Finite Group Databasebeta

← #11786500

Subgroups — #11786500

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3C2×#63645C211yesmaximal, characteristic, complemented
4#10592686C211yesmaximal, characteristic
5C2×#63635C211yesmaximal, characteristic, complemented
6C32×#340C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68877—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#64101—22no—
21#63658—21no—
22#63647C414yescomplemented
23#63645—22no—
24#63635—22no—
25C2×#892—34no—
26C2×(C2×D3)⋊C8—34no—
27C2×#818—34no—
28#4987—34no—
29C2×#808—34no—
30C3×#340D314yescomplemented
31#4529—34no—
32C23×C3⋊D3D411yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3C2×C412yes—
44C2×C4×C3⋊D3Q812yes—
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8C2×C412yes—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D412yes—
52#3752—24no—
53#3752—42no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D412yes—
58C4×C3⋊Dic3—24no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)C2×C412yes—
62#1854—91noSylow
63C22×C4×D3—34no—
64C22×C3×C8C2×D314yes—
65C2×C3×C4⋊C4C2×D314yes—
66C2×C3×C4⋊C4C2×D314yes—
67C2×(C2×D3)⋊C4—64no—
68C2×(C2×D3)⋊C4—64no—
69C2×C4⋊Dic3—34no—
70C2×C4⋊Dic3—34no—
71C2×C4×Dic3—64no—
72C22×C3⋊C8—34no—
73#892—68no—
74#892—68no—
75C3⋊#95—64no—
76(C2×D3)⋊C8—316no—
77#818—68no—
78#808—68no—
79C23×C32C2×D411yescharacteristic
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3—21no—
83C22×C3⋊D3—21no—
84C22×C3⋊D3—21no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3C4⋊C412yes—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×Q811yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3C4⋊C412yes—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—22no—
111C4×C3⋊D3—22no—
112C32×C8—22no—
113C3⋊(C3⋊C8)—22no—
114C2×#117—91no—
115C2×#107—91no—
116C2×#106—91no—
117C2×C22⋊C8—91no—
118#380—91no—
119#340—91no—
120#340C3⋊D311yescharacteristic, complemented
121C23×D3—34no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4C22×D314yes—
125C22×Dic3—34no—
126C22×Dic3—64no—
127C22×Dic3—64no—
128C2×C4×D3—38no—
129C2×C4×D3—38no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C3×C8—24no—
135C2×C3×C8—24no—
136C2×C3×C8C4×D318yes—
137C3×C4⋊C4—24no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4D1218yes—
141(C2×D3)⋊C4—616no—
142(C2×D3)⋊C4—128no—
143C4⋊Dic3—38no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146C4⋊Dic3—64no—
147C4×Dic3—616no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—64no—
150C2×C3⋊C8—64no—
151C22×C32C2×C4⋊C411yescharacteristic
152C22×C32#12011yescharacteristic
153C22×C32#12311yescharacteristic
154C22×C32#13511yescharacteristic
155C22×C32#13511yescharacteristic
156C22×C32AGL(1,ℤ/8)11yescharacteristic
157C22×C32#13711yescharacteristic
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—41no—
162C2×C3⋊D3—41no—
163C2×C3⋊D3—41no—
164C2×C3⋊D3—41no—
165C32×C4—42no—
166C32×C4—81no—
167C32×C4C4×D411yescharacteristic
168C32×C4C4×D411yescharacteristic
169C32×C4C22⋊Q811yescharacteristic
170C32×C4C22⋊Q811yescharacteristic
171C3⋊Dic3—22no—
172C3⋊Dic3—42no—
173C3⋊Dic3—81no—
174C23×C4—91no—
175C22×C8—91no—
176C22×C8C2×C3⋊D311yescharacteristic
177#117—182no—
178#117—182no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—91no—
181C2×C4⋊C4C2×C3⋊D311yescharacteristic
182C2×C4⋊C4C2×C3⋊D311yescharacteristic
183C2×C22⋊C4—181no—
184C2×C22⋊C4—181no—
185C2×C42—181no—
186#107—182no—
187#106—182no—
188C22⋊C8—94no—
189#95—181no—
190C23×C3D3×D414yes—
191C22×D3—38no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—64no—
197C22×D3—64no—
