Finite Group Databasebeta

← #11795082

Subgroups — #11795082

Order 1152.

553 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592634C211yesmaximal, characteristic
2C3×#4928C211yesmaximal, characteristic
3C2×#63575C212yesmaximal
4C3×#4524C211yesmaximal, characteristic
5#10589164C212yesmaximal
6#69607—31nomaximal
7#68639—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)—21no—
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C22×C3×C3⋊C8C2212yes—
16C3×C3⋊#95—21no—
17#63575—24no—
18C3×#389—31no—
19C2×#818—32no—
20C2×#807—32no—
21#4935—31no—
22#4935—31no—
23#4935—61no—
24#4928D311yescharacteristic
25C3×#336—31no—
26#4551—32no—
27#4529—32no—
28#4524D311yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—22no—
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35C32×C42—22no—
36C4⋊(C3⋊Dic3)—22no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)—42no—
39C4⋊(C3⋊Dic3)—42no—
40C3×C4⋊Dic3—21no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3D412yes—
43C3×Dic3⋊C4—42no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8Q814yes—
47#2083—91noSylow
48C22×C3×C8—32no—
49C2×C3×C4⋊C4—31no—
50C2×C3×C4⋊C4—31no—
51C2×C3×C4⋊C4—61no—
52C2×C3×C42—21no—
53C2×C3×C42C2×D311yescharacteristic
54C2×C3×C42C2×D311yescharacteristic
55C2×C4⋊Dic3—32no—
56C2×C4⋊Dic3—32no—
57C2×C4⋊Dic3—62no—
58C2×C4⋊Dic3—62no—
59C2×C4⋊Dic3—62no—
60C2×C4⋊Dic3—61no—
61C2×C4⋊Dic3—61no—
62C2×C4⋊Dic3—61no—
63C2×C4⋊Dic3—61no—
64C2×C4⋊Dic3C2×D311yescharacteristic
65C2×C4⋊Dic3C2×D311yescharacteristic
66C2×Dic3⋊C4—21no—
67C22×C3⋊C8C2×D312yes—
68C3×#95—61no—
69C3⋊#95—21no—
70#818—64no—
71#807—64no—
72C23×C32C2×D411yescharacteristic
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4D812yes—
78C2×C32×C4Q1612yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×Q812yes—
81C2×C32×C4#4111yescharacteristic
82C2×C32×C4#4112yes—
83C2×C3⋊Dic3—42no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—42no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—41no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C3×C3⋊C8—24no—
93C2×#107—92no—
94#389—31no—
95#384—91no—
96#340—92no—
97#336—31no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4—61no—
102C22×C3×C4—61no—
103C22×C3×C4D1211yescharacteristic
104C22×C3×C4D1211yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C22×C3×C4#6711yescharacteristic
107C22×C3×C4C22×D311yescharacteristic
108C22×C3×C4C22×D311yescharacteristic
109C22×Dic3—21no—
110C22×Dic3—21no—
111C22×Dic3—64no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C2×C3×C8—34no—
115C2×C3×C8—62no—
116C2×C3×C8—62no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—61no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—122no—
121C3×C42—24no—
122C3×C42—22no—
123C3×C42—22no—
124C4⋊Dic3—21no—
125C4⋊Dic3—22no—
126C4⋊Dic3—62no—
127C4⋊Dic3—62no—
128C4⋊Dic3—62no—
129C4⋊Dic3—62no—
130C4⋊Dic3—122no—
131C4⋊Dic3—122no—
132C4⋊Dic3—124no—
133C4⋊Dic3—122no—
134C4⋊Dic3—122no—
135C4⋊Dic3—124no—
136C4⋊Dic3—122no—
137C4⋊Dic3—122no—
138C4⋊Dic3D1212yes—
139Dic3⋊C4—42no—
140C2×C3⋊C8—22no—
141C2×C3⋊C8—22no—
142C2×C3⋊C8Dic614yes—
143C22×C32#12111yescharacteristic
144C22×C32#12311yescharacteristic
145C22×C32C4⋊Q811yescharacteristic
146C22×C32C2×D811yescharacteristic
147C22×C32C2×Q1611yescharacteristic
148C22×C32AGL(1,ℤ/8)11yescharacteristic
149C22×C32#13711yescharacteristic
150C32×C4—22no—
151C32×C4—22no—
152C32×C4C22⋊Q812yes—
153C32×C4#12512yes—
154C3⋊Dic3—82no—
155C3×Dic3—42no—
156C3×Dic3—81no—
157C22×C8—32no—
158C2×C4⋊C4—31no—
159C2×C4⋊C4—31no—
160C2×C4⋊C4—61no—
161C2×C4⋊C4—92no—
162C2×C4⋊C4—181no—
163C2×C4⋊C4—181no—
164C2×C42D3211yescharacteristic
165#107—184no—
166#95—61no—
167C23×C3—21no—
168C23×C3C2×D1211yescharacteristic
169C23×C3C2×#6711yescharacteristic
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—22no—
188C2×C3×C4—62no—
189C2×C3×C4—121no—
190C2×C3×C4—121no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4—121no—
