Finite Group Databasebeta

← #11785809

Subgroups — #11785809

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3#10592686C211yesmaximal, characteristic
4C32×#340C211yesmaximal, characteristic, complemented
5#10589417C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68813—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3—21no—
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19#64101—22no—
20#64101C414yescomplemented
21#63658—21no—
22#63647—22no—
23C2×#892—34no—
24C2×(C2×D3)⋊C8—34no—
25#4987—34no—
26C3×#340D314yescomplemented
27#4551—34no—
28#4529—34no—
29#4529—34no—
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4—21no—
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3C2×C412yes—
42C2×C4×C3⋊D3D412yes—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2×C412yes—
50#3752—24no—
51#3752—42no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)C2×C412yes—
56C4×C3⋊Dic3—24no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60#1825—91noSylow
61C22×C4×D3—34no—
62C22×C3×C8C2×D314yes—
63C2×C3×C4⋊C4C2×D314yes—
64C2×C3×C4⋊C4C2×D314yes—
65C2×(C2×D3)⋊C4—64no—
66C2×(C2×D3)⋊C4—64no—
67C2×C4⋊Dic3—34no—
68C2×C4⋊Dic3—34no—
69C2×C4×Dic3—64no—
70C22×C3⋊C8—34no—
71#892—316no—
72#892—68no—
73C3⋊#95—64no—
74(C2×D3)⋊C8—68no—
75C23×C32C2×D411yescharacteristic
76C22×C3⋊D3—21no—
77C22×C3⋊D3—21no—
78C22×C3⋊D3—21no—
79C22×C3⋊D3—21no—
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3C22⋊C412yes—
83C2×C32×C4—22no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4#4111yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C22⋊C412yes—
104C4×C3⋊D3—22no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—22no—
108C32×C8—41no—
109C3⋊(C3⋊C8)—41no—
110C2×#117—91no—
111C2×C22⋊C8—91no—
112#380—91no—
113#340—91no—
114#340—91no—
115#340—91no—
116#340C3⋊D311yescharacteristic, complemented
117C23×D3—34no—
118C22×C3×C4—24no—
119C22×C3×C4—24no—
120C22×C3×C4C22×D314yes—
121C22×Dic3—34no—
122C22×Dic3—64no—
123C22×Dic3—64no—
124C2×C4×D3—38no—
125C2×C4×D3—38no—
126C2×C4×D3—64no—
127C2×C4×D3—64no—
128C2×C4×D3—64no—
129C2×C4×D3—64no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C2×C3×C8—24no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4C4×D318yes—
137(C2×D3)⋊C4—616no—
138(C2×D3)⋊C4—128no—
139C4⋊Dic3—38no—
140C4⋊Dic3—64no—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143C4×Dic3—616no—
144C2×C3⋊C8—64no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32#12311yescharacteristic
149C22×C32#12311yescharacteristic
150C22×C32#13511yescharacteristic
151C22×C32#13511yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C22×C32#13711yescharacteristic
154C2×C3⋊D3—22no—
155C2×C3⋊D3—22no—
156C2×C3⋊D3—22no—
157C2×C3⋊D3—41no—
158C2×C3⋊D3—41no—
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C32×C4—42no—
162C32×C4—81no—
163C32×C4#11711yescharacteristic
164C32×C4#11711yescharacteristic
165C32×C4#12311yescharacteristic
166C32×C4#12311yescharacteristic
167C3⋊Dic3—22no—
168C3⋊Dic3—42no—
169C3⋊Dic3—81no—
170C23×C4—91no—
171C22×C8—91no—
172C22×C8C2×C3⋊D311yescharacteristic
173#117—94no—
174#117—182no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4C2×C3⋊D311yescharacteristic
178C2×C4⋊C4C2×C3⋊D311yescharacteristic
179C2×C22⋊C4—181no—
180C2×C22⋊C4—181no—
181C2×C42—181no—
182C22⋊C8—182no—
183#95—181no—
184C23×C3D3×D414yes—
185C22×D3—38no—
186C22×D3—64no—
187C22×D3—64no—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—64no—
192C2×C3×C4—28no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4—44no—
