Finite Group Databasebeta

← #11783192

Subgroups — #11783192

Order 1152.

902 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 135 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×#64283C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic
4#10590074C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624—21no—
7C2×#3792C2212yes—
8#64283—22no—
9#64283C414yescomplemented
10C2×#3788—21no—
11C2×#3787—21no—
12C3×#926—21no—
13C2×C3×C4×Dic3—21no—
14#63974—21no—
15#63957C2212yes—
16C2×Dic32C2212yes—
17#63900C412yescomplemented
18C4×#624—22no—
19C4×#624—21no—
20C4×#624C414yescomplemented
21#63874C412yescomplemented
22#63849—21no—
23D3×#117—61no—
24C2×C42×D3—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C4×C3⋊D3C2×C412yes—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3Q812yes—
36C22×C3×Dic3—22no—
37C2×#624—28no—
38C2×#624—24no—
39C2×#624—22no—
40#3792—22no—
41#3792C2×C414yescomplemented
42C2×#622—22no—
43#3788—24no—
44#3787—24no—
45C3×#217—22no—
46C3×C4⋊Dic3—22no—
47C3×C4×Dic3—24no—
48C3×C4×Dic3—22no—
49#3724C2×C414yescomplemented
50#3722—22no—
51Dic32—22no—
52Dic32—22no—
53Dic32C2×C414yescomplemented
54C2×#339—91nomaximal, Sylow
55C22×C4×D3—61no—
56C22×C4×D3—61no—
57C22×C4×D3—62no—
58C3×#117—61no—
59C2×C3×C42—61no—
60#926—21no—
61C2×C4×Dic3—21no—
62C2×C4×Dic3—62no—
63#892—62no—
64D3×C4⋊C4—62no—
65D3×C22⋊C4—62no—
66#877—62no—
67#872—62no—
68C42×D3—64no—
69C42×D3—64no—
70C42×D3—62no—
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3—24no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C22×C3⋊D3C22⋊C412yes—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3⋊D3C4⋊C412yes—
77C2×C32×C4C22⋊C412yes—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C4⋊C412yes—
81C2×C3⋊Dic3C22×C411yescharacteristic
82C2×C3⋊Dic3C22×C411yescharacteristic
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×Q811yescharacteristic
87C4×C3⋊D3C4212yes—
88C4×C3⋊D3C4212yes—
89C4×C3⋊D3C22⋊C412yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C4⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C2×C3×Dic3—28no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98#624—216no—
99#624—44no—
100#622—24no—
101C22×M16—91no—
102C2×#117—91no—
103C22×C42—91no—
104#339—94no—
105C23×D3—61no—
106C23×D3—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×Dic3—22no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—68no—
130C2×C4×D3—616no—
131C2×C4×D3—64no—
132C3×C4⋊C4—62no—
133C3×C22⋊C4—62no—
134C3×C42—64no—
135C3×C42—62no—
136#217—22no—
137(C2×D3)⋊C4—64no—
138C4⋊Dic3—22no—
139Dic3⋊C4—64no—
140C4×Dic3—24no—
141C4×Dic3—22no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C4×Dic3—64no—
145C22×C32—22no—
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C2×C4⋊C411yescharacteristic
149C2×C3⋊D3—22no—
150C2×C3⋊D3—24no—
151C2×C3⋊D3—24no—
152C2×C3⋊D3#9512yes—
153C2×C3⋊D3#9512yes—
154C2×C3⋊D3#10414yes—
155C32×C4#9512yes—
156C32×C4#9512yes—
157C3⋊Dic3C2×C4211yescharacteristic
158C3⋊Dic3C2×C22⋊C411yescharacteristic
159C3⋊Dic3C2×C4⋊C411yescharacteristic
160C3⋊Dic3C2×C4⋊C411yescharacteristic
161C3×Dic3—28no—
162C3×Dic3—44no—
163C23×C4—91no—
164C23×C4—181no—
165C2×M16—94no—
166C2×M16—92no—
167C2×M16—181no—
168C2×M16—182no—
169C22×C8—181no—
170#117—61no—
