Finite Group Databasebeta

← #11868937

Subgroups — #11868937

Order 1152.

1194 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
1#10595992C211yesmaximal, characteristic
2#10595990C211yesmaximal, characteristic, complemented
3C32×#424C211yesmaximal, characteristic, complemented
4#10592830C211yesmaximal, characteristic
5#10592820C211yesmaximal, characteristic, complemented
6C2×#63648C211yesmaximal, characteristic
7#10592805C211yesmaximal, characteristic, complemented
8#10592546C212yesmaximal, complemented
9#10592546C212yesmaximal, complemented
10#10592545C212yesmaximal, complemented
11#10592541C212yesmaximal, complemented
12#79090—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20#64102—21no—
21#64102—21no—
22#64099—21no—
23#64097—21no—
24C22⋊C4×C3⋊D3—22no—
25#64087—22no—
26C4×C4⋊(C3⋊D3)C2212yes—
27C4×C4⋊(C3⋊D3)C2212yes—
28#64079C2212yescomplemented
29#64078C2212yescomplemented
30C32×C4⋊C8C2212yescomplemented
31C32×C4⋊C8C2212yescomplemented
32#63648C2212yes—
33#63648C2212yes—
34#63648C2212yes—
35#63648C2212yes—
36#63645C2211yescharacteristic, complemented
37#63645C2212yescomplemented
38#63645C2211yescharacteristic, complemented
39#63644C2211yescharacteristic, complemented
40#63644C2212yescomplemented
41#63644C2211yescharacteristic, complemented
42#5521—34no—
43#5519—34no—
44C3×#424D314yescomplemented
45#5131—34no—
46#5121—34no—
47C2×#821—34no—
48#5106—34no—
49#4847—38no—
50#4847—38no—
51#4846—38no—
52#4842—38no—
53C23×C3⋊D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)Q814yescomplemented
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×#634—22no—
63C32×M16—22no—
64C2×C32×C8—22no—
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2312yes—
67C2×C32×C8C2311yescharacteristic
68C32×C4⋊C4D411yescharacteristic
69C32×C4⋊C4D411yescharacteristic
70C32×C22⋊C4D412yes—
71C32×C42C2312yes—
72#3757—21no—
73#3757—21no—
74#3752—22no—
75#3752—22no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—22no—
84#3750—22no—
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—21no—
87#3081—91noSylow
88C22×D12—34no—
89C2×C3×M16C2×D314yes—
90C22×C3×C8C2×D314yes—
91C3×#117C2×D314yes—
92#926—34no—
93#926—34no—
94C2×C4⋊Dic3—34no—
95#893—64no—
96#893—64no—
97#890—64no—
98#888—64no—
99D3×C22⋊C4—68no—
100#878—68no—
101C4×D12—38no—
102C4×D12—38no—
103#870—38no—
104#869—38no—
105C3×C4⋊C8C2×D318yescomplemented
106C3×C4⋊C8C2×D318yescomplemented
107#821—38no—
108#821—38no—
109#821—38no—
110#821—38no—
111#818—38no—
112#818—34no—
113#818—34no—
114#817—38no—
115#817—34no—
116#817—34no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—24no—
120C22×C3⋊D3—81no—
121C22×C3⋊D3—81no—
122C2×C32×C4C2×D412yes—
123C2×C32×C4C2×D412yes—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q812yes—
126C2×C32×C4#4112yes—
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—81no—
