Finite Group Databasebeta

← #11783294

Subgroups — #11783294

Order 1152.

822 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#3788C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4#10590075C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624—21no—
7C22×#622C2212yes—
8C2×#3788—22no—
9C2×#3788—22no—
10C2×#3788C414yescomplemented
11C2×C3×C4⋊Dic3—21no—
12C2×C3×C4×Dic3—21no—
13C2×#3724C2212yes—
14C2×#3724C2212yes—
15C2×#3722—21no—
16#63900—22no—
17#63900C414yescomplemented
18#63874—22no—
19#63874C414yescomplemented
20C2×D3×C4⋊C4—61no—
21C2×#872—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C4×C3⋊D3C2×C412yes—
26C2×C4×C3⋊D3C2×C412yes—
27C2×C4×C3⋊D3C2×C412yes—
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3Q812yes—
31C22×C3×Dic3—22no—
32C22×C3×Dic3—22no—
33C2×#624—24no—
34C2×#624—44no—
35C2×#622—22no—
36C2×#622—22no—
37C2×#622C2×C414yescomplemented
38#3788—28no—
39C3×C4⋊Dic3—24no—
40C3×C4×Dic3—24no—
41#3724—22no—
42#3724—22no—
43#3724C2×C414yes—
44#3724C2×C414yescomplemented
45#3722—24no—
46#1736—91nomaximal, Sylow
47C22×C4×D3—61no—
48C22×C4×D3—61no—
49C22×C4×D3—62no—
50C2×C3×C4⋊C4—61no—
51C2×C3×C42—61no—
52C2×(C2×D3)⋊C4—62no—
53C2×C4⋊Dic3—21no—
54C2×Dic3⋊C4—62no—
55C2×Dic3⋊C4—62no—
56C2×C4×Dic3—21no—
57D3×C4⋊C4—64no—
58D3×C4⋊C4—64no—
59#872—64no—
60#872—64no—
61C23×C32C2×D411yescharacteristic
62C22×C3⋊D3—22no—
63C22×C3⋊D3—22no—
64C22×C3⋊D3C22⋊C412yes—
65C22×C3⋊D3C22⋊C412yes—
66C22×C3⋊D3C4⋊C412yes—
67C2×C32×C4C22⋊C412yes—
68C2×C32×C4C22⋊C412yes—
69C2×C32×C4C4⋊C412yes—
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C22×C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×Q811yescharacteristic
76C4×C3⋊D3C4214yes—
77C4×C3⋊D3C22⋊C414yes—
78C4×C3⋊D3C4⋊C414yes—
79C4×C3⋊D3C4⋊C414yes—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—44no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—42no—
85#624—48no—
86#622—24no—
87C22×M16—91no—
88C2×#117—91no—
89C22×C4⋊C4—91no—
90#340—94no—
91C23×D3—61no—
92C23×D3—61no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—62no—
96C22×C3×C4—62no—
97C22×Dic3—22no—
98C22×Dic3—22no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—68no—
114C2×C4×D3—128no—
115C3×C4⋊C4—64no—
116C3×C42—64no—
117(C2×D3)⋊C4—68no—
118C4⋊Dic3—24no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121Dic3⋊C4—64no—
122Dic3⋊C4—64no—
123C4×Dic3—24no—
124C22×C32C2×C22⋊C411yescharacteristic
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32C2×C4⋊C411yescharacteristic
127C22×C32AGL(1,ℤ/8)12yes—
128C22×C32#13712yes—
129C2×C3⋊D3—24no—
130C2×C3⋊D3—22no—
131C2×C3⋊D3—22no—
132C2×C3⋊D3—24no—
133C2×C3⋊D3#9514yes—
134C32×C4#9514yes—
135C3⋊Dic3C2×C4211yescharacteristic
136C3⋊Dic3C2×C22⋊C411yescharacteristic
137C3⋊Dic3C2×C4⋊C411yescharacteristic
138C3⋊Dic3C2×C4⋊C411yescharacteristic
139C3×Dic3—44no—
140C3×Dic3—44no—
141C23×C4—91no—
142C23×C4—181no—
143C2×M16—94no—
144C2×M16—182no—
145C2×M16—182no—
146C22×C8—92no—
147#117—94no—
148#117—182no—
149C2×C4⋊C4—61no—
150C2×C4⋊C4—94no—
151C2×C4⋊C4—92no—
152C2×C4⋊C4—92no—
153C2×C4⋊C4—182no—
