Finite Group Databasebeta

← #11895924

Subgroups — #11895924

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2#10596048C211yesmaximal, characteristic
3#10592787C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592766C212yesmaximal, complemented
6#10592765C212yesmaximal, complemented
7#10592726C211yesmaximal, characteristic, complemented
8#10592726C212yesmaximal, complemented
9#10592725C212yesmaximal, complemented
10C4×#3755C211yesmaximal, characteristic, complemented
11#10592723C211yesmaximal, characteristic, complemented
12#83690—34nomaximal
13C2×#3832—21no—
14C32×C4⋊Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#125—22no—
17C32×#125C2212yes—
18C32×C4×Q8—21no—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2212yes—
21C32×C4×Q8C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3755C2212yes—
24#64104—21no—
25#64104—22no—
26#64083C2211yescharacteristic
27#64083C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yes—
30#63662C2211yescharacteristic
31#63636C2212yes—
32#63636C2212yes—
33#63636C2212yes—
34#63636C2211yescharacteristic
35#63636C2212yes—
36#63635C2211yescharacteristic
37#63634C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40#63630C2212yes—
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×#557D314yescomplemented
43#5577—34no—
44#5088—34no—
45#5087—34no—
46#5067—38no—
47#5066—38no—
48#5027—38no—
49#5027—34no—
50#5026—38no—
51C4×#215—34no—
52#5024—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×Q8C2311yescharacteristic
56#3832—44no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2311yescharacteristic
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—21no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—22no—
70C32×C4⋊C4D411yescharacteristic
71C32×C4⋊C4D412yes—
72C32×C4⋊C4C2312yes—
73C32×C4⋊C4C2311yescharacteristic
74C32×C42—22no—
75C32×C42—21no—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78#3755—22no—
79#3755—24no—
80#3752—22no—
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86#3368—91noSylow
87C2×#239—64no—
88C3×C4⋊Q8—24no—
89C3×C4⋊Q8C2×D314yes—
90C3×#125—28no—
91C3×#125C2×D318yes—
92C3×C4×Q8—24no—
93C3×C4×Q8C2×D314yes—
94C3×C4×Q8C2×D318yes—
95C3×C4×Q8C2×D314yes—
96C2×#215—34no—
97C2×#215—38no—
98#895—64no—
99#895—68no—
100#874—38no—
101#874—34no—
102C4×D12—34no—
103C4×D12—38no—
104#835—34no—
105#809—34no—
106#809—38no—
107#809—38no—
108#809—38no—
109#809—38no—
110#808—34no—
111#807—38no—
112C4⋊(C3⋊C8)—38no—
113C4⋊(C3⋊C8)—34no—
114#803—38no—
115C4×C3⋊C8—34no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—21no—
118C32×Q8—22no—
119C32×Q8—21no—
120C32×Q8—42no—
121C32×Q8#4112yescomplemented
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4C2×D412yes—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—21no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—44no—
136C4⋊(C3⋊D3)—42no—
137C4⋊(C3⋊D3)—82no—
138C4⋊(C3⋊D3)—81no—
139C4×C3⋊D3—44no—
140C4×C3⋊D3—42no—
141C3⋊(C3⋊C8)—21no—
142C3⋊(C3⋊C8)—22no—
143C3⋊(C3⋊C8)—21no—
144#557C3⋊D311yescharacteristic, complemented
145#550—91no—
146#490—92no—
147#486—91no—
148#478—92no—
149#474—91no—
150#460—92no—
151#460—91no—
152#446—91no—
153#440—92no—
154C4×SD16—91no—
155C2×C3×Q8—24no—
156C2×C3×Q8#6714yes—
157C2×C3×Q8C22×D314yes—
158#239—1216no—
159C2×D12—34no—
160C2×D12—38no—
161C2×D12—68no—
162C2×D12—64no—
163C2×D12—68no—
164C2×D12—64no—
165C2×C4×D3—68no—
166C2×C4×D3—64no—
167C3×C4⋊C4—28no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—28no—
170C3×C4⋊C4—24no—
171C3×C4⋊C4—28no—
172C3×C4⋊C4#6714yes—
173C3×C4⋊C4#6718yes—
174C3×C4⋊C4C22×D318yes—
175C3×C4⋊C4C22×D314yes—
176C3×C42—28no—
177C3×C42—24no—
178C3×C42C22×D314yes—
179C3×C42C22×D318yes—
180#215—68no—
181#215—616no—
182(C2×D3)⋊C4—68no—
183(C2×D3)⋊C4—64no—
184C4⋊Dic3—34no—
185C2×C3⋊C8—34no—
186C2×C3⋊C8—34no—
187C2×C3⋊C8—38no—
188C22×C32C22×D411yescharacteristic
189C2×C3⋊D3—42no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—41no—
195C32×C4—22no—
196C32×C4—22no—
197C32×C4—22no—
