Finite Group Databasebeta

← #11785268

Subgroups — #11785268

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63641C211yesmaximal, characteristic
5#10592676C211yesmaximal, characteristic
6#10589417C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#70222—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12Q8×C3⋊Dic3—22no—
13Q8×C3⋊Dic3C414yescomplemented
14C2×C4⋊(C3⋊Dic3)—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C32×#103—22no—
21#63662—22no—
22#63658—21no—
23#63658—21no—
24#63641—22no—
25C2×Q8×Dic3—34no—
26C2×C3×#103D314yes—
27C2×#835—34no—
28C2×Dic3⋊C8—34no—
29#4977—34no—
30#4551—34no—
31#4529—34no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8C2×C412yes—
36C2×C32×Q8D412yes—
37C2×C32×Q8Q812yes—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—24no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C412yes—
55C4×C3⋊Dic3—24no—
56C4×C3⋊Dic3C2×C412yes—
57C4×C3⋊Dic3D412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61#1805—91noSylow
62C22×C3×Q8C2×D314yes—
63C22×C3×C8C2×D314yes—
64C2×C3×C4⋊C4C2×D314yes—
65Q8×Dic3—316no—
66Q8×Dic3—68no—
67C2×C4⋊Dic3—34no—
68C2×C4⋊Dic3—34no—
69C2×C4⋊Dic3—64no—
70C2×C4×Dic3—34no—
71C2×C4×Dic3—64no—
72C22×C3⋊C8—34no—
73C3×#103—28no—
74#835—68no—
75C3⋊#95—64no—
76C3⋊#95—64no—
77Dic3⋊C8—68no—
78C23×C32C2×D411yescharacteristic
79C32×Q8—22no—
80C32×Q8—22no—
81C32×Q8—22no—
82C32×Q8C4⋊C414yes—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×Q811yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3C22⋊C412yes—
106C2×C3⋊Dic3C22⋊C412yes—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109C2×C4×Q8—91no—
110C2×C4⋊C8—91no—
111C2×#103—91no—
112C2×#103C3⋊D311yescharacteristic
113#382—91no—
114#340—91no—
115#340—91no—
116C2×C3×Q8—24no—
117C2×C3×Q8—24no—
118C2×C3×Q8—24no—
119C2×C3×Q8Dic618yes—
120C2×C3×Q8C4×D318yes—
121C2×C3×Q8#6718yes—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4C22×D314yes—
125C22×Dic3—34no—
126C22×Dic3—34no—
127C22×Dic3—64no—
128C22×Dic3—64no—
129C2×C3×C8—24no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C3×C4⋊C4—24no—
133C3×C4⋊C4—24no—
134C4⋊Dic3—38no—
135C4⋊Dic3—616no—
136C4⋊Dic3—64no—
137C4⋊Dic3—64no—
138C4⋊Dic3—64no—
139C4×Dic3—38no—
140C4×Dic3—38no—
141C4×Dic3—616no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144C2×C3⋊C8—64no—
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#12111yescharacteristic
147C22×C32C22⋊Q811yescharacteristic
148C22×C32#13511yescharacteristic
149C22×C32#13511yescharacteristic
150C22×C32#13711yescharacteristic
151C22×C32#13711yescharacteristic
152C32×C4—24no—
153C32×C4—81no—
154C32×C4C2×C4⋊C411yescharacteristic
155C32×C4#11711yescharacteristic
156C32×C4#12111yescharacteristic
157C32×C4C22⋊Q811yescharacteristic
158C3⋊Dic3—22no—
159C3⋊Dic3—22no—
160C3⋊Dic3—42no—
161C3⋊Dic3—81no—
162C22×Q8C2×C3⋊D311yescharacteristic
163C22×C8—91no—
164C22×C8C2×C3⋊D311yescharacteristic
165C4×Q8—94no—
166C4×Q8—182no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4—91no—
169C2×C4⋊C4—181no—
170C2×C4⋊C4C2×C3⋊D311yescharacteristic
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—182no—
174#103—22no—
175#103—182no—
176#95—181no—
177#95—181no—
178C23×C3D3×D414yes—
179C3×Q8—28no—