154C2×C22⋊C4—181no—
155C2×C42—61no—
156C23×C3—21no—
157C23×C3—21no—
158C22×D3—62no—
159C22×D3—62no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—62no—
163C22×D3—62no—
164C22×D3—64no—
165C22×D3—64no—
166C22×D3—122no—
167C22×D3—122no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—64no—
175C2×C3×C4—64no—
176C2×C3×C4—124no—
177C2×C3×C4—122no—
178C2×C3×C4—122no—
179C2×Dic3—24no—
180C2×Dic3—24no—
181C2×Dic3—44no—
182C2×Dic3—42no—
183C2×Dic3—42no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C4×D3—64no—
197C4×D3—64no—
198C4×D3—64no—
199C4×D3—64no—
200C4×D3—64no—
201C4×D3—64no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—1216no—
205C2×C32C2×#9511yescharacteristic
206C2×C32#41712yes—
207C2×C32#41811yescharacteristic
208C2×C32#41911yescharacteristic
209C2×C32#42812yes—
210C3⋊D3—24no—
211C24—91no—
212C22×C4—62no—
213C22×C4—62no—
214C22×C4—91no—
215C22×C4—92no—
216C22×C4—92no—
217C22×C4—92no—
218C22×C4—92no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—184no—
222C22×C4—364no—
223C22×C4GO+(4,𝔽2)11yescharacteristic
224M16—188no—
225C2×C8—94no—
226C2×C8—182no—
227C2×C8—182no—
228C4⋊C4—64no—
229C4⋊C4—94no—
230C4⋊C4—94no—
231C4⋊C4—182no—
232C4⋊C4—182no—
233C22⋊C4—184no—
234C42—64no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C2×D3—64no—
246C2×D3—64no—
247C2×D3—64no—
248C2×D3—68no—
249C2×D3—64no—
250C2×D3—68no—
251C2×D3—124no—
252C2×D3—122no—
253C2×D3—122no—
254C2×D3—124no—
255C3×C4—24no—
256C3×C4—24no—
257C3×C4—124no—
258C3×C4—124no—
259Dic3—44no—
260Dic3—44no—
261Dic3—61no—
262Dic3—61no—
263Dic3—61no—
264Dic3—61no—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268Dic3—61no—
269C32#173611yescharacteristic, complemented, Sylow
270C23—92no—
271C23—92no—
272C23—92no—
273C23—182no—
274C23—182no—
275C23C2×GO+(4,𝔽2)11yescharacteristic
276C2×C4—64no—
277C2×C4—64no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—94no—
285C2×C4—94no—
286C2×C4—94no—
287C2×C4—94no—
288C2×C4—124no—
289C2×C4—122no—
290C2×C4—122no—
291C2×C4—368no—
292C2×C4D32⋊C412yes—
293C2×C4D32⋊C412yes—
294C2×C4#377312yes—
295C8—184no—
296C2×C3—22no—
297C2×C3—22no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—22no—
303C2×C3—22no—
304C2×C3—21no—
305C2×C3—21no—
306D3—68no—
307D3—124no—
308C22—94no—
309C22—184no—
310C22—182no—
311C22—182no—
312C22—184no—
313C22#6422412yes—
314C22#6422612yes—
315C22C2×D32⋊C411yescharacteristic
316C22C2×D32⋊C411yescharacteristic
317C22C2×#377311yescharacteristic
318C4—91no—
319C4—91no—
320C4—91no—
321C4—91no—
322C4—124no—
323C4—124no—
324C4#6373714yes—
325C3—21no—
326C3—21no—
327C2—184no—
328C2#1059336012yes—
329C2#1059336311yescharacteristic
330C2#1059337411yescharacteristic
331C2#1059339412yes—
332C2C2×#6373711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1736
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590075C2semidirect
10. C2×#3788C4semidirect
17. #63900C4semidirect
19. #63874C4semidirect
37. C2×#622C2×C4semidirect
44. #3724C2×C4semidirect
269. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
C2×#639002
C2×#638742
#105900752
#17369