Finite Group Databasebeta

← #11790834

Subgroups — #11790834

Order 1152.

1224 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C2×#63661C214yesmaximal, complemented
3#10592911C211yesmaximal, characteristic, complemented
4C4×#3757C211yesmaximal, characteristic, complemented
5#71686—34nomaximal
6C22×C32×D4C411yescharacteristic, complemented
7C22×C32×D4C2212yes—
8C23×C32×C4C2211yescharacteristic
9C32×#121—21no—
10C32×#121—21no—
11C32×#121—21no—
12C32×#121—21no—
13C2×C32×C4⋊C4C411yescharacteristic, complemented
14C2×C32×C22⋊C4C412yescomplemented
15C2×#3757C2212yes—
16C2×#3757C2212yes—
17C2×C4⋊(C3⋊Dic3)—21no—
18C2×C4×C3⋊Dic3—21no—
19#63661—28no—
20#63658—21no—
21#63658—21no—
22C2×C3×#121D314yes—
23C2×#834—316no—
24#5212—34no—
25C4×#217—34no—
26C24×C32C2×C412yes—
27C24×C32C2311yescharacteristic
28C2×C32×D4—22no—
29C2×C32×D4—22no—
30C2×C32×D4—24no—
31C2×C32×D4—24no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C32×D4—42no—
35C22×C32×C4—42no—
36C22×C32×C4C2×C412yes—
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3—22no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C22⋊C4—22no—
48C32×C22⋊C4—22no—
49#3757—22no—
50#3757—24no—
51#3757D414yescomplemented
52C4⋊(C3⋊Dic3)—42no—
53C4×C3⋊Dic3—42no—
54#1964—91noSylow
55C22×C3×D4Dic314yescomplemented
56C22×C3×D4C2×D318yes—
57C23×C3×C4C2×D314yes—
58C3×#121—24no—
59C3×#121—24no—
60C3×#121—24no—
61C3×#121—24no—
62C2×C3×C4⋊C4Dic314yescomplemented
63C2×C3×C22⋊C4Dic318yescomplemented
64C2×#217—38no—
65C2×#217—38no—
66C2×C4⋊Dic3—64no—
67C2×C4×Dic3—64no—
68#834—632no—
69C3⋊#95—64no—
70C3⋊#95—64no—
71C23×C32—22no—
72C23×C32—24no—
73C23×C32—41no—
74C23×C32—41no—
75C23×C32—42no—
76C23×C32—42no—
77C23×C32C22×C411yescharacteristic
78C23×C32C2×D412yes—
79C23×C32C2×D411yescharacteristic
80C23×C32C2×D411yescharacteristic
81C23×C32#4112yes—
82C32×D4—42no—
83C32×D4—44no—
84C32×D4—42no—
85C32×D4—42no—
86C32×D4—42no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—24no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C3⋊Dic3—24no—
100C2×C3⋊Dic3—42no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3—42no—
103C2×C3⋊Dic3—42no—
104C2×C3⋊Dic3—42no—
105C2×#121C3⋊D311yescharacteristic
106C2×#99—94no—
107#380—91no—
108C4×C22⋊C4—91no—
109C24×C3C2×Dic318yes—
110C24×C3C22×D314yes—
111C2×C3×D4—216no—
112C2×C3×D4—216no—
113C2×C3×D4—28no—
114C2×C3×D4—28no—
115C2×C3×D4—24no—
116C2×C3×D4—24no—
117C2×C3×D4—48no—
118C22×C3×C4—48no—
119C22×C3×C4C2×Dic318yes—
120C22×C3×C4C2×Dic314yes—
121C22×C3×C4C2×Dic314yes—
122C22×C3×C4#6714yes—
123C22×C3×C4#6714yes—
124C22×C3×C4#6714yes—
125C22×C3×C4#6714yes—
126C22×Dic3—68no—
127C22×Dic3—68no—
128C3×C4⋊C4—24no—
129C3×C4⋊C4—24no—
130C3×C22⋊C4—28no—
131C3×C22⋊C4—28no—
132#217—316no—
133#217—68no—
134#217—616no—
135C4⋊Dic3—128no—
136C4×Dic3—128no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—42no—
144C22×C32—42no—
145C22×C32—42no—
146C22×C32—42no—
147C22×C32—42no—
148C22×C32—84no—
149C22×C32C2×C22⋊C411yescharacteristic
150C22×C32C4×D412yes—
151C22×C32#12112yes—
152C22×C32#12411yescharacteristic
153C22×C32#12711yescharacteristic
154C32×C4—21no—
155C32×C4—21no—
156C32×C4—21no—
157C32×C4—42no—
158C32×C4#9912yescomplemented
159C3⋊Dic3—44no—
160C3⋊Dic3—82no—
161C22×D4C3⋊Dic311yescharacteristic, complemented
162C22×D4C2×C3⋊D312yes—
163C23×C4C2×C3⋊D311yescharacteristic
164#121—21no—
165#121—21no—
166#121—21no—
167#121—21no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4C3⋊Dic311yescharacteristic, complemented
170C2×C22⋊C4—92no—
171C2×C22⋊C4—92no—
172C2×C22⋊C4C3⋊Dic312yescomplemented
173C2×C42—181no—
174#99—188no—
175#95—181no—
176#95—181no—
177C23×C3—28no—
178C23×C3—216no—
179C23×C3—44no—
180C23×C3—44no—
181C23×C3—48no—
182C23×C3—48no—
183C23×C3D3×D418yes—
