Finite Group Databasebeta

← #11783383

Subgroups — #11783383

Order 1152.

750 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 127 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×#64286C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4#10590076C214yesmaximal
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157C2212yes—
7#64286—22no—
8#64286C414yescomplemented
9C2×C4⋊#157—21no—
10C2×C4×#157—21no—
11C3×#926—21no—
12C2×C3×C4×Dic3—21no—
13#63974C2212yes—
14C2×#3724—21no—
15C2×#3722C2212yes—
16#63957—21no—
17#63900C412yescomplemented
18C4×#624C412yescomplemented
19#63874—22no—
20#63874—21no—
21#63874C414yescomplemented
22#63849—21no—
23D3×#117—61no—
24C2×#872—61no—
25C23×C3⋊D3C2311yescharacteristic
26C22×#157—22no—
27C22×C32×C4D411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3Q812yes—
37C22×C3×Dic3—22no—
38C2×#624C2×C414yes—
39C22⋊#157—22no—
40C22⋊#157C2×C414yes—
41C4⋊#157—24no—
42C4×#157—24no—
43C3×#217—22no—
44C3×C4⋊Dic3—22no—
45C3×C4×Dic3—24no—
46C3×C4×Dic3—22no—
47#3724—24no—
48#3724—22no—
49#3722—22no—
50#3722—22no—
51#3722C2×C414yes—
52Dic32—22no—
53#1740—91nomaximal, Sylow
54C22×C4×D3—61no—
55C22×C4×D3—61no—
56C3×#117—61no—
57C2×C3×C42—61no—
58C2×(C2×D3)⋊C4—62no—
59#926—21no—
60C2×Dic3⋊C4—62no—
61C2×C4×Dic3—21no—
62#892—62no—
63D3×C4⋊C4—62no—
64D3×C22⋊C4—62no—
65#877—62no—
66#872—64no—
67#872—64no—
68#872—62no—
69C42×D3—62no—
70C23×C32C2×D411yescharacteristic
71C22×C3⋊D3—42no—
72C22×C3⋊D3C22×C411yescharacteristic
73C22×C3⋊D3C22×C411yescharacteristic
74C22×C3⋊D3C22×C411yescharacteristic
75C22×C3⋊D3C2×D411yescharacteristic
76C22×C3⋊D3C2×D411yescharacteristic
77C22×C3⋊D3C2×Q811yescharacteristic
78C2×#157—24no—
79C2×#157—44no—
80C2×C32×C4C22⋊C412yes—
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C4⋊C412yes—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C412yes—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C4⋊C412yes—
88C4×C3⋊D3C4212yes—
89C4×C3⋊D3C4212yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C22⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C4×C3⋊D3C4⋊C412yes—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—44no—
99#624—44no—
100C2×#117—91no—
101C2×#117—91no—
102C2×#117—91no—
103#342—94no—
104C23×D3—61no—
105C23×D3—61no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—62no—
109C22×Dic3—22no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C2×C4×D3—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—62no—
122C2×C4×D3—62no—
123C2×C4×D3—61no—
124C2×C4×D3—62no—
125C2×C4×D3—61no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—64no—
129C3×C4⋊C4—62no—
130C3×C22⋊C4—62no—
131C3×C42—62no—
132C3×C42—64no—
133#217—22no—
134(C2×D3)⋊C4—64no—
135(C2×D3)⋊C4—64no—
136(C2×D3)⋊C4—64no—
137C4⋊Dic3—22no—
138Dic3⋊C4—68no—
139Dic3⋊C4—64no—
140C4×Dic3—22no—
141C4×Dic3—24no—
142C4×Dic3—64no—
143C22×C32—22no—
144C22×C32C2×C22⋊C411yescharacteristic
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32C2×C4⋊C411yescharacteristic
147C2×C3⋊D3—22no—
148C2×C3⋊D3—22no—
149C2×C3⋊D3—41no—
150C2×C3⋊D3—41no—
151C2×C3⋊D3—41no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3C2×C4211yescharacteristic
154C2×C3⋊D3C2×C22⋊C411yescharacteristic
155C2×C3⋊D3C2×C4⋊C411yescharacteristic
156C2×C3⋊D3C2×C4⋊C411yescharacteristic
157#157—44no—
158C32×C4#9512yes—
159C32×C4#9512yes—
160C3⋊Dic3#9512yes—
161C3⋊Dic3#9512yes—
162C3×Dic3—44no—
163C3×Dic3—44no—
164C23×C4—91no—
165#117—61no—
166#117—94no—
167#117—94no—
168#117—182no—
169#117—181no—
