Finite Group Databasebeta

← #11787172

Subgroups — #11787172

Order 1152.

1224 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C22×#3748C211yesmaximal, characteristic, complemented
3C2×#63657C212yesmaximal, complemented
4C2×#63657C211yesmaximal, characteristic, complemented
5#10589390C212yesmaximal, complemented
6#71611—34nomaximal
7C22×C32×D4C411yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C32×C4×D4—22no—
11C32×C4×D4—22no—
12C2×C32×C4⋊C4C411yescharacteristic
13C2×C32×C22⋊C4C411yescharacteristic
14C2×C32×C22⋊C4C411yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3748—22no—
17C2×#3748—24no—
18C22×C3⋊(C3⋊C8)C2212yes—
19C22×C3⋊(C3⋊C8)C2212yes—
20#63657—22no—
21#63657—24no—
22C2×C3×C4×D4D314yes—
23C22×#208—34no—
24C2×#830—38no—
25C2×#830—34no—
26#4524—38no—
27C24×C32C2×C411yescharacteristic
28C24×C32C2×C411yescharacteristic
29C2×C32×D4—22no—
30C2×C32×D4—22no—
31C2×C32×D4—22no—
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4—21no—
35C22×C32×C4—21no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4D412yes—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C32×C4⋊C4—22no—
46C32×C22⋊C4—22no—
47C32×C22⋊C4—22no—
48C32×C42—21no—
49C32×C42—21no—
50#3748—28no—
51C2×C3⋊(C3⋊C8)—22no—
52C2×C3⋊(C3⋊C8)—22no—
53C2×C3⋊(C3⋊C8)—22no—
54C2×C3⋊(C3⋊C8)—22no—
55C2×C3⋊(C3⋊C8)—22no—
56C2×C3⋊(C3⋊C8)D414yescomplemented
57#1870—91noSylow
58C22×C3×D4Dic314yes—
59C23×C3×C4C2×D314yes—
60C23×C3×C4C2×D314yes—
61C3×C4×D4—28no—
62C3×C4×D4—28no—
63C2×C3×C4⋊C4Dic314yes—
64C2×C3×C22⋊C4Dic314yes—
65C2×C3×C22⋊C4Dic314yes—
66C2×C3×C42C2×D314yes—
67C2×#208—616no—
68C2×#208—68no—
69C22×C3⋊C8—38no—
70C22×C3⋊C8—38no—
71#830—616no—
72#830—68no—
73C23×C32—21no—
74C23×C32—22no—
75C23×C32—22no—
76C23×C32—21no—
77C23×C32—21no—
78C23×C32—21no—
79C23×C32—22no—
80C23×C32—22no—
81C23×C32C22⋊C412yes—
82C23×C32M1612yescomplemented
83C23×C32C22×C411yescharacteristic
84C32×D4—28no—
85C2×C32×C4—21no—
86C2×C32×C4—22no—
87C2×C32×C4—21no—
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—22no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—41no—
96C2×C32×C4—42no—
97C2×C32×C4—41no—
98C2×C32×C4C22⋊C412yes—
99C2×C32×C4M1612yescomplemented
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4112yes—
104C3⋊(C3⋊C8)—24no—
105C3⋊(C3⋊C8)—42no—
106C22×M16—91no—
107C2×C4×D4C3⋊D311yescharacteristic
108C2×C22⋊C8—92no—
109C2×C22⋊C8—91no—
110#336—92no—
111C24×C3C2×Dic314yes—
112C24×C3C2×Dic314yes—
113C2×C3×D4—28no—
114C2×C3×D4—28no—
115C2×C3×D4—28no—
116C22×C3×C4—28no—
117C22×C3×C4—28no—
118C22×C3×C4—28no—
119C22×C3×C4—28no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4C2×Dic314yes—
123C22×C3×C4C2×Dic314yes—
124C22×C3×C4C2×Dic314yes—
125C22×C3×C4C2×Dic314yes—
126C22×C3×C4#6718yes—
127C22×C3×C4#6718yes—
128C22×C3×C4C22×D314yes—
129C3×C4⋊C4—28no—
130C3×C22⋊C4—28no—
131C3×C22⋊C4—28no—
132C3×C42—24no—
133C3×C42—24no—
134#208—632no—
135C2×C3⋊C8—316no—
136C2×C3⋊C8—68no—
137C2×C3⋊C8—68no—
138C2×C3⋊C8—68no—
139C2×C3⋊C8—68no—
140C2×C3⋊C8—68no—
141C22×C32—22no—
142C22×C32—22no—
143C22×C32—22no—
144C22×C32—22no—
145C22×C32—24no—
146C22×C32—41no—
147C22×C32—41no—
148C22×C32—42no—
149C22×C32—42no—
150C22×C32—42no—
151C22×C32C2×C22⋊C411yescharacteristic
152C22×C32C4×D412yes—
153C22×C32C2×M1611yescharacteristic
154C22×C32C2×M1611yescharacteristic
155C22×C32#13112yes—
156C32×C4—22no—
157C32×C4—22no—
158C32×C4—41no—
159C32×C4—41no—
160C32×C4#12011yescharacteristic
161C32×C4#12112yes—
162C32×C4#12311yescharacteristic
163C22×D4C3⋊Dic311yescharacteristic
164C23×C4C2×C3⋊D311yescharacteristic
165C23×C4C2×C3⋊D311yescharacteristic
166C2×M16—184no—
167C2×M16—182no—
168C22×C8—92no—
169C22×C8—92no—
170C4×D4—22no—
171C4×D4—22no—