180C3×Q8—28no—
181C3×Q8—28no—
182C3×Q8Dic3⋊C4116yes—
183C2×C3×C4—28no—
184C2×C3×C4—28no—
185C2×C3×C4—28no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—44no—
189C2×C3×C4C2×Dic614yes—
190C2×C3×C4C2×C4×D314yes—
191C2×C3×C4D3×D414yes—
192C2×C3×C4#23714yes—
193C2×C3×C4#23714yes—
194C2×C3×C4C2×#6714yes—
195C2×Dic3—38no—
196C2×Dic3—38no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—68no—
202C2×Dic3—124no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C3×C8—44no—
208C3⋊C8—124no—
209C2×C32#38011yescharacteristic
210C2×C32#41611yescharacteristic
211C2×C32#41911yescharacteristic
212C2×C32#46411yescharacteristic
213C2×C32#46411yescharacteristic
214C2×C32#47911yescharacteristic
215C2×C32#47911yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—21no—
219C2×Q8#63412yes—
220C2×Q8C4×C3⋊D312yes—
221C2×Q8#63812yes—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—181no—
227C22×C4—181no—
228C22×C4C22×C3⋊D311yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—181no—
233C2×C8—181no—
234C2×C8—181no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—92no—
238C4⋊C4—184no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C42—92no—
243C42—92no—
244C42—184no—
245C22×C3#87814yes—
246C22×C3D3×C22⋊C414yes—
247C22×C3#91514yes—
248C22×C3#91614yes—
249C22×C3#91814yes—
250C22×C3#91914yes—
251C22×C3#93914yes—
252C3×C4—216no—
253C3×C4—84no—
254C3×C4#87714yes—
255C3×C4#87814yes—
256C3×C4C2×Dic3⋊C414yes—
257C3×C4#93914yes—
258Dic3—68no—
259Dic3—68no—
260Dic3—128no—
261Dic3—244no—
262C32#180511yescharacteristic, complemented, Sylow
263C23D4×C3⋊D311yescharacteristic
264Q8—22no—
265Q8—22no—
266Q8—22no—
267Q8#375014yes—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—182no—
281C2×C4—361no—
282C2×C4—361no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4—361no—
286C2×C4C2×#63411yescharacteristic
287C2×C4C2×C4×C3⋊D311yescharacteristic
288C2×C4D4×C3⋊D311yescharacteristic
289C2×C4#383011yescharacteristic
290C2×C4#383011yescharacteristic
291C2×C4C2×#63811yescharacteristic
292C8—41no—
293C8—361no—
294C2×C3#479614yes—
295C2×C3#479914yes—
296C2×C3#480214yes—
297C2×C3#480414yes—
298C2×C3#494214yes—
299C2×C3#516614yes—
300C2×C3#518514yes—
301C22#6408711yescharacteristic
302C22C22⋊C4×C3⋊D311yescharacteristic
303C22#6412411yescharacteristic
304C22#6412511yescharacteristic
305C22#6412711yescharacteristic
306C22#6412811yescharacteristic
307C22#6414811yescharacteristic
308C4—24no—
309C4—81no—
310C4—182no—
311C4—182no—
312C4—362no—
313C4—721no—
314C4#6408611yescharacteristic
315C4#6408711yescharacteristic
316C4C2×#375011yescharacteristic
317C4#6414811yescharacteristic
318C3#7022214yescomplemented
319C2#1059249511yescharacteristic
320C2#1059249811yescharacteristic
321C2#1059250111yescharacteristic
322C2#1059250311yescharacteristic
323C2#1059264111yescharacteristic
324C2#1059286511yescharacteristic
325C2#1059288411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1805
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
13. Q8×C3⋊Dic3C4semidirect
262. C32#1805semidirect
318. 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×C32×#1032
C2×#636622
C2×#636412
#105926762
#105894172
#105893952
#702223