Finite Group Databasebeta

← #11783270

Subgroups — #11783270

Order 1152.

1344 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic
2C2×#64101C211yesmaximal, characteristic
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
4C32×#340C211yesmaximal, characteristic, complemented
5#10589417C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68867—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—
18C2×C4×C3⋊Dic3—21no—
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C2×#3743—22no—
21C2×#3743—22no—
22C2×#3743C414yescomplemented
23#64101—22no—
24#64101C414yescomplemented
25C4⋊C4×C3⋊D3—22no—
26C4⋊C4×C3⋊D3C414yescomplemented
27C22×ΓL(1,𝔽25)—34no—
28C2×#892—34no—
29C2×D3×C4⋊C4—34no—
30C3×#340D314yescomplemented
31#4551—34no—
32#4529—34no—
33#4529—34no—
34C23×C3⋊D3D411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3—24no—
42C2×C4×C3⋊D3—42no—
43C2×C4×C3⋊D3—42no—
44C2×C4×C3⋊D3C2×C412yes—
45C2×C4×C3⋊D3C2×C412yes—
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3D412yes—
48C2×C4×C3⋊D3D412yes—
49C2×C4×C3⋊D3Q812yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8C2×C412yescomplemented
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2×C412yes—
56C32×C4⋊C4C2×C412yescomplemented
57#3752—24no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2×C412yes—
61C4⋊(C3⋊Dic3)C2×C412yescomplemented
62#3750—24no—
63C4×C3⋊Dic3—24no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)C2×C412yescomplemented
67#3743—28no—
68#1736—91noSylow
69C22×C4×D3—34no—
70C22×C4×D3—64no—
71C22×C3×C8C2×D314yes—
72C2×C3×C4⋊C4C2×D314yes—
73C2×C3×C4⋊C4C2×D314yes—
74C2×(C2×D3)⋊C4—64no—
75C2×C4⋊Dic3—34no—
76C2×C4⋊Dic3—34no—
77C2×Dic3⋊C4—64no—
78C2×C4×Dic3—64no—
79C22×C3⋊C8—34no—
80C2×ΓL(1,𝔽25)—316no—
81C2×ΓL(1,𝔽25)—68no—
82C2×ΓL(1,𝔽25)—68no—
83#892—316no—
84#892—68no—
85D3×C4⋊C4—316no—
86D3×C4⋊C4—68no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—21no—
92C22×C3⋊D3C22⋊C412yes—
93C22×C3⋊D3C22⋊C412yes—
94C22×C3⋊D3C4⋊C412yes—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3⋊Dic3C22⋊C412yes—
115C2×C3⋊Dic3C4⋊C412yes—
116C4×C3⋊D3—48no—
117C4×C3⋊D3C4214yes—
118C4×C3⋊D3C22⋊C414yes—
119C4×C3⋊D3C4⋊C414yes—
120C4×C3⋊D3C4⋊C414yes—
121C32×C8—22no—
122C3⋊(C3⋊C8)—22no—
123C22×M16—91no—
124C2×#117—91no—
125C22×C4⋊C4—91no—
126#340—91no—
127#340—91no—
128#340—91no—
129#340C3⋊D311yescharacteristic, complemented
130C23×D3—34no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4C22×D314yes—
134C22×Dic3—34no—
135C22×Dic3—64no—
136C22×Dic3—64no—
137C2×C4×D3—38no—
138C2×C4×D3—38no—
139C2×C4×D3—38no—
140C2×C4×D3—38no—
141C2×C4×D3—38no—
142C2×C4×D3—38no—
143C2×C4×D3—616no—
144C2×C4×D3—128no—
145C2×C4×D3—128no—
146C2×C3×C8—24no—
147C2×C3×C8—24no—
148C2×C3×C8C4×D318yescomplemented
149C3×C4⋊C4—24no—
150C3×C4⋊C4—24no—
151C3×C4⋊C4C4×D318yes—
152C3×C4⋊C4C4×D318yescomplemented
