Finite Group Databasebeta

← #11783267

Subgroups — #11783267

Order 1152.

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

normal subgroups only

This group has 758 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×#64286C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4#10590049C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—21no—
7#64286—22no—
8#64286C414yescomplemented
9C2×C4⋊#157C2212yes—
10C2×C4×#157—21no—
11C3×#926—21no—
12C22×C3×C3⋊C8—21no—
13#63974—21no—
14#63957C412yescomplemented
15#63900C2212yes—
16C4×#624—21no—
17#63874C412yescomplemented
18#63849—21no—
19C2×#3710—21no—
20C2×#3710—22no—
21C2×#3710C414yescomplemented
22C2×#3710C2212yes—
23C22×D3×C8—61no—
24D3×#117—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—22no—
27C22×C32×C4D411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2×C412yes—
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3Q812yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#624—22no—
38C22⋊#157—24no—
39C4⋊#157—22no—
40C4⋊#157C2×C414yes—
41C4×#157—24no—
42C3×#217—22no—
43C3×C4⋊Dic3—22no—
44C3×C4×Dic3—22no—
45C2×C3×C3⋊C8—24no—
46C2×C3×C3⋊C8—22no—
47#3724C2×C414yes—
48#3722—22no—
49Dic32—22no—
50#3710—24no—
51#3710—22no—
52#3710C2×C414yes—
53#1735—91nomaximal, Sylow
54C22×C4×D3—61no—
55C22×C4×D3—61no—
56C22×C3×C8—61no—
57C3×#117—61no—
58#926—21no—
59C22×C3⋊C8—21no—
60C2×D3×C8—64no—
61C2×D3×C8—62no—
62C2×D3×C8—62no—
63C2×D3×C8—64no—
64#892—62no—
65D3×C4⋊C4—62no—
66D3×C22⋊C4—62no—
67#877—62no—
68#872—62no—
69C42×D3—62no—
70C23×C32C22⋊C411yescharacteristic
71C22×C3⋊D3—24no—
72C22×C3⋊D3C22⋊C411yescharacteristic
73C22×C3⋊D3C22⋊C412yes—
74C22×C3⋊D3C4⋊C412yes—
75C22×C3⋊D3C2×D411yescharacteristic
76C2×#157—24no—
77C2×#157—44no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C412yes—
80C2×C32×C4C4⋊C412yes—
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C4212yes—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C4⋊C412yes—
85C2×C3⋊Dic3C22×C411yescharacteristic
86C4×C3⋊D3C4212yes—
87C4×C3⋊D3C22⋊C412yes—
88C4×C3⋊D3C22⋊C412yes—
89C4×C3⋊D3C4⋊C412yes—
90C4×C3⋊D3C4⋊C412yes—
91C4×C3⋊D3C4⋊C412yes—
92C4×C3⋊D3C22×C411yescharacteristic
93C4×C3⋊D3C22×C411yescharacteristic
94C4×C3⋊D3C2×D411yescharacteristic
95C4×C3⋊D3C2×Q811yescharacteristic
96C2×C3×Dic3—24no—
97#624—44no—
98C3×C3⋊C8—24no—
99C23×C8—91no—
100C2×#117—91no—
101C2×#117—91no—
102#340—94no—
103C23×D3—61no—
104C23×D3—61no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—62no—
114C2×C4×D3—61no—
115C2×C4×D3—62no—
116C2×C4×D3—61no—
117C2×C4×D3—62no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—61no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C3×C8—62no—
127C2×C3×C8—64no—
128C3×C4⋊C4—62no—
129C3×C22⋊C4—62no—
130C3×C42—62no—
131#217—22no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—22no—
134Dic3⋊C4—64no—
135C4×Dic3—22no—
136C4×Dic3—64no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8—24no—
139D3×C8—64no—
140D3×C8—68no—
141D3×C8—64no—
142C22×C32—22no—
143C22×C32#9512yes—
144C22×C32C2×C22⋊C411yescharacteristic
145C2×C3⋊D3—22no—
146C2×C3⋊D3—24no—
147C2×C3⋊D3—24no—
148C2×C3⋊D3#9512yes—
149C2×C3⋊D3C2×C22⋊C411yescharacteristic
150C2×C3⋊D3C2×C4⋊C411yescharacteristic
151C2×C3⋊D3#13514yes—
152#157—44no—
153C32×C4#9512yes—
154C32×C4C2×C22⋊C411yescharacteristic
155C32×C4C2×C4⋊C411yescharacteristic
156C3⋊Dic3#9512yes—
157C3⋊Dic3C2×C4211yescharacteristic
