Finite Group Databasebeta

← #11785287

Subgroups — #11785287

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal
3#10591230C211yesmaximal, characteristic
4C2×#63572C211yesmaximal, characteristic
5#10589164C212yesmaximal
6#70222—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8Q8×C3⋊Dic3—22no—
9Q8×C3⋊Dic3C414yescomplemented
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C4×C3⋊Dic3—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C3×#835—24no—
17#63579—21no—
18#63579—21no—
19#63572—22no—
20C2×Q8×Dic3—32no—
21C2×Q8×Dic3—61no—
22C2×C3×#103—32no—
23C2×#835D312yes—
24C2×Dic3⋊C8—32no—
25#4977—32no—
26#4551—32no—
27#4529—32no—
28C2×C32×Q8—21no—
29C2×C32×Q8—21no—
30C2×C32×Q8—21no—
31C2×C32×Q8C2×C412yes—
32C2×C32×Q8D412yes—
33C2×C32×Q8Q812yes—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3×Dic3—22no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—24no—
42C4⋊(C3⋊Dic3)C2×C412yes—
43C4×C3⋊Dic3—24no—
44C4×C3⋊Dic3C2×C412yes—
45C4×C3⋊Dic3D412yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51#1805—91noSylow
52C22×C3×Q8—21no—
53C22×C3×Q8C2×D312yes—
54C22×C3×C8—32no—
55C2×C3×C4⋊C4—32no—
56Q8×Dic3—38no—
57Q8×Dic3—64no—
58Q8×Dic3—64no—
59Q8×Dic3—64no—
60C2×C4⋊Dic3—32no—
61C2×C4⋊Dic3—61no—
62C2×C4⋊Dic3—62no—
63C2×C4⋊Dic3—62no—
64C2×C4⋊Dic3C2×D312yes—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—62no—
68C2×C4×Dic3—62no—
69C22×C3⋊C8C2×D312yes—
70C3×#103—64no—
71#835—24no—
72C3⋊#95—62no—
73C3⋊#95—62no—
74Dic3⋊C8—64no—
75C23×C32C2×D411yescharacteristic
76C32×Q8—22no—
77C32×Q8—22no—
78C32×Q8—22no—
79C32×Q8C4⋊C414yes—
80C2×C32×C4—22no—
81C2×C32×C4—22no—
82C2×C32×C4—22no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q811yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C2×C32×C4#4111yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—42no—
93C2×C3⋊Dic3C22⋊C412yes—
94C2×C3⋊Dic3C22⋊C412yes—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—42no—
98C3×C3⋊C8—42no—
99C2×C4×Q8—91no—
100C2×C4⋊C8—91no—
101C2×#103—32no—
102#382—91no—
103#340—92no—
104C2×C3×Q8—22no—
105C2×C3×Q8—22no—
106C2×C3×Q8—22no—
107C2×C3×Q8—22no—
108C2×C3×Q8—22no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8Dic614yes—
114C2×C3×Q8C4×D314yes—
115C2×C3×Q8#6714yes—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×C3×C4C22×D312yes—
121C22×Dic3—22no—
122C22×Dic3—32no—
123C22×Dic3—32no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C2×C3×C8—62no—
129C2×C3×C8—62no—
130C2×C3×C8—62no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—62no—
133C4⋊Dic3—22no—
134C4⋊Dic3—22no—
135C4⋊Dic3—34no—
136C4⋊Dic3—62no—
137C4⋊Dic3—68no—
138C4⋊Dic3—68no—
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C4×Dic3—68no—
146C4×Dic3—68no—
147C2×C3⋊C8—22no—
148C2×C3⋊C8—22no—
149C2×C3⋊C8—22no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32#12111yescharacteristic
152C22×C32C22⋊Q811yescharacteristic
153C22×C32#13512yes—
154C22×C32#13712yes—
155C32×C4—24no—
156C32×C4C2×C4⋊C411yescharacteristic
157C32×C4#11711yescharacteristic
158C32×C4#12111yescharacteristic
159C32×C4C22⋊Q811yescharacteristic
160C3⋊Dic3—22no—
161C3⋊Dic3—22no—
162C3⋊Dic3—42no—
163C3×Dic3—82no—
164C22×Q8D3211yescharacteristic
165C22×C8—32no—
166C4×Q8—94no—
167C4×Q8—182no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—182no—