198C2×C3×C4—28no—
199C2×C3×C4—44no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4C2×D1214yes—
206C2×C3×C4#23514yes—
207C2×C3×C4D3×D414yes—
208C2×C3×C4#23714yes—
209C2×C3×C4D3×Q814yes—
210C2×Dic3—38no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—68no—
214C2×Dic3—124no—
215C2×Dic3—124no—
216C2×Dic3—124no—
217C2×Dic3—124no—
218C2×Dic3—124no—
219C4×D3—68no—
220C4×D3—68no—
221C4×D3—68no—
222C4×D3—68no—
223C3×C8—28no—
224C3⋊C8—68no—
225C2×C32#38511yescharacteristic
226C2×C32#42711yescharacteristic
227C2×C32#42811yescharacteristic
228C2×C32#44911yescharacteristic
229C2×C32#45211yescharacteristic
230C2×C32#48211yescharacteristic
231C2×C32#48511yescharacteristic
232C3⋊D3—42no—
233C24—91no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—91no—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—181no—
240C22×C4—181no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4C22×C3⋊D311yescharacteristic
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—92no—
249C2×C8—181no—
250C2×C8—181no—
251C2×C8C4×C3⋊D312yes—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C4⋊C4C4⋊(C3⋊D3)12yes—
260C22⋊C4—184no—
261C22⋊C4—362no—
262C42—184no—
263C22×C3#88214yes—
264C22×C3#88314yes—
265C22×C3D3×C4⋊C414yes—
266C22×C3#91214yes—
267C22×C3#91414yes—
268C22×C3#91514yes—
269C22×C3#91914yes—
270C2×D3—68no—
271C2×D3—68no—
272C2×D3—68no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—124no—
276C2×D3—124no—
277C3×C4—48no—
278C3×C4—84no—
279C3×C4C4×D1214yes—
280C3×C4#67⋊C414yes—
281C3×C4#89614yes—
282C3×C4#89714yes—
283Dic3—68no—
284Dic3—128no—
285Dic3—244no—
286C32#185411yescharacteristic, complemented, Sylow
287C23—92no—
288C23—181no—
289C23—181no—
290C23—181no—
291C23—181no—
292C23—181no—
293C23—181no—
294C23D4×C3⋊D311yescharacteristic
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—92no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4C2×C4×C3⋊D311yescharacteristic
315C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
316C2×C4#382811yescharacteristic
317C2×C4D4×C3⋊D311yescharacteristic
318C2×C4#383011yescharacteristic
319C2×C4Q8×C3⋊D311yescharacteristic
320C8—22no—
321C8—182no—
322C2×C3#466814yes—
323C2×C3#478314yes—
324C2×C3#478414yes—
325C2×C3#481014yes—
326C2×C3#481414yes—
327C2×C3#486114yes—
328C2×C3#488014yes—
329D3—128no—
330C22—182no—
331C22—182no—
332C22—182no—
333C22—361no—
334C22—361no—
335C22—361no—
336C22—361no—
337C22#6409111yescharacteristic
338C22#6409211yescharacteristic
339C22C4⋊C4×C3⋊D311yescharacteristic
340C22#6412111yescharacteristic
341C22#6412311yescharacteristic
342C22#6412411yescharacteristic
343C22#6412811yescharacteristic
344C4—42no—
345C4—81no—
346C4—182no—
347C4—362no—
348C4—721no—
349C4C4×C4⋊(C3⋊D3)11yescharacteristic
350C4#6409011yescharacteristic
351C4#6410511yescharacteristic
352C4#6410611yescharacteristic
353C3#6887714yescomplemented
354C2—362no—
355C2#1059236711yescharacteristic
356C2#1059248211yescharacteristic
357C2#1059248311yescharacteristic
358C2#1059250911yescharacteristic
359C2#1059251311yescharacteristic
360C2#1059256011yescharacteristic
361C2#1059257911yescharacteristic
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#1854
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
3. C2×#63645C2semidirect
5. C2×#63635C2semidirect
6. C32×#340C2semidirect
7. #10589395C2semidirect
22. #63647C4semidirect
30. C3×#340D3semidirect
120. #340C3⋊D3semidirect
286. C32#1854semidirect
353. C3#68877semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#636472
C2×#636452
#105926862
C2×#636352
C32×#3402
#105893952
#688773