Finite Group Databasebeta

← #11786957

Subgroups — #11786957

Order 1152.

894 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×C32×#106C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic
4#10592671C211yesmaximal, characteristic
5C2×#63637C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#70588—34nomaximal
9C22×#634C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×#3750—21no—
16C2×C4×C3⋊Dic3—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19#64096—22no—
20#64096—22no—
21C32×#106—22no—
22#63658—21no—
23#63643C414yescomplemented
24#63637—22no—
25C2×#887—34no—
26C2×C3×#106D314yes—
27C2×#816—34no—
28#4972—34no—
29C2×#810—34no—
30#4550—34no—
31#4529—34no—
32C22×C32×C4—21no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×#634—21no—
40C2×#634—21no—
41C2×#634—21no—
42C2×#634C2×C412yes—
43C2×#634D412yes—
44C2×#634Q812yes—
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—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)C2×C412yes—
54#3750—24no—
55#3750—42no—
56C4×C3⋊Dic3—24no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1865—91noSylow
63C22×Dic6—34no—
64C22×C3×C8C2×D314yes—
65C2×C3×C4⋊C4C2×D314yes—
66C2×C3×C4⋊C4C2×D314yes—
67C2×C4⋊Dic3—34no—
68C2×Dic3⋊C4—64no—
69C2×Dic3⋊C4—64no—
70C2×C4×Dic3—34no—
71C2×C4×Dic3—64no—
72C22×C3⋊C8—34no—
73#887—68no—
74#887—68no—
75C3×#106—28no—
76C3⋊#95—64no—
77#816—316no—
78#810—68no—
79C23×C32C2×D411yescharacteristic
80C2×C32×C4—22no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×Q811yescharacteristic
90C2×C32×C4#4111yescharacteristic
91C2×C32×C4#4111yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3SD1612yes—
104#634—22no—
105#634—22no—
106#634—22no—
107#634C4⋊C414yescomplemented
108C32×C8—22no—
109C3⋊(C3⋊C8)—41no—
110C2×C4×Q8—91no—
111C2×#106C3⋊D311yescharacteristic
112C2×#103—91no—
113C2×#103—91no—
114#389—91no—
115#340—91no—
116#336—91no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4C22×D314yes—
120C22×Dic3—34no—
121C22×Dic3—34no—
122C22×Dic3—64no—
123C22×Dic3—64no—
124C2×Dic6—38no—
125C2×Dic6—38no—
126C2×Dic6—38no—
127C2×Dic6—64no—
128C2×Dic6—64no—
129C2×Dic6—64no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C2×C3×C8C4×D318yes—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4#6718yes—
137C4⋊Dic3—38no—
138C4⋊Dic3—64no—
139Dic3⋊C4—616no—
140Dic3⋊C4—128no—
141C4×Dic3—616no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C2×C3⋊C8—64no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12011yescharacteristic
149C22×C32C22⋊Q811yescharacteristic
150C22×C32C2×SD1611yescharacteristic
151C22×C32#13511yescharacteristic
152C22×C32#13711yescharacteristic
153C22×C32#13711yescharacteristic
154C32×C4—42no—
155C32×C4—81no—
156C32×C4C2×C4⋊C411yescharacteristic
157C32×C4C4×D411yescharacteristic
158C32×C4C22⋊Q811yescharacteristic
159C32×C4#12311yescharacteristic
160C3⋊Dic3—24no—
161C3⋊Dic3—22no—
162C3⋊Dic3—42no—
163C3⋊Dic3—41no—
164C22×Q8—91no—
165C22×C8—91no—
166C22×C8C2×C3⋊D311yescharacteristic
167C4×Q8—182no—
168C4×Q8—182no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171C2×C4⋊C4—181no—
172C2×C4⋊C4C2×C3⋊D311yescharacteristic
173C2×C4⋊C4C2×C3⋊D311yescharacteristic
174C2×C42—91no—
175C2×C42—181no—
176#106—22no—
177#103—94no—
178#103—182no—
179#95—181no—
180C23×C3D3×D414yes—
181C2×C3×C4—28no—
182C2×C3×C4—44no—
183C2×C3×C4—44no—
