Finite Group Databasebeta

← #11786404

Subgroups — #11786404

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#208C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×#63572C212yesmaximal, complemented
5#10589156C212yesmaximal, complemented
6#71995—31nomaximal
7#69951—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3757C412yes—
10C2×C4×C3⋊Dic3C2212yes—
11C2×C3×#208—22no—
12C2×C3×#208—24no—
13C22×C3×C3⋊C8C2211yescharacteristic
14C22×C3×C3⋊C8C2211yescharacteristic
15C22×C3×C3⋊C8C2212yes—
16#63658C411yescharacteristic
17#63658C411yescharacteristic
18C3×#830—22no—
19#63572—24no—
20C22×C3×M16—31no—
21C22×#208D311yescharacteristic
22C2×C3×C22⋊C8—31no—
23C4×#217—31no—
24C4×#217—31no—
25C4×#217—61no—
26C2×#830D311yescharacteristic
27C2×Dic3⋊C8—32no—
28C2×Dic3⋊C8—32no—
29#4550—32no—
30#4550—32no—
31C24×C32C2×C411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D412yes—
36C22×C32×C4Q812yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2×C412yes—
39C22×C3⋊Dic3C2×C412yes—
40#3757—24no—
41C4×C3⋊Dic3—22no—
42C4×C3⋊Dic3—22no—
43C3×#208—28no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—21no—
48C2×C3×C3⋊C8—21no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8D414yes—
51#1851—91noSylow
52C23×C3×C4—21no—
53C23×C3×C4C2×D311yescharacteristic
54C23×C3×C4C2×D311yescharacteristic
55C2×C3×M16—64no—
56C2×C3×M16—62no—
57C22×C3×C8—32no—
58C22×C3×C8—31no—
59C22×C3×C8—31no—
60C2×#217—32no—
61C2×#217—32no—
62C2×#217—62no—
63C2×C4×Dic3—32no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—62no—
66C2×#208—22no—
67C2×#208—24no—
68C22×C3⋊C8C2×D311yescharacteristic
69C22×C3⋊C8C2×D311yescharacteristic
70C22×C3⋊C8C2×D312yes—
71C3×C22⋊C8—62no—
72C3⋊#95—31no—
73C3⋊#95—31no—
74C3⋊#95—31no—
75C3⋊#95—31no—
76C3⋊#95—61no—
77C3⋊#95—61no—
78#830—22no—
79Dic3⋊C8—64no—
80Dic3⋊C8—64no—
81C23×C32—22no—
82C23×C32—22no—
83C23×C32—21no—
84C23×C32—21no—
85C23×C32C4⋊C412yes—
86C23×C32C22×C411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—22no—
91C2×C32×C4C4⋊C412yes—
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q811yescharacteristic
95C2×C32×C4#4112yes—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3M1614yescomplemented
102C3×C3⋊C8—24no—
103C3×C3⋊C8—41no—
104C3×C3⋊C8—41no—
105C22×M16—31no—
106C2×C4⋊C8—92no—
107C2×C22⋊C8—31no—
108C4×C22⋊C4—91no—
109#336—92no—
110C24×C3—21no—
111C24×C3C4×D311yescharacteristic
112C24×C3C4×D311yescharacteristic
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4—42no—
122C22×C3×C4—42no—
123C22×C3×C4Dic612yes—
124C22×C3×C4Dic612yes—
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4C4×D311yescharacteristic
127C22×C3×C4#6712yes—
128C22×C3×C4#6712yes—
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—32no—
134C22×Dic3—32no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C3×M16—68no—
138C2×C3×C8—34no—
139C2×C3×C8—62no—
140C2×C3×C8—62no—
141C2×C3×C8—62no—
142C2×C3×C8—62no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145#217—64no—
146#217—64no—
147#217—68no—
148C4×Dic3—62no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—122no—
153C4×Dic3—122no—
154#208—28no—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8#6714yes—
162C22×C32—22no—
163C22×C32—22no—
164C22×C32—22no—
165C22×C32—42no—
166C22×C32—42no—
167C22×C32C2×C4⋊C411yescharacteristic
168C22×C32C4×D412yes—
169C22×C32C2×M1612yes—
170C22×C32#13111yescharacteristic
171C22×C32#13111yescharacteristic
172C32×C4—22no—
173C32×C4#12011yescharacteristic
174C32×C4C22⋊Q812yes—
175C32×C4#12311yescharacteristic
176C3⋊Dic3—24no—
177C3⋊Dic3—42no—
178C23×C4D3211yescharacteristic
179C2×M16—64no—
180C2×M16—62no—
181C22×C8—32no—
182C22×C8—31no—
183C22×C8—31no—
184C2×C22⋊C4—92no—
185C2×C42—92no—
186C4⋊C8—184no—
187C22⋊C8—62no—
188#95—91no—
189#95—91no—
190C23×C3—24no—
191C23×C3—22no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—21no—
201C23×C3—42no—
202C23×C3—41no—
203C23×C3—41no—
204C23×C3Dic3⋊C412yes—
205C23×C3Dic3⋊C412yes—
206C23×C3C2×C4×D311yescharacteristic
207C23×C3C2×C4×D311yescharacteristic
