Finite Group Databasebeta

← #11785754

Subgroups — #11785754

Order 1152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3#10592686C211yesmaximal, characteristic
4C32×#340C211yesmaximal, characteristic, complemented
5#10589417C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68871—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⋊D3C414yescomplemented
21#63658—21no—
22#63647—22no—
23C2×D3×C4⋊C4—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⋊D3—24no—
42C2×C4×C3⋊D3—42no—
43C2×C4×C3⋊D3—42no—
44C2×C4×C3⋊D3C2×C412yes—
45C2×C4×C3⋊D3D412yes—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C2×C32×C8—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4C2×C412yes—
53#3752—42no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)C2×C412yes—
58#3750—24no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1823—91noSylow
63C22×C4×D3—34no—
64C22×C4×D3—64no—
65C22×C3×C8C2×D314yes—
66C2×C3×C4⋊C4C2×D314yes—
67C2×C3×C4⋊C4C2×D314yes—
68C2×(C2×D3)⋊C4—64no—
69C2×C4⋊Dic3—34no—
70C2×C4⋊Dic3—34no—
71C2×Dic3⋊C4—64no—
72C22×C3⋊C8—34no—
73D3×C4⋊C4—316no—
74D3×C4⋊C4—68no—
75C3⋊#95—64no—
76(C2×D3)⋊C8—68no—
77C23×C32C2×D411yescharacteristic
78C22×C3⋊D3—21no—
79C22×C3⋊D3—21no—
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3C22⋊C412yes—
83C22×C3⋊D3D812yes—
84C22×C3⋊D3SD1612yes—
85C2×C32×C4—22no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3C22⋊C412yes—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—48no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—41no—
113C22×C4⋊C4—91no—
114C2×C22⋊C8—91no—
115#380—91no—
116#340—91no—
117#340—91no—
118#340—91no—
119#340C3⋊D311yescharacteristic, complemented
120C23×D3—34no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4C22×D314yes—
124C22×Dic3—34no—
125C22×Dic3—64no—
126C22×Dic3—64no—
127C2×C4×D3—38no—
128C2×C4×D3—38no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—616no—
134C2×C4×D3—128no—
135C2×C4×D3—128no—
136C2×C3×C8—24no—
137C2×C3×C8—24no—
138C2×C3×C8—24no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—24no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4C4×D318yes—
143(C2×D3)⋊C4—128no—
144C4⋊Dic3—38no—
145C4⋊Dic3—64no—
146C4⋊Dic3—64no—
147C4⋊Dic3—64no—
148Dic3⋊C4—616no—
149C2×C3⋊C8—64no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152C22×C32C2×C22⋊C411yescharacteristic
153C22×C32#12311yescharacteristic
154C22×C32#12311yescharacteristic
155C22×C32C2×D811yescharacteristic
156C22×C32C2×SD1611yescharacteristic
157C22×C32#13711yescharacteristic
158C22×C32#13711yescharacteristic
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—22no—
162C2×C3⋊D3—22no—
163C2×C3⋊D3—22no—
164C2×C3⋊D3—22no—
165C2×C3⋊D3#10214yes—
166C32×C4—42no—
167C32×C4—81no—
168C32×C4#11711yescharacteristic
169C32×C4#11711yescharacteristic
170C32×C4#12311yescharacteristic
171C32×C4#12311yescharacteristic
172C3⋊Dic3—22no—
173C3⋊Dic3—42no—
174C3⋊Dic3—81no—
175C23×C4—91no—
176C23×C4—181no—
177C22×C8—91no—
178C22×C8C2×C3⋊D311yescharacteristic
179C2×C4⋊C4—91no—
180C2×C4⋊C4—94no—
181C2×C4⋊C4—91no—
182C2×C4⋊C4—182no—
183C2×C4⋊C4—181no—
184C2×C4⋊C4C2×C3⋊D311yescharacteristic
185C2×C4⋊C4C2×C3⋊D311yescharacteristic
186C2×C22⋊C4—181no—
187C22⋊C8—182no—
188#95—181no—
189C23×C3D3×D414yes—
190C22×D3—38no—
191C22×D3—38no—
192C22×D3—38no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—64no—
197C2×C3×C4—28no—
198C2×C3×C4—44no—
199C2×C3×C4—44no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4C2×C4×D314yes—
204C2×C3×C4#23514yes—
