Finite Group Databasebeta

← #11792621

Subgroups — #11792621

Order 1152.

1110 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×Q16C211yesmaximal, characteristic
2C2×#64153C211yesmaximal, characteristic
3C22×#3756C211yesmaximal, characteristic
4#10592928C211yesmaximal, characteristic
5C2×#63662C211yesmaximal, characteristic
6C2×#63643C211yesmaximal, characteristic
7#10589416C211yesmaximal, characteristic
8#72073—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C32×Q16—22no—
13C2×C32×Q16—22no—
14C2×C32×Q16—22no—
15C22×C32×C8C2211yescharacteristic
16#64153—22no—
17#64153—22no—
18C2×#3756—22no—
19C2×#3756—22no—
20C2×#3756—22no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750—22no—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#63662—22no—
26#63658—22no—
27#63643—22no—
28C22×C3×Q16D314yes—
29C2×#944—34no—
30C22×#216—34no—
31#5229—34no—
32C2×#835—34no—
33C2×#816—34no—
34#4550—34no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8D412yes—
46C2×C32×Q8D412yes—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D412yes—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634D412yes—
59C32×Q16—28no—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C2×C32×C8D412yes—
63#3756—28no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66#3750—28no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D412yes—
72#2016—91noSylow
73C22×C3×Q8C2×D314yes—
74C22×C3×Q8C2×D314yes—
75C22×Dic6—34no—
76C2×C3×Q16—28no—
77C2×C3×Q16—28no—
78C2×C3×Q16—28no—
79C22×C3×C8C2×D314yes—
80#944—68no—
81#944—68no—
82C2×#216—68no—
83C2×#216—68no—
84C2×#216—68no—
85C2×C4⋊Dic3—34no—
86C2×Dic3⋊C4—68no—
87C2×C4×Dic3—34no—
88C22×C3⋊C8—34no—
89#835—68no—
90C3⋊#95—68no—
91#816—68no—
92C23×C32C2×D411yescharacteristic
93C32×Q8—22no—
94C32×Q8—22no—
95C32×Q8—22no—
96C32×Q8—22no—
97C32×Q8—41no—
98C32×Q8—41no—
99C32×Q8—41no—
100C32×Q8—41no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—42no—
120C2×C3⋊Dic3Q1614yescomplemented
121#634—22no—
122#634—22no—
123#634—41no—
124#634—41no—
125C32×C8—22no—
126C3⋊(C3⋊C8)—22no—
127C22×Q16—91no—
128C22×Q16C3⋊D311yescharacteristic
129C2×C4⋊Q8—91no—
130C2×#103—91no—
131C2×#103—91no—
132#391—91no—
133#336—91no—
134C2×C3×Q8—24no—
135C2×C3×Q8—24no—
136C2×C3×Q8—24no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—24no—
140C2×C3×Q8—24no—
141C2×C3×Q8—24no—
142C2×C3×Q8—24no—
143C2×C3×Q8—24no—
144C2×C3×Q8#6718yes—
145C2×C3×Q8#6718yes—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4C22×D314yes—
149C22×Dic3—38no—
150C22×Dic3—64no—
151C22×Dic3—64no—
152C2×Dic6—38no—
153C2×Dic6—64no—
154C2×Dic6—64no—
155C2×Dic6—64no—
156C2×Dic6—64no—
157C2×Dic6—64no—
158C3×Q16—232no—
159C2×C3×C8—24no—
160C2×C3×C8—24no—
161C2×C3×C8#6718yes—
162#216—632no—
163C4⋊Dic3—64no—
164C4⋊Dic3—64no—
165Dic3⋊C4—632no—
166C4×Dic3—64no—
167C4×Dic3—64no—
168C2×C3⋊C8—38no—
169C2×C3⋊C8—64no—
170C2×C3⋊C8—64no—
171C22×C32#12011yescharacteristic
172C22×C32#12111yescharacteristic
173C22×C32#12711yescharacteristic
174C22×C32C2×Q1612yes—
175C22×C32#13712yes—
176C32×C4—42no—
177C32×C4—42no—
178C32×C4#12011yescharacteristic
179C32×C4#12011yescharacteristic
180C32×C4#12111yescharacteristic
181C32×C4#12111yescharacteristic
182C3⋊Dic3—24no—
183C3⋊Dic3—42no—
184C3⋊Dic3—81no—
185C22×Q8—91no—
186C22×Q8C2×C3⋊D311yescharacteristic
187C22×Q8C2×C3⋊D311yescharacteristic
188C2×Q16—22no—
189C2×Q16—22no—
190C2×Q16—22no—
