Finite Group Databasebeta

← #11773861

Subgroups — #11773861

Order 1152.

1217 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 1217 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C3×#5207C212yesmaximal, complemented
3#10589146C214yesmaximal, complemented
4#69967—32nomaximal
5C24×C3⋊D3C411yescharacteristic
6C23×C32×C4C2211yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C2×#3752—22no—
9C2×#3752—22no—
10C2×#3752C412yes—
11C2×#3752C2212yes—
12C2×C3×#208—22no—
13C3×#830—22no—
14C3×#830C2214yescomplemented
15C22×(C2×D3)⋊C4—32no—
16C22×(C2×D3)⋊C4—61no—
17C3×#407—32no—
18#5207D312yescomplemented
19#4468—38no—
20C24×C32C2×C411yescharacteristic
21C23×C3⋊D3—21no—
22C23×C3⋊D3—21no—
23C23×C3⋊D3—24no—
24C23×C3⋊D3—42no—
25C23×C3⋊D3—42no—
26C23×C3⋊D3C2×C412yes—
27C22×C32×C4—42no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D412yes—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—42no—
35C22×C3⋊Dic3C2×C412yes—
36#3752—24no—
37#3752—24no—
38C3×#208—44no—
39C2×C3×C3⋊C8—24no—
40#1462—91noSylow
41C24×D3—32no—
42C24×D3—61no—
43C23×C3×C4—21no—
44C23×C3×C4C2×D312yes—
45C23×Dic3—32no—
46C23×Dic3—61no—
47C2×C3×M16—62no—
48C2×(C2×D3)⋊C4—34no—
49C2×(C2×D3)⋊C4—34no—
50C2×(C2×D3)⋊C4—62no—
51C2×(C2×D3)⋊C4—62no—
52C2×(C2×D3)⋊C4—64no—
53C2×(C2×D3)⋊C4—64no—
54C2×(C2×D3)⋊C4—62no—
55C2×(C2×D3)⋊C4—62no—
56C2×(C2×D3)⋊C4—62no—
57C2×(C2×D3)⋊C4—62no—
58C2×#208—22no—
59C3×C22⋊C8—34no—
60C3×C22⋊C8—62no—
61#830—22no—
62#830C2×D314yescomplemented
63C23×C32—22no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32C22⋊C411yescharacteristic
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22×C411yescharacteristic
69C22×C3⋊D3—24no—
70C22×C3⋊D3—24no—
71C22×C3⋊D3—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—416no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3—42no—
77C22×C3⋊D3—42no—
78C22×C3⋊D3—42no—
79C22×C3⋊D3—42no—
80C22×C3⋊D3M1614yescomplemented
81C2×C32×C4—24no—
82C2×C32×C4—41no—
83C2×C32×C4—42no—
84C2×C32×C4—41no—
85C2×C32×C4C22⋊C412yes—
86C2×C32×C4C2×D412yes—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3—42no—
90C2×C3⋊Dic3—42no—
91C3×C3⋊C8—44no—
92C22×C22⋊C4—91no—
93#407—32no—
94#323—94no—
95C24×C3—21no—
96C24×C3C4×D312yes—
97C23×D3—34no—
98C23×D3—62no—
99C23×D3—68no—
100C23×D3—62no—
101C23×D3—62no—
102C23×D3—68no—
103C23×D3—62no—
104C23×D3—62no—
105C23×D3—124no—
106C23×D3—124no—
107C23×D3—124no—
108C23×D3—124no—
109C22×C3×C4—21no—
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×C3×C4—21no—
113C22×C3×C4—44no—
114C22×C3×C4—44no—
115C22×C3×C4C4×D312yes—
116C22×C3×C4D1212yes—
117C22×C3×C4D1212yes—
118C22×C3×C4#6712yes—
119C22×C3×C4#6712yes—
120C22×C3×C4C22×D312yes—
121C22×Dic3—34no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C22×Dic3—124no—
128C22×Dic3—124no—
129C3×M16—124no—
130C2×C3×C8—64no—
131(C2×D3)⋊C4—68no—
132(C2×D3)⋊C4—68no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135(C2×D3)⋊C4—64no—
136(C2×D3)⋊C4—64no—
137#208—44no—
138C2×C3⋊C8—24no—
139C22×C32—28no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32#9912yes—
147C22×C32#10012yes—
148C22×C32C2×C22⋊C411yescharacteristic
149C22×C32C2×M1612yes—
150C2×C3⋊D3—24no—
151C2×C3⋊D3—48no—
152C2×C3⋊D3—48no—
153C2×C3⋊D3—44no—
154C2×C3⋊D3—42no—
155C2×C3⋊D3—42no—
156C2×C3⋊D3—44no—
157C32×C4—22no—
158C32×C4—22no—
159C3⋊Dic3—42no—
160C25—91no—
161C23×C4—91no—
162C23×C4D3211yescharacteristic
163C2×M16—62no—
164C2×C22⋊C4—92no—
165C2×C22⋊C4—92no—
166C2×C22⋊C4—182no—
167C2×C22⋊C4—182no—
168C22⋊C8—34no—
169C22⋊C8—62no—
170C23×C3—24no—
171C23×C3—24no—
172C23×C3—24no—
173C23×C3—24no—
174C23×C3—24no—
175C23×C3—24no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3(C2×D3)⋊C412yes—