172C2×C4⋊C4C3⋊Dic311yescharacteristic
173C2×C22⋊C4C3⋊Dic311yescharacteristic
174C2×C22⋊C4C3⋊Dic311yescharacteristic
175C2×C42C2×C3⋊D311yescharacteristic
176C22⋊C8—184no—
177C22⋊C8—182no—
178C23×C3—24no—
179C23×C3—24no—
180C23×C3—24no—
181C23×C3—28no—
182C23×C3—28no—
183C23×C3—28no—
184C23×C3—28no—
185C23×C3—24no—
186C23×C3#20818yescomplemented
187C23×C3#21718yes—
188C23×C3C22×Dic314yes—
189C3×D4—232no—
190C2×C3×C4—24no—
191C2×C3×C4—28no—
192C2×C3×C4—24no—
193C2×C3×C4—28no—
194C2×C3×C4—28no—
195C2×C3×C4—216no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—48no—
203C2×C3×C4#20818yescomplemented
204C2×C3×C4#21718yes—
205C2×C3×C4D3×D418yes—
206C2×C3×C4#23718yes—
207C2×C3×C4C2×#6714yes—
208C2×C3×C4C2×#6714yes—
209C3⋊C8—616no—
210C3⋊C8—128no—
211C2×C32—42no—
212C2×C32—42no—
213C2×C32#38611yescharacteristic
214C2×C32#40711yescharacteristic
215C2×C32#40811yescharacteristic
216C2×C32#43512yes—
217C2×C32#43612yes—
218C24C2×C3⋊Dic311yescharacteristic
219C24C2×C3⋊Dic311yescharacteristic
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4C2×C3⋊Dic311yescharacteristic
230C22×C4C2×C3⋊Dic311yescharacteristic
231C22×C4C2×C3⋊Dic311yescharacteristic
232C22×C4C2×C3⋊Dic311yescharacteristic
233C22×C4#63812yes—
234C22×C4#63812yes—
235C22×C4C22×C3⋊D311yescharacteristic
236M16—188no—
237C2×C8—94no—
238C2×C8—182no—
239C2×C8—182no—
240C2×C8—182no—
241C2×C8—182no—
242C2×C8—182no—
243C4⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C42—21no—
247C42—21no—
248C22×C3—28no—
249C22×C3—28no—
250C22×C3—28no—
251C22×C3—28no—
252C22×C3—216no—
253C22×C3—44no—
254C22×C3—44no—
255C22×C3—48no—
256C22×C3—48no—
257C22×C3—48no—
258C22×C3C2×#20814yes—
259C22×C3C2×#20814yes—
260C22×C3D4×Dic318yes—
261C22×C3#94818yes—
262C22×C3C2×#21714yes—
263C3×C4—28no—
264C3×C4—28no—
265C3×C4—44no—
266C3×C4—44no—
267C3×C4#93514yes—
268C3×C4#93714yes—
269C3×C4#93918yes—
270C32#187011yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—21no—
279C23#374812yescomplemented
280C23#375712yes—
281C23C22×C3⋊Dic311yescharacteristic
282D4—28no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4#374812yescomplemented
297C2×C4#375712yes—
298C2×C4D4×C3⋊D312yes—
299C2×C4#383012yes—
300C2×C4C2×#63811yescharacteristic
301C2×C4C2×#63811yescharacteristic
302C8—184no—
303C8—362no—
304C2×C3—48no—
305C2×C3—48no—
306C2×C3#501118yes—
307C2×C3#501218yes—
308C2×C3#520714yes—
309C2×C3#522014yes—
310C2×C3#523414yes—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—24no—
316C22—41no—
317C22—41no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22C2×#374811yescharacteristic
322C22C2×#374811yescharacteristic
323C22D4×C3⋊Dic312yes—
324C22#6415712yes—
325C22C2×#375711yescharacteristic
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4#6414411yescharacteristic
331C4#6414611yescharacteristic
332C4#6414812yes—
333C3#7161114yescomplemented
334C2—42no—
335C2—42no—
336C2#1059271012yes—
337C2#1059271112yes—
338C2#1059290611yescharacteristic
339C2#1059291911yescharacteristic
340C2#1059293311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×C3⋊D3
commutator, socleC23×C32C22×C4
FittingC2×C32×C4×D4C2
prime radicalC22×C32×D4C4
cosocleC22×C32×C4C23
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#1870
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3748C2semidirect
3. C2×#63657C2semidirect
4. C2×#63657C2semidirect
5. #10589390C2semidirect
56. C2×C3⋊(C3⋊C8)D4semidirect
82. C23×C32M16semidirect
99. C2×C32×C4M16semidirect
186. C23×C3#208semidirect
203. C2×C3×C4#208semidirect
270. C32#1870semidirect
279. C23#3748semidirect
296. C2×C4#3748semidirect
333. C3#71611semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C22×#37482
C2×#636572
#105893902
#716113