—91no—
224#103—92no—
225#103C2×C3⋊D312yes—
226#103C2×C3⋊D312yes—
227#102—91no—
228#102—91no—
229#102—92no—
230#97—92no—
231C4×C8C2×C3⋊D311yescharacteristic
232C22×D3—64no—
233C22×D3—64no—
234C3×Q8—28no—
235C3×Q8—28no—
236C3×Q8—48no—
237C2×C3×C4—28no—
238C2×C3×C4—28no—
239C2×C3×C4D3×D414yes—
240C2×C3×C4D3×D414yes—
241C2×C3×C4C23×D314yes—
242C2×Dic3—38no—
243C2×Dic3—38no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246D12—38no—
247D12—64no—
248D12—64no—
249D12—64no—
250C4×D3—1216no—
251C4×D3—128no—
252C4×D3—128no—
253Dic6—68no—
254Dic6—1216no—
255C3×C8—24no—
256C3×C8—24no—
257C3⋊C8—68no—
258C2×C32#54811yescharacteristic
259C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
260C2×C32#57811yescharacteristic
261C3⋊D3—42no—
262C3⋊D3—81no—
263C2×Q8—21no—
264C2×Q8—91no—
265C2×Q8—182no—
266C2×Q8—364no—
267C2×Q8C22×C3⋊D312yes—
268C2×D4—91no—
269C2×D4—91no—
270C22×C4—182no—
271C22×C4—181no—
272C22×C4—181no—
273SD16—184no—
274D8—182no—
275C2×C8—92no—
276C2×C8C22×C3⋊D311yescharacteristic
277C2×C8C22×C3⋊D311yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—91no—
282C4⋊C4—92no—
283C4⋊C4—91no—
284C4⋊C4—91no—
285C4⋊C4—182no—
286C4⋊C4—182no—
287C4⋊C4C22×C3⋊D312yes—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C22⋊C4—181no—
292C22⋊C4—181no—
293C42—92no—
294C42—182no—
295C42C22×C3⋊D311yescharacteristic
296C22×C3C2×D3×D414yes—
297C2×D3—68no—
298C2×D3—124no—
299C2×D3—124no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C3×C4—24no—
304C3×C4—48no—
305C3×C4—48no—
306C3×C4#91418yes—
307C3×C4D3×#4114yes—
308C3×C4#101014yes—
309Dic3—68no—
310Dic3—68no—
311Dic3—124no—
312Dic3—124no—
313C32#336711yescharacteristic, complemented, Sylow
314C23—181no—
315C23—181no—
316Q8—22no—
317Q8—22no—
318Q8—42no—
319Q8—182no—
320Q8—364no—
321D4—92no—
322D4—181no—
323D4—181no—
324D4—181no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—364no—
332C2×C4—362no—
333C2×C4—362no—
334C2×C4D4×C3⋊D311yescharacteristic
335C2×C4D4×C3⋊D311yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—21no—
338C8—21no—
339C8—182no—
340C2×C3#567714yes—
341C2×C3C2×#91414yes—
342C2×C3#576614yes—
343D3—128no—
344D3—244no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22—361no—
349C22—361no—
350C22—361no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—42no—
354C4—42no—
355C4—182no—
356C4—182no—
357C4—361no—
358C4—361no—
359C4#6412312yes—
360C4#41×C3⋊D311yescharacteristic
361C4#6436711yescharacteristic
362C3#8162214yescomplemented
363C2—362no—
364C2—721no—
365C2#1059614811yescharacteristic
366C2C2×#6412311yescharacteristic
367C2#1059623711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#487C3⋊D3
hypocenterC32#3367
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
1. #10596203C2semidirect
2. #10596198C2semidirect
3. C32×#487C2semidirect
4. #10592786C2semidirect
5. #10592782C2semidirect
7. #10592516C2semidirect
8. #10592493C2semidirect
9. #10592492C2semidirect
11. #10592378C2semidirect
44. C3×#487D3semidirect
145. #487C3⋊D3semidirect
313. C32#3367semidirect
362. C3#81622semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105961982
C32×#4872
#105927862
#105927822
#105925182
#105925162
#105924932
#105924922
C4×#37452
#105923782
#816223