Finite Group Databasebeta

← #11868940

Subgroups — #11868940

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#10596269C211yesmaximal, characteristic
2#10595990C211yesmaximal, characteristic, complemented
3C32×#418C211yesmaximal, characteristic
4C2×#63659C211yesmaximal, characteristic
5#10592820C211yesmaximal, characteristic, complemented
6#10592818C211yesmaximal, characteristic, complemented
7#10592697C211yesmaximal, characteristic, complemented
8#10592465C212yesmaximal, complemented
9#10592462C212yesmaximal, complemented
10#10592460C212yesmaximal, complemented
11#10592458C212yesmaximal, complemented
12#78918—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3757—22no—
17D4×C3⋊Dic3—21no—
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3C2212yes—
20D4×C3⋊Dic3C2212yes—
21#64135C2211yescharacteristic
22#64135C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64099C2212yescomplemented
26#64097C2212yescomplemented
27#64087—22no—
28#64079—21no—
29#64078—21no—
30C32×#102C2212yes—
31C32×#102C2212yes—
32#63659C2212yes—
33#63659C2212yes—
34#63645C2212yescomplemented
35#63644C2212yescomplemented
36#63641C2212yescomplemented
37#63641C2212yescomplemented
38#63635C2211yescharacteristic, complemented
39#63635C2211yescharacteristic, complemented
40#63634C2211yescharacteristic, complemented
41#63634C2211yescharacteristic, complemented
42#5798—34no—
43#5519—34no—
44C3×#418D314yes—
45C2×#832—34no—
46#5121—34no—
47#5119—34no—
48#4998—34no—
49#4766—38no—
50#4763—38no—
51#4761—38no—
52#4759—38no—
53C24×C32—21no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4Q814yescomplemented
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3—22no—
62C2×#634—22no—
63C32×M16—22no—
64C2×C32×C8C2312yes—
65C32×C4⋊C4C2311yescharacteristic
66C32×C4⋊C4C2311yescharacteristic
67C32×C22⋊C4—21no—
68C32×C42—21no—
69#3757—21no—
70#3757—22no—
71#3757—22no—
72#3757D412yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)D411yescharacteristic
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81#3750—22no—
82C4×C3⋊Dic3—21no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3081—91noSylow
88C22×C3×D4C2×D314yes—
89C2×C3×M16C2×D314yes—
90C3×#117C2×D314yes—
91C2×#217—68no—
92D4×Dic3—38no—
93D4×Dic3—38no—
94D4×Dic3—64no—
95D4×Dic3—64no—
96#926—34no—
97#926—34no—
98C2×C4⋊Dic3—34no—
99C22×C3⋊C8—34no—
100#890—38no—
101#888—38no—
102#878—68no—
103#870—64no—
104#869—64no—
105C3×#102C2×D318yes—
106C3×#102C2×D318yes—
107#832—38no—
108#832—38no—
109#818—38no—
110#817—38no—
111Dic3⋊C8—38no—
112Dic3⋊C8—38no—
113#808—34no—
114#808—34no—
115#807—34no—
116#807—34no—
117C23×C32—22no—
118C23×C32—24no—
119C23×C32—81no—
120C23×C32—81no—
121C23×C32C2×D411yescharacteristic
122C32×D4—24no—
123C32×D4—22no—
124C32×D4C2×Q814yes—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q812yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—82no—
135C2×C3⋊Dic3—82no—
136C2×C3⋊Dic3—81no—
137C2×C3⋊Dic3C2×D412yes—
138C2×C3⋊Dic3C2×D412yes—
139#634—82no—
140C32×C8—22no—
141C3⋊(C3⋊C8)—21no—
142C3⋊(C3⋊C8)—21no—
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#424—91no—
152#418C3⋊D311yescharacteristic
153C2×#102—91no—
154C24×C3—24no—
155C2×C3×D4—24no—
156C2×C3×D4—28no—
157C2×C3×D4Dic6116yescomplemented
158C2×C3×D4C22×D318yes—
159C22×C3×C4C22×D314yes—
160C22×Dic3—68no—
161C22×Dic3—68no—
162C22×Dic3—64no—
163C2×Dic6—68no—
164C3×M16—28no—
165C2×C3×C8C22×D318yes—
166C3×C4⋊C4C22×D314yes—
167C3×C4⋊C4C22×D314yes—
168C3×C22⋊C4—24no—
169C3×C42—24no—
170#217—38no—
171#217—68no—
172#217—68no—
173#217—64no—
174C4⋊Dic3—34no—
175C4⋊Dic3—34no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—38no—
179C4⋊Dic3—68no—
180C4⋊Dic3—64no—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183C4×Dic3—38no—
184C4×Dic3—64no—
185C2×C3⋊C8—34no—
186C2×C3⋊C8—34no—
187C2×C3⋊C8—68no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—24no—
191C22×C32—42no—
192C22×C32—42no—
193C22×C32—84no—
194C22×C32C22⋊Q812yes—
195C22×C32C22×D411yescharacteristic
196C32×C4—41no—
197C32×C4—41no—
