Finite Group Databasebeta

← #11794651

Subgroups — #11794651

Order 1152.

822 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×#63648C211yesmaximal, characteristic
2#10592687C211yesmaximal, characteristic
3#10592674C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic
5C32×#340C211yesmaximal, characteristic, complemented
6#10589416C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68902—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×#3750—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20#63648—22no—
21#63636—22no—
22C2×#821—34no—
23#4988—34no—
24#4975—34no—
25C2×#809—34no—
26C3×#340D314yescomplemented
27#4550—34no—
28#4529—34no—
29C23×C3⋊D3—21no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)D412yes—
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49#3752—42no—
50#3752—42no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53#3750—42no—
54#3750—42no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60#2071—91noSylow
61C22×D12—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×Dic3⋊C4—64no—
69C2×Dic3⋊C4—64no—
70C2×C4×Dic3—34no—
71C22×C3⋊C8—34no—
72#821—68no—
73#809—68no—
74C23×C32C2×D411yescharacteristic
75C22×C3⋊D3—22no—
76C22×C3⋊D3—41no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3—41no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4#4111yescharacteristic
90C2×C32×C4#4111yescharacteristic
91C2×C32×C4#4111yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3D812yes—
102C2×C3⋊Dic3SD1612yes—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109C2×#102—91no—
110C2×#102—91no—
111#390—91no—
112#384—91no—
113#340—91no—
114#340C3⋊D311yescharacteristic, complemented
115#336—91no—
116C23×D3—64no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4C22×D314yes—
120C22×Dic3—34no—
121C22×Dic3—34no—
122C22×Dic3—64no—
123C2×D12—38no—
124C2×D12—64no—
125C2×D12—64no—
126C2×D12—64no—
127C2×D12—64no—
128C2×D12—64no—
129C2×C3×C8—24no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C3×C4⋊C4—24no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—24no—
136(C2×D3)⋊C4—128no—
137(C2×D3)⋊C4—128no—
138C4⋊Dic3—64no—
139C4⋊Dic3—64no—
140Dic3⋊C4—128no—
141Dic3⋊C4—128no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C2×C3⋊C8—64no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32#12111yescharacteristic
148C22×C32#12311yescharacteristic
149C22×C32#12411yescharacteristic
150C22×C32C2×D811yescharacteristic
151C22×C32C2×SD1611yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C22×C32#13711yescharacteristic
154C2×C3⋊D3—42no—
155C2×C3⋊D3—42no—
156C2×C3⋊D3—42no—
157C2×C3⋊D3—81no—
158C2×C3⋊D3—81no—
159C2×C3⋊D3—81no—
160C2×C3⋊D3—81no—
161C32×C4—81no—
162C32×C4—81no—
163C32×C4#12311yescharacteristic
164C32×C4#12311yescharacteristic
165C32×C4#12611yescharacteristic
166C32×C4#12611yescharacteristic
167C3⋊Dic3—22no—
168C3⋊Dic3—22no—
169C3⋊Dic3—81no—
170C22×D4—91no—
171C22×C8—91no—
172C22×C8C2×C3⋊D311yescharacteristic
173C2×C4⋊C4—91no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4—181no—
176C2×C4⋊C4C2×C3⋊D311yescharacteristic
177C2×C4⋊C4C2×C3⋊D311yescharacteristic
178C2×C22⋊C4—181no—
179C2×C22⋊C4—181no—
180C2×C42—91no—
181#102—182no—
182#102—182no—
183C23×C3D3×D414yes—
184C22×D3—68no—
185C22×D3—124no—
186C22×D3—124no—
187C22×D3—124no—
188C22×D3—124no—
189C22×D3—124no—
190C22×D3—124no—
191C2×C3×C4—44no—
192C2×C3×C4—44no—
193C2×C3×C4—44no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4—44no—
