Finite Group Databasebeta

← #11897524

Subgroups — #11897524

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#10596050C211yesmaximal, characteristic, complemented
2Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4#10592546C212yesmaximal, complemented
5#10592545C211yesmaximal, characteristic, complemented
6#10592541C211yesmaximal, characteristic, complemented
7#10592541C212yesmaximal, complemented
8#10592410C212yesmaximal
9#10592401C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic
11#10592379C211yesmaximal, characteristic, complemented
12#79975—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16C2×#3745C2211yescharacteristic
17#64106—21no—
18#64106—22no—
19#64105—22no—
20C4⋊C4×C3⋊D3—21no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2212yes—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2212yes—
25#64079C2212yes—
26#64078C2211yescharacteristic
27#64078C2212yes—
28#64078C2211yescharacteristic
29C32×C4⋊C8C2211yescharacteristic
30C32×C4⋊C8C2212yes—
31C32×#97C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63648C2211yescharacteristic
34#63648C2212yes—
35#63648C2212yes—
36#63648C2211yescharacteristic
37#63645C2212yes—
38#63645C2211yescharacteristic
39#63644C2212yes—
40#63644C2212yes—
41#63644C2212yes—
42#5579—34no—
43Q8×D12—34no—
44C3×#446D314yescomplemented
45#4847—38no—
46#4846—34no—
47#4842—38no—
48#4842—34no—
49#4711—38no—
50#4702—38no—
51C4×D24—34no—
52#4680—34no—
53C2×C32×Q8D411yescharacteristic
54Q8×C3⋊D3—44no—
55C2×C4⋊(C3⋊D3)C2311yescharacteristic
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634—21no—
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2312yes—
66C2×C32×C8C2311yescharacteristic
67C32×C4⋊C4D411yescharacteristic
68C32×C4⋊C4D412yes—
69C32×C42C2311yescharacteristic
70C32×C42C2312yes—
71#3752—21no—
72#3752—22no—
73#3752—22no—
74#3752—21no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2312yes—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—22no—
83#3750—22no—
84#3745Q814yescomplemented
85#3384—91noSylow
86C2×D3×Q8—64no—
87C3×C4×Q8C2×D314yes—
88#946—64no—
89C2×D24—34no—
90#897—64no—
91#897—68no—
92#896—68no—
93D3×C4⋊C4—64no—
94C4×D12—34no—
95C4×D12—34no—
96C4×D12—38no—
97C4×D12—38no—
98#870—38no—
99#869—34no—
100#869—34no—
101#869—38no—
102C3×C4⋊C8C2×D314yes—
103C3×C4⋊C8C2×D318yes—
104C3×#97C2×D318yes—
105C3×C4×C8C2×D314yes—
106#821—34no—
107#821—34no—
108#821—38no—
109#821—38no—
110#818—34no—
111#818—38no—
112#817—38no—
113#817—38no—
114#817—38no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—21no—
117C32×Q8—22no—
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C4⋊(C3⋊D3)—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)C2×Q812yes—
130C4⋊(C3⋊D3)C2×Q812yescomplemented
131C4×C3⋊D3—44no—
132C4×C3⋊D3—42no—
133C4×C3⋊D3—42no—
134C4×C3⋊D3—82no—
135#634—44no—
136#634—42no—
137#634—81no—
138C32×C8—21no—
139C32×C8—22no—
140C32×C8C2×Q812yescomplemented
141#554—91no—
142D4×Q8—91no—
143#501—92no—
144#498—91no—
145#478—92no—
146#476—92no—
147#476—91no—
148#474—91no—
149#446C3⋊D311yescharacteristic, complemented
150#442—92no—
151C4×D8—91no—
152C2×C3×Q8D1214yes—
153D3×Q8—1216no—
154C2×D12—34no—
155C2×D12—34no—
156C2×C4×D3—64no—
157C2×C4×D3—68no—
158C2×C4×D3—64no—
159C2×C4×D3—68no—
160C2×Dic6—68no—
161C2×Dic6—64no—
162C2×Dic6—64no—
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D318yes—
165C2×C3×C8C22×D314yes—
166C3×C4⋊C4D1214yes—
167C3×C4⋊C4D1218yes—
168C3×C42C22×D314yes—
169C3×C42C22×D318yes—
170(C2×D3)⋊C4—64no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—68no—
173(C2×D3)⋊C4—64no—
174C4⋊Dic3—38no—
175C4⋊Dic3—38no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—64no—
179C4⋊Dic3—68no—
180C4⋊Dic3—64no—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183D24—316no—
184C22×C32C22×D411yescharacteristic
185C2×C3⋊D3—22no—
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C32×C4—22no—
192C32×C4—21no—
193C32×C4—22no—
194C32×C4AGL(1,ℤ/8)12yes—
195C32×C4C22×Q811yescharacteristic
196C32×C42−1+411yescharacteristic
197C3⋊Dic3—41no—
198C3⋊Dic3—42no—
199C3⋊Dic3—41no—
200C3⋊Dic3—42no—
