Finite Group Databasebeta

← #11783766

Subgroups — #11783766

Order 1152.

1037 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 1037 conjugacy classes of subgroups — too many to draw. Only its 190 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
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal
3#10591705C212yesmaximal, complemented
4#10589187C212yesmaximal, complemented
5Dic3×#99—32nomaximal
6C22×C32×D4C2211yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic, complemented
8C23×C3⋊Dic3C2211yescharacteristic
9C2×#3757C411yescharacteristic, complemented
10C2×#3757C2211yescharacteristic
11D4×C3⋊Dic3—22no—
12D4×C3⋊Dic3—22no—
13C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
14C2×C4×C3⋊Dic3C411yescharacteristic, complemented
15C2×C3×#217C2214yes—
16C2×Dic32—22no—
17C3×#834C418yescomplemented
18#63579—22no—
19C2×D4×Dic3—32no—
20C2×D4×Dic3—61no—
21C2×C3×#99—32no—
22C2×#834D312yes—
23Dic3×C22⋊C4—34no—
24#4527—34no—
25C24×C32C2×C411yescharacteristic
26C24×C32C2311yescharacteristic
27C2×C32×D4—22no—
28C2×C32×D4—22no—
29C2×C32×D4C2×C414yes—
30C22×C32×C4C2×C411yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—42no—
34C22×C3⋊Dic3—42no—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3D412yes—
40C22×C3⋊Dic3D412yes—
41C22×C3×Dic3—24no—
42#3757—22no—
43#3757—22no—
44C4⋊(C3⋊Dic3)—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C3×#217—24no—
48C3×#217C2×C418yescomplemented
49Dic32—44no—
50C4×#99—91noSylow
51C22×C3×D4—21no—
52C22×C3×D4C2×D312yes—
53C23×Dic3—32no—
54C23×Dic3—32no—
55C23×Dic3—61no—
56C23×Dic3—61no—
57C2×C3×C22⋊C4—34no—
58C2×#217—32no—
59C2×#217—32no—
60C2×#217—61no—
61C2×#217—61no—
62C2×#217C2×D314yes—
63D4×Dic3—64no—
64D4×Dic3—64no—
65D4×Dic3—64no—
66D4×Dic3—64no—
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—61no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—64no—
72C3×#99—38no—
73#834Dic318yescomplemented
74C3⋊#95—64no—
75C23×C32—21no—
76C23×C32—21no—
77C23×C32—41no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32—41no—
81C23×C32C4212yescomplemented
82C23×C32C22×C411yescharacteristic
83C23×C32C22×C412yes—
84C23×C32C2×D412yes—
85C23×C32#4112yes—
86C32×D4—28no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4C4212yescomplemented
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—42no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C412yes—
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3×Dic3—28no—
104C2×C3×Dic3—44no—
105C2×C3×Dic3—44no—
106C2×C4×D4—91no—
107C2×#99—32no—
108C4×C22⋊C4—92no—
109#342—92no—
110C24×C3—21no—
111C24×C3—21no—
112C24×C3C4×D312yes—
113C24×C3C22×D312yes—
114C2×C3×D4—24no—
115C2×C3×D4—24no—
116C2×C3×D4—24no—
117C2×C3×D4—24no—
118C2×C3×D4—24no—
119C2×C3×D4C4×D314yes—
120C2×C3×D4C2×Dic314yes—
121C22×C3×C4—21no—
122C22×C3×C4—64no—
123C22×C3×C4C4×D312yes—
124C22×Dic3—24no—
125C22×Dic3—32no—
126C22×Dic3—34no—
127C22×Dic3—32no—
128C22×Dic3—34no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—62no—
140C22×Dic3—62no—
141C22×Dic3—124no—
142C22×Dic3—124no—
143C22×Dic3—124no—
144C22×Dic3—124no—
145C3×C22⋊C4—38no—
146C3×C22⋊C4—64no—
147#217—24no—
148#217—64no—
149#217—64no—
150#217—64no—
151#217—64no—
152#217C2×Dic318yescomplemented
153C4⋊Dic3—64no—
154C4⋊Dic3—64no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C4×Dic3—62no—
159C4×Dic3—128no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32—22no—
163C22×C32—22no—
164C22×C32—22no—
165C22×C32—42no—
166C22×C32—42no—
167C22×C32—42no—
168C22×C32—42no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32C2×C4211yescharacteristic
172C22×C32C2×C22⋊C411yescharacteristic
173C22×C32#11711yescharacteristic
174C22×C32C4×D414yes—
175C32×C4—22no—
176C3⋊Dic3—21no—
177C3⋊Dic3—22no—
178C3⋊Dic3—41no—
179C3⋊Dic3—41no—
180C3⋊Dic3#9912yescomplemented
181C3×Dic3—48no—
182C22×D4D3211yescharacteristic
183C23×C4—91no—
184C23×C4—91no—
185C4×D4—182no—
186C4×D4—182no—
187C2×C4⋊C4—91no—
188C2×C22⋊C4—34no—
189C2×C22⋊C4—91no—
190C2×C22⋊C4—91no—
191C2×C42—91no—
192C2×C42—182no—
193#99—38no—
194#95—182no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—22no—
201C23×C3—22no—
202C23×C3—21no—
203C23×C3—22no—
204C23×C3—42no—
205C23×C3—42no—
