Finite Group Databasebeta

← #11802871

Subgroups — #11802871

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic, complemented
3C3×#4935C211yesmaximal, characteristic, complemented
4#10591325C212yesmaximal
5#10591274C212yesmaximal, complemented
6#10591266C214yesmaximal
7#10591263C214yesmaximal, complemented
8#74358—31nomaximal
9#74224—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2212yes—
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64081C418yescomplemented
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4⋊Dic3C2214yes—
19C2×#3722C2214yes—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24C2×#872—31no—
25C2×#872—31no—
26C2×#872—61no—
27C3×#384—31no—
28C3×#382—31no—
29#4990—34no—
30#4987—32no—
31#4987—32no—
32#4978—34no—
33Dic3×C4⋊C4—32no—
34Dic3×C4⋊C4—32no—
35#4936D311yescharacteristic, complemented
36#4935D311yescharacteristic, complemented
37#4670—34no—
38#4655—34no—
39C23×C3⋊D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3C2×C414yes—
47C22×C3×Dic3C2314yes—
48C22×C3×Dic3C2314yes—
49C32×C42C2×C414yes—
50#3752C2×C418yes—
51#3750C2×C418yes—
52C4×C3⋊Dic3C2×C414yes—
53C3×C4⋊Dic3—24no—
54C3×C4⋊Dic3—24no—
55C3×C4⋊Dic3—44no—
56#3722—44no—
57Dic32—44no—
58#2314—91noSylow
59C22×C4×D3—31no—
60C22×C4×D3—31no—
61C22×C4×D3—61no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—32no—
64C2×C3×C4⋊C4—34no—
65C2×C3×C42—21no—
66C2×C3×C42C2×D311yescharacteristic
67C2×C3×C42C2×D311yescharacteristic
68C2×(C2×D3)⋊C4—32no—
69C2×(C2×D3)⋊C4—32no—
70C2×(C2×D3)⋊C4—34no—
71C2×(C2×D3)⋊C4—34no—
72C2×(C2×D3)⋊C4—62no—
73C2×C4⋊Dic3C2×D312yes—
74C2×C4⋊Dic3C2×D312yes—
75C2×C4⋊Dic3C2×D314yes—
76C2×Dic3⋊C4—32no—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—62no—
79C2×C4×Dic3—31no—
80C2×C4×Dic3—31no—
81C2×C4×Dic3—34no—
82C2×C4×Dic3—34no—
83C2×C4×Dic3—61no—
84#872—38no—
85#872—38no—
86#872—68no—
87C3×#95—34no—
88C3⋊#95—34no—
89C3⋊#95—34no—
90C3⋊#95—34no—
91C3⋊#95—34no—
92C3⋊#95C2×D314yes—
93C23×C32C2411yescharacteristic
94C22×C3⋊D3—21no—
95C22×C3⋊D3—21no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3C22×C412yes—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4C22×C414yes—
102C2×C32×C4C22×C412yes—
103C2×C32×C4#4112yes—
104C2×C32×C4#4112yes—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C22×C414yes—
110C2×C3⋊Dic3C22×C412yes—
111C4×C3⋊D3—28no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×#117—91no—
119#388—94no—
120#387—94no—
121#384—31no—
122#382—31no—
123#380—92no—
124C4×C4⋊C4—92no—
125C23×D3—31no—
126C23×D3—31no—
127C23×D3—61no—
128C22×C3×C4—21no—
129C22×C3×C4—22no—
130C22×C3×C4—34no—
131C22×C3×C4—34no—
132C22×C3×C4C22×D312yes—
133C22×C3×C4C22×D312yes—
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C22×Dic3—31no—
137C22×Dic3—31no—
138C22×Dic3—32no—
139C22×Dic3—32no—
140C22×Dic3—61no—
141C22×Dic3—62no—
142C22×Dic3C22×D314yes—
143C22×Dic3C22×D314yes—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×C4×D3—64no—
147C2×C4×D3—64no—
148C2×C4×D3—64no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C3×C4⋊C4—64no—
154C3×C4⋊C4—64no—
155C3×C4⋊C4—124no—
156C3×C42—24no—
157C3×C42C4×D314yes—
158C3×C42C4×D314yes—
159(C2×D3)⋊C4—38no—
160(C2×D3)⋊C4—38no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—124no—
163(C2×D3)⋊C4—124no—
164C4⋊Dic3—24no—
165C4⋊Dic3—24no—
166C4⋊Dic3—44no—
167Dic3⋊C4—38no—
168Dic3⋊C4—38no—
169Dic3⋊C4—68no—
170C4×Dic3—34no—
171C4×Dic3—34no—
172C4×Dic3—64no—
173C4×Dic3—124no—
174C4×Dic3—124no—
175C22×C32C23×C411yescharacteristic
176C22×C32C2×#4111yescharacteristic
177C22×C32C2×#4111yescharacteristic
178C22×C32H(5,𝔽2)12yes—
179C22×C322−1+412yes—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—24no—
182C2×C3⋊D3—41no—
183C2×C3⋊D3—41no—
184C2×C3⋊D3—42no—
185C32×C4—24no—
186C32×C4#11714yes—
187C3⋊Dic3—22no—
188C3⋊Dic3—24no—
189C3×Dic3—44no—
190C3×Dic3—44no—
191C23×C4—91no—
192#117—98no—
193C2×C4⋊C4—32no—
194C2×C4⋊C4—32no—
195C2×C4⋊C4—34no—
196C2×C4⋊C4—92no—
197C2×C22⋊C4—92no—
198C2×C22⋊C4—94no—
199C2×C42—91no—
200C2×C42—94no—
201C2×C42D3211yescharacteristic
202#95—34no—
203#95—94no—
204#95—94no—
205C23×C3—21no—
206C23×C3C23×D311yescharacteristic
207C23×C3C23×D311yescharacteristic
208C22×D3—32no—
