Finite Group Databasebeta

← #11807514

Subgroups — #11807514

Order 1152.

1656 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#10592677C212yesmaximal, complemented
5#10592644C212yesmaximal, complemented
6#10592644C212yesmaximal, complemented
7C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
8C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
9C4×#3750C212yesmaximal, complemented
10#76308—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×C4×C3⋊Dic3C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2212yes—
28#63658C2212yes—
29#63658C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33C2×#935—34no—
34C3×#390D314yes—
35#5220—34no—
36#4978—38no—
37#4945—38no—
38#4945—38no—
39Dic3×C22⋊C4—38no—
40Dic3×C22⋊C4—38no—
41C4×Dic3⋊C4—38no—
42C24×C32C2311yescharacteristic
43C24×C32C2311yescharacteristic
44C2×C32×D4—41no—
45C2×C32×D4—41no—
46C2×C32×D4C2×C414yes—
47C22×C32×C4C2312yes—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C3⋊Dic3—24no—
51C22×C3⋊Dic3—41no—
52C22×C3⋊Dic3—41no—
53C22×C3⋊Dic3—41no—
54C22×C3⋊Dic3C2×C414yescomplemented
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2312yes—
59C32×C4⋊C4—41no—
60C32×C22⋊C4—24no—
61C32×C22⋊C4—24no—
62C32×C42—41no—
63#3757—24no—
64#3757—41no—
65#3757C2×C418yes—
66#3757C2×C414yescomplemented
67#3750—24no—
68#3750C2×C418yescomplemented
69C4×C3⋊Dic3—24no—
70C4×C3⋊Dic3—42no—
71C4×C3⋊Dic3—42no—
72#2374—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×C4×Dic3—38no—
88C2×C4×Dic3—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—22no—
97C23×C32—22no—
98C23×C32—22no—
99C23×C32—21no—
100C23×C32—21no—
101C23×C32—21no—
102C23×C32—21no—
103C23×C32C22×C412yes—
104C23×C32C22×C412yes—
105C23×C32C2411yescharacteristic
106C32×D4—44no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4C22×C412yes—
115C2×C32×C4#4114yes—
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—44no—
126C2×C3⋊Dic3—44no—
127C2×C3⋊Dic3C22×C414yes—
128C2×C3⋊Dic3C22×C414yes—
129C2×C3⋊Dic3#4114yes—
130C2×#123—91no—
131#390C3⋊D311yescharacteristic
132#388—92no—
133#388—92no—
134#387—92no—
135#386—91no—
136C4×C4⋊C4—92no—
137C4×C22⋊C4—92no—
138C4×C22⋊C4—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×D314yes—
146C22×C3×C4C22×D318yes—
147C22×Dic3—38no—
148C22×Dic3—38no—
149C22×Dic3—38no—
150C22×Dic3—316no—
151C22×Dic3—38no—
152C22×Dic3—616no—
153C22×Dic3—124no—
154C22×Dic3—124no—
155C22×Dic3—124no—
156C3×C4⋊C4—44no—
157C3×C22⋊C4—216no—
158C3×C22⋊C4—216no—
159C3×C42—44no—
160#217—332no—
161#217—316no—
162#217—616no—
163#217—124no—
164Dic3⋊C4—332no—
165Dic3⋊C4—616no—
166C4×Dic3—616no—
167C4×Dic3—128no—
168C4×Dic3—128no—
169C22×C32—24no—
170C22×C32—24no—
171C22×C32—22no—
172C22×C32—22no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32—42no—
176C22×C32—42no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32C23×C411yescharacteristic
180C22×C32C2×#4112yes—
181C22×C32C2×#4112yes—
182C22×C32H(5,𝔽2)11yescharacteristic
183C22×C32H(5,𝔽2)11yescharacteristic
184C32×C4—22no—
185C32×C4—24no—
186C32×C4—42no—
187C3⋊Dic3—24no—
188C3⋊Dic3—24no—
189C3⋊Dic3—24no—
