Finite Group Databasebeta

← #11807641

Subgroups — #11807641

Order 1152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic
3#10592919C211yesmaximal, characteristic
4#10592675C212yesmaximal, complemented
5#10592645C212yesmaximal, complemented
6#10592644C212yesmaximal, complemented
7#10592643C212yesmaximal, complemented
8#10592641C212yesmaximal, complemented
9#10592632C212yesmaximal, complemented
10#76309—34nomaximal
11C22×C32×D4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4C2212yes—
16C2×C32×C22⋊C4C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×#3757C2212yes—
19C2×#3757C2211yescharacteristic
20C2×#3757C2212yes—
21C2×#3757C2211yescharacteristic
22#64144C418yescomplemented
23C2×#3750C2212yes—
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×#3750C2212yes—
27C2×C4×C3⋊Dic3C2212yes—
28#63658C2212yes—
29#63658C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33C2×#935—34no—
34C3×#390D314yes—
35#5220—34no—
36#4976—38no—
37#4946—38no—
38#4945—38no—
39#4944—38no—
40#4942—38no—
41#4933—38no—
42C24×C32C2311yescharacteristic
43C24×C32C2311yescharacteristic
44C2×C32×D4—41no—
45C2×C32×D4—41no—
46C2×C32×D4C2×C414yes—
47C22×C32×C4C2312yes—
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—41no—
51C22×C3⋊Dic3—41no—
52C22×C3⋊Dic3—41no—
53C22×C3⋊Dic3—42no—
54C22×C3⋊Dic3C2×C414yescomplemented
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2312yes—
59C32×C4⋊C4—41no—
60C32×C22⋊C4—42no—
61C32×C22⋊C4—42no—
62C32×C42—41no—
63#3757—42no—
64#3757—41no—
65#3757C2×C418yes—
66#3757C2×C414yescomplemented
67#3750—42no—
68#3750—42no—
69#3750—42no—
70#3750C2×C418yescomplemented
71C4×C3⋊Dic3—42no—
72#2376—91noSylow
73C22×C3×D4C2×D314yes—
74C23×Dic3—34no—
75C23×Dic3—34no—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C22⋊C4C2×D318yes—
78C2×C3×C22⋊C4C2×D318yes—
79C2×C3×C42C2×D314yes—
80C2×#217—38no—
81C2×#217—34no—
82C2×#217—38no—
83C2×#217—34no—
84#935—332no—
85C2×Dic3⋊C4—38no—
86C2×Dic3⋊C4—38no—
87C2×Dic3⋊C4—38no—
88C2×Dic3⋊C4—38no—
89C2×C4×Dic3—38no—
90C3⋊#95—38no—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C3⋊#95—38no—
94C3⋊#95—38no—
95C23×C32—22no—
96C23×C32—21no—
97C23×C32—22no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32—21no—
101C23×C32—22no—
102C23×C32—22no—
103C23×C32C22×C412yes—
104C23×C32C22×C412yes—
105C23×C32C2411yescharacteristic
106C32×D4—44no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4C22×C412yes—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—44no—
127C2×C3⋊Dic3—44no—
128C2×C3⋊Dic3C22×C414yes—
129C2×C3⋊Dic3C22×C414yes—
130C2×#123—91no—
131#390C3⋊D311yescharacteristic
132#389—92no—
133#388—92no—
134#388—92no—
135#387—92no—
136#386—91no—
137#385—92no—
138#380—92no—
139C24×C3C22×D314yes—
140C24×C3C22×D314yes—
141C2×C3×D4—44no—
142C2×C3×D4—44no—
143C2×C3×D4C4×D3116yes—
144C22×C3×C4C22×D318yes—
145C22×C3×C4C22×D318yes—
146C22×C3×C4C22×D314yes—
147C22×Dic3—38no—
148C22×Dic3—38no—
149C22×Dic3—316no—
150C22×Dic3—38no—
151C22×Dic3—38no—
152C22×Dic3—124no—
153C22×Dic3—124no—
154C22×Dic3—124no—
155C22×Dic3—128no—
156C3×C4⋊C4—44no—
157C3×C22⋊C4—48no—
158C3×C22⋊C4—48no—
159C3×C42—44no—
160#217—332no—
161#217—316no—
162#217—128no—
163#217—124no—
164Dic3⋊C4—332no—
165Dic3⋊C4—128no—
166Dic3⋊C4—128no—
167Dic3⋊C4—128no—
168C4×Dic3—128no—
169C22×C32—22no—
170C22×C32—22no—
171C22×C32—24no—
172C22×C32—24no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32—42no—
176C22×C32—42no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32C23×C411yescharacteristic
180C22×C32H(5,𝔽2)11yescharacteristic
181C22×C32H(5,𝔽2)11yescharacteristic
182C22×C32H(5,𝔽2)12yes—
183C22×C322−1+412yes—
184C32×C4—22no—
185C32×C4—42no—
186C32×C4—42no—
187C3⋊Dic3—24no—
188C3⋊Dic3—24no—
189C3⋊Dic3—42no—
190C3⋊Dic3—42no—
191C22×D4C2×C3⋊D311yescharacteristic
192C23×C4—91no—
193C23×C4—91no—
