Finite Group Databasebeta

← #11795081

Subgroups — #11795081

Order 1152.

545 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592627C211yesmaximal, characteristic
2C3×#4935C211yesmaximal, characteristic
3C2×#63575C212yesmaximal
4C3×#4524C211yesmaximal, characteristic
5#10589164C212yesmaximal
6#69569—31nomaximal
7#68639—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×#3750—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16#63658—21no—
17#63575—24no—
18C3×#384—31no—
19C2×#818—32no—
20C2×#807—32no—
21#4935D311yescharacteristic
22#4928—31no—
23#4928—31no—
24#4928—61no—
25C3×#336—31no—
26#4551—32no—
27#4529—32no—
28#4524D311yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C22×C3×Dic3—22no—
35C32×C42—22no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)D412yes—
39#3750—42no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3—42no—
43C3×C4⋊Dic3—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—32no—
50C2×C3×C4⋊C4—61no—
51C2×C3×C4⋊C4—61no—
52C2×C3×C42—21no—
53C2×C3×C42C2×D311yescharacteristic
54C2×C3×C42C2×D311yescharacteristic
55C2×C4⋊Dic3—21no—
56C2×C4⋊Dic3—21no—
57C2×C4⋊Dic3—31no—
58C2×C4⋊Dic3—31no—
59C2×C4⋊Dic3—31no—
60C2×C4⋊Dic3—31no—
61C2×C4⋊Dic3—61no—
62C2×C4⋊Dic3—61no—
63C2×C4⋊Dic3C2×D312yes—
64C2×Dic3⋊C4—62no—
65C2×Dic3⋊C4—61no—
66C2×Dic3⋊C4—61no—
67C22×C3⋊C8C2×D312yes—
68C3⋊#95—62no—
69C3⋊#95—61no—
70C3⋊#95—61no—
71#818—64no—
72#807—64no—
73C23×C32C2×D411yescharacteristic
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4D812yes—
79C2×C32×C4Q1612yes—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×Q812yes—
82C2×C32×C4#4112yes—
83C2×C32×C4#4111yescharacteristic
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C3×C3⋊C8—24no—
94C2×#107—92no—
95#389—91no—
96#384—31no—
97#340—92no—
98#336—31no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—62no—
103C22×C3×C4D1211yescharacteristic
104C22×C3×C4D1211yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C22×C3×C4#6711yescharacteristic
107C22×C3×C4C22×D311yescharacteristic
108C22×C3×C4C22×D311yescharacteristic
109C22×Dic3—22no—
110C22×Dic3—62no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—62no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C2×C3×C8—34no—
117C2×C3×C8—62no—
118C2×C3×C8—62no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—62no—
121C3×C4⋊C4—122no—
122C3×C4⋊C4—122no—
123C3×C42—22no—
124C3×C42—22no—
125C3×C42—42no—
126C4⋊Dic3—22no—
127C4⋊Dic3—22no—
128C4⋊Dic3—32no—
129C4⋊Dic3—32no—
130C4⋊Dic3—42no—
131C4⋊Dic3—42no—
132C4⋊Dic3—62no—
133C4⋊Dic3—62no—
134C4⋊Dic3—61no—
135C4⋊Dic3—61no—
136C4⋊Dic3—62no—
137C4⋊Dic3—62no—
138C4⋊Dic3—122no—
139Dic3⋊C4—124no—
140Dic3⋊C4—122no—
141Dic3⋊C4—122no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8Dic614yes—
145C22×C32#12111yescharacteristic
146C22×C32#12311yescharacteristic
147C22×C32C4⋊Q811yescharacteristic
148C22×C32C2×D811yescharacteristic
149C22×C32C2×Q1611yescharacteristic
150C22×C32AGL(1,ℤ/8)11yescharacteristic
151C22×C32#13711yescharacteristic
152C32×C4—22no—
153C32×C4—22no—
154C32×C4C22⋊Q812yes—
155C32×C4#12512yes—
156C3⋊Dic3—42no—
157C3⋊Dic3—81no—
158C3×Dic3—82no—
159C22×C8—32no—
160C2×C4⋊C4—32no—
161C2×C4⋊C4—61no—
162C2×C4⋊C4—61no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4—181no—
166C2×C42D3211yescharacteristic
167#107—184no—
168#95—181no—
169C23×C3—21no—
170C23×C3C2×D1211yescharacteristic
171C23×C3C2×#6711yescharacteristic
172C2×C3×C4—21no—
173C2×C3×C4—21no—
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—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—22no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—122no—
191C2×C3×C4—122no—
192C2×C3×C4—122no—
193C2×C3×C4D2412yes—
194C2×C3×C4Dic1212yes—
195C2×C3×C4#21312yes—