197C2×C3×C4—44no—
198C2×C3×C4C2×C4×D314yes—
199C2×C3×C4#23514yes—
200C2×C3×C4#23514yes—
201C2×C3×C4D3×D414yes—
202C2×C3×C4#23714yes—
203C2×C3×C4#23914yes—
204C2×Dic3—38no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—68no—
208C2×Dic3—124no—
209C2×Dic3—124no—
210C2×Dic3—124no—
211C2×Dic3—124no—
212C2×Dic3—124no—
213C4×D3—68no—
214C4×D3—68no—
215C4×D3—68no—
216C4×D3—68no—
217C3×C8—44no—
218C3⋊C8—124no—
219C2×C32#38111yescharacteristic
220C2×C32#41611yescharacteristic
221C2×C32#41711yescharacteristic
222C2×C32#48211yescharacteristic
223C2×C32#48211yescharacteristic
224C2×C32#48511yescharacteristic
225C2×C32#48511yescharacteristic
226C3⋊D3—42no—
227C24—91no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—91no—
231C22×C4—92no—
232C22×C4—92no—
233C22×C4—181no—
234C22×C4—181no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4—181no—
239C22×C4C22×C3⋊D311yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—181no—
244C2×C8—181no—
245C2×C8—181no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—92no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C4⋊C4C4×C3⋊D312yes—
254C22⋊C4—184no—
255C22⋊C4—362no—
256C42—184no—
257C22×C3D3×C22⋊C414yes—
258C22×C3#88314yes—
259C22×C3#89414yes—
260C22×C3#91114yes—
261C22×C3#91514yes—
262C22×C3#91614yes—
263C22×C3#91914yes—
264C2×D3—68no—
265C2×D3—68no—
266C2×D3—68no—
267C2×D3—124no—
268C2×D3—124no—
269C2×D3—124no—
270C2×D3—124no—
271C3×C4—48no—
272C3×C4—84no—
273C3×C4#87214yes—
274C3×C4#88314yes—
275C3×C4#89214yes—
276C3×C4#89414yes—
277Dic3—68no—
278Dic3—128no—
279Dic3—244no—
280C32#182511yescharacteristic, complemented, Sylow
281C23—92no—
282C23—181no—
283C23—181no—
284C23—181no—
285C23—181no—
286C23—181no—
287C23—181no—
288C23D4×C3⋊D311yescharacteristic
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—92no—
296C2×C4—181no—
297C2×C4—181no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—361no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4C2×C4×C3⋊D311yescharacteristic
309C2×C4#382811yescharacteristic
310C2×C4#382811yescharacteristic
311C2×C4D4×C3⋊D311yescharacteristic
312C2×C4#383011yescharacteristic
313C2×C4#383211yescharacteristic
314C8—41no—
315C8—361no—
316C2×C3#466414yes—
317C2×C3#477114yes—
318C2×C3#477914yes—
319C2×C3#480414yes—
320C2×C3#481414yes—
321C2×C3#486814yes—
322C2×C3#488514yes—
323D3—128no—
324C22—182no—
325C22—182no—
326C22—182no—
327C22—361no—
328C22—361no—
329C22—361no—
330C22—361no—
331C22C22⋊C4×C3⋊D311yescharacteristic
332C22#6409211yescharacteristic
333C22#6410311yescharacteristic
334C22#6412011yescharacteristic
335C22#6412411yescharacteristic
336C22#6412511yescharacteristic
337C22#6412811yescharacteristic
338C4—42no—
339C4—81no—
340C4—182no—
341C4—362no—
342C4—721no—
343C4#6408111yescharacteristic
344C4#6409211yescharacteristic
345C4#6410111yescharacteristic
346C4#6410311yescharacteristic
347C3#6881314yescomplemented
348C2—362no—
349C2#1059236311yescharacteristic
350C2#1059247011yescharacteristic
351C2#1059247811yescharacteristic
352C2#1059250311yescharacteristic
353C2#1059251311yescharacteristic
354C2#1059256711yescharacteristic
355C2#1059258411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1825
LCSG ▷ C2×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
20. #64101C4semidirect
26. C3×#340D3semidirect
116. #340C3⋊D3semidirect
280. C32#1825semidirect
347. C3#68813semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#636472
#105926862
C32×#3402
#105894172
#105893952
#688133