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⋊C4C2×C3⋊D311yescharacteristic
198C2×C22⋊C4—92no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—92no—
201C2×C22⋊C4—91no—
202C2×C22⋊C4C2×C3⋊D312yes—
203C2×C22⋊C4C2×C3⋊D312yes—
204C2×C42—92no—
205C2×C42—92no—
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—28no—
215C23×C3—24no—
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—28no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—28no—
231C2×C3×C4—28no—
232C2×C3×C4C2×C4×D318yes—
233C2×C3×C4#237116yes—
234C2×Dic3—316no—
235C2×Dic3—316no—
236C2×Dic3—316no—
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×C32C4×#4112yes—
251C2×C32#51811yescharacteristic
252C2×C32#55111yescharacteristic
253C2×C32#55312yes—
254C2×C32#55911yescharacteristic
255C24C22×C3⋊D311yescharacteristic
256C24C22×C3⋊D311yescharacteristic
257C2×D4—41no—
258C2×D4—41no—
259C2×D4C4×C3⋊D314yes—
260C22×C4—92no—
261C22×C4—92no—
262C22×C4—92no—
263C22×C4—94no—
264C22×C4—92no—
265C22×C4—184no—
266C22×C4—361no—
267C22×C4—361no—
268C22×C4—361no—
269C22×C4C22×C3⋊D312yes—
270C22×C4C22×C3⋊D311yescharacteristic
271C22×C4C22×C3⋊D312yes—
272C4⋊C4—41no—
273C4⋊C4—98no—
274C4⋊C4—184no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—94no—
278C22⋊C4—98no—
279C22⋊C4—184no—
280C22⋊C4—361no—
281C42—41no—
282C42—184no—
283C42—362no—
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×C3C2×#23718yes—
297C22×C3#100414yes—
298C22×C3#100414yes—
299C22×C3D3×#4118yes—
300C3×C4—28no—
301C3×C4—216no—
302C3×C4—48no—
303Dic3—616no—
304Dic3—616no—
305Dic3—616no—
306Dic3—128no—
307C32#237411yescharacteristic, 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—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—94no—
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—364no—
340C2×C4—364no—
341C2×C4C2×C4×C3⋊D312yes—
342C2×C4#383014yes—
343C2×C3—48no—
344C2×C3—48no—
345C2×C3#548614yes—
346C2×C3C4×#23718yes—
347C2×C3#560118yes—
348C2×C3#567914yes—
349C2×C3#571314yes—
350C22—22no—
351C22—22no—
352C22—24no—
353C22—24no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22C22×C4×C3⋊D311yescharacteristic
361C22C2×#383012yes—
362C22#6436111yescharacteristic
363C22#6436111yescharacteristic
364C22#41×C3⋊D312yes—
365C4—22no—
366C4—24no—
367C4—42no—
368C4—184no—
369C4—184no—
370C4—184no—
371C4—362no—
372C3#7630814yescomplemented
373C2—42no—
374C2—42no—
375C2#1059595711yescharacteristic
376C2C4×#383012yes—
377C2#1059607212yes—
378C2#1059615011yescharacteristic
379C2#1059618411yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#390C2
socle, cosocleC23×C32C24
prime radicalC22×C32×D4C22
hypercenter#390C3⋊D3
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
4. #10592677C2semidirect
5. #10592644C2semidirect
6. #10592644C2semidirect
7. C22⋊C4×C3⋊Dic3C2semidirect
8. C22⋊C4×C3⋊Dic3C2semidirect
9. C4×#3750C2semidirect
22. #64144C4semidirect
54. C22×C3⋊Dic3C2×C4semidirect
66. #3757C2×C4semidirect
68. #3750C2×C4semidirect
307. C32#2374semidirect
372. C3#76308semidirect

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
#105926772
#105926442
C22⋊C4×C3⋊Dic32
C4×#37502
#763083