Finite Group Databasebeta

← #11785749

Subgroups — #11785749

Order 1152.

532 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#10594969C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4#10590052C212yesmaximal, complemented
5#10590052C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3788C2212yes—
8C3×#926—21no—
9#63974C412yes—
10#63957—21no—
11#63900C2211yescharacteristic
12#63900C2211yescharacteristic
13C4×#624C412yes—
14#63874—21no—
15#63849—21no—
16C2×#3712C2212yes—
17C22⋊#622—21no—
18#63778—21no—
19C3×#830—21no—
20#63557—21no—
21D3×#117—61no—
22#4726—61no—
23C23×C3⋊D3C2×C411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C4×C3⋊D3—24no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#624C2×C412yes—
32C2×#624C2×C412yes—
33C2×#622—22no—
34#3788—24no—
35C3×#217—22no—
36C3×C4⋊Dic3—21no—
37C3×C4⋊Dic3—21no—
38C3×C4×Dic3—22no—
39C2×C3×C3⋊C8—22no—
40#3724—21no—
41#3724—21no—
42#3722—22no—
43Dic32—22no—
44#3712—24no—
45#1822—91nomaximal, Sylow
46C22×C4×D3—61no—
47C22×C4×D3—61no—
48C3×#117—61no—
49#926—21no—
50C2×ΓL(1,𝔽25)—62no—
51#892—61no—
52#892—61no—
53D3×C4⋊C4—61no—
54D3×C4⋊C4—61no—
55D3×C22⋊C4—62no—
56#877—62no—
57#872—62no—
58C42×D3—62no—
59C3×C22⋊C8—61no—
60#830—21no—
61(C2×D3)⋊C8—62no—
62C23×C32C22⋊C411yescharacteristic
63C22×C3⋊D3—22no—
64C22×C3⋊D3—41no—
65C22×C3⋊D3—41no—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C22×C3⋊D3C22×C411yescharacteristic
68C2×C32×C4—22no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C4×C3⋊D3—22no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3#4114yes—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80#624—42no—
81#624—42no—
82#622—42no—
83C3×C3⋊C8—42no—
84C2×#117—91no—
85#407—91no—
86#407—91no—
87#343—92no—
88#343—92no—
89C23×D3—61no—
90C23×D3—61no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—68no—
106C2×C4×D3—124no—
107C2×C3×C8—62no—
108C3×C4⋊C4—61no—
109C3×C4⋊C4—61no—
110C3×C22⋊C4—62no—
111C3×C42—62no—
112#217—22no—
113(C2×D3)⋊C4—62no—
114(C2×D3)⋊C4—62no—
115C4⋊Dic3—21no—
116C4⋊Dic3—21no—
117Dic3⋊C4—62no—
118Dic3⋊C4—62no—
119C4×Dic3—22no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C2×C3⋊C8—22no—
123ΓL(1,𝔽25)—124no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—21no—
133C2×C3⋊D3—44no—
134C2×C3⋊D3#11712yes—
135C32×C4—21no—
136C32×C4#12312yes—
137C3⋊Dic3—21no—
138C3⋊Dic3#12312yes—
139C3×Dic3—42no—
140C3×Dic3—42no—
141C23×C4—91no—
142C2×M16—92no—
143C2×M16—92no—
144#117—61no—
145#117—181no—
146#117—181no—
147#117—181no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C22⋊C4—92no—
151C2×C42—92no—
152C22⋊C8—61no—
153C22⋊C8—181no—
154C22⋊C8—181no—
155C22⋊C8—181no—
156C23×C3—21no—
157C23×C3—21no—
158C22×D3—61no—
159C22×D3—61no—
160C22×D3—61no—
161C22×D3—61no—
162C22×D3—64no—
163C22×D3—122no—
164C22×D3—122no—
165C22×D3—122no—
166C22×D3—122no—
167C22×D3—122no—
168C2×C3×C4—24no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—42no—
174C2×C3×C4—62no—
175C2×C3×C4—62no—
176C2×Dic3—22no—
177C2×Dic3—22no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—64no—
183C2×Dic3—122no—
184C4×D3—64no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—64no—
189C4×D3—122no—
190C4×D3—122no—
191C4×D3—122no—
192C4×D3—124no—
193C4×D3—124no—
194C3×C8—122no—
195C3⋊C8—42no—
196C2×C32—41no—
197C2×C32#38111yescharacteristic
198C2×C32#41311yescharacteristic
199C2×C32#41311yescharacteristic
200C3⋊D3—22no—
201C3⋊D3—41no—
202C24—91no—
203C22×C4—92no—
204C22×C4—92no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—184no—
211C22×C4GO+(4,𝔽2)11yescharacteristic
212M16—184no—
213M16—184no—
214C2×C8—62no—
215C2×C8—182no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C22⋊C4—62no—
221C22⋊C4—182no—
222C42—62no—
223C42—182no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3—41no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—62no—
236C2×D3—62no—
237C2×D3—62no—
238C2×D3—121no—
239C2×D3—121no—
240C2×D3—121no—
241C2×D3—121no—
242C2×D3—121no—
243C2×D3—121no—
244C2×D3—128no—
245C2×D3—128no—
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—41no—
250C3×C4—122no—
251C3×C4—122no—
252Dic3—42no—
253Dic3—42no—
254Dic3—62no—
255Dic3—62no—
256Dic3—62no—
257Dic3—121no—
258C32#182211yescharacteristic, complemented, Sylow
259C23—91no—
260C23—91no—
261C23—182no—
262C23—361no—
263C23—361no—
264C23D32⋊C411yescharacteristic
265C2×C4—22no—
266C2×C4—62no—
267C2×C4—62no—
268C2×C4—91no—
269C2×C4—94no—
270C2×C4—91no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—362no—
276C2×C4—362no—
277C2×C4D32⋊C411yescharacteristic
278C2×C4C2×GO+(4,𝔽2)11yescharacteristic
279C8—122no—
280C8—362no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—42no—
288C2×C3—42no—
289D3—64no—
290D3—122no—
291D3—122no—
292D3—122no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—92no—
297C22—181no—
298C22—181no—
299C22—181no—
300C22—181no—
301C22—181no—
302C22—364no—
303C22C2×D32⋊C411yescharacteristic
304C4—21no—
305C4—92no—
306C4—122no—
307C4—122no—
308C4—181no—
309C4#6423312yes—
310C3—21no—
311C3—21no—
312C2—41no—
313C2—182no—
314C2—361no—
315C2#1059331111yescharacteristic
316C2#1059331311yescharacteristic
317C2#1059348811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1822
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590052C2semidirect
5. #10590052C2semidirect
258. C32#1822semidirect

Maximal subgroups

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

subgroupindex
#105949692
#105938032
#105911592
#105900522
#18229