Finite Group Databasebeta

← #11791125

Subgroups — #11791125

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic
3C2×#63659C211yesmaximal, characteristic
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×#63634C211yesmaximal, characteristic, complemented
6#10592628C211yesmaximal, characteristic, complemented
7C2×#63630C211yesmaximal, characteristic, complemented
8#69649—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4—22no—
13C2×C32×C42C2211yescharacteristic
14C2×#3754—22no—
15C2×#3754—22no—
16C2×#3754C414yescomplemented
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20#63659—22no—
21#63658—22no—
22#63637—22no—
23#63634—22no—
24#63630—22no—
25C22×#214—34no—
26C3×#390D314yes—
27C2×#832—34no—
28C2×#810—34no—
29C2×#807—34no—
30#4929—34no—
31C2×#803—34no—
32C24×C32—21no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4C2×C412yes—
39C22×C32×C4—21no—
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C22⋊C4—44no—
53C32×C42—21no—
54C32×C42—21no—
55#3754—28no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C2×C3⋊(C3⋊C8)D412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63C2×C3⋊(C3⋊C8)D412yes—
64#1973—91noSylow
65C22×C3×D4C2×D314yes—
66C22×Dic6—34no—
67C2×C3×C4⋊C4C2×D314yes—
68C2×C3×C22⋊C4—28no—
69C2×C3×C42C2×D314yes—
70C2×#214—316no—
71C2×#214—68no—
72C2×#214—68no—
73C2×C4⋊Dic3—34no—
74C22×C3⋊C8—34no—
75C22×C3⋊C8—34no—
76#832—68no—
77C3⋊#95—68no—
78#810—68no—
79#807—68no—
80#803—68no—
81C23×C32—22no—
82C23×C32—41no—
83C23×C32—41no—
84C23×C32—42no—
85C23×C32—42no—
86C23×C32C2×D411yescharacteristic
87C32×D4—22no—
88C32×D4—22no—
89C32×D4—41no—
90C32×D4—41no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4—42no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—42no—
107#634—22no—
108#634—22no—
109#634—41no—
110#634—41no—
111C3⋊(C3⋊C8)—22no—
112C3⋊(C3⋊C8)C22⋊C414yescomplemented
113C22×SD16—91no—
114C2×#107—91no—
115C2×#103—91no—
116C2×#102—91no—
117C2×#97—91no—
118#391—91no—
119#390C3⋊D311yescharacteristic
120C24×C3—24no—
121C2×C3×D4—24no—
122C2×C3×D4—24no—
123C2×C3×D4—24no—
124C2×C3×D4—24no—
125C2×C3×D4—24no—
126C2×C3×D4C4×D318yes—
127C22×C3×C4—24no—
128C22×C3×C4#6718yes—
129C22×C3×C4C22×D314yes—
130C22×Dic3—64no—
131C22×Dic3—64no—
132C2×Dic6—38no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C2×Dic6—64no—
137C2×Dic6—64no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—24no—
140C3×C22⋊C4—416no—
141C3×C42—24no—
142C3×C42—24no—
143#214—632no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146C2×C3⋊C8—38no—
147C2×C3⋊C8—38no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—38no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152C22×C32—42no—
153C22×C32—44no—
154C22×C32—82no—
155C22×C32—81no—
156C22×C32—81no—
157C22×C32C4×D411yescharacteristic
158C22×C32#12111yescharacteristic
159C22×C32#12711yescharacteristic
160C22×C32AGL(1,ℤ/8)12yes—
161C22×C32#13712yes—
162C32×C4—42no—
163C32×C4—81no—
164C32×C4C2×C22⋊C411yescharacteristic
165C32×C4C4×D411yescharacteristic
166C32×C4#12111yescharacteristic
167C32×C4#12411yescharacteristic
168C3⋊Dic3—42no—
169C3⋊Dic3—81no—
170C22×Q8—91no—
171C22×D4C2×C3⋊D311yescharacteristic
172C2×SD16—94no—
173C2×SD16—182no—
174C2×SD16—182no—
175C22×C8—91no—
176C22×C8—91no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4C2×C3⋊D311yescharacteristic
179C2×C22⋊C4—22no—
180C2×C42C2×C3⋊D311yescharacteristic
181#107—182no—