134C4⋊(C3⋊D3)—24no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)C2×Q814yes—
137C4×C3⋊D3—82no—
138C4×C3⋊D3—82no—
139#634—82no—
140C32×C8—21no—
141C32×C8—21no—
142C32×C8—22no—
143#544—91no—
144#518—91no—
145#478—92no—
146#478—92no—
147#476—92no—
148#474—92no—
149#428—91no—
150#427—91no—
151#424C3⋊D311yescharacteristic, complemented
152#418—91no—
153C2×#102—91no—
154C23×D3—64no—
155C22×C3×C4C22×D314yes—
156C22×Dic3—64no—
157C2×D12—316no—
158C2×D12—38no—
159C2×D12—64no—
160C2×D12—68no—
161C2×C4×D3—68no—
162C2×C4×D3—68no—
163C2×Dic6—68no—
164C3×M16—28no—
165C2×C3×C8—28no—
166C2×C3×C8C22×D314yes—
167C2×C3×C8C22×D318yes—
168C2×C3×C8C22×D314yes—
169C3×C4⋊C4D1214yes—
170C3×C4⋊C4D1214yes—
171C3×C22⋊C4D1218yes—
172C3×C42C22×D318yes—
173#217—64no—
174#217—64no—
175(C2×D3)⋊C4—68no—
176(C2×D3)⋊C4—68no—
177C4⋊Dic3—34no—
178C4⋊Dic3—34no—
179C4⋊Dic3—34no—
180C4⋊Dic3—38no—
181C4⋊Dic3—34no—
182C4⋊Dic3—68no—
183C4⋊Dic3—64no—
184Dic3⋊C4—68no—
185Dic3⋊C4—68no—
186C4×Dic3—64no—
187C4×Dic3—64no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32C22⋊Q812yes—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—24no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—84no—
196C32×C4—22no—
197C32×C4—22no—
198C32×C4C22⋊Q812yes—
199C32×C4C22×Q811yescharacteristic
200C32×C4C2×#4111yescharacteristic
201C3⋊Dic3—41no—
202C3⋊Dic3—42no—
203C3⋊Dic3—41no—
204C3⋊Dic3—41no—
205C3⋊Dic3—41no—
206C22×D4—91no—
207C2×M16C2×C3⋊D311yescharacteristic
208C22×C8C2×C3⋊D311yescharacteristic
209C4⋊Q8—92no—
210C4⋊Q8—181no—
211#125—92no—
212#125—181no—
213C22⋊Q8—182no—
214C4×D4—92no—
215C4×D4—92no—
216C4×D4—181no—
217C4×D4—181no—
218#117—91no—
219#117—91no—
220#117C2×C3⋊D311yescharacteristic
221C2×C4⋊C4—91no—
222C2×C22⋊C4—182no—
223#107—91no—
224#107—91no—
225#107—92no—
226#106—91no—
227#106—91no—
228#106—92no—
229C4⋊C8C2×C3⋊D312yescomplemented
230C4⋊C8C2×C3⋊D312yescomplemented
231#102—92no—
232#102—92no—
233#102—92no—
234#102—92no—
235C23×C3C2×D1214yes—
236C22×D3—68no—
237C22×D3—616no—
238C22×D3—244no—
239C22×D3—244no—
240C2×C3×C4C2×D1218yes—
241C2×C3×C4C2×D1218yes—
242C2×C3×C4C2×D1214yes—
243C2×C3×C4#23718yes—
244C2×C3×C4D3×Q818yes—
245C2×C3×C4C23×D314yes—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—68no—
251C2×Dic3—244no—
252D12—316no—
253D12—616no—
254D12—68no—
255C4×D3—248no—
256C4×D3—248no—
257Dic6—248no—
258C3×C8—24no—
259C3×C8—24no—
260C3×C8—28no—
261C2×C32—22no—
262C2×C32C2×C22⋊Q811yescharacteristic
263C2×C32#57611yescharacteristic
264C2×C32#57711yescharacteristic
265C3⋊D3—44no—
266C24—181no—
267C2×Q8—182no—
268C2×D4—92no—
269C2×D4—94no—
270C2×D4—181no—
271C2×D4—182no—
272C22×C4—181no—
273C22×C4—182no—
274C22×C4—182no—
275C22×C4C22×C3⋊D311yescharacteristic
276M16—22no—
277C2×C8—22no—
278C2×C8C22×C3⋊D311yescharacteristic
279C2×C8C22×C3⋊D312yes—
280C2×C8C22×C3⋊D311yescharacteristic