205C2×C3×C4#23514yes—
206C2×C3×C4D3×D414yes—
207C2×C3×C4#23714yes—
208C2×C3×C4#23914yes—
209C2×Dic3—38no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—68no—
213C2×Dic3—124no—
214C2×Dic3—124no—
215C2×Dic3—124no—
216C2×Dic3—124no—
217C2×Dic3—124no—
218C4×D3—68no—
219C4×D3—68no—
220C4×D3—68no—
221C4×D3—68no—
222C4×D3—1232no—
223C3×C8—44no—
224C3⋊C8—124no—
225C2×C32#38111yescharacteristic
226C2×C32C2×#10211yescharacteristic
227C2×C32#41911yescharacteristic
228C2×C32#48011yescharacteristic
229C2×C32#48011yescharacteristic
230C2×C32#48311yescharacteristic
231C2×C32#48311yescharacteristic
232C3⋊D3—24no—
233C24—91no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—91no—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—184no—
240C22×C4—181no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4—181no—
246C22×C4—362no—
247C22×C4—362no—
248C22×C4C22×C3⋊D311yescharacteristic
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—181no—
253C2×C8—181no—
254C2×C8—181no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—92no—
259C4⋊C4—184no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C4⋊C4—181no—
263C4⋊C4C4×C3⋊D312yes—
264C22⋊C4—362no—
265C22×C3D3×C22⋊C414yes—
266C22×C3#88314yes—
267C22×C3#89414yes—
268C22×C3D3×D814yes—
269C22×C3D3×SD1614yes—
270C22×C3#91514yes—
271C22×C3#91814yes—
272C2×D3—316no—
273C2×D3—68no—
274C2×D3—68no—
275C2×D3—68no—
276C2×D3—68no—
277C2×D3—68no—
278C2×D3—68no—
279C3×C4—48no—
280C3×C4—84no—
281C3×C4#87214yes—
282C3×C4#88314yes—
283C3×C4#89214yes—
284C3×C4#89414yes—
285Dic3—68no—
286Dic3—128no—
287Dic3—244no—
288C32#182311yescharacteristic, complemented, Sylow
289C23—92no—
290C23—92no—
291C23—92no—
292C23—181no—
293C23—181no—
294C23—181no—
295C23—181no—
296C23D4×C3⋊D311yescharacteristic
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—92no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—368no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4C2×C4×C3⋊D311yescharacteristic
318C2×C4#382811yescharacteristic
319C2×C4#382811yescharacteristic
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4#383011yescharacteristic
322C2×C4#383211yescharacteristic
323C8—41no—
324C8—361no—
325C2×C3#466414yes—
326C2×C3D3×#10214yes—
327C2×C3#477414yes—
328C2×C3#480214yes—
329C2×C3#480514yes—
330C2×C3#486214yes—
331C2×C3#488214yes—
332D3—616no—
333C22—94no—
334C22—182no—
335C22—182no—
336C22—182no—
337C22—182no—
338C22—182no—
339C22—182no—
340C22C22⋊C4×C3⋊D311yescharacteristic
341C22#6409211yescharacteristic
342C22#6410311yescharacteristic
343C22D8×C3⋊D311yescharacteristic
344C22SD16×C3⋊D311yescharacteristic
345C22#6412411yescharacteristic
346C22#6412711yescharacteristic
347C4—42no—
348C4—81no—
349C4—182no—
350C4—362no—
351C4—721no—
352C4#6408111yescharacteristic
353C4#6409211yescharacteristic
354C4#6410111yescharacteristic
355C4#6410311yescharacteristic
356C3#6887114yescomplemented
357C2—184no—
358C2#1059236311yescharacteristic
359C2C3⋊D3×#10211yescharacteristic
360C2#1059247311yescharacteristic
361C2#1059250111yescharacteristic
362C2#1059250411yescharacteristic
363C2#1059256111yescharacteristic
364C2#1059258111yescharacteristic
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#1823
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. C4⋊C4×C3⋊D3C4semidirect
26. C3×#340D3semidirect
119. #340C3⋊D3semidirect
288. C32#1823semidirect
356. C3#68871semidirect

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×#636472
#105926862
C32×#3402
#105894172
#105893952
#688713