Finite Group Databasebeta

← #11803211

Subgroups — #11803211

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic
3C3×#4932C211yesmaximal, characteristic
4#10591360C212yesmaximal
5#10591229C212yesmaximal
6#10591213C212yesmaximal
7#10591212C212yesmaximal
8#10591197C214yesmaximal
9#73625—31nomaximal
10#73386—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C4×#634C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2214yes—
21C3×C3⋊#95C2211yescharacteristic
22C3×C3⋊#95C2212yes—
23C3×C3⋊#95C2211yescharacteristic
24C3×C3⋊#95C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C4×Dic6—31no—
29C2×C4×Dic6—31no—
30C2×C4×Dic6—61no—
31C3×C4×C4⋊C4—31no—
32C3×#376—31no—
33#4973—32no—
34#4972—32no—
35C4×C4⋊Dic3D311yescharacteristic
36#4933—34no—
37#4932D311yescharacteristic
38#4929—32no—
39#4928—32no—
40#4652—34no—
41#4651—32no—
42#4651—32no—
43#4650—32no—
44#4650—32no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C2×#634—24no—
51C2×#634C2×C414yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2312yes—
55C32×C42C2×C414yes—
56C4⋊(C3⋊Dic3)C2×C414yes—
57#3750C2×C418yes—
58C4×C3⋊Dic3C2×C418yes—
59C3×C4⋊Dic3—24no—
60C3×C4×Dic3—24no—
61C3×C4×Dic3—42no—
62#3724—44no—
63#2320—91noSylow
64C22×Dic6—31no—
65C22×Dic6—31no—
66C22×Dic6—61no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C42—21no—
69C2×C3×C42—32no—
70C2×C3×C42—32no—
71C2×C3×C42C2×D311yescharacteristic
72C2×C3×C42C2×D311yescharacteristic
73C2×C4⋊Dic3—31no—
74C2×C4⋊Dic3—31no—
75C2×C4⋊Dic3—61no—
76C2×C4⋊Dic3C2×D312yes—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4—34no—
81C2×Dic3⋊C4—62no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—62no—
85C2×C4×Dic3C2×D312yes—
86C2×C4×Dic3C2×D312yes—
87C4×Dic6—38no—
88C4×Dic6—38no—
89C4×Dic6—68no—
90C3×#95—31no—
91C3×#95—32no—
92C3×#95—31no—
93C3×#95—32no—
94C3⋊#95—34no—
95C3⋊#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95—34no—
99C3⋊#95—34no—
100C3⋊#95C2×D311yescharacteristic
101C3⋊#95C2×D312yes—
102C3⋊#95C2×D311yescharacteristic
103C3⋊#95C2×D312yes—
104C23×C32C2411yescharacteristic
105C2×C32×C4—22no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C412yes—
111C2×C32×C4#4114yes—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3C22×C414yes—
116C2×C3⋊Dic3C22×C414yes—
117#634—28no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—22no—
127C2×C4×Q8—91no—
128#391—92no—
129#389—92no—
130#387—94no—
131#383—92no—
132#382—92no—
133C4×C4⋊C4—31no—
134#376—31no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—32no—
139C22×C3×C4—34no—
140C22×C3×C4—32no—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—32no—
150C22×Dic3—32no—
151C22×Dic3—62no—
152C22×Dic3—62no—
153C22×Dic3C22×D312yes—
154C22×Dic3C22×D314yes—
155C22×Dic3C22×D312yes—
156C2×Dic6—34no—
157C2×Dic6—34no—
158C2×Dic6—64no—
159C2×Dic6—68no—
160C2×Dic6—64no—
161C2×Dic6—64no—
162C3×C4⋊C4—64no—
163C3×C42—24no—
164C3×C42—64no—
165C3×C42—122no—
166C3×C42C4×D314yes—
167C3×C42C4×D314yes—
168C4⋊Dic3—24no—
169C4⋊Dic3—34no—
170C4⋊Dic3—34no—
171C4⋊Dic3—64no—
172Dic3⋊C4—38no—
173Dic3⋊C4—38no—
174Dic3⋊C4—68no—
175Dic3⋊C4—124no—
176Dic3⋊C4—124no—
177C4×Dic3—24no—
178C4×Dic3—38no—
179C4×Dic3—38no—
180C4×Dic3—42no—
181C4×Dic3—68no—
182C22×C32C23×C411yescharacteristic
183C22×C32C2×#4112yes—
184C22×C32H(5,𝔽2)11yescharacteristic
185C22×C322−1+411yescharacteristic
186C22×C322−1+412yes—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4#11714yes—
190C3⋊Dic3—24no—
191C3⋊Dic3—24no—
192C3×Dic3—42no—
193C3×Dic3—42no—
194C3×Dic3—44no—
195C22×Q8—91no—
196C4×Q8—98no—
197C2×C4⋊C4—32no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—94no—
201C2×C42—32no—
202C2×C42—32no—