184C2×C3×C4—44no—
185C2×C3×C4—44no—
186C2×C3×C4—44no—
187C2×C3×C4C2×C4×D314yes—
188C2×C3×C4#23514yes—
189C2×C3×C4D3×D414yes—
190C2×C3×C4D3×Q814yes—
191C2×C3×C4#23914yes—
192C2×C3×C4C2×#6714yes—
193C2×Dic3—38no—
194C2×Dic3—68no—
195C2×Dic3—68no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—68no—
199C2×Dic3—68no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205Dic6—316no—
206Dic6—68no—
207Dic6—68no—
208Dic6—68no—
209C3×C8—28no—
210C3⋊C8—124no—
211C2×C32#38511yescharacteristic
212C2×C32C4×SD1611yescharacteristic
213C2×C32#44111yescharacteristic
214C2×C32#44811yescharacteristic
215C2×C32#45211yescharacteristic
216C2×C32#47511yescharacteristic
217C2×C32#47911yescharacteristic
218C2×Q8—92no—
219C2×Q8—92no—
220C2×Q8—92no—
221C2×Q8—181no—
222C2×Q8—181no—
223C2×Q8—181no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—181no—
229C22×C4—181no—
230C22×C4C22×C3⋊D311yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—181no—
234C2×C8—181no—
235C2×C8—181no—
236C2×C8C4×C3⋊D312yes—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—92no—
241C4⋊C4—184no—
242C4⋊C4—181no—
243C4⋊C4—362no—
244C4⋊C4#63812yes—
245C42—184no—
246C42—181no—
247C42—181no—
248C22×C3#89314yes—
249C22×C3#89614yes—
250C22×C3D3×SD1614yes—
251C22×C3#91514yes—
252C22×C3#91514yes—
253C22×C3#91614yes—
254C22×C3#93714yes—
255C3×C4—48no—
256C3×C4—84no—
257C3×C4D3×C4⋊C414yes—
258C3×C4#89414yes—
259C3×C4C4×#6714yes—
260C3×C4#94614yes—
261Dic3—68no—
262Dic3—616no—
263Dic3—124no—
264Dic3—128no—
265C32#186511yescharacteristic, complemented, Sylow
266C23D4×C3⋊D311yescharacteristic
267Q8—94no—
268Q8—182no—
269Q8—182no—
270Q8—182no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—92no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—182no—
283C2×C4—182no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4—361no—
288C2×C4—361no—
289C2×C4C2×C4×C3⋊D311yescharacteristic
290C2×C4#382811yescharacteristic
291C2×C4D4×C3⋊D311yescharacteristic
292C2×C4Q8×C3⋊D311yescharacteristic
293C2×C4#383211yescharacteristic
294C2×C4C2×#63811yescharacteristic
295C8—22no—
296C8—361no—
297C2×C3#485214yes—
298C2×C3#485314yes—
299C2×C3#485414yes—
300C2×C3#485714yes—
301C2×C3#498914yes—
302C2×C3#517014yes—
303C2×C3#517314yes—
304C22#6410211yescharacteristic
305C22#6410511yescharacteristic
306C22SD16×C3⋊D311yescharacteristic
307C22#6412411yescharacteristic
308C22#6412411yescharacteristic
309C22#6412511yescharacteristic
310C22#6414611yescharacteristic
311C4—42no—
312C4—81no—
313C4—182no—
314C4—184no—
315C4—362no—
316C4—361no—
317C4C4⋊C4×C3⋊D311yescharacteristic
318C4#6410311yescharacteristic
319C4C4×#63811yescharacteristic
320C4#6415511yescharacteristic
321C3#7058814yescomplemented
322C2#1059255111yescharacteristic
323C2#1059255211yescharacteristic
324C2#1059255311yescharacteristic
325C2#1059255611yescharacteristic
326C2#1059268811yescharacteristic
327C2#1059286911yescharacteristic
328C2#1059287211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#106C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#106C3⋊D3
hypocenterC32#1865
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
23. #63643C4semidirect
107. #634C4⋊C4semidirect
265. C32#1865semidirect
321. C3#70588semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C32×#1062
C2×#636432
#105926712
C2×#636372
#105894162
#105893952
#705883