153(C2×D3)⋊C4—616no—
154C4⋊Dic3—38no—
155C4⋊Dic3—38no—
156C4⋊Dic3—64no—
157C4⋊Dic3—64no—
158Dic3⋊C4—616no—
159C4×Dic3—616no—
160C2×C3⋊C8—38no—
161C2×C3⋊C8—64no—
162C2×C3⋊C8—64no—
163ΓL(1,𝔽25)—632no—
164C22×C32C2×C22⋊C411yescharacteristic
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32C2×C4⋊C411yescharacteristic
167C22×C32AGL(1,ℤ/8)11yescharacteristic
168C22×C32AGL(1,ℤ/8)11yescharacteristic
169C22×C32#13711yescharacteristic
170C22×C32#13711yescharacteristic
171C2×C3⋊D3—22no—
172C2×C3⋊D3—22no—
173C2×C3⋊D3—22no—
174C2×C3⋊D3—22no—
175C2×C3⋊D3—22no—
176C2×C3⋊D3—22no—
177C2×C3⋊D3#9514yes—
178C32×C4—42no—
179C32×C4—42no—
180C32×C4C2×C4211yescharacteristic
181C32×C4C2×C22⋊C411yescharacteristic
182C32×C4C2×C4⋊C411yescharacteristic
183C32×C4C2×C4⋊C411yescharacteristic
184C3⋊Dic3—42no—
185C3⋊Dic3—42no—
186C3⋊Dic3#9514yes—
187C23×C4—91no—
188C23×C4—181no—
189C2×M16—94no—
190C2×M16—182no—
191C2×M16—182no—
192C22×C8—91no—
193C22×C8C2×C3⋊D311yescharacteristic
194#117—94no—
195#117—182no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—94no—
199C2×C4⋊C4—182no—
200C2×C4⋊C4—181no—
201C2×C4⋊C4C2×C3⋊D311yescharacteristic
202C2×C4⋊C4C2×C3⋊D311yescharacteristic
203C2×C22⋊C4—181no—
204C2×C42—181no—
205C23×C3D3×D414yes—
206C22×D3—38no—
207C22×D3—38no—
208C22×D3—38no—
209C22×D3—64no—
210C22×D3—64no—
211C22×D3—64no—
212C22×D3—64no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4—44no—
216C2×C3×C4—44no—
217C2×C3×C4—44no—
218C2×C3×C4—44no—
219C2×C3×C4C2×C4×D314yes—
220C2×C3×C4C2×C4×D314yes—
221C2×C3×C4C2×C4×D314yes—
222C2×C3×C4D3×D414yes—
223C2×C3×C4D3×D414yes—
224C2×C3×C4D3×Q814yes—
225C2×Dic3—38no—
226C2×Dic3—38no—
227C2×Dic3—38no—
228C2×Dic3—68no—
229C2×Dic3—68no—
230C2×Dic3—124no—
231C2×Dic3—124no—
232C2×Dic3—124no—
233C2×Dic3—124no—
234C4×D3—316no—
235C4×D3—316no—
236C4×D3—316no—
237C4×D3—316no—
238C4×D3—1232no—
239C3×C8—28no—
240C3⋊C8—68no—
241C2×C32C2×#9511yescharacteristic
242C2×C32#41711yescharacteristic
243C2×C32#41711yescharacteristic
244C2×C32#41811yescharacteristic
245C2×C32#41911yescharacteristic
246C2×C32#42811yescharacteristic
247C2×C32#42811yescharacteristic
248C3⋊D3—24no—
249C24—91no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—91no—
253C22×C4—92no—
254C22×C4—92no—
255C22×C4—92no—
256C22×C4—92no—
257C22×C4—92no—
258C22×C4—92no—
259C22×C4—184no—
260C22×C4—181no—
261C22×C4—181no—
262C22×C4—362no—
263C22×C4—362no—
264C22×C4C22×C3⋊D311yescharacteristic
265M16—188no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—92no—
269C2×C8—181no—
270C2×C8—181no—
271C2×C8C4×C3⋊D312yescomplemented
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—92no—
275C4⋊C4—92no—
276C4⋊C4—184no—
277C4⋊C4—181no—
278C4⋊C4—181no—
279C4⋊C4C4×C3⋊D312yes—
280C4⋊C4C4×C3⋊D312yescomplemented
281C22⋊C4—184no—
282C42—184no—
283C22×C3D3×C22⋊C414yes—
284C22×C3D3×C22⋊C414yes—