196C2×C3×C4#21612yes—
197C2×C3×C4C2×Dic612yes—
198C2×C3×C4#23512yes—
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4#23711yescharacteristic
202C2×C3×C4#23712yes—
203C2×C3×C4D3×Q812yes—
204C2×C3×C4#23911yescharacteristic
205C2×Dic3—42no—
206C2×Dic3—42no—
207C2×Dic3—42no—
208C2×Dic3—64no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C2×Dic3—121no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226C3×C8—64no—
227C3⋊C8—24no—
228C2×C32#39811yescharacteristic
229C2×C32#45911yescharacteristic
230C2×C32#46211yescharacteristic
231C2×C32#48011yescharacteristic
232C2×C32#48411yescharacteristic
233C2×C32#50011yescharacteristic
234C2×C32#50111yescharacteristic
235C22×C4—62no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4#62611yescharacteristic
239C22×C4#62611yescharacteristic
240C22×C4C2×D3211yescharacteristic
241C2×C8—34no—
242C2×C8—62no—
243C2×C8—62no—
244C4⋊C4—62no—
245C4⋊C4—62no—
246C4⋊C4—92no—
247C4⋊C4—122no—
248C4⋊C4—122no—
249C4⋊C4—181no—
250C4⋊C4—182no—
251C4⋊C4—362no—
252C42—22no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3#86911yescharacteristic
261C22×C3#88611yescharacteristic
262C22×C3#89511yescharacteristic
263C22×C3C2×D2411yescharacteristic
264C22×C3C2×Dic1211yescharacteristic
265C22×C3#90811yescharacteristic
266C22×C3#90911yescharacteristic
267C22×C3#92911yescharacteristic
268C22×C3C2×#21311yescharacteristic
269C22×C3#93211yescharacteristic
270C22×C3#93811yescharacteristic
271C22×C3#94211yescharacteristic
272C22×C3C2×#21611yescharacteristic
273C22×C3#94411yescharacteristic
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—42no—
281C3×C4—42no—
282C3×C4—242no—
283C3×C4#87812yes—
284C3×C4#88912yes—
285C3×C4#89012yes—
286C3×C4#89612yes—
287Dic3—82no—
288Dic3—124no—
289Dic3—122no—
290Dic3—122no—
291Dic3—242no—
292Dic3—241no—
293Dic3—241no—
294C32#208311yescharacteristic, complemented, Sylow
295C23C2×#62611yescharacteristic
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—122no—
301C2×C4—122no—
302C2×C4—122no—
303C2×C4—182no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4—361no—
309C2×C4#371412yes—
310C2×C4#371912yes—
311C2×C4D3×Dic612yes—
312C2×C4#379611yescharacteristic
313C2×C4#380211yescharacteristic
314C2×C4#380412yes—
315C8—64no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3#466111yescharacteristic
324C2×C3#468211yescharacteristic
325C2×C3#470211yescharacteristic
326C2×C3#472211yescharacteristic
327C2×C3#473611yescharacteristic
328C2×C3#484311yescharacteristic
329C2×C3#484911yescharacteristic
330C2×C3#496711yescharacteristic
331C2×C3#497011yescharacteristic
332C2×C3#498311yescharacteristic
333C2×C3#507211yescharacteristic
334C2×C3#507811yescharacteristic
335C2×C3#508111yescharacteristic
336C2×C3#509011yescharacteristic
337C22C2×#371411yescharacteristic
338C22#6383011yescharacteristic
339C22#6383311yescharacteristic
340C22C2×#371911yescharacteristic
341C22#6386611yescharacteristic
342C22#6391611yescharacteristic
343C22#6396611yescharacteristic
344C4—22no—
345C4—22no—
346C4—242no—
347C4—362no—
348C4—721no—
349C4#6384612yes—
350C4#6389912yes—
351C3—21no—
352C3#6863911yescharacteristic, complemented
353C3#6956911yescharacteristic, complemented
354C2#1059030511yescharacteristic
355C2#1059031111yescharacteristic
356C2#1059035511yescharacteristic
357C2#1059038811yescharacteristic
358C2#1059113311yescharacteristic
359C2#1059113511yescharacteristic
360C2#1059135811yescharacteristic
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
294. C32#2083semidirect
352. C3#68639semidirect
353. C3#69569semidirect

Maximal subgroups

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

subgroupindex
#105926272
C3×#49352
C2×#635752
C3×#45242
#105891642
#695693
#686393