203C2×C42—92no—
204C2×C42D3211yescharacteristic
205#95—31no—
206#95—31no—
207#95—32no—
208#95—32no—
209#95—94no—
210#95—94no—
211#95—94no—
212C23×C3—21no—
213C23×C3C23×D311yescharacteristic
214C23×C3C23×D311yescharacteristic
215C2×C3×C4—24no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—62no—
229C2×C3×C4—62no—
230C2×C3×C4—64no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4C2×C4×D312yes—
238C2×C3×C4C2×C4×D312yes—
239C2×C3×C4C2×C4×D312yes—
240C2×C3×C4C2×C4×D312yes—
241C2×C3×C4C2×C4×D312yes—
242C2×C3×C4C2×C4×D312yes—
243C2×C3×C4#23514yes—
244C2×C3×C4#23514yes—
245C2×Dic3—22no—
246C2×Dic3—22no—
247C2×Dic3—24no—
248C2×Dic3—24no—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—24no—
254C2×Dic3—34no—
255C2×Dic3—34no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—68no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269Dic6—616no—
270Dic6—68no—
271Dic6—68no—
272C2×C32C2×#11711yescharacteristic
273C2×C32#51911yescharacteristic
274C2×C32#52011yescharacteristic
275C2×C32#54112yes—
276C2×C32#54212yes—
277C2×Q8—94no—
278C2×Q8—184no—
279C22×C4—32no—
280C22×C4—32no—
281C22×C4—34no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4C2×D3211yescharacteristic
285C22×C4C2×D3211yescharacteristic
286C22×C4C2×D3211yescharacteristic
287C4⋊C4—64no—
288C4⋊C4—98no—
289C4⋊C4—94no—
290C4⋊C4—364no—
291C42—64no—
292C42—98no—
293C42—122no—
294C42#62414yes—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3C22×C4×D311yescharacteristic
301C22×C3C22×C4×D311yescharacteristic
302C22×C3C2×#23512yes—
303C22×C3C2×#23512yes—
304C22×C3#100411yescharacteristic
305C22×C3#100711yescharacteristic
306C22×C3#100911yescharacteristic
307C22×C3#101011yescharacteristic
308C22×C3#101012yes—
309C22×C3#101012yes—
310C3×C4—24no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—24no—
316C3×C4—42no—
317C3×C4—124no—
318C3×C4—122no—
319C3×C4—122no—
320C3×C4#87214yes—
321C3×C4#87214yes—
322Dic3—42no—
323Dic3—42no—
324Dic3—44no—
325Dic3—68no—
326Dic3—64no—
327Dic3—64no—
328Dic3—64no—
329Dic3—64no—
330Dic3—124no—
331C32#232011yescharacteristic, complemented, Sylow
332C23C22×D3211yescharacteristic
333Q8—188no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—64no—
341C2×C4—62no—
342C2×C4—62no—
343C2×C4—64no—
344C2×C4—64no—
345C2×C4—62no—
346C2×C4—94no—
347C2×C4—94no—
348C2×C4—182no—
349C2×C4—184no—
350C2×C4—182no—
351C2×C4#379814yes—
352C2×C4C2×#62412yes—
353C2×C4C2×#62412yes—
354C2×C4C2×#62412yes—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—22no—
358C2×C3—21no—
359C2×C3—22no—
360C2×C3C2×#87211yescharacteristic
361C2×C3C2×#87211yescharacteristic
362C2×C3#550411yescharacteristic
363C2×C3#551611yescharacteristic
364C2×C3#551611yescharacteristic
365C2×C3#551812yes—
366C2×C3#552311yescharacteristic
367C2×C3#553412yes—
368C2×C3#556112yes—
369C2×C3#558312yes—
370C22#6429711yescharacteristic
371C22#6429812yes—
372C22C2×#379812yes—
373C22#6430711yescharacteristic
374C22C22×#62411yescharacteristic
375C4—22no—
376C4—22no—
377C4—122no—
378C4—122no—
379C4—124no—
380C4—184no—
381C4—184no—
382C4#6387414yes—
383C3—21no—
384C3#7338611yescharacteristic, complemented
385C3#7362511yescharacteristic, complemented
386C2#1059388012yes—
387C2#1059398312yes—
388C2#1059482811yescharacteristic
389C2C2×#6387411yescharacteristic
390C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2320
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. C4×#634C4semidirect
331. C32#2320semidirect
384. C3#73386semidirect
385. C3#73625semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×C4×C4⋊Dic32
C3×#49322
#105913602
#105912292
#105912132
#105912122
#105911972
#736253
#733863