Finite Group Databasebeta

← #11783759

Subgroups — #11783759

Order 1152.

1037 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1037 conjugacy classes of subgroups — too many to draw. Only its 158 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×#64090C211yesmaximal, characteristic
2#10591705C212yesmaximal, complemented
3C2×#63581C212yesmaximal
4C3×#4526C212yesmaximal, complemented
5#68952—32nomaximal
6C22×#638C2211yescharacteristic
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic, complemented
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3752C411yescharacteristic, complemented
11C2×#3750C411yescharacteristic, complemented
12C2×C4×C3⋊Dic3C411yescharacteristic, complemented
13#64090—22no—
14#64090—22no—
15C2×C3×#217C2214yes—
16C2×Dic32—22no—
17#63581C418yescomplemented
18#63579—22no—
19C2×#67⋊C4—32no—
20C2×#67⋊C4—61no—
21C2×#806—34no—
22Dic3×C22⋊C4—34no—
23C3×#342—32no—
24#4526D312yescomplemented
25C24×C32C2311yescharacteristic
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C2×#638—22no—
30C2×#638—22no—
31C2×#638C2×C414yes—
32C22×C3⋊Dic3—42no—
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3D412yes—
37C22×C3⋊Dic3D412yes—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—42no—
41C22×C3×Dic3—24no—
42C32×C22⋊C4—22no—
43#3752—22no—
44#3750—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C3×#217—24no—
48C3×#217C2×C418yescomplemented
49Dic32—44no—
50C4×#99—91noSylow
51C22×#67—32no—
52C22×#67—61no—
53C23×Dic3—32no—
54C23×Dic3—61no—
55C22×C4×D3—32no—
56C22×C4×D3—61no—
57C2×C3×C22⋊C4—21no—
58C2×C3×C22⋊C4—34no—
59C2×C3×C22⋊C4C2×D312yes—
60C2×#217C2×D314yes—
61C2×(C2×D3)⋊C4—32no—
62C2×(C2×D3)⋊C4—61no—
63C2×Dic3⋊C4—32no—
64C2×Dic3⋊C4—61no—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—64no—
68#67⋊C4—64no—
69#67⋊C4—64no—
70#67⋊C4—64no—
71#67⋊C4—64no—
72C3⋊#95—64no—
73#806—316no—
74C23×C32—41no—
75C23×C32—41no—
76C23×C32C22×C411yescharacteristic
77C23×C32C22×C412yes—
78C23×C32C2×D412yes—
79C23×C32#4112yes—
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3—41no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3C4212yescomplemented
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89#638—28no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3C4212yescomplemented
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C412yes—
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C4×C3⋊D3—42no—
101C4×C3⋊D3—42no—
102C2×C3×Dic3—28no—
103C2×C3×Dic3—44no—
104C2×C3×Dic3—44no—
105C2×C4×D4—91no—
106C2×#99—92no—
107C4×C22⋊C4—92no—
108#342—32no—
109C24×C3—21no—
110C24×C3C22×D312yes—
111C23×D3—32no—
112C23×D3—61no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—64no—
116C22×C3×C4C4×D312yes—
117C22×C3×C4C4×D312yes—
118C2×#67—38no—
119C2×#67—64no—
120C2×#67—64no—
121C2×#67—64no—
122C2×#67—64no—
123C2×#67—62no—
124C2×#67—62no—
125C22×Dic3—24no—
126C22×Dic3—32no—
127C22×Dic3—32no—
128C22×Dic3—34no—
129C22×Dic3—32no—
130C22×Dic3—34no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C22×Dic3—61no—
136C22×Dic3—124no—
137C22×Dic3—124no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—124no—
143C2×C4×D3—124no—
144C3×C22⋊C4—24no—
145C3×C22⋊C4—24no—
146C3×C22⋊C4—38no—
147C3×C22⋊C4—64no—
148#217—24no—
149#217C4×D318yescomplemented
150(C2×D3)⋊C4—64no—
151(C2×D3)⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154C4×Dic3—62no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C4×Dic3—128no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32—22no—
162C22×C32—22no—
163C22×C32—42no—
164C22×C32—42no—
165C22×C32C2×C4211yescharacteristic
166C22×C32C2×C22⋊C411yescharacteristic
167C22×C32#11711yescharacteristic
168C22×C32C4×D414yes—
169C2×C3⋊D3—22no—
170C2×C3⋊D3—42no—
171C2×C3⋊D3—41no—
172C2×C3⋊D3—41no—
173C2×C3⋊D3—42no—
174C32×C4—41no—
175C32×C4—41no—
176C3⋊Dic3—22no—
177C3⋊Dic3—21no—
178C3⋊Dic3—22no—
179C3⋊Dic3#9912yescomplemented
180C3×Dic3—48no—
181C22×D4—91no—
182C23×C4—91no—
183C23×C4—91no—
184C4×D4—182no—
185C4×D4—182no—
186C2×C4⋊C4—91no—
187C2×C22⋊C4—34no—
188C2×C22⋊C4—91no—
189C2×C22⋊C4D3211yescharacteristic
190C2×C42—91no—
191C2×C42—182no—
192#99—98no—
193#95—182no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—21no—