281C4⋊C4—92no—
282C4⋊C4—91no—
283C4⋊C4—91no—
284C4⋊C4—91no—
285C4⋊C4—91no—
286C4⋊C4—181no—
287C4⋊C4—182no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
291C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
292C22⋊C4—181no—
293C22⋊C4—181no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C22⋊C4C4⋊(C3⋊D3)12yes—
297C42—181no—
298C42—181no—
299C42C22×C3⋊D312yes—
300C22×C3—24no—
301C22×C3—24no—
302C22×C3#89718yes—
303C22×C3C22×D1214yes—
304C2×D3—616no—
305C2×D3—128no—
306C2×D3—128no—
307C2×D3—2416no—
308C3×C4—28no—
309C3×C4—28no—
310C3×C4#89718yes—
311C3×C4C2×#23714yes—
312C3×C4C2×D3×Q814yes—
313Dic3—124no—
314Dic3—124no—
315Dic3—124no—
316Dic3—128no—
317Dic3—124no—
318C32#308111yescharacteristic, complemented, Sylow
319C23—182no—
320C23—184no—
321C23—721no—
322C23—721no—
323C23C2×C4⋊(C3⋊D3)11yescharacteristic
324Q8—722no—
325D4—94no—
326D4—182no—
327D4—184no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—181no—
332C2×C4—182no—
333C2×C4—722no—
334C2×C4—722no—
335C2×C4—721no—
336C2×C4C2×C4⋊(C3⋊D3)12yes—
337C2×C4C2×C4⋊(C3⋊D3)12yes—
338C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
339C2×C4#383012yes—
340C2×C4Q8×C3⋊D312yes—
341C2×C4C23×C3⋊D311yescharacteristic
342C8—21no—
343C8—21no—
344C8—22no—
345C2×C3—28no—
346C2×C3C2×#89714yes—
347C2×C3#575114yes—
348C2×C3#575214yes—
349D3—1216no—
350C22—21no—
351C22—21no—
352C22—184no—
353C22—362no—
354C22—362no—
355C22—724no—
356C22#6410612yes—
357C22C22×C4⋊(C3⋊D3)11yescharacteristic
358C4—22no—
359C4—22no—
360C4—361no—
361C4—361no—
362C4—361no—
363C4—362no—
364C4—361no—
365C4#6410612yes—
366C4C2×#383011yescharacteristic
367C4C2×Q8×C3⋊D311yescharacteristic
368C3#7909014yescomplemented
369C2—22no—
370C2—364no—
371C2C2×#6410611yescharacteristic
372C2#1059622211yescharacteristic
373C2#1059622311yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#424C2
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#424C3⋊D3
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #10595990C2semidirect
3. C32×#424C2semidirect
5. #10592820C2semidirect
7. #10592805C2semidirect
8. #10592546C2semidirect
9. #10592546C2semidirect
10. #10592545C2semidirect
11. #10592541C2semidirect
28. #64079C22semidirect
29. #64078C22semidirect
30. C32×C4⋊C8C22semidirect
31. C32×C4⋊C8C22semidirect
36. #63645C22semidirect
37. #63645C22semidirect
38. #63645C22semidirect
39. #63644C22semidirect
40. #63644C22semidirect
41. #63644C22semidirect
44. C3×#424D3semidirect
58. C2×C4⋊(C3⋊D3)Q8semidirect
105. C3×C4⋊C8C2×D3semidirect
106. C3×C4⋊C8C2×D3semidirect
151. #424C3⋊D3semidirect
229. C4⋊C8C2×C3⋊D3semidirect
230. C4⋊C8C2×C3⋊D3semidirect
318. C32#3081semidirect
368. C3#79090semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105959902
C32×#4242
#105928302
#105928202
C2×#636482
#105928052
#105925462
#105925452
#105925412
#790903