206C23×C3—42no—
207C23×C3—42no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—42no—
211C23×C3—42no—
212C23×C3C4×Dic314yescomplemented
213C23×C3C2×C4×D312yes—
214C23×C3C2×C4×D312yes—
215C23×C3D3×D414yes—
216C23×C3#23714yes—
217C23×C3C22×Dic312yes—
218C3×D4—216no—
219C3×D4—28no—
220C3×D4—28no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—68no—
227C2×C3×C4—124no—
228C2×C3×C4—124no—
229C2×C3×C4C4×Dic314yescomplemented
230C2×Dic3—28no—
231C2×Dic3—32no—
232C2×Dic3—32no—
233C2×Dic3—34no—
234C2×Dic3—44no—
235C2×Dic3—44no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—62no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—124no—
247C2×Dic3—124no—
248C2×Dic3—124no—
249C2×Dic3—122no—
250C2×Dic3—124no—
251C2×Dic3—124no—
252C2×Dic3—124no—
253C2×Dic3—124no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32—24no—
262C2×C32—42no—
263C2×C32C4×C22⋊C411yescharacteristic
264C2×C32C2×#9911yescharacteristic
265C2×C32#41011yescharacteristic
266C24#62411yescharacteristic
267C24C2×D3211yescharacteristic
268C2×D4—22no—
269C2×D4—22no—
270C2×D4D3×Dic314yes—
271C22×C4—64no—
272C22×C4—91no—
273C22×C4—92no—
274C22×C4—91no—
275C22×C4—92no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4—362no—
281C22×C4—362no—
282C22×C4#62411yescharacteristic
283C4⋊C4—182no—
284C22⋊C4—38no—
285C22⋊C4—64no—
286C22⋊C4—182no—
287C22⋊C4—182no—
288C42—181no—
289C42—181no—
290C42—364no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—24no—
294C22×C3—22no—
295C22×C3—24no—
296C22×C3—22no—
297C22×C3—24no—
298C22×C3—24no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—24no—
302C22×C3—21no—
303C22×C3—42no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—44no—
307C22×C3—42no—
308C22×C3—44no—
309C22×C3—42no—
310C22×C3—44no—
311C22×C3—44no—
312C22×C3—44no—
313C22×C3—44no—
314C22×C3—44no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3#87712yes—
319C22×C3D3×C22⋊C412yes—
320C22×C3#67⋊C414yes—
321C22×C3C2×C4×Dic312yes—
322C22×C3D4×Dic314yes—
323C3×C4—24no—
324C3×C4—24no—
325C3×C4—128no—
326Dic3—34no—
327Dic3—48no—
328Dic3—62no—
329Dic3—62no—
330Dic3—62no—
331Dic3—64no—
332Dic3—122no—
333Dic3—122no—
334Dic3—122no—
335Dic3—122no—
336Dic3—122no—
337C32C4×#9911yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23Dic3212yescomplemented
345C23C2×D3×Dic312yes—
346C23#380512yes—
347C23C2×#62411yescharacteristic
348C23#381112yes—
349D4—28no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—68no—
353C2×C4—91no—
354C2×C4—91no—
355C2×C4—92no—
356C2×C4—124no—
357C2×C4—124no—
358C2×C4—184no—
359C2×C4—182no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4—362no—
363C2×C4—362no—
364C2×C4—361no—
365C2×C4—362no—
366C2×C4—361no—
367C2×C4—361no—
368C2×C4Dic3212yescomplemented
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—24no—
372C2×C3—24no—
373C2×C3—22no—
374C2×C3—22no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—44no—
379C2×C3—44no—
380C2×C3—44no—
381C2×C3#474012yes—
382C2×C3D3×#9912yes—
383C2×C3Dic3×C22⋊C412yes—
384C22—22no—
385C22—21no—
386C22—22no—
387C22—21no—
388C22—22no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22C2×Dic3211yescharacteristic
396C22#6395711yescharacteristic
397C22#67⋊Dic314yes—
398C22#6397411yescharacteristic
399C4—22no—
400C4—92no—
401C4—128no—
402C4—181no—
403C4—182no—
404C4—361no—
405C4—361no—
406C3—21no—
407C3Dic3×#9912yescomplemented
408C2—24no—
409C2—21no—
410C2—21no—
411C2—42no—
412C2#1059152711yescharacteristic
413C2#1059152911yescharacteristic
414C2#1059170511yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C2×C22⋊C4
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591705C2semidirect
4. #10589187C2semidirect
7. C23×C3⋊Dic3C4semidirect
9. C2×#3757C4semidirect
13. C2×C4⋊(C3⋊Dic3)C4semidirect
14. C2×C4×C3⋊Dic3C4semidirect
17. C3×#834C4semidirect
48. C3×#217C2×C4semidirect
73. #834Dic3semidirect
81. C23×C32C42semidirect
89. C2×C32×C4C42semidirect
152. #217C2×Dic3semidirect
180. C3⋊Dic3#99semidirect
212. C23×C3C4×Dic3semidirect
229. C2×C3×C4C4×Dic3semidirect
337. C32C4×#99semidirect
344. C23Dic32semidirect
368. C2×C4Dic32semidirect
407. C3Dic3×#99semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#8342
#105917052
#105891872
Dic3×#993