198C32×C4—21no—
199C32×C4—42no—
200C32×C4—41no—
201C32×C4AGL(1,ℤ/8)12yes—
202C32×C4C2×#4111yescharacteristic
203C32×C42−1+411yescharacteristic
204C3⋊Dic3—41no—
205C2×#41—181no—
206C2×SD16—91no—
207C2×SD16—92no—
208C4⋊Q8—21no—
209C4⋊Q8C2×C3⋊D311yescharacteristic
210#127—91no—
211#127—92no—
212#125—22no—
213#125C2×C3⋊D312yes—
214#121—181no—
215#121—182no—
216C4×Q8—21no—
217C4×Q8C2×C3⋊D311yescharacteristic
218C4×Q8C2×C3⋊D312yes—
219C4×Q8C2×C3⋊D311yescharacteristic
220C4×D4—91no—
221C4×D4—92no—
222#107—92no—
223#106—91no—
224C4⋊C8—91no—
225C4⋊C8—92no—
226#103—91no—
227#102—91no—
228#102—92no—
229#102—92no—
230#102—92no—
231#102—92no—
232#97—92no—
233C4×C8—91no—
234C22×D3—68no—
235C22×D3—64no—
236C3×Q8—28no—
237C3×Q8—24no—
238C3×Q8—48no—
239C3×Q8#23918yescomplemented
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—28no—
243C2×C3×C4C2×#6718yes—
244C2×C3×C4C2×#6714yes—
245C2×C3×C4C2×#6718yes—
246C2×C3×C4C2×#6714yes—
247C2×C3×C4C23×D314yes—
248C2×Dic3—64no—
249D12—64no—
250D12—68no—
251D12—64no—
252D12—68no—
253D12—1216no—
254D12—128no—
255D12—248no—
256D12—244no—
257C4×D3—1216no—
258C4×D3—128no—
259C3⋊C8—64no—
260C3⋊C8—68no—
261C3⋊C8—64no—
262C2×C32#54811yescharacteristic
263C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
264C2×C32#57711yescharacteristic
265C3⋊D3—82no—
266C3⋊D3—81no—
267#41—364no—
268C2×Q8—21no—
269C2×Q8#63811yescharacteristic
270C2×Q8C22×C3⋊D311yescharacteristic
271C2×D4—91no—
272C2×D4—92no—
273C2×D4—182no—
274C2×D4—181no—
275C2×D4—182no—
276C2×D4—181no—
277C22×C4—182no—
278C22×C4—181no—
279SD16—182no—
280SD16—184no—
281C2×C8—91no—
282C2×C8—91no—
283C2×C8—92no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—91no—
290C4⋊C4#63811yescharacteristic
291C4⋊C4#63812yes—
292C4⋊C4C22×C3⋊D311yescharacteristic
293C4⋊C4C22×C3⋊D312yes—
294C22⋊C4—182no—
295C22⋊C4—181no—
296C42—22no—
297C42—21no—
298C42C22×C3⋊D311yescharacteristic
299C42C22×C3⋊D312yes—
300C22×C3C22×#6714yes—
301C2×D3—128no—
302C2×D3—124no—
303C2×D3—128no—
304C2×D3—124no—
305C2×D3—128no—
306C2×D3—124no—
307C3×C4—28no—
308C3×C4—28no—
309C3×C4—28no—
310C3×C4—24no—
311C3×C4—48no—
312C3×C4—44no—
313C3×C4#94918yes—
314C3×C4C2×#23914yes—
315C3×C4#100714yes—
316Dic3—124no—
317C32#336811yescharacteristic, complemented, Sylow
318C23—182no—
319C23—181no—
320Q8—21no—
321Q8—22no—
322Q8—42no—
323Q8#383212yescomplemented
324D4—181no—
325D4—182no—
326D4—181no—
327D4—182no—
328D4—364no—
329D4—362no—
330D4—722no—
331D4—721no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—181no—
336C2×C4—364no—
337C2×C4—362no—
338C2×C4C2×#63812yes—
339C2×C4C2×#63811yescharacteristic
340C2×C4C2×#63812yes—
341C2×C4C2×#63811yescharacteristic
342C2×C4C23×C3⋊D311yescharacteristic
343C8—181no—
344C8—182no—
345C8—181no—
346C2×C3#581714yes—
347C2×C3C2×#94914yes—
348C2×C3#583714yes—
349D3—248no—
350D3—244no—
351C22—362no—
352C22—361no—
353C22—362no—
354C22—361no—
355C22—362no—
356C22—361no—
357C22C22×#63811yescharacteristic
358C4—22no—
359C4—22no—
360C4—22no—
361C4—21no—
362C4—42no—
363C4—41no—
364C4—361no—
365C4#6415812yes—
366C4C2×#383211yescharacteristic
367C4#6436411yescharacteristic
368C3#8369014yescomplemented
369C2—722no—
370C2—721no—
371C2#1059628811yescharacteristic
372C2C2×#6415811yescharacteristic
373C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radical#10596048C2
hypercenter#557C3⋊D3
hypocenterC32#3368
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. #10592787C2semidirect
4. #10592786C2semidirect
5. #10592766C2semidirect
6. #10592765C2semidirect
7. #10592726C2semidirect
8. #10592726C2semidirect
9. #10592725C2semidirect
10. C4×#3755C2semidirect
11. #10592723C2semidirect
42. C3×#557D3semidirect
121. C32×Q8#41semidirect
144. #557C3⋊D3semidirect
239. C3×Q8#239semidirect
317. C32#3368semidirect
323. Q8#3832semidirect
368. C3#83690semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
#105960482
#105927872
#105927862
#105927662
#105927652
#105927262
#105927252
C4×#37552
#105927232
#836903