174#103—64no—
175#95—181no—
176#95—181no—
177C23×C3—21no—
178C23×C3D3×D412yes—
179C3×Q8—24no—
180C3×Q8—24no—
181C3×Q8—24no—
182C3×Q8—24no—
183C3×Q8—24no—
184C3×Q8—24no—
185C3×Q8—24no—
186C3×Q8Dic3⋊C418yes—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—122no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202C2×C3×C4C2×Dic612yes—
203C2×C3×C4C2×C4×D312yes—
204C2×C3×C4D3×D412yes—
205C2×C3×C4#23712yes—
206C2×C3×C4#23712yes—
207C2×C3×C4C2×#6712yes—
208C2×Dic3—34no—
209C2×Dic3—34no—
210C2×Dic3—42no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—64no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—122no—
223C2×Dic3—124no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C3×C8—122no—
227C3⋊C8—42no—
228C2×C32#38011yescharacteristic
229C2×C32#41611yescharacteristic
230C2×C32#41911yescharacteristic
231C2×C32#46412yes—
232C2×C32#47912yes—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8#62412yes—
237C2×Q8#62512yes—
238C2×Q8#62712yes—
239C22×C4—21no—
240C22×C4—62no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—181no—
244C22×C4C2×D3211yescharacteristic
245C2×C8—62no—
246C2×C8—62no—
247C2×C8—62no—
248C4⋊C4—62no—
249C4⋊C4—62no—
250C4⋊C4—92no—
251C4⋊C4—184no—
252C4⋊C4—181no—
253C42—92no—
254C42—92no—
255C42—184no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3#87812yes—
262C22×C3D3×C22⋊C412yes—
263C22×C3#91512yes—
264C22×C3#91612yes—
265C22×C3#91812yes—
266C22×C3#91912yes—
267C22×C3#93912yes—
268C3×C4—28no—
269C3×C4—28no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—242no—
275C3×C4#87712yes—
276C3×C4#87812yes—
277C3×C4C2×Dic3⋊C412yes—
278C3×C4#93912yes—
279Dic3—64no—
280Dic3—64no—
281Dic3—64no—
282Dic3—82no—
283Dic3—122no—
284Dic3—124no—
285Dic3—124no—
286C32#180511yescharacteristic, complemented, Sylow
287C23#381111yescharacteristic
288Q8—22no—
289Q8—22no—
290Q8—22no—
291Q8#372414yes—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—92no—
296C2×C4—92no—
297C2×C4—122no—
298C2×C4—122no—
299C2×C4—122no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—362no—
304C2×C4#380511yescharacteristic
305C2×C4#380511yescharacteristic
306C2×C4C2×#62411yescharacteristic
307C2×C4C2×#62511yescharacteristic
308C2×C4C2×#62711yescharacteristic
309C2×C4#381111yescharacteristic
310C8—122no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—22no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3#479612yes—
317C2×C3#479912yes—
318C2×C3#480212yes—
319C2×C3#480412yes—
320C2×C3#494212yes—
321C2×C3#516612yes—
322C2×C3#518512yes—
323C22#6395012yes—
324C22#6395112yes—
325C22#6397411yescharacteristic
326C22#6398011yescharacteristic
327C22#6398211yescharacteristic
328C4—24no—
329C4—182no—
330C4—182no—
331C4—242no—
332C4—362no—
333C4#6395711yescharacteristic
334C4C2×#372411yescharacteristic
335C4#6398011yescharacteristic
336C4#6398211yescharacteristic
337C3—21no—
338C3#7022212yescomplemented
339C2#1059156011yescharacteristic
340C2#1059156211yescharacteristic
341C2#1059161212yes—
342C2#1059161512yes—
343C2#1059172011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1805
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
9. Q8×C3⋊Dic3C4semidirect
286. C32#1805semidirect
338. C3#70222semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#8352
#105912302
C2×#635722
#105891642
#702223