Finite Group Databasebeta

← #11786447

Subgroups — #11786447

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×C32×#106C211yesmaximal, characteristic, complemented
3C2×#63647C211yesmaximal, characteristic
4#10592686C211yesmaximal, characteristic
5C2×#63635C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70579—34nomaximal
9C22×C4×C3⋊D3—21no—
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750—21no—
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C4⋊C4×C3⋊D3—22no—
20C4⋊C4×C3⋊D3—22no—
21C32×#106—22no—
22#63658—21no—
23#63647C414yescomplemented
24#63635—22no—
25C2×D3×C4⋊C4—34no—
26C2×C3×#106D314yescomplemented
27C2×(C2×D3)⋊C8—34no—
28#4987—34no—
29C2×#808—34no—
30#4551—34no—
31#4529—34no—
32C23×C3⋊D3D411yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—24no—
44C2×C4×C3⋊D3—42no—
45C2×C4×C3⋊D3—42no—
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3Q812yes—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8C2×C412yescomplemented
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D412yes—
55#3752—42no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D412yes—
60#3750—24no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)C2×C412yescomplemented
64#1853—91noSylow
65C22×C4×D3—34no—
66C22×C4×D3—64no—
67C22×C3×C8C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69C2×C3×C4⋊C4C2×D314yes—
70C2×(C2×D3)⋊C4—64no—
71C2×C4⋊Dic3—34no—
72C2×C4⋊Dic3—34no—
73C2×Dic3⋊C4—64no—
74C22×C3⋊C8—34no—
75D3×C4⋊C4—68no—
76D3×C4⋊C4—68no—
77C3×#106—28no—
78C3⋊#95—64no—
79(C2×D3)⋊C8—316no—
80#808—68no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—21no—
83C22×C3⋊D3—21no—
84C22×C3⋊D3—21no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3C4⋊C412yes—
87C22×C3⋊D3SD1612yes—
88C22×C3⋊D3SD1612yes—
89C2×C32×C4—22no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×Q811yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3C4⋊C412yes—
110C4×C3⋊D3—22no—
111C4×C3⋊D3—22no—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—22no—
114C4×C3⋊D3—48no—
115C32×C8—22no—
116C3⋊(C3⋊C8)—22no—
117C22×C4⋊C4—91no—
118C2×#106—91no—
119C2×#106C3⋊D311yescharacteristic, complemented
120C2×C22⋊C8—91no—
121#380—91no—
122#340—91no—
123#340—91no—
124C23×D3—34no—
125C22×C3×C4—24no—
126C22×C3×C4—24no—
127C22×C3×C4C22×D314yes—
128C22×Dic3—34no—
129C22×Dic3—64no—
130C22×Dic3—64no—
131C2×C4×D3—38no—
132C2×C4×D3—38no—
133C2×C4×D3—64no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—616no—
138C2×C4×D3—128no—
139C2×C4×D3—128no—
140C2×C3×C8—24no—
141C2×C3×C8—24no—
142C2×C3×C8C4×D318yescomplemented
143C3×C4⋊C4—24no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4#6718yes—
147(C2×D3)⋊C4—128no—
148C4⋊Dic3—38no—
149C4⋊Dic3—64no—
150C4⋊Dic3—64no—
151C4⋊Dic3—64no—
152Dic3⋊C4—616no—
153C2×C3⋊C8—38no—
154C2×C3⋊C8—64no—
155C2×C3⋊C8—64no—
156C22×C32C2×C4⋊C411yescharacteristic
157C22×C32#12011yescharacteristic
158C22×C32#12311yescharacteristic
159C22×C32C2×SD1611yescharacteristic
160C22×C32C2×SD1611yescharacteristic
161C22×C32AGL(1,ℤ/8)11yescharacteristic
162C22×C32#13711yescharacteristic
163C2×C3⋊D3—22no—
164C2×C3⋊D3—22no—
165C2×C3⋊D3—22no—
166C2×C3⋊D3—22no—
167C2×C3⋊D3—22no—
168C2×C3⋊D3—22no—
169C2×C3⋊D3#10614yescomplemented
170C32×C4—42no—
171C32×C4—81no—
172C32×C4C4×D411yescharacteristic
173C32×C4C4×D411yescharacteristic
174C32×C4C22⋊Q811yescharacteristic
175C32×C4C22⋊Q811yescharacteristic
176C3⋊Dic3—22no—
177C3⋊Dic3—42no—
178C3⋊Dic3—81no—
179C23×C4—91no—
180C23×C4—181no—
181C22×C8—91no—
182C22×C8C2×C3⋊D311yescharacteristic
183C2×C4⋊C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—182no—
186C2×C4⋊C4—181no—
187C2×C4⋊C4—182no—
188C2×C4⋊C4C2×C3⋊D311yescharacteristic
189C2×C4⋊C4C2×C3⋊D311yescharacteristic
190C2×C22⋊C4—181no—
191#106—22no—
192#106—182no—
193C22⋊C8—94no—
194#95—181no—
195C23×C3D3×D414yes—
196C22×D3—38no—
197C22×D3—38no—
198C22×D3—38no—
199C22×D3—64no—
200C22×D3—64no—
201C22×D3—64no—
202C22×D3—64no—