209C22×D3—32no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—61no—
214C22×D3—61no—
215C22×D3—62no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—62no—
221C22×D3—122no—
222C22×D3—122no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—24no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—64no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4—64no—
239C2×C3×C4C2×C4×D314yes—
240C2×C3×C4C2×C4×D314yes—
241C2×C3×C4C2×C4×D312yes—
242C2×C3×C4C2×C4×D312yes—
243C2×C3×C4#23712yes—
244C2×C3×C4#23712yes—
245C2×C3×C4#23912yes—
246C2×C3×C4#23912yes—
247C2×Dic3—24no—
248C2×Dic3—24no—
249C2×Dic3—24no—
250C2×Dic3—24no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3—34no—
254C2×Dic3—34no—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—62no—
258C2×Dic3—64no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—62no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—122no—
270C2×Dic3—122no—
271C4×D3—616no—
272C4×D3—68no—
273C4×D3—68no—
274C2×C32C2×#11711yescharacteristic
275C2×C32#52012yes—
276C2×C32#54011yescharacteristic
277C2×C32#54111yescharacteristic
278C2×C32#54212yes—
279C3⋊D3—42no—
280C24—91no—
281C22×C4—34no—
282C22×C4—34no—
283C22×C4—91no—
284C22×C4—92no—
285C22×C4—94no—
286C22×C4—182no—
287C22×C4—182no—
288C22×C4C2×D3212yes—
289C22×C4C2×D3211yescharacteristic
290C4⋊C4—64no—
291C4⋊C4—64no—
292C4⋊C4—98no—
293C4⋊C4—124no—
294C22⋊C4—98no—
295C22⋊C4—364no—
296C42—94no—
297C42—364no—
298C42#62414yes—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—21no—
304C22×C3C22×C4×D311yescharacteristic
305C22×C3C22×C4×D311yescharacteristic
306C22×C3C2×#23711yescharacteristic
307C22×C3C2×#23711yescharacteristic
308C22×C3#100412yes—
309C22×C3C2×#23911yescharacteristic
310C22×C3C2×#23911yescharacteristic
311C22×C3#100712yes—
312C22×C3#100912yes—
313C22×C3#101012yes—
314C2×D3—64no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—64no—
318C2×D3—64no—
319C2×D3—124no—
320C2×D3—122no—
321C2×D3—122no—
322C2×D3—124no—
323C2×D3—122no—
324C2×D3—121no—
325C2×D3—121no—
326C2×D3—121no—
327C2×D3—121no—
328C2×D3—122no—
329C3×C4—24no—
330C3×C4—24no—
331C3×C4—24no—
332C3×C4—44no—
333C3×C4—124no—
334C3×C4—124no—
335C3×C4#89214yes—
336C3×C4#89214yes—
337Dic3—44no—
338Dic3—44no—
339Dic3—64no—
340Dic3—62no—
341Dic3—62no—
342Dic3—64no—
343Dic3—64no—
344Dic3—124no—
345C32#231411yescharacteristic, complemented, Sylow
346C23—92no—
347C23—181no—
348C23—181no—
349C23—182no—
350C23—182no—
351C23C22×D3211yescharacteristic
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—64no—
355C2×C4—64no—
356C2×C4—64no—
357C2×C4—64no—
358C2×C4—64no—
359C2×C4—64no—
360C2×C4—94no—
361C2×C4—92no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—188no—
367C2×C4#379612yes—
368C2×C4#379612yes—
369C2×C4C2×#62414yes—
370C2×C4C2×#62412yes—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3C2×#89211yescharacteristic
377C2×C3C2×#89211yescharacteristic
378C2×C3#550412yes—
379C2×C3#552312yes—
380C2×C3#568212yes—
381C2×C3#569711yescharacteristic
382C2×C3#569811yescharacteristic
383C2×C3#571911yescharacteristic
384C2×C3#573111yescharacteristic
385C2×C3#573312yes—
386D3—124no—
387D3—122no—
388D3—122no—
389C22—182no—
390C22—184no—
391C22—361no—
392C22—361no—
393C22—362no—
394C22C2×#379611yescharacteristic
395C22C2×#379611yescharacteristic
396C22#6429712yes—
397C22#6430712yes—
398C22C22×#62411yescharacteristic
399C4—24no—
400C4—124no—
401C4—124no—
402C4—182no—
403C4—184no—
404C4#6384914yes—
405C3—21no—
406C3#7422411yescharacteristic, complemented
407C3#7435811yescharacteristic, complemented
408C2—362no—
409C2#1059386711yescharacteristic
410C2#1059395011yescharacteristic
411C2#1059395512yes—
412C2C2×#6384911yescharacteristic
413C2#1059499012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2314
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4936C2semidirect
3. C3×#4935C2semidirect
5. #10591274C2semidirect
7. #10591263C2semidirect
15. #64081C4semidirect
35. #4936D3semidirect
36. #4935D3semidirect
345. C32#2314semidirect
406. C3#74224semidirect
407. C3#74358semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#49362
C3×#49352
#105913252
#105912742
#105912662
#105912632
#743583
#742243