191C2×Q16—182no—
192C2×Q16—182no—
193C2×Q16—182no—
194C22×C8—91no—
195C22×C8C2×C3⋊D311yescharacteristic
196C4⋊Q8—182no—
197C4⋊Q8—182no—
198C2×C4⋊C4—91no—
199C2×C4⋊C4—182no—
200C2×C42—91no—
201#103—182no—
202#103—182no—
203#95—182no—
204C23×C3D3×D414yes—
205C3×Q8—28no—
206C3×Q8—28no—
207C3×Q8—28no—
208C3×Q8—28no—
209C3×Q8—44no—
210C3×Q8—44no—
211C3×Q8—44no—
212C3×Q8—44no—
213C2×C3×C4—28no—
214C2×C3×C4—28no—
215C2×C3×C4—44no—
216C2×C3×C4—44no—
217C2×C3×C4—44no—
218C2×C3×C4—44no—
219C2×C3×C4D3×D414yes—
220C2×C3×C4D3×D414yes—
221C2×C3×C4#23714yes—
222C2×C3×C4C2×#6714yes—
223C2×C3×C4C2×#6714yes—
224C2×C3×C4C2×#6714yes—
225C2×Dic3—316no—
226C2×Dic3—68no—
227C2×Dic3—68no—
228C2×Dic3—68no—
229C2×Dic3—124no—
230C2×Dic3—124no—
231C2×Dic3—128no—
232C2×Dic3—124no—
233Dic6—68no—
234Dic6—68no—
235Dic6—124no—
236Dic6—124no—
237C3×C8—28no—
238C3⋊C8—68no—
239C2×C32#39211yescharacteristic
240C2×C32#45112yes—
241C2×C32#46212yes—
242C2×C32#49411yescharacteristic
243C2×C32#49711yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—92no—
255C2×Q8—181no—
256C2×Q8—181no—
257C2×Q8—181no—
258C2×Q8—181no—
259C2×Q8—181no—
260C2×Q8#63812yes—
261C2×Q8#63812yes—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—92no—
265C22×C4—181no—
266C22×C4—181no—
267C22×C4C22×C3⋊D311yescharacteristic
268Q16—28no—
269Q16—188no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—92no—
273C2×C8—181no—
274C2×C8—181no—
275C2×C8#63812yes—
276C4⋊C4—188no—
277C4⋊C4—181no—
278C4⋊C4—181no—
279C42—181no—
280C42—181no—
281C22×C3D3×Q1618yes—
282C22×C3#91818yes—
283C22×C3#93714yes—
284C22×C3#93914yes—
285C22×C3#94014yes—
286C3×C4—48no—
287C3×C4—48no—
288C3×C4#93714yes—
289C3×C4#93814yes—
290C3×C4#93914yes—
291C3×C4#95314yes—
292Dic3—616no—
293Dic3—128no—
294Dic3—244no—
295C32#201611yescharacteristic, complemented, Sylow
296C23D4×C3⋊D311yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—22no—
300Q8—22no—
301Q8—41no—
302Q8—41no—
303Q8—41no—
304Q8—41no—
305Q8—182no—
306Q8—182no—
307Q8—361no—
308Q8—361no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—94no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—362no—
322C2×C4—361no—
323C2×C4D4×C3⋊D311yescharacteristic
324C2×C4D4×C3⋊D311yescharacteristic
325C2×C4#383011yescharacteristic
326C2×C4C2×#63811yescharacteristic
327C2×C4C2×#63811yescharacteristic
328C2×C4C2×#63811yescharacteristic
329C8—22no—
330C8—182no—
331C2×C3#518218yes—
332C2×C3#518314yes—
333C2×C3#518618yes—
334C2×C3#519014yes—
335C2×C3#522314yes—
336C22Q16×C3⋊D312yes—
337C22#6412712yes—
338C22#6414611yescharacteristic
339C22#6414811yescharacteristic
340C22#6414911yescharacteristic
341C4—42no—
342C4—42no—
343C4—184no—
344C4—362no—
345C4—721no—
346C4#6414611yescharacteristic
347C4#6414711yescharacteristic
348C4#6414811yescharacteristic
349C4#6416211yescharacteristic
350C3#7207314yescomplemented
351C2#1059288112yes—
352C2#1059288211yescharacteristic
353C2#1059288512yes—
354C2#1059288911yescharacteristic
355C2#1059292211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×Q16C2
socle, prime radicalC23×C32C2×D4
hypercenterC22×Q16C3⋊D3
hypocenterC32#2016
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
120. C2×C3⋊Dic3Q16semidirect
295. C32#2016semidirect
350. C3#72073semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Q162
C2×#641532
C22×#37562
#105929282
C2×#636622
C2×#636432
#105894162
#720733