Finite Group Databasebeta

← #11805938

Subgroups — #11805938

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C3×#5229C212yesmaximal
3#10591360C212yesmaximal
4#10591359C211yesmaximal, characteristic
5C4×#3724C211yesmaximal, characteristic
6#10591271C214yesmaximal
7Dic3×C4⋊Dic3C212yesmaximal
8#10591257C212yesmaximal
9#76489—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11Q8×C3⋊Dic3C418yescomplemented
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4×C3⋊Dic3C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2212yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2212yes—
21C2×#3724C2211yescharacteristic
22C2×Dic32C2214yes—
23C3×C3⋊#95C2214yes—
24C3×C3⋊#95C2214yes—
25#63579C2214yes—
26#63579C2212yes—
27C2×Q8×Dic3—32no—
28C2×Q8×Dic3—61no—
29C3×#391—32no—
30#5229D312yes—
31#4975—32no—
32Dic3×C4⋊C4—32no—
33C4×C4⋊Dic3—32no—
34C4×Dic3⋊C4—32no—
35#4654—34no—
36#4653—34no—
37#4650—34no—
38#4649—34no—
39C2×C32×Q8—22no—
40C2×C32×Q8—22no—
41C2×C32×Q8C2×C414yes—
42C22×C32×C4C2312yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3×Dic3C2312yes—
48C22×C3×Dic3C2314yes—
49C22×C3×Dic3C2312yes—
50C4⋊(C3⋊Dic3)C2×C418yes—
51C4⋊(C3⋊Dic3)C2×C414yes—
52C4×C3⋊Dic3C2×C418yes—
53C4×C3⋊Dic3C2×C414yes—
54C3×C4⋊Dic3—24no—
55C3×C4×Dic3—24no—
56#3724—24no—
57#3724—22no—
58#3724—42no—
59#3724Q814yescomplemented
60Dic32—44no—
61#2355—91noSylow
62C22×C3×Q8—21no—
63C22×C3×Q8C2×D312yes—
64C2×C3×C4⋊C4—32no—
65C2×C3×C42—32no—
66Q8×Dic3—316no—
67Q8×Dic3—68no—
68C2×C4⋊Dic3—34no—
69C2×C4⋊Dic3—32no—
70C2×C4⋊Dic3—61no—
71C2×C4⋊Dic3—62no—
72C2×C4⋊Dic3C2×D312yes—
73C2×Dic3⋊C4—32no—
74C2×Dic3⋊C4—34no—
75C2×Dic3⋊C4—32no—
76C2×Dic3⋊C4—34no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—34no—
80C2×C4×Dic3—34no—
81C2×C4×Dic3—62no—
82C2×C4×Dic3—61no—
83C2×C4×Dic3C2×D312yes—
84C3×#95—34no—
85C3×#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—32no—
89C3⋊#95—32no—
90C3⋊#95C2×D314yes—
91C3⋊#95C2×D314yes—
92C23×C32C2411yescharacteristic
93C32×Q8—28no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4C22×C414yes—
97C2×C32×C4C22×C412yes—
98C2×C32×C4#4112yes—
99C2×C32×C4#4112yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3C22×C414yes—
105C2×C3⋊Dic3C22×C412yes—
106C2×C3⋊Dic3C22×C412yes—
107C2×C3⋊Dic3C2×Q812yes—
108C2×C3⋊Dic3#4112yes—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3C2×Q814yes—
118C2×C4×Q8—91no—
119#391—32no—
120#387—94no—
121#384—91no—
122#382—92no—
123C4×C4⋊C4—92no—
124C4×C4⋊C4—91no—
125C4×C4⋊C4—92no—
126C2×C3×Q8—24no—
127C2×C3×Q8—24no—
128C2×C3×Q8—24no—
129C2×C3×Q8—24no—
130C2×C3×Q8—24no—
131C2×C3×Q8C4×D318yes—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—32no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4C22×D314yes—
138C22×C3×C4C22×D312yes—
139C22×Dic3—32no—
140C22×Dic3—34no—
141C22×Dic3—32no—
142C22×Dic3—61no—
143C22×Dic3—62no—
144C22×Dic3—61no—
145C22×Dic3C22×D312yes—
146C22×Dic3C22×D314yes—
147C22×Dic3C22×D312yes—
148C3×C4⋊C4—64no—
149C3×C42—64no—
150C4⋊Dic3—24no—
151C4⋊Dic3—316no—
152C4⋊Dic3—38no—
153C4⋊Dic3—68no—
154C4⋊Dic3—64no—
155Dic3⋊C4—38no—
156Dic3⋊C4—68no—
157Dic3⋊C4—64no—
158Dic3⋊C4—124no—
159C4×Dic3—24no—
160C4×Dic3—316no—
161C4×Dic3—38no—
162C4×Dic3—68no—
163C4×Dic3—64no—
164C4×Dic3—124no—
165C4×Dic3—124no—
166C22×C32C23×C411yescharacteristic
167C22×C32C22×Q811yescharacteristic
168C22×C32C2×#4111yescharacteristic
169C22×C32C2×#4111yescharacteristic
170C22×C32C2×#4111yescharacteristic
171C22×C32H(5,𝔽2)11yescharacteristic
172C22×C322−1+411yescharacteristic
173C32×C4—24no—
174C32×C4#11714yes—
175C3⋊Dic3—24no—
176C3⋊Dic3—22no—
177C3⋊Dic3C4×Q814yes—
178C3×Dic3—24no—
179C3×Dic3—42no—
180C3×Dic3—44no—
181C22×Q8D3211yescharacteristic
182C4×Q8—98no—