184C23×C3#23718yes—
185C23×C3C22×Dic314yes—
186C23×C3C2×#6714yes—
187C23×C3C2×#6714yes—
188C3×D4—48no—
189C3×D4—48no—
190C3×D4—416no—
191C3×D4—48no—
192C3×D4—48no—
193C2×C3×C4—28no—
194C2×C3×C4—28no—
195C2×C3×C4—28no—
196C2×C3×C4—216no—
197C2×C3×C4—28no—
198C2×C3×C4—44no—
199C2×C3×C4—44no—
200C2×C3×C4—44no—
201C2×C3×C4#21714yes—
202C2×C3×C4#21714yes—
203C2×C3×C4#21714yes—
204C2×C3×C4#21714yes—
205C2×Dic3—616no—
206C2×Dic3—128no—
207C2×Dic3—128no—
208C2×Dic3—128no—
209C2×Dic3—128no—
210C2×Dic3—128no—
211C2×C32—22no—
212C2×C32—21no—
213C2×C32—22no—
214C2×C32—21no—
215C2×C32—82no—
216C2×C32#39011yescharacteristic
217C2×C32C2×#9911yescharacteristic
218C2×C32#41011yescharacteristic
219C24C2×C3⋊Dic312yes—
220C24C22×C3⋊D311yescharacteristic
221C2×D4—24no—
222C2×D4—24no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4—42no—
228C22×C4—42no—
229C22×C4—182no—
230C22×C4—182no—
231C22×C4C2×C3⋊Dic312yes—
232C22×C4C2×C3⋊Dic311yescharacteristic
233C22×C4C2×C3⋊Dic311yescharacteristic
234C22×C4#63811yescharacteristic
235C22×C4#63811yescharacteristic
236C22×C4#63811yescharacteristic
237C22×C4#63811yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—362no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—94no—
244C22⋊C4—182no—
245C22⋊C4—184no—
246C42—362no—
247C22×C3—24no—
248C22×C3—24no—
249C22×C3—24no—
250C22×C3—24no—
251C22×C3—24no—
252C22×C3—24no—
253C22×C3—48no—
254C22×C3—48no—
255C22×C3—48no—
256C22×C3—48no—
257C22×C3—48no—
258C22×C3—816no—
259C22×C3D4×Dic318yes—
260C22×C3#93614yes—
261C22×C3#93818yes—
262C22×C3#94014yes—
263C22×C3C2×#21714yes—
264C3×C4—24no—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—48no—
268C3×C4#83418yescomplemented
269Dic3—1216no—
270Dic3—248no—
271C32#196411yescharacteristic, complemented, Sylow
272C23—22no—
273C23—24no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23D4×C3⋊D312yes—
279C23#383012yes—
280C23C22×C3⋊Dic311yescharacteristic
281C23C2×#63811yescharacteristic
282C23C2×#63811yescharacteristic
283D4—42no—
284D4—42no—
285D4—44no—
286D4—42no—
287D4—42no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—184no—
297C2×C4—362no—
298C2×C4—362no—
299C2×C4—362no—
300C2×C4—362no—
301C2×C4—362no—
302C2×C4#375711yescharacteristic
303C2×C4#375711yescharacteristic
304C2×C4#375711yescharacteristic
305C2×C4#375711yescharacteristic
306C2×C3—28no—
307C2×C3—24no—
308C2×C3—28no—
309C2×C3—24no—
310C2×C3—88no—
311C2×C3C2×#83414yes—
312C2×C3#522114yes—
313C2×C3#524014yes—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—84no—
326C22D4×C3⋊Dic312yes—
327C22#6414511yescharacteristic
328C22#6414712yes—
329C22#6414911yescharacteristic
330C22C2×#375711yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—364no—
336C4—722no—
337C4#6366112yescomplemented
338C3#7168614yescomplemented
339C2—22no—
340C2—21no—
341C2—22no—
342C2—21no—
343C2—82no—
344C2C2×#6366111yescharacteristic
345C2#1059292011yescharacteristic
346C2#1059293911yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC23×C32C22×C4
FrattiniC24C22×C3⋊D3
Fitting, prime radicalC2×C32×#121C2
socleC22×C32C2×C22⋊C4
cosocleC24×C32C23
hypercenterC2×#121C3⋊D3
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#63661C2semidirect
3. #10592911C2semidirect
4. C4×#3757C2semidirect
6. C22×C32×D4C4semidirect
13. C2×C32×C4⋊C4C4semidirect
14. C2×C32×C22⋊C4C4semidirect
51. #3757D4semidirect
55. C22×C3×D4Dic3semidirect
62. C2×C3×C4⋊C4Dic3semidirect
63. C2×C3×C22⋊C4Dic3semidirect
158. C32×C4#99semidirect
161. C22×D4C3⋊Dic3semidirect
169. C2×C4⋊C4C3⋊Dic3semidirect
172. C2×C22⋊C4C3⋊Dic3semidirect
268. C3×C4#834semidirect
271. C32#1964semidirect
337. C4#63661semidirect
338. C3#71686semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×#636612
#105929112
C4×#37572
#716863