180C23×C3(C2×D3)⋊C412yes—
181C23×C3C2×C4×D312yes—
182C22×D3—38no—
183C22×D3—64no—
184C22×D3—64no—
185C22×D3—68no—
186C22×D3—68no—
187C22×D3—68no—
188C22×D3—68no—
189C22×D3—64no—
190C22×D3—64no—
191C22×D3—64no—
192C22×D3—124no—
193C22×D3—124no—
194C22×D3—124no—
195C22×D3—124no—
196C22×D3—1232no—
197C22×D3—1232no—
198C22×D3—124no—
199C22×D3—124no—
200C22×D3—124no—
201C22×D3—124no—
202C22×D3—124no—
203C22×D3—124no—
204C22×D3—124no—
205C22×D3—124no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—44no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—44no—
217C2×C3×C4—42no—
218C2×C3×C4(C2×D3)⋊C412yes—
219C2×C3×C4(C2×D3)⋊C412yes—
220C2×C3×C4C2×D1212yes—
221C2×C3×C4C2×#6712yes—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—124no—
225C2×Dic3—124no—
226C2×Dic3—124no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229C2×Dic3—124no—
230C3×C8—124no—
231C3⋊C8—44no—
232C2×C32—22no—
233C2×C32—22no—
234C2×C32—22no—
235C2×C32#40711yescharacteristic
236C2×C32C2×#9911yescharacteristic
237C2×C32C2×#10011yescharacteristic
238C3⋊D3—44no—
239C24—92no—
240C24—184no—
241C24—181no—
242C24—181no—
243C24—362no—
244C24—362no—
245C24#62411yescharacteristic
246C22×C4—42no—
247C22×C4—92no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4—362no—
251C22×C4#62411yescharacteristic
252C22×C4#62612yes—
253C22×C4#62612yes—
254C22×C4C2×D3211yescharacteristic
255M16—124no—
256C2×C8—64no—
257C22⋊C4—184no—
258C22⋊C4—184no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—216no—
266C22×C3—216no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—21no—
277C22×C3#80614yes—
278C22×C3#82314yes—
279C22×C3D3×M1614yes—
280C22×C3C2×(C2×D3)⋊C412yes—
281C2×D3—68no—
282C2×D3—68no—
283C2×D3—128no—
284C2×D3—1216no—
285C2×D3—128no—
286C2×D3—1216no—
287C2×D3—1216no—
288C2×D3—1216no—
289C2×D3—128no—
290C2×D3—124no—
291C2×D3—124no—
292C2×D3—124no—
293C2×D3—124no—
294C2×D3—128no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—22no—
298C3×C4—22no—
299C3×C4—42no—
300C3×C4—42no—
301Dic3—124no—
302Dic3—124no—
303C32#146211yescharacteristic, complemented, Sylow
304C23—22no—
305C23—22no—
306C23—22no—
307C23—94no—
308C23—184no—
309C23—184no—
310C23—182no—
311C23—182no—
312C23—362no—
313C23—362no—
314C23—3616no—
315C23—362no—
316C23—362no—
317C23—362no—
318C23—362no—
319C23#372211yescharacteristic
320C23#372211yescharacteristic
321C23C2×#62411yescharacteristic
322C2×C4—24no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—182no—
327C2×C4—362no—
328C2×C4—362no—
329C2×C4—362no—
330C2×C4#372212yes—
331C2×C4C2×#62612yes—
332C8—124no—
333C2×C3—24no—
334C2×C3—24no—
335C2×C3—24no—
336C2×C3—24no—
337C2×C3—24no—
338C2×C3—24no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3C2×#80612yes—
343C2×C3#512612yes—
344C2×C3C2×#82312yes—
345D3—128no—
346D3—128no—
347C22—28no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—184no—
355C22—364no—
356C22—368no—
357C22—364no—
358C22—368no—
359C22—362no—
360C22—362no—
361C22#6355912yes—
362C22#6358112yes—
363C22#6381812yes—
364C22C2×#372211yescharacteristic
365C4—22no—
366C4—22no—
367C4—362no—
368C3—21no—
369C3#6996712yescomplemented
370C2—22no—
371C2—22no—
372C2—22no—
373C2—364no—
374C2#1059107411yescharacteristic
375C2C2×#6355911yescharacteristic
376C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1462
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5207C2semidirect
3. #10589146C2semidirect
14. C3×#830C22semidirect
18. #5207D3semidirect
62. #830C2×D3semidirect
80. C22×C3⋊D3M16semidirect
303. C32#1462semidirect
369. C3#69967semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C3×#52072
#105891462
#699673