285C22×C3D3×C4⋊C414yes—
286C22×C3#91114yes—
287C22×C3#91414yes—
288C22×C3#91514yes—
289C22×C3#91814yes—
290C2×D3—316no—
291C2×D3—68no—
292C2×D3—68no—
293C2×D3—68no—
294C2×D3—68no—
295C2×D3—68no—
296C2×D3—68no—
297C3×C4—48no—
298C3×C4—48no—
299C3×C4C42×D314yes—
300C3×C4D3×C22⋊C414yes—
301C3×C4D3×C4⋊C414yes—
302C3×C4D3×C4⋊C414yes—
303Dic3—316no—
304Dic3—128no—
305Dic3—128no—
306C32#173611yescharacteristic, complemented, Sylow
307C23—92no—
308C23—92no—
309C23—92no—
310C23—181no—
311C23—181no—
312C23—181no—
313C23—181no—
314C23D4×C3⋊D311yescharacteristic
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—94no—
325C2×C4—94no—
326C2×C4—94no—
327C2×C4—94no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—368no—
331C2×C4—361no—
332C2×C4—361no—
333C2×C4—361no—
334C2×C4—361no—
335C2×C4C2×C4×C3⋊D311yescharacteristic
336C2×C4C2×C4×C3⋊D311yescharacteristic
337C2×C4C2×C4×C3⋊D311yescharacteristic
338C2×C4D4×C3⋊D311yescharacteristic
339C2×C4D4×C3⋊D311yescharacteristic
340C2×C4Q8×C3⋊D311yescharacteristic
341C8—22no—
342C8—182no—
343C2×C3D3×#9514yes—
344C2×C3#477014yes—
345C2×C3#477114yes—
346C2×C3#480214yes—
347C2×C3#480314yes—
348C2×C3#486114yes—
349C2×C3#488114yes—
350D3—616no—
351C22—94no—
352C22—182no—
353C22—182no—
354C22—182no—
355C22—182no—
356C22—182no—
357C22—182no—
358C22C22⋊C4×C3⋊D311yescharacteristic
359C22C22⋊C4×C3⋊D311yescharacteristic
360C22C4⋊C4×C3⋊D311yescharacteristic
361C22#6412011yescharacteristic
362C22#6412311yescharacteristic
363C22#6412411yescharacteristic
364C22#6412711yescharacteristic
365C4—42no—
366C4—42no—
367C4—94no—
368C4—362no—
369C4—362no—
370C4C42×C3⋊D311yescharacteristic
371C4C22⋊C4×C3⋊D311yescharacteristic
372C4C4⋊C4×C3⋊D311yescharacteristic
373C4C4⋊C4×C3⋊D311yescharacteristic
374C3#6886714yescomplemented
375C2—184no—
376C2C3⋊D3×#9511yescharacteristic
377C2#1059246911yescharacteristic
378C2#1059247011yescharacteristic
379C2#1059250111yescharacteristic
380C2#1059250211yescharacteristic
381C2#1059256011yescharacteristic
382C2#1059258011yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC32×C4C2×C42
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1736
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C32×#340C2semidirect
5. #10589417C2semidirect
6. #10589395C2semidirect
7. #10589395C2semidirect
22. C2×#3743C4semidirect
24. #64101C4semidirect
26. C4⋊C4×C3⋊D3C4semidirect
30. C3×#340D3semidirect
52. C2×C32×C8C2×C4semidirect
56. C32×C4⋊C4C2×C4semidirect
61. C4⋊(C3⋊Dic3)C2×C4semidirect
66. C2×C3⋊(C3⋊C8)C2×C4semidirect
129. #340C3⋊D3semidirect
148. C2×C3×C8C4×D3semidirect
152. C3×C4⋊C4C4×D3semidirect
271. C2×C8C4×C3⋊D3semidirect
280. C4⋊C4C4×C3⋊D3semidirect
306. C32#1736semidirect
374. C3#68867semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#641012
C2×C4⋊C4×C3⋊D32
C32×#3402
#105894172
#105893952
#688673