197C23×C3—22no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3C2×C4×D314yes—
203C23×C3C2×C4×D312yes—
204C23×C3D3×D414yes—
205C23×C3#23712yes—
206C23×C3#23912yes—
207C22×D3—34no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—122no—
214C22×D3—122no—
215C22×D3—122no—
216C22×D3—122no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—42no—
225C2×C3×C4—68no—
226C2×C3×C4—124no—
227C2×C3×C4—124no—
228#67—616no—
229#67—68no—
230#67—68no—
231C2×Dic3—28no—
232C2×Dic3—32no—
233C2×Dic3—34no—
234C2×Dic3—32no—
235C2×Dic3—34no—
236C2×Dic3—44no—
237C2×Dic3—44no—
238C2×Dic3—62no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—62no—
242C2×Dic3—68no—
243C2×Dic3—64no—
244C2×Dic3—62no—
245C2×Dic3—64no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—124no—
250C2×Dic3—124no—
251C2×Dic3—122no—
252C2×Dic3—124no—
253C2×Dic3—122no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—124no—
257C4×D3—124no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32—24no—
261C2×C32C4×C22⋊C411yescharacteristic
262C2×C32C2×#9911yescharacteristic
263C2×C32#41011yescharacteristic
264C3⋊D3—42no—
265C24—91no—
266C24C2×D3211yescharacteristic
267C2×D4—94no—
268C2×D4—182no—
269C2×D4—182no—
270C22×C4—64no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—92no—
274C22×C4—91no—
275C22×C4—92no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4—362no—
279C22×C4—362no—
280C22×C4#62411yescharacteristic
281C22×C4#62411yescharacteristic
282C4⋊C4—182no—
283C22⋊C4—22no—
284C22⋊C4—38no—
285C22⋊C4—64no—
286C22⋊C4—182no—
287C42—181no—
288C42—181no—
289C42—364no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—24no—
293C22×C3—22no—
294C22×C3—24no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—24no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—42no—
301C22×C3—42no—
302C22×C3—44no—
303C22×C3—42no—
304C22×C3—42no—
305C22×C3—44no—
306C22×C3—44no—
307C22×C3C42×D312yes—
308C22×C3D3×C22⋊C412yes—
309C22×C3#67⋊C414yes—
310C22×C3#89212yes—
311C22×C3#89314yes—
312C2×D3—64no—
313C2×D3—64no—
314C2×D3—122no—
315C2×D3—124no—
316C2×D3—124no—
317C2×D3—124no—
318C2×D3—122no—
319C2×D3—122no—
320C2×D3—122no—
321C2×D3—124no—
322C3×C4—42no—
323C3×C4—42no—
324C3×C4—42no—
325C3×C4—42no—
326C3×C4—128no—
327Dic3—34no—
328Dic3—48no—
329Dic3—62no—
330Dic3—62no—
331Dic3—64no—
332Dic3—64no—
333Dic3—62no—
334Dic3—64no—
335Dic3—122no—
336C32C4×#9911yescharacteristic, complemented, Sylow
337C23—41no—
338C23—41no—
339C23—92no—
340C23—181no—
341C23—181no—
342C23—361no—
343C23—361no—
344C23#379612yes—
345C23C4×D3212yes—
346C23C2×#62411yescharacteristic
347C23#381112yes—
348D4—188no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—68no—
354C2×C4—91no—
355C2×C4—92no—
356C2×C4—91no—
357C2×C4—92no—
358C2×C4—124no—
359C2×C4—124no—
360C2×C4—184no—
361C2×C4—182no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—362no—
365C2×C4—362no—
366C2×C4—362no—
367C2×C4—361no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—24no—
371C2×C3—24no—
372C2×C3—22no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—44no—
378C2×C3#466612yes—
379C2×C3#474012yes—
380C2×C3D3×#9912yes—
381D3—124no—
382D3—124no—
383C22—21no—
384C22—22no—
385C22—21no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—182no—
390C22—362no—
391C22—362no—
392C22—361no—
393C22—361no—
394C22#6384911yescharacteristic
395C22#6388114yes—
396C22C4×#62411yescharacteristic
397C22#6397411yescharacteristic
398C4—41no—
399C4—41no—
400C4—92no—
401C4—128no—
402C4—182no—
403C4—181no—
404C4—182no—
405C3—21no—
406C3#6895212yescomplemented
407C2—24no—
408C2—21no—
409C2—21no—
410C2—362no—
411C2#1059126011yescharacteristic
412C2#1059152711yescharacteristic
413C2#1059152911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591705C2semidirect
4. C3×#4526C2semidirect
8. C22×C4×C3⋊D3C4semidirect
10. C2×#3752C4semidirect
11. C2×#3750C4semidirect
12. C2×C4×C3⋊Dic3C4semidirect
17. #63581C4semidirect
24. #4526D3semidirect
48. C3×#217C2×C4semidirect
84. C22×C3⋊D3C42semidirect
96. C2×C3⋊Dic3C42semidirect
149. #217C4×D3semidirect
179. C3⋊Dic3#99semidirect
336. C32C4×#99semidirect
406. C3#68952semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
#105917052
C2×#635812
C3×#45262
#689523