182#103—182no—
183#102—182no—
184#97—182no—
185#95—182no—
186C23×C3—28no—
187C23×C3—48no—
188C23×C3—44no—
189C23×C3—44no—
190C23×C3—48no—
191C23×C3C2×#6714yes—
192C3×D4—28no—
193C3×D4—28no—
194C3×D4—44no—
195C3×D4—44no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—28no—
199C2×C3×C4—48no—
200C2×C3×C4—44no—
201C2×C3×C4C2×C4×D314yes—
202C2×C3×C4#23514yes—
203C2×C3×C4D3×D414yes—
204C2×C3×C4D3×D414yes—
205C2×C3×C4D3×D414yes—
206C2×C3×C4#23714yes—
207C2×Dic3—68no—
208C2×Dic3—124no—
209C2×Dic3—124no—
210C2×Dic3—128no—
211C2×Dic3—124no—
212Dic6—68no—
213Dic6—68no—
214Dic6—124no—
215Dic6—124no—
216C3⋊C8—316no—
217C3⋊C8—68no—
218C2×C32—82no—
219C2×C32#39011yescharacteristic
220C2×C32#44012yes—
221C2×C32#46812yes—
222C2×C32#49611yescharacteristic
223C2×C32#49711yescharacteristic
224C24—21no—
225C2×Q8—92no—
226C2×Q8—181no—
227C2×Q8—181no—
228C2×Q8—181no—
229C2×Q8—181no—
230C2×Q8—181no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4C4×C3⋊D312yes—
237C22×C4—21no—
238C22×C4—181no—
239C22×C4—181no—
240C22×C4#63812yes—
241C22×C4C22×C3⋊D311yescharacteristic
242SD16—188no—
243C2×C8—92no—
244C2×C8—92no—
245C2×C8—92no—
246C2×C8—92no—
247C2×C8—181no—
248C2×C8—181no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C22⋊C4—44no—
254C42—21no—
255C42—21no—
256C22×C3—48no—
257C22×C3—416no—
258C22×C3—88no—
259C22×C3—84no—
260C22×C3—84no—
261C22×C3C4×#6714yes—
262C22×C3#93218yes—
263C22×C3#93914yes—
264C22×C3#94014yes—
265C22×C3#95118yes—
266C3×C4—48no—
267C3×C4—84no—
268C3×C4D3×C22⋊C414yes—
269C3×C4#67⋊C414yes—
270C3×C4#88414yes—
271C3×C4#88514yes—
272Dic3—128no—
273Dic3—244no—
274C32#197311yescharacteristic, complemented, Sylow
275C23—22no—
276C23—42no—
277C23—41no—
278C23—41no—
279C23—42no—
280C23C2×#63811yescharacteristic
281Q8—182no—
282Q8—182no—
283Q8—361no—
284Q8—361no—
285D4—22no—
286D4—22no—
287D4—41no—
288D4—41no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—182no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4—362no—
298C2×C4—361no—
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4#382811yescharacteristic
301C2×C4D4×C3⋊D311yescharacteristic
302C2×C4D4×C3⋊D311yescharacteristic
303C2×C4D4×C3⋊D311yescharacteristic
304C2×C4#383011yescharacteristic
305C8—94no—
306C8—182no—
307C2×C3—88no—
308C2×C3#495714yes—
309C2×C3#501818yes—
310C2×C3#504218yes—
311C2×C3#506014yes—
312C2×C3#507414yes—
313C22—42no—
314C22—44no—
315C22—81no—
316C22—82no—
317C22—81no—
318C22C4×#63811yescharacteristic
319C22#6414112yes—
320C22#6414811yescharacteristic
321C22#6414911yescharacteristic
322C22#6416012yes—
323C4—42no—
324C4—81no—
325C4—362no—
326C4—721no—
327C4C22⋊C4×C3⋊D311yescharacteristic
328C4#6409011yescharacteristic
329C4#6409311yescharacteristic
330C4#6409411yescharacteristic
331C3#6964914yescomplemented
332C2—82no—
333C2#1059265611yescharacteristic
334C2#1059271712yes—
335C2#1059274112yes—
336C2#1059275911yescharacteristic
337C2#1059277311yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C32×C4C23
hypercenter#390C3⋊D3
hypocenterC32#1973
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
4. C2×#63637C2semidirect
5. C2×#63634C2semidirect
6. #10592628C2semidirect
7. C2×#63630C2semidirect
16. C2×#3754C4semidirect
112. C3⋊(C3⋊C8)C22⋊C4semidirect
274. C32#1973semidirect
331. C3#69649semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C32×#3902
C2×#636592
C2×#636372
C2×#636342
#105926282
C2×#636302
#696493