Finite Group Databasebeta

← #11789890

Subgroups — #11789890

Order 1152.

852 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
2C2×#63642C211yesmaximal, characteristic, complemented
3#10592687C211yesmaximal, characteristic
4#10592683C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68857—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)—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19#63658—21no—
20#63648—22no—
21#63642—22no—
22#63636C414yescomplemented
23C2×#821—34no—
24C2×#815—34no—
25#4988—34no—
26#4984—34no—
27C2×#809—34no—
28C3×#340D314yescomplemented
29#4529—34no—
30C23×C3⋊D3—21no—
31C22×C32×C4—21no—
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
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⋊D3)—21no—
42C2×C4⋊(C3⋊D3)C2×C412yes—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C2×C32×C8D412yes—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2×C412yes—
50#3752—42no—
51#3752—42no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—42no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)C2×C412yes—
60#1936—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×C4⋊Dic3—64no—
69C2×C4×Dic3—34no—
70C22×C3⋊C8—34no—
71C3⋊#95—64no—
72#821—68no—
73#815—68no—
74#809—316no—
75C23×C32C2×D411yescharacteristic
76C22×C3⋊D3—22no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3—41no—
82C22×C3⋊D3—41no—
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—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—22no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C32×C8—22no—
109C3⋊(C3⋊C8)—22no—
110C2×#102—91no—
111C2×#102—91no—
112C2×#97—91no—
113#390—91no—
114#389—91no—
115#340—91no—
116#340C3⋊D311yescharacteristic, complemented
117C23×D3—64no—
118C22×C3×C4—24no—
119C22×C3×C4—24no—
120C22×C3×C4C22×D314yes—
121C22×Dic3—34no—
122C22×Dic3—34no—
123C22×Dic3—64no—
124C2×D12—38no—
125C2×D12—64no—
126C2×D12—64no—
127C2×D12—64no—
128C2×D12—64no—
129C2×D12—64no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C2×C3×C8D1218yes—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4C4×D318yes—
137(C2×D3)⋊C4—128no—
138(C2×D3)⋊C4—128no—
139C4⋊Dic3—64no—
140C4⋊Dic3—64no—
141C4⋊Dic3—128no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C2×C3⋊C8—38no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12111yescharacteristic
149C22×C32#12411yescharacteristic
150C22×C32AGL(1,ℤ/8)11yescharacteristic
151C22×C32AGL(1,ℤ/8)11yescharacteristic
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—42no—
162C32×C4—81no—
163C32×C4#11711yescharacteristic
164C32×C4C4×D411yescharacteristic
165C32×C4#12311yescharacteristic
166C32×C4#12611yescharacteristic
167C3⋊Dic3—41no—
168C3⋊Dic3—41no—
169C3⋊Dic3—81no—
170C22×D4—91no—
171C22×C8—91no—
172C22×C8C2×C3⋊D311yescharacteristic
173C2×C4⋊C4—91no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4C2×C3⋊D311yescharacteristic
176C2×C4⋊C4C2×C3⋊D311yescharacteristic
177C2×C22⋊C4—181no—
178C2×C22⋊C4—181no—
179C2×C42—91no—
180#102—94no—
181#102—182no—
182#97—182no—
183#95—181no—
184C23×C3D3×D414yes—
185C22×D3—68no—
186C22×D3—124no—
187C22×D3—124no—
188C22×D3—124no—
189C22×D3—124no—
190C22×D3—124no—
191C22×D3—124no—
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×C4C2×D1214yes—
200C2×C3×C4#23514yes—
201C2×C3×C4#23714yes—
202C2×C3×C4#23714yes—
203C2×C3×C4#23914yes—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—124no—
211C2×Dic3—124no—
212C2×Dic3—124no—
213D12—68no—
214D12—68no—
215D12—124no—
216D12—124no—
217C3×C8—28no—
218C3⋊C8—68no—
219C2×C32#38811yescharacteristic
220C2×C32#44011yescharacteristic
221C2×C32#44211yescharacteristic
222C2×C32#46811yescharacteristic
223C2×C32#46911yescharacteristic
224C2×C32#48911yescharacteristic
225C2×C32#49011yescharacteristic
226C3⋊D3—82no—
227C24—181no—
228C2×D4—92no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4—181no—
232C2×D4—181no—
233C2×D4—181no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—181no—
239C22×C4C22×C3⋊D311yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—92no—
243C2×C8—181no—
244C2×C8—181no—
245C2×C8C4⋊(C3⋊D3)12yes—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—362no—
252C4⋊C4C4×C3⋊D312yes—
253C22⋊C4—362no—
254C22⋊C4—362no—
255C42—181no—
256C42—181no—
257C22×C3#67⋊C414yes—
258C22×C3#88514yes—
259C22×C3#89514yes—
260C22×C3#91114yes—
261C22×C3#91414yes—
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—48no—
272C3×C4—84no—
273C3×C4C4×D1214yes—
274C3×C4#88614yes—
275C3×C4#89214yes—
276C3×C4#89814yes—
277Dic3—124no—
278Dic3—124no—
279Dic3—244no—
280C32#193611yescharacteristic, 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—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—181no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4C2×C4×C3⋊D311yescharacteristic
309C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
310C2×C4#382811yescharacteristic
311C2×C4#383011yescharacteristic
312C2×C4#383011yescharacteristic
313C2×C4#383211yescharacteristic
314C8—22no—
315C8—182no—
316C2×C3#467014yes—
317C2×C3#476414yes—
318C2×C3#478514yes—
319C2×C3#479414yes—
320C2×C3#481714yes—
321C2×C3#486514yes—
322C2×C3#488614yes—
323D3—248no—
324C22—362no—
325C22—362no—
326C22—362no—
327C22—721no—
328C22—721no—
329C22—721no—
330C22—721no—
331C22#6409011yescharacteristic
332C22#6409411yescharacteristic
333C22#6410411yescharacteristic
334C22#6412011yescharacteristic
335C22#6412311yescharacteristic
336C22#6412311yescharacteristic
337C22#6412711yescharacteristic
338C4—42no—
339C4—81no—
340C4—361no—
341C4—361no—
342C4—721no—
343C4C4×C4⋊(C3⋊D3)11yescharacteristic
344C4#6409511yescharacteristic
345C4#6410111yescharacteristic
346C4#6410711yescharacteristic
347C3#6885714yescomplemented
348C2—722no—
349C2#1059236911yescharacteristic
350C2#1059246311yescharacteristic
351C2#1059248411yescharacteristic
352C2#1059249311yescharacteristic
353C2#1059251611yescharacteristic
354C2#1059256411yescharacteristic
355C2#1059258511yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1936
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
2. C2×#63642C2semidirect
4. #10592683C2semidirect
6. C32×#340C2semidirect
7. #10589395C2semidirect
22. #63636C4semidirect
28. C3×#340D3semidirect
116. #340C3⋊D3semidirect
280. C32#1936semidirect
347. C3#68857semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
C2×#636422
#105926872
#105926832
C2×#636362
C32×#3402
#105893952
#688573