203C2×C3×C4—28no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4#23514yes—
211C2×C3×C4D3×D414yes—
212C2×C3×C4D3×Q814yes—
213C2×C3×C4#23914yes—
214C2×C3×C4C2×#6714yes—
215C2×Dic3—38no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—68no—
219C2×Dic3—124no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224C4×D3—68no—
225C4×D3—68no—
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—1232no—
229C3×C8—28no—
230C3⋊C8—68no—
231C2×C32#38511yescharacteristic
232C2×C32C2×#10611yescharacteristic
233C2×C32#42811yescharacteristic
234C2×C32#44811yescharacteristic
235C2×C32#45011yescharacteristic
236C2×C32#48111yescharacteristic
237C2×C32#48311yescharacteristic
238C3⋊D3—24no—
239C24—91no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—91no—
243C22×C4—92no—
244C22×C4—92no—
245C22×C4—184no—
246C22×C4—181no—
247C22×C4—181no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4—181no—
251C22×C4—181no—
252C22×C4—362no—
253C22×C4—362no—
254C22×C4C22×C3⋊D311yescharacteristic
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—92no—
258C2×C8—181no—
259C2×C8—181no—
260C2×C8C4×C3⋊D312yescomplemented
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—92no—
265C4⋊C4—184no—
266C4⋊C4—181no—
267C4⋊C4—181no—
268C4⋊C4—181no—
269C4⋊C4#63812yes—
270C22⋊C4—362no—
271C22×C3D3×C4⋊C414yes—
272C22×C3#89414yes—
273C22×C3D3×SD1614yes—
274C22×C3D3×SD1614yes—
275C22×C3#91414yes—
276C22×C3#91514yes—
277C22×C3#93714yes—
278C2×D3—316no—
279C2×D3—68no—
280C2×D3—68no—
281C2×D3—68no—
282C2×D3—68no—
283C2×D3—68no—
284C2×D3—68no—
285C3×C4—48no—
286C3×C4—84no—
287C3×C4#89314yes—
288C3×C4#89614yes—
289C3×C4C4×#6714yes—
290C3×C4#94614yes—
291Dic3—68no—
292Dic3—128no—
293Dic3—244no—
294C32#185311yescharacteristic, complemented, Sylow
295C23—92no—
296C23—92no—
297C23—92no—
298C23—181no—
299C23—181no—
300C23—181no—
301C23—181no—
302C23D4×C3⋊D311yescharacteristic
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—92no—
310C2×C4—181no—
311C2×C4—181no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4—368no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4C2×C4×C3⋊D311yescharacteristic
324C2×C4#382811yescharacteristic
325C2×C4D4×C3⋊D311yescharacteristic
326C2×C4Q8×C3⋊D311yescharacteristic
327C2×C4#383211yescharacteristic
328C2×C4C2×#63811yescharacteristic
329C8—22no—
330C8—182no—
331C2×C3D3×#10614yes—
332C2×C3#486114yes—
333C2×C3#486214yes—
334C2×C3#486314yes—
335C2×C3#498914yes—
336C2×C3#516914yes—
337C2×C3#517014yes—
338D3—616no—
339C22—94no—
340C22—182no—
341C22—182no—
342C22—182no—
343C22—182no—
344C22—182no—
345C22—182no—
346C22C4⋊C4×C3⋊D311yescharacteristic
347C22#6410311yescharacteristic
348C22SD16×C3⋊D311yescharacteristic
349C22SD16×C3⋊D311yescharacteristic
350C22#6412311yescharacteristic
351C22#6412411yescharacteristic
352C22#6414611yescharacteristic
353C4—42no—
354C4—81no—
355C4—182no—
356C4—362no—
357C4—721no—
358C4#6410211yescharacteristic
359C4#6410511yescharacteristic
360C4C4×#63811yescharacteristic
361C4#6415511yescharacteristic
362C3#7057914yescomplemented
363C2—184no—
364C2C3⋊D3×#10611yescharacteristic
365C2#1059256011yescharacteristic
366C2#1059256111yescharacteristic
367C2#1059256211yescharacteristic
368C2#1059268811yescharacteristic
369C2#1059286811yescharacteristic
370C2#1059286911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#106C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×#106C3⋊D3
hypocenterC32#1853
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C32×#106C2semidirect
5. C2×#63635C2semidirect
6. #10589417C2semidirect
7. #10589395C2semidirect
23. #63647C4semidirect
26. C2×C3×#106D3semidirect
50. C2×C32×C8C2×C4semidirect
63. C2×C3⋊(C3⋊C8)C2×C4semidirect
119. C2×#106C3⋊D3semidirect
142. C2×C3×C8C4×D3semidirect
169. C2×C3⋊D3#106semidirect
260. C2×C8C4×C3⋊D3semidirect
294. C32#1853semidirect
362. C3#70579semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C32×#1062
C2×#636472
#105926862
C2×#636352
#105894172
#105893952
#705793