201C22×Q8—181no—
202C2×D8—91no—
203C4⋊Q8—91no—
204C4⋊Q8—92no—
205C4⋊Q8—91no—
206#125—92no—
207C22⋊Q8—181no—
208C22⋊Q8—181no—
209C22⋊Q8—182no—
210C22⋊Q8—182no—
211C4×Q8C2×C3⋊D311yescharacteristic
212C4×D4—91no—
213C4×D4—92no—
214C4×D4—91no—
215C4×D4—92no—
216C2×C4⋊C4—181no—
217#107—91no—
218#107—92no—
219#106—92no—
220#106—92no—
221#106—92no—
222C4⋊C8C2×C3⋊D311yescharacteristic
223C4⋊C8C2×C3⋊D312yes—
224#102—91no—
225#102—91no—
226#102—92no—
227#102—92no—
228#97C2×C3⋊D312yes—
229C4×C8C2×C3⋊D311yescharacteristic
230C22×D3—64no—
231C22×D3—64no—
232C3×Q8—28no—
233C2×C3×C4C2×D1218yes—
234C2×C3×C4C2×D1218yes—
235C2×C3×C4C2×D1214yes—
236C2×C3×C4C2×D1214yes—
237C2×C3×C4C23×D314yes—
238C2×Dic3—64no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241C2×Dic3—68no—
242D12—38no—
243D12—38no—
244D12—64no—
245D12—64no—
246C4×D3—1216no—
247C4×D3—128no—
248C4×D3—128no—
249C4×D3—248no—
250Dic6—1216no—
251Dic6—128no—
252Dic6—244no—
253C3×C8—24no—
254C3×C8—28no—
255C3×C8D3×Q818yescomplemented
256C2×C32D4×Q811yescharacteristic
257C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
258C2×C32#57711yescharacteristic
259C3⋊D3—42no—
260C3⋊D3—42no—
261C2×Q8—182no—
262C2×Q8—181no—
263C2×Q8—181no—
264C2×Q8—364no—
265C2×Q8C4⋊(C3⋊D3)11yescharacteristic
266C2×D4—91no—
267C2×D4—91no—
268C22×C4—181no—
269C22×C4—182no—
270C22×C4—181no—
271C22×C4—182no—
272D8—94no—
273C2×C8C22×C3⋊D311yescharacteristic
274C2×C8C22×C3⋊D312yes—
275C2×C8C22×C3⋊D311yescharacteristic
276C4⋊C4—92no—
277C4⋊C4—91no—
278C4⋊C4—92no—
279C4⋊C4—91no—
280C4⋊C4—182no—
281C4⋊C4—181no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4—182no—
285C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
286C4⋊C4C4⋊(C3⋊D3)12yes—
287C22⋊C4—181no—
288C22⋊C4—182no—
289C22⋊C4—181no—
290C22⋊C4—182no—
291C42C22×C3⋊D311yescharacteristic
292C42C22×C3⋊D312yes—
293C22×C3C22×D1214yes—
294C2×D3—68no—
295C2×D3—68no—
296C2×D3—124no—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—124no—
300C3×C4—28no—
301C3×C4—24no—
302C3×C4—28no—
303C3×C4#90818yes—
304C3×C4C2×D3×Q814yes—
305C3×C4#101014yes—
306Dic3—124no—
307Dic3—128no—
308Dic3—124no—
309Dic3—128no—
310C32#338411yescharacteristic, complemented, Sylow
311C23—181no—
312C23—181no—
313Q8—22no—
314Q8—364no—
315Q8—362no—
316Q8—721no—
317D4—92no—
318D4—92no—
319D4—181no—
320D4—181no—
321C2×C4—181no—
322C2×C4—182no—
323C2×C4—182no—
324C2×C4—181no—
325C2×C4—364no—
326C2×C4—362no—
327C2×C4—362no—
328C2×C4—722no—
329C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
330C2×C4C2×C4⋊(C3⋊D3)12yes—
331C2×C4C2×C4⋊(C3⋊D3)12yes—
332C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
333C2×C4C23×C3⋊D311yescharacteristic
334C8—21no—
335C8—22no—
336C8Q8×C3⋊D312yescomplemented
337C2×C3Q8×D1214yes—
338C2×C3C2×#90814yes—
339C2×C3#575114yes—
340D3—128no—
341D3—128no—
342C22—182no—
343C22—182no—
344C22—361no—
345C22—361no—
346C22—361no—
347C22—361no—
348C22C22×C4⋊(C3⋊D3)11yescharacteristic
349C4—22no—
350C4—22no—
351C4—21no—
352C4—362no—
353C4—361no—
354C4—361no—
355C4—362no—
356C4#6411712yes—
357C4C2×Q8×C3⋊D311yescharacteristic
358C4#6436711yescharacteristic
359C3#7997514yescomplemented
360C2—362no—
361C2—362no—
362C2Q8×C4⋊(C3⋊D3)11yescharacteristic
363C2C2×#6411711yescharacteristic
364C2#1059622211yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#446C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#446C3⋊D3
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. Q8×C4⋊(C3⋊D3)C2semidirect
3. C32×#446C2semidirect
4. #10592546C2semidirect
5. #10592545C2semidirect
6. #10592541C2semidirect
7. #10592541C2semidirect
9. #10592401C2semidirect
11. #10592379C2semidirect
44. C3×#446D3semidirect
84. #3745Q8semidirect
130. C4⋊(C3⋊D3)C2×Q8semidirect
140. C32×C8C2×Q8semidirect
149. #446C3⋊D3semidirect
255. C3×C8D3×Q8semidirect
310. C32#3384semidirect
336. C8Q8×C3⋊D3semidirect
359. C3#79975semidirect

Maximal subgroups

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

subgroupindex
#105960502
Q8×C4⋊(C3⋊D3)2
C32×#4462
#105925462
#105925452
#105925412
#105924102
#105924012
C4×#37452
#105923792
#799753