194C2×C3×C4D2412yes—
195C2×C3×C4Dic1212yes—
196C2×C3×C4#21312yes—
197C2×C3×C4#21612yes—
198C2×C3×C4C2×Dic612yes—
199C2×C3×C4C2×D1211yescharacteristic
200C2×C3×C4#23511yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4#23712yes—
203C2×C3×C4#23712yes—
204C2×C3×C4D3×Q812yes—
205C2×C3×C4#23911yescharacteristic
206C2×Dic3—22no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209C2×Dic3—41no—
210C2×Dic3—41no—
211C2×Dic3—41no—
212C2×Dic3—124no—
213C2×Dic3—124no—
214C2×Dic3—124no—
215C2×Dic3—122no—
216C2×Dic3—122no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C2×Dic3—122no—
221C3×C8—64no—
222C3⋊C8—24no—
223C2×C32#39811yescharacteristic
224C2×C32#45911yescharacteristic
225C2×C32#46211yescharacteristic
226C2×C32#48011yescharacteristic
227C2×C32#48411yescharacteristic
228C2×C32#50011yescharacteristic
229C2×C32#50111yescharacteristic
230C22×C4—61no—
231C22×C4—61no—
232C22×C4—182no—
233C22×C4#62611yescharacteristic
234C22×C4#62611yescharacteristic
235C22×C4C2×D3211yescharacteristic
236C2×C8—34no—
237C2×C8—62no—
238C2×C8—62no—
239C4⋊C4—32no—
240C4⋊C4—61no—
241C4⋊C4—62no—
242C4⋊C4—122no—
243C4⋊C4—182no—
244C4⋊C4—182no—
245C4⋊C4—362no—
246C4⋊C4—362no—
247C42—22no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3#86911yescharacteristic
256C22×C3#88611yescharacteristic
257C22×C3#89511yescharacteristic
258C22×C3C2×D2411yescharacteristic
259C22×C3C2×Dic1211yescharacteristic
260C22×C3#90811yescharacteristic
261C22×C3#90911yescharacteristic
262C22×C3#93011yescharacteristic
263C22×C3C2×#21311yescharacteristic
264C22×C3#93511yescharacteristic
265C22×C3C2×#21611yescharacteristic
266C22×C3#94411yescharacteristic
267C22×C3#94911yescharacteristic
268C22×C3#95111yescharacteristic
269C3×C4—24no—
270C3×C4—24no—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—122no—
278C3×C4—241no—
279C3×C4#87812yes—
280C3×C4#88912yes—
281C3×C4#89012yes—
282C3×C4#89712yes—
283Dic3—42no—
284Dic3—81no—
285Dic3—244no—
286Dic3—242no—
287Dic3—242no—
288C32#208311yescharacteristic, complemented, Sylow
289C23C2×#62611yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—62no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—121no—
300C2×C4—362no—
301C2×C4—362no—
302C2×C4—362no—
303C2×C4#371412yes—
304C2×C4#371912yes—
305C2×C4D3×Dic612yes—
306C2×C4#379911yescharacteristic
307C2×C4D3×D1211yescharacteristic
308C2×C4#380512yes—
309C8—64no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3#466111yescharacteristic
318C2×C3#468211yescharacteristic
319C2×C3#470211yescharacteristic
320C2×C3#472211yescharacteristic
321C2×C3#473611yescharacteristic
322C2×C3#484311yescharacteristic
323C2×C3#484911yescharacteristic
324C2×C3#498111yescharacteristic
325C2×C3#501511yescharacteristic
326C2×C3#503111yescharacteristic
327C2×C3#503311yescharacteristic
328C2×C3#504411yescharacteristic
329C2×C3#506411yescharacteristic
330C2×C3#507811yescharacteristic
331C22C2×#371411yescharacteristic
332C22#6382511yescharacteristic
333C22#6383111yescharacteristic
334C22C2×#371911yescharacteristic
335C22#6386611yescharacteristic
336C22#6390911yescharacteristic
337C22#6396211yescharacteristic
338C4—22no—
339C4—22no—
340C4—122no—
341C4—241no—
342C4—722no—
343C4#6384512yes—
344C4#6389312yes—
345C3—21no—
346C3#6863911yescharacteristic, complemented
347C3#6960711yescharacteristic, complemented
348C2#1059030611yescharacteristic
349C2#1059031111yescharacteristic
350C2#1059034911yescharacteristic
351C2#1059038511yescharacteristic
352C2#1059109411yescharacteristic
353C2#1059110311yescharacteristic
354C2#1059135311yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32#2083
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
288. C32#2083semidirect
346. C3#68639semidirect
347. C3#69607semidirect

Maximal subgroups

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

subgroupindex
#105926342
C3×#49282
C2×#635752
C3×#45242
#105891642
#696073
#686393