171#117—92no—
172#117—92no—
173#117—181no—
174C2×C4⋊C4—92no—
175C2×C22⋊C4—181no—
176C2×C42—61no—
177C2×C42—94no—
178C2×C42—92no—
179C2×C42—181no—
180C2×C42—182no—
181C23×C3—21no—
182C23×C3—21no—
183C22×D3—61no—
184C22×D3—62no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—62no—
188C22×D3—61no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—68no—
192C22×D3—124no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—64no—
202C2×C3×C4—68no—
203C2×C3×C4—64no—
204C2×Dic3—24no—
205C2×Dic3—28no—
206C2×Dic3—24no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—62no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—632no—
236C4×D3—128no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32C2×#9511yescharacteristic
240C2×C32C2×#10412yes—
241C3⋊D3—22no—
242C3⋊D3#33914yescomplemented
243C24—91no—
244C22×C4—62no—
245C22×C4—91no—
246C22×C4—92no—
247C22×C4—92no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—92no—
253C22×C4—92no—
254C22×C4—184no—
255C22×C4—188no—
256C22×C4—182no—
257C22×C4GO+(4,𝔽2)11yescharacteristic
258M16—94no—
259M16—184no—
260M16—182no—
261C2×C8—184no—
262C2×C8—182no—
263C4⋊C4—62no—
264C4⋊C4—94no—
265C22⋊C4—62no—
266C22⋊C4—182no—
267C42—64no—
268C42—62no—
269C42—94no—
270C42—182no—
271C42—182no—
272C22×C3—24no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—42no—
280C2×D3—62no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—62no—
286C2×D3—68no—
287C2×D3—68no—
288C2×D3—64no—
289C2×D3—124no—
290C2×D3—124no—
291C2×D3—122no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—68no—
297C3×C4—124no—
298Dic3—28no—
299Dic3—44no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303Dic3—61no—
304Dic3—61no—
305Dic3—61no—
306Dic3—61no—
307Dic3—61no—
308C32C2×#33911yescharacteristic, complemented, Sylow
309C23—91no—
310C23—91no—
311C23—92no—
312C23—92no—
313C23—184no—
314C23C2×GO+(4,𝔽2)11yescharacteristic
315C2×C4—68no—
316C2×C4—64no—
317C2×C4—64no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—92no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—1816no—
333C2×C4—364no—
334C2×C4D32⋊C412yes—
335C2×C4D32⋊C411yescharacteristic
336C2×C4D32⋊C411yescharacteristic
337C2×C4#377312yes—
338C8—184no—
339C2×C3—22no—
340C2×C3—22no—
341C2×C3—22no—
342C2×C3—22no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—41no—
346C2×C3—41no—
347D3—64no—
348D3—64no—
349D3—64no—
350D3—122no—
351C22—22no—
352C22—94no—
353C22—92no—
354C22—92no—
355C22—184no—
356C22—184no—
357C22—182no—
358C22C2×D32⋊C411yescharacteristic
359C22C2×D32⋊C411yescharacteristic
360C22C2×#377311yescharacteristic
361C4—68no—
362C4—91no—
363C4—91no—
364C4—91no—
365C4—91no—
366C4—124no—
367C4#6373712yes—
368C4#6373712yes—
369C3—21no—
370C3—21no—
371C2—21no—
372C2—21no—
373C2—94no—
374C2—182no—
375C2#1059338012yes—
376C2C2×#6373711yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#339
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590074C2semidirect
9. #64283C4semidirect
17. #63900C4semidirect
20. C4×#624C4semidirect
21. #63874C4semidirect
41. #3792C2×C4semidirect
49. #3724C2×C4semidirect
53. Dic32C2×C4semidirect
242. C3⋊D3#339semidirect
308. C32C2×#339semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
#105949692
C2×C4×#6242
#105900742
C2×#3399