170#117—181no—
171#117—181no—
172#117—182no—
173C2×C4⋊C4—92no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4—181no—
176C2×C22⋊C4—92no—
177C2×C22⋊C4—92no—
178C2×C22⋊C4—92no—
179C2×C42—61no—
180C2×C42—92no—
181C2×C42—181no—
182C23×C3—21no—
183C23×C3—21no—
184C22×D3—61no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—61no—
188C22×D3—61no—
189C22×D3—61no—
190C22×D3—61no—
191C22×D3—61no—
192C22×D3—61no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—61no—
196C22×D3—124no—
197C22×D3—124no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—64no—
207C2×C3×C4—64no—
208C2×C3×C4—124no—
209C2×Dic3—24no—
210C2×Dic3—24no—
211C2×Dic3—44no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—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—62no—
236C4×D3—128no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32C2×#9511yescharacteristic
240C2×C32#41012yes—
241C3⋊D3—21no—
242C3⋊D3—21no—
243C3⋊D3—21no—
244C3⋊D3—21no—
245C24—91no—
246C22×C4—62no—
247C22×C4—94no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—92no—
252C22×C4—92no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—92no—
256C22×C4—92no—
257C22×C4—182no—
258C22×C4GO+(4,𝔽2)11yescharacteristic
259C4⋊C4—62no—
260C4⋊C4—182no—
261C4⋊C4—184no—
262C4⋊C4—184no—
263C22⋊C4—62no—
264C22⋊C4—94no—
265C22⋊C4—94no—
266C22⋊C4—182no—
267C22⋊C4—182no—
268C22⋊C4—182no—
269C42—64no—
270C42—62no—
271C42—182no—
272C42—184no—
273C22×C3—24no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—42no—
281C2×D3—61no—
282C2×D3—61no—
283C2×D3—61no—
284C2×D3—61no—
285C2×D3—61no—
286C2×D3—61no—
287C2×D3—61no—
288C2×D3—61no—
289C2×D3—64no—
290C2×D3—122no—
291C2×D3—122no—
292C2×D3—122no—
293C2×D3—122no—
294C2×D3—122no—
295C2×D3—122no—
296C2×D3—122no—
297C2×D3—122no—
298C2×D3—122no—
299C2×D3—122no—
300C2×D3—122no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—124no—
306C3×C4—124no—
307Dic3—44no—
308Dic3—44no—
309Dic3—62no—
310Dic3—62no—
311Dic3—62no—
312Dic3—62no—
313C32#174011yescharacteristic, complemented, Sylow
314C23—91no—
315C23—91no—
316C23—91no—
317C23—91no—
318C23—91no—
319C23—91no—
320C23—362no—
321C23C2×GO+(4,𝔽2)11yescharacteristic
322C2×C4—64no—
323C2×C4—64no—
324C2×C4—91no—
325C2×C4—92no—
326C2×C4—91no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—92no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—124no—
337C2×C4—184no—
338C2×C4—364no—
339C2×C4—364no—
340C2×C4D32⋊C412yes—
341C2×C4D32⋊C411yescharacteristic
342C2×C4D32⋊C411yescharacteristic
343C2×C4#377312yes—
344C2×C3—22no—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352D3—62no—
353D3—62no—
354D3—121no—
355D3—121no—
356D3—121no—
357D3—121no—
358D3—121no—
359D3—121no—
360C22—22no—
361C22—91no—
362C22—91no—
363C22—91no—
364C22—91no—
365C22—182no—
366C22—182no—
367C22—361no—
368C22—361no—
369C22—361no—
370C22—361no—
371C22C2×D32⋊C411yescharacteristic
372C22C2×D32⋊C411yescharacteristic
373C22C2×#377311yescharacteristic
374C4—92no—
375C4—92no—
376C4—124no—
377C4—124no—
378C4—364no—
379C4#6373712yes—
380C4#6373712yes—
381C3—21no—
382C3—21no—
383C2—21no—
384C2—21no—
385C2—181no—
386C2—181no—
387C2—181no—
388C2—181no—
389C2#1059334512yes—
390C2C2×#6373711yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1740
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #64286C4semidirect
17. #63900C4semidirect
18. C4×#624C4semidirect
21. #63874C4semidirect
313. C32#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105949692
C2×#638742
#105900762
#17409