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—22no—
221C2×C3×C4—42no—
222C2×C3×C4—44no—
223C2×C3×C4—42no—
224C2×C3×C4—42no—
225C2×C3×C4Dic3⋊C412yes—
226C2×C3×C4Dic3⋊C412yes—
227C2×C3×C4C2×Dic611yescharacteristic
228C2×C3×C4C2×Dic611yescharacteristic
229C2×C3×C4#23512yes—
230C2×C3×C4D3×D412yes—
231C2×C3×C4#23712yes—
232C2×C3×C4C2×#6711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×C3×C4C2×#6712yes—
235C2×Dic3—34no—
236C2×Dic3—34no—
237C2×Dic3—64no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—64no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—122no—
250C2×Dic3—122no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C3×C8—64no—
254C3×C8—121no—
255C3×C8—121no—
256C3⋊C8—24no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C2×C32—42no—
260C2×C32#38511yescharacteristic
261C2×C32#42311yescharacteristic
262C2×C32#42411yescharacteristic
263C2×C32#43512yes—
264C2×C32#43612yes—
265C24#62411yescharacteristic
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—92no—
269C22×C4—92no—
270C22×C4#62411yescharacteristic
271C22×C4#62512yes—
272C22×C4#62712yes—
273C22×C4C2×D3211yescharacteristic
274M16—68no—
275C2×C8—34no—
276C2×C8—62no—
277C2×C8—62no—
278C2×C8—62no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8—62no—
282C22⋊C4—184no—
283C42—182no—
284C42—182no—
285C22×C3—24no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—44no—
300C22×C3—44no—
301C22×C3—42no—
302C22×C3—42no—
303C22×C3—42no—
304C22×C3—42no—
305C22×C3#67⋊C412yes—
306C22×C3#90111yescharacteristic
307C22×C3#90111yescharacteristic
308C22×C3D3×M1612yes—
309C22×C3D3×M1612yes—
310C22×C3#90711yescharacteristic
311C22×C3#90711yescharacteristic
312C22×C3C2×Dic3⋊C411yescharacteristic
313C22×C3C2×Dic3⋊C411yescharacteristic
314C22×C3C4×#6712yes—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—21no—
318C3×C4—22no—
319C3×C4—21no—
320C3×C4—42no—
321C3×C4#87812yes—
322C3×C4#92412yes—
323C3×C4#92911yescharacteristic
324C3×C4#93511yescharacteristic
325C3×C4#93711yescharacteristic
326C3×C4#95311yescharacteristic
327Dic3—64no—
328Dic3—64no—
329Dic3—124no—
330Dic3—124no—
331Dic3—122no—
332Dic3—122no—
333C32#185111yescharacteristic, complemented, Sylow
334C23—21no—
335C23—21no—
336C23—22no—
337C23—22no—
338C23#372412yes—
339C23C2×#62411yescharacteristic
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—94no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4#372412yes—
351C2×C4#380412yes—
352C2×C4C2×#62511yescharacteristic
353C2×C4C2×#62711yescharacteristic
354C2×C4D3×#6712yes—
355C8—64no—
356C8—121no—
357C8—121no—
358C2×C3—22no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—44no—
364C2×C3—42no—
365C2×C3—42no—
366C2×C3#472812yes—
367C2×C3#472912yes—
368C2×C3#494611yescharacteristic
369C2×C3#510211yescharacteristic
370C2×C3#511811yescharacteristic
371C2×C3#511811yescharacteristic
372C2×C3#511911yescharacteristic
373C2×C3#512712yes—
374C2×C3#512812yes—
375C2×C3#521011yescharacteristic
376C22—22no—
377C22—22no—
378C22—22no—
379C22—42no—
380C22—42no—
381C22#6381711yescharacteristic
382C22#6381711yescharacteristic
383C22#6381812yes—
384C22#6395212yes—
385C22C2×#372411yescharacteristic
386C4—22no—
387C4—184no—
388C4—362no—
389C4#6396111yescharacteristic
390C4#6396412yes—
391C4#6397611yescharacteristic
392C3—21no—
393C3#6995111yescharacteristic, complemented
394C3#7199511yescharacteristic, complemented
395C2—42no—
396C2#1059105112yes—
397C2#1059111911yescharacteristic
398C2#1059112011yescharacteristic
399C2#1059114912yes—
400C2#1059169311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socleC23×C32C22×C4
FittingC23×C32×C4C22
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1851
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63572C2semidirect
5. #10589156C2semidirect
101. C2×C3⋊Dic3M16semidirect
333. C32#1851semidirect
393. C3#69951semidirect
394. C3#71995semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2082
C4×#37572
C2×C3×#8302
C2×#635722
#105891562
#719953
#699513