198C32×C4C22⋊Q812yes—
199C32×C4C22×Q811yescharacteristic
200C32×C4C2×#4111yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—42no—
204C3⋊Dic3—41no—
205C3⋊Dic3—41no—
206C22×D4C2×C3⋊D311yescharacteristic
207C2×M16C2×C3⋊D311yescharacteristic
208C22×C8—91no—
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—92no—
224#107—91no—
225#107—91no—
226#106—92no—
227#106—91no—
228#106—91no—
229C4⋊C8—92no—
230C4⋊C8—92no—
231#102—92no—
232#102—92no—
233#102C2×C3⋊D312yes—
234#102C2×C3⋊D312yes—
235C23×C3—28no—
236C23×C3—216no—
237C23×C3—84no—
238C23×C3—84no—
239C23×C3D3×D414yes—
240C3×D4—216no—
241C3×D4—28no—
242C3×D4C2×Dic6116yes—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4C2×Dic618yes—
246C2×C3×C4D3×D414yes—
247C2×C3×C4#23718yes—
248C2×C3×C4C23×D314yes—
249C2×Dic3—38no—
250C2×Dic3—38no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—68no—
254C2×Dic3—248no—
255C2×Dic3—248no—
256C2×Dic3—244no—
257Dic6—248no—
258C3×C8—28no—
259C3⋊C8—64no—
260C3⋊C8—64no—
261C2×C32—22no—
262C2×C32—44no—
263C2×C32C2×C22⋊Q811yescharacteristic
264C2×C32#57611yescharacteristic
265C2×C32#57711yescharacteristic
266C24—21no—
267C2×Q8—182no—
268C2×D4—21no—
269C2×D4—22no—
270C2×D4#63414yescomplemented
271C2×D4C22×C3⋊D312yes—
272C22×C4—182no—
273C22×C4—182no—
274C22×C4—181no—
275C22×C4C22×C3⋊D311yescharacteristic
276M16—22no—
277C2×C8—91no—
278C2×C8—91no—
279C2×C8—182no—
280C2×C8C22×C3⋊D312yes—
281C4⋊C4—91no—
282C4⋊C4—91no—
283C4⋊C4—92no—
284C4⋊C4—91no—
285C4⋊C4—91no—
286C4⋊C4—182no—
287C4⋊C4—182no—
288C4⋊C4—182no—
289C4⋊C4—181no—
290C4⋊C4C22×C3⋊D311yescharacteristic
291C4⋊C4C22×C3⋊D311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—92no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C22⋊C4—181no—
297C42—21no—
298C42—92no—
299C42—181no—
300C22×C3—24no—
301C22×C3—24no—
302C22×C3—216no—
303C22×C3—48no—
304C22×C3—48no—
305C22×C3—816no—
306C22×C3#87818yes—
307C22×C3C2×D3×D414yes—
308C3×C4—44no—
309C3×C4—44no—
310C3×C4#87818yes—
311C3×C4C22×Dic614yes—
312C3×C4C2×#23714yes—
313Dic3—68no—
314Dic3—68no—
315Dic3—128no—
316Dic3—124no—
317Dic3—124no—
318C32#308111yescharacteristic, complemented, Sylow
319C23—22no—
320C23—24no—
321C23—81no—
322C23—81no—
323C23D4×C3⋊D311yescharacteristic
324Q8—722no—
325D4—24no—
326D4—22no—
327D4C2×#63414yes—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—181no—
333C2×C4—181no—
334C2×C4—182no—
335C2×C4—722no—
336C2×C4—722no—
337C2×C4—721no—
338C2×C4C2×#63412yes—
339C2×C4D4×C3⋊D311yescharacteristic
340C2×C4#383012yes—
341C2×C4C23×C3⋊D311yescharacteristic
342C8—22no—
343C8—181no—
344C8—181no—
345C2×C3—28no—
346C2×C3—416no—
347C2×C3C2×#87814yes—
348C2×C3#577414yes—
349C2×C3#577514yes—
350C22—21no—
351C22—21no—
352C22—24no—
353C22—42no—
354C22—42no—
355C22—84no—
356C22#6408712yes—
357C22C2×D4×C3⋊D311yescharacteristic
358C4—41no—
359C4—41no—
360C4—182no—
361C4—182no—
362C4—361no—
363C4—362no—
364C4—361no—
365C4#6408712yes—
366C4C22×#63411yescharacteristic
367C4C2×#383011yescharacteristic
368C3#7891814yescomplemented
369C2—22no—
370C2—44no—
371C2C2×#6408711yescharacteristic
372C2#1059624511yescharacteristic
373C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenter#418C3⋊D3
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #10595990C2semidirect
5. #10592820C2semidirect
6. #10592818C2semidirect
7. #10592697C2semidirect
8. #10592465C2semidirect
9. #10592462C2semidirect
10. #10592460C2semidirect
11. #10592458C2semidirect
25. #64099C22semidirect
26. #64097C22semidirect
34. #63645C22semidirect
35. #63644C22semidirect
36. #63641C22semidirect
37. #63641C22semidirect
38. #63635C22semidirect
39. #63635C22semidirect
40. #63634C22semidirect
41. #63634C22semidirect
56. C2×C32×D4Q8semidirect
157. C2×C3×D4Dic6semidirect
270. C2×D4#634semidirect
318. C32#3081semidirect
368. C3#78918semidirect

Maximal subgroups

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

subgroupindex
#105962692
#105959902
C32×#4182
C2×#636592
#105928202
#105928182
#105926972
#105924652
#105924622
#105924602
#105924582
#789183