194#123—98no—
195C2×C4⋊C4—92no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4C2×C3⋊D311yescharacteristic
200C2×C22⋊C4—92no—
201C2×C22⋊C4—91no—
202C2×C22⋊C4—92no—
203C2×C22⋊C4—91no—
204C2×C22⋊C4C2×C3⋊D312yes—
205C2×C22⋊C4C2×C3⋊D312yes—
206C2×C42—92no—
207C2×C42C2×C3⋊D311yescharacteristic
208#95—92no—
209#95—92no—
210#95—92no—
211#95—92no—
212#95—92no—
213C23×C3—28no—
214C23×C3—24no—
215C23×C3—28no—
216C23×C3—24no—
217C23×C3—24no—
218C23×C3—24no—
219C23×C3—28no—
220C23×C3—28no—
221C23×C3C2×C4×D318yes—
222C23×C3C2×C4×D318yes—
223C23×C3C23×D314yes—
224C3×D4—416no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—28no—
231C2×C3×C4—28no—
232C2×C3×C4—28no—
233C2×C3×C4C2×C4×D318yes—
234C2×Dic3—316no—
235C2×Dic3—316no—
236C2×Dic3—68no—
237C2×Dic3—68no—
238C2×Dic3—68no—
239C2×Dic3—68no—
240C2×Dic3—68no—
241C2×Dic3—68no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C2×Dic3—1216no—
247C2×Dic3—1216no—
248C2×C32—42no—
249C2×C32—42no—
250C2×C32#51811yescharacteristic
251C2×C32#52012yes—
252C2×C32#56011yescharacteristic
253C2×C32#56212yes—
254C2×C32#56311yescharacteristic
255C24C22×C3⋊D311yescharacteristic
256C24C22×C3⋊D311yescharacteristic
257C2×D4—41no—
258C2×D4—41no—
259C2×D4C4×C3⋊D314yes—
260C22×C4—92no—
261C22×C4—92no—
262C22×C4—94no—
263C22×C4—92no—
264C22×C4—92no—
265C22×C4—361no—
266C22×C4—361no—
267C22×C4—362no—
268C22×C4—361no—
269C22×C4C22×C3⋊D312yes—
270C22×C4C22×C3⋊D312yes—
271C22×C4C22×C3⋊D311yescharacteristic
272C4⋊C4—41no—
273C4⋊C4—98no—
274C4⋊C4—362no—
275C4⋊C4—362no—
276C4⋊C4—362no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—94no—
280C22⋊C4—98no—
281C22⋊C4—362no—
282C22⋊C4—361no—
283C42—41no—
284C42—362no—
285C22×C3—28no—
286C22×C3—28no—
287C22×C3—216no—
288C22×C3—216no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—48no—
294C22×C3—48no—
295C22×C3C22×C4×D314yes—
296C22×C3#100414yes—
297C22×C3#100418yes—
298C22×C3#100414yes—
299C22×C3#101018yes—
300C3×C4—28no—
301C3×C4—48no—
302C3×C4—48no—
303Dic3—616no—
304Dic3—616no—
305Dic3—128no—
306Dic3—128no—
307C32#237611yescharacteristic, complemented, Sylow
308C23—22no—
309C23—22no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—22no—
315C23—22no—
316C23C2×C4×C3⋊D312yes—
317C23C2×C4×C3⋊D312yes—
318C23C23×C3⋊D311yescharacteristic
319D4—44no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—94no—
329C2×C4—94no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—364no—
341C2×C4—364no—
342C2×C4C2×C4×C3⋊D312yes—
343C2×C3—48no—
344C2×C3—48no—
345C2×C3#548614yes—
346C2×C3#554618yes—
347C2×C3#562118yes—
348C2×C3#567214yes—
349C2×C3#572014yes—
350C22—22no—
351C22—22no—
352C22—24no—
353C22—24no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22C22×C4×C3⋊D311yescharacteristic
361C22#6436111yescharacteristic
362C22#6436112yes—
363C22#6436111yescharacteristic
364C22#6436712yes—
365C4—22no—
366C4—42no—
367C4—42no—
368C4—184no—
369C4—184no—
370C4—362no—
371C4—362no—
372C3#7630914yescomplemented
373C2—42no—
374C2—42no—
375C2#1059595711yescharacteristic
376C2#1059601712yes—
377C2#1059609212yes—
378C2#1059614311yescharacteristic
379C2#1059619111yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#390C2
socle, cosocleC23×C32C24
prime radicalC22×C32×D4C22
hypercenter#390C3⋊D3
hypocenterC32#2376
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #10592675C2semidirect
5. #10592645C2semidirect
6. #10592644C2semidirect
7. #10592643C2semidirect
8. #10592641C2semidirect
9. #10592632C2semidirect
22. #64144C4semidirect
54. C22×C3⋊Dic3C2×C4semidirect
66. #3757C2×C4semidirect
70. #3750C2×C4semidirect
307. C32#2376semidirect
372. C3#76309semidirect

Maximal subgroups

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

subgroupindex
C2×#641442
C32×#3902
#105929192
#105926752
#105926452
#105926442
#105926432
#105926412
#105926322
#763093