183C2×C4⋊C4—32no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—92no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—92no—
189C2×C4⋊C4—92no—
190C2×C42—32no—
191C2×C42—92no—
192C2×C42—91no—
193C2×C42—94no—
194#95—34no—
195#95—34no—
196#95—94no—
197#95—92no—
198C23×C3—21no—
199C23×C3C23×D312yes—
200C3×Q8—216no—
201C3×Q8—216no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—24no—
209C2×C3×C4—22no—
210C2×C3×C4—34no—
211C2×C3×C4—62no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×C3×C4C2×C4×D318yes—
220C2×C3×C4C2×C4×D314yes—
221C2×C3×C4#23714yes—
222C2×C3×C4#23714yes—
223C2×Dic3—22no—
224C2×Dic3—22no—
225C2×Dic3—22no—
226C2×Dic3—24no—
227C2×Dic3—22no—
228C2×Dic3—22no—
229C2×Dic3—24no—
230C2×Dic3—24no—
231C2×Dic3—34no—
232C2×Dic3—34no—
233C2×Dic3—34no—
234C2×Dic3—38no—
235C2×Dic3—34no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—64no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C2×Dic3—64no—
244C2×Dic3—62no—
245C2×Dic3—122no—
246C2×Dic3—121no—
247C2×Dic3—122no—
248C2×Dic3—121no—
249C2×Dic3D3×Q814yes—
250C2×C32C2×#11711yescharacteristic
251C2×C32C2×C4×Q811yescharacteristic
252C2×C32#52011yescharacteristic
253C2×C32#55411yescharacteristic
254C2×C32#55611yescharacteristic
255C2×C32#55711yescharacteristic
256C2×C32#55911yescharacteristic
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8#62414yes—
260C22×C4—32no—
261C22×C4—32no—
262C22×C4—34no—
263C22×C4—91no—
264C22×C4—92no—
265C22×C4—91no—
266C22×C4C2×D3212yes—
267C22×C4C2×D3211yescharacteristic
268C4⋊C4—64no—
269C4⋊C4—94no—
270C4⋊C4—98no—
271C4⋊C4—94no—
272C4⋊C4—182no—
273C4⋊C4—184no—
274C4⋊C4—362no—
275C42—64no—
276C42—98no—
277C42—94no—
278C42—364no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3C22×C4×D312yes—
287C22×C3C2×#23712yes—
288C22×C3C2×#23712yes—
289C22×C3C2×D3×Q812yes—
290C22×C3#100712yes—
291C22×C3D3×#4112yes—
292C22×C3#100912yes—
293C3×C4—28no—
294C3×C4—28no—
295C3×C4—24no—
296C3×C4—64no—
297C3×C4—122no—
298C3×C4—124no—
299C3×C4#87718yes—
300Dic3—24no—
301Dic3—38no—
302Dic3—42no—
303Dic3—44no—
304Dic3—64no—
305Dic3—68no—
306Dic3—64no—
307Dic3—124no—
308Dic3—122no—
309C32#235511yescharacteristic, complemented, Sylow
310C23C22×D3211yescharacteristic
311Q8—28no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—34no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—64no—
319C2×C4—62no—
320C2×C4—64no—
321C2×C4—62no—
322C2×C4—64no—
323C2×C4—92no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—94no—
327C2×C4—92no—
328C2×C4—182no—
329C2×C4—181no—
330C2×C4—182no—
331C2×C4—181no—
332C2×C4#380512yes—
333C2×C4#380512yes—
334C2×C4C2×#62414yes—
335C2×C4C2×#62412yes—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3C2×#87712yes—
344C2×C3C4×D3×Q812yes—
345C2×C3#557412yes—
346C2×C3#563512yes—
347C2×C3#564112yes—
348C2×C3#568112yes—
349C2×C3#572112yes—
350C22#6431611yescharacteristic
351C22D32×Q811yescharacteristic
352C22#6431911yescharacteristic
353C22#6432011yescharacteristic
354C22C2×#380511yescharacteristic
355C22C2×#380511yescharacteristic
356C22C22×#62411yescharacteristic
357C4—24no—
358C4—64no—
359C4—94no—
360C4—124no—
361C4—122no—
362C4—184no—
363C4—182no—
364C4#6395714yes—
365C3—21no—
366C3#7648912yescomplemented
367C2#1059533811yescharacteristic
368C2#1059535311yescharacteristic
369C2Q8×#62411yescharacteristic
370C2#1059539211yescharacteristic
371C2#1059540711yescharacteristic
372C2#1059541311yescharacteristic
373C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, prime radical, cosocleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
11. Q8×C3⋊Dic3C4semidirect
59. #3724Q8semidirect
309. C32#2355semidirect
366. C3#76489semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C3×#52292
#105913602
#105913592
C4×#37242
#105912712
Dic3×C4⋊Dic32
#105912572
#764893