158C3⋊Dic3C2×C4⋊C411yescharacteristic
159C3×Dic3—44no—
160C23×C4—91no—
161C22×C8—61no—
162C22×C8—92no—
163C22×C8—94no—
164C22×C8—181no—
165C22×C8—182no—
166#117—61no—
167#117—92no—
168#117—92no—
169#117—94no—
170#117—181no—
171#117—182no—
172C2×C4⋊C4—92no—
173C2×C4⋊C4—92no—
174C2×C22⋊C4—181no—
175C2×C22⋊C4—181no—
176C2×C42—181no—
177C2×C42—181no—
178C23×C3—21no—
179C23×C3—21no—
180C22×D3—61no—
181C22×D3—62no—
182C22×D3—62no—
183C22×D3—61no—
184C22×D3—61no—
185C22×D3—61no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—68no—
189C22×D3—124no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—64no—
199C2×Dic3—24no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C4×D3—62no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—62no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—61no—
223C4×D3—61no—
224C4×D3—61no—
225C4×D3—61no—
226C4×D3—61no—
227C4×D3—61no—
228C4×D3—128no—
229C3×C8—64no—
230C3⋊C8—24no—
231C2×C32—22no—
232C2×C32C2×#9511yescharacteristic
233C2×C32#41612yes—
234C3⋊D3—22no—
235C3⋊D3#41612yes—
236C3⋊D3#42712yes—
237C24—91no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—182no—
248C22×C4—182no—
249C22×C4GO+(4,𝔽2)11yescharacteristic
250C2×C8—62no—
251C2×C8—64no—
252C2×C8—94no—
253C2×C8—182no—
254C2×C8—184no—
255C4⋊C4—62no—
256C4⋊C4—94no—
257C4⋊C4—94no—
258C4⋊C4—182no—
259C22⋊C4—62no—
260C22⋊C4—182no—
261C22⋊C4—184no—
262C42—62no—
263C42—182no—
264C42—184no—
265C22×C3—24no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—42no—
271C2×D3—62no—
272C2×D3—61no—
273C2×D3—61no—
274C2×D3—61no—
275C2×D3—61no—
276C2×D3—64no—
277C2×D3—64no—
278C2×D3—62no—
279C2×D3—68no—
280C2×D3—68no—
281C2×D3—64no—
282C2×D3—124no—
283C2×D3—124no—
284C2×D3—122no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—124no—
292Dic3—44no—
293Dic3—62no—
294Dic3—62no—
295Dic3—61no—
296Dic3—61no—
297Dic3—61no—
298Dic3—61no—
299C32#173511yescharacteristic, complemented, Sylow
300C23—91no—
301C23—91no—
302C23—92no—
303C23—92no—
304C23—184no—
305C23D32⋊C411yescharacteristic
306C2×C4—64no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—92no—
310C2×C4—92no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—92no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—92no—
317C2×C4—92no—
318C2×C4—92no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—184no—
322C2×C4—364no—
323C2×C4—364no—
324C2×C4D32⋊C412yes—
325C2×C4D32⋊C411yescharacteristic
326C2×C4#377312yes—
327C2×C4C2×GO+(4,𝔽2)11yescharacteristic
328C8—64no—
329C2×C3—24no—
330C2×C3—22no—
331C2×C3—22no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—42no—
335D3—62no—
336D3—62no—
337D3—62no—
338D3—62no—
339D3—64no—
340D3—122no—
341C22—22no—
342C22—94no—
343C22—91no—
344C22—91no—
345C22—92no—
346C22—184no—
347C22—184no—
348C22—182no—
349C22#6373712yes—
350C22C2×D32⋊C411yescharacteristic
351C4—92no—
352C4—91no—
353C4—91no—
354C4—124no—
355C4—364no—
356C4#6373712yes—
357C4C2×D32⋊C411yescharacteristic
358C4C2×#377311yescharacteristic
359C3—21no—
360C3—21no—
361C2—22no—
362C2—92no—
363C2—92no—
364C2—182no—
365C2#1059331712yes—
366C2C2×#6373711yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1735
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. #10590049C2semidirect
8. #64286C4semidirect
14. #63957C4semidirect
17. #63874C4semidirect
21. C2×#3710C4semidirect
299. C32#1735semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105949692
C22×#37102
#105900492
#17359