197C2×C3×C4#23514yes—
198C2×C3×C4#23514yes—
199C2×C3×C4#23514yes—
200C2×C3×C4D3×D414yes—
201C2×C3×C4#23714yes—
202C2×C3×C4#23914yes—
203C2×Dic3—38no—
204C2×Dic3—38no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—124no—
210C2×Dic3—124no—
211C2×Dic3—124no—
212D12—68no—
213D12—68no—
214D12—124no—
215D12—124no—
216C3×C8—44no—
217C3⋊C8—124no—
218C2×C32#39711yescharacteristic
219C2×C32#45911yescharacteristic
220C2×C32#46111yescharacteristic
221C2×C32#48011yescharacteristic
222C2×C32#48111yescharacteristic
223C2×C32#48611yescharacteristic
224C2×C32#48911yescharacteristic
225C3⋊D3—82no—
226C24—181no—
227C2×D4—92no—
228C2×D4—181no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4—181no—
232C2×D4—181no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—181no—
238C22×C4C22×C3⋊D311yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—181no—
243C2×C8—181no—
244C2×C8—181no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—362no—
252C4⋊C4—362no—
253C22⋊C4—362no—
254C22⋊C4—362no—
255C42—181no—
256C42—181no—
257C22×C3#88414yes—
258C22×C3#88514yes—
259C22×C3#89414yes—
260C22×C3D3×D814yes—
261C22×C3D3×SD1614yes—
262C22×C3#91414yes—
263C22×C3#91814yes—
264C2×D3—128no—
265C2×D3—128no—
266C2×D3—128no—
267C2×D3—244no—
268C2×D3—244no—
269C2×D3—244no—
270C2×D3—244no—
271C3×C4—84no—
272C3×C4—84no—
273C3×C4#87614yes—
274C3×C4#88314yes—
275C3×C4#89414yes—
276C3×C4#89814yes—
277Dic3—68no—
278Dic3—68no—
279Dic3—244no—
280C32#207111yescharacteristic, complemented, Sylow
281C23—182no—
282C23—361no—
283C23—361no—
284C23—361no—
285C23—361no—
286C23—361no—
287C23—361no—
288C23D4×C3⋊D311yescharacteristic
289D4—182no—
290D4—182no—
291D4—361no—
292D4—361no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—92no—
300C2×C4—92no—
301C2×C4—181no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4#382811yescharacteristic
309C2×C4#382811yescharacteristic
310C2×C4#382811yescharacteristic
311C2×C4D4×C3⋊D311yescharacteristic
312C2×C4#383011yescharacteristic
313C2×C4#383211yescharacteristic
314C8—41no—
315C8—361no—
316C2×C3#467514yes—
317C2×C3#476014yes—
318C2×C3#478614yes—
319C2×C3#479414yes—
320C2×C3#481814yes—
321C2×C3#486314yes—
322C2×C3#488214yes—
323D3—248no—
324C22—362no—
325C22—362no—
326C22—362no—
327C22—721no—
328C22—721no—
329C22—721no—
330C22—721no—
331C22#6409311yescharacteristic
332C22#6409411yescharacteristic
333C22#6410311yescharacteristic
334C22D8×C3⋊D311yescharacteristic
335C22SD16×C3⋊D311yescharacteristic
336C22#6412311yescharacteristic
337C22#6412711yescharacteristic
338C4—81no—
339C4—81no—
340C4—182no—
341C4—182no—
342C4—721no—
343C4#6408511yescharacteristic
344C4#6409211yescharacteristic
345C4#6410311yescharacteristic
346C4#6410711yescharacteristic
347C3#6890214yescomplemented
348C2—722no—
349C2#1059237411yescharacteristic
350C2#1059245911yescharacteristic
351C2#1059248511yescharacteristic
352C2#1059249311yescharacteristic
353C2#1059251711yescharacteristic
354C2#1059256211yescharacteristic
355C2#1059258111yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#340C3⋊D3
hypocenterC32#2071
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. #10592674C2semidirect
5. C32×#340C2semidirect
6. #10589416C2semidirect
7. #10589395C2semidirect
26. C3×#340D3semidirect
114. #340C3⋊D3semidirect
280. C32#2071semidirect
347. C3#68902semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
#105926872
#105926742
C2×#636362
C32×#3402
#105894162
#105893952
#689023