Finite Group Databasebeta

← #11773216

Subgroups — #11773216

Order 1152.

986 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 191 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×C4×#157C211yesmaximal, characteristic
2C22×#3773C212yesmaximal
3C2×#63737C212yesmaximal
4#10591370C212yesmaximal
5C23×#157C2211yescharacteristic
6C23×#157C2211yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C2214yes—
9C2×C4×#157—24no—
10C2×C4×#157C414yescomplemented
11C2×#3773—24no—
12C2×#3773—24no—
13C2×#3773C418yescomplemented
14#63737—24no—
15C3×C3⋊#95—22no—
16#63579—22no—
17D3×#95—62no—
18C23×C3⋊D3C2311yescharacteristic
19C22×#157—22no—
20C22×#157—22no—
21C22×#157C2×C412yes—
22C22×#157C2×C412yes—
23C22×#157C2×C414yes—
24C22×#157D412yes—
25C22×#157D414yes—
26C22×#157D412yes—
27C22×#157Q812yes—
28C22×#157Q812yes—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3Q812yes—
35C22×C3×Dic3—24no—
36C2×#624—24no—
37C2×#624—24no—
38C2×#624—24no—
39C2×#624—24no—
40C2×#624—24no—
41C2×#624C2×C418yes—
42C4×#157—28no—
43#3773—216no—
44C4⋊#95—91nomaximal, Sylow
45C22×C4×D3—64no—
46C22×C4×D3—62no—
47C3×#95—62no—
48C3⋊#95—22no—
49C3⋊#95—64no—
50C23×C32C2×D411yescharacteristic
51C22×C3⋊D3C22×C411yescharacteristic
52C22×C3⋊D3C22×C412yes—
53C22×C3⋊D3C2×D412yes—
54C22×C3⋊D3C2×D411yescharacteristic
55C22×C3⋊D3C2×D411yescharacteristic
56C22×C3⋊D3C2×Q811yescharacteristic
57C22×C3⋊D3C2×Q811yescharacteristic
58C22×C3⋊D3C2×Q811yescharacteristic
59C22×C3⋊D3#4112yes—
60C22×C3⋊D3#4112yes—
61C2×#157—22no—
62C2×#157—22no—
63C2×#157—24no—
64C2×#157—24no—
65C2×#157C4214yes—
66C2×#157C22⋊C418yes—
67C2×#157C22⋊C414yes—
68C2×#157C4⋊C414yes—
69C2×#157C4⋊C418yes—
70C2×#157C4⋊C414yescomplemented
71C2×C32×C4—22no—
72C2×C32×C4C4⋊C412yescomplemented
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3C4⋊C412yescomplemented
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3—24no—
78C2×C3×Dic3—28no—
79C2×C3×Dic3—44no—
80C2×C3×Dic3—44no—
81#624—28no—
82#624—28no—
83#624—44no—
84#624—44no—
85C22×C4⋊C4—92no—
86C22×C42—91no—
87C2×#95—92no—
88C2×#95—92no—
89C23×D3—62no—
90C22×C3×C4—22no—
91C22×C3×C4—64no—
92C22×Dic3—24no—
93C22×Dic3—62no—
94C2×C4×D3—68no—
95C2×C4×D3—64no—
96C2×C4×D3—64no—
97C2×C4×D3—68no—
98C2×C4×D3—124no—
99C2×C4×D3—124no—
100C2×C4×D3—124no—
101C2×C4×D3—124no—
102C2×C4×D3—124no—
103C2×C4×D3—124no—
104C22×C32C2×C4⋊C411yescharacteristic
105C22×C32C4×D412yes—
106C22×C32#12112yes—
107C22×C32#12711yescharacteristic
108C22×C32C4⋊Q811yescharacteristic
109C2×C3⋊D3C2×C4211yescharacteristic
110C2×C3⋊D3C2×C22⋊C411yescharacteristic
111C2×C3⋊D3C2×C22⋊C412yes—
112C2×C3⋊D3C2×C4⋊C411yescharacteristic
113C2×C3⋊D3C2×C4⋊C412yes—
114C2×C3⋊D3C2×C4⋊C411yescharacteristic
115C2×C3⋊D3#11711yescharacteristic
116C2×C3⋊D3#11711yescharacteristic
117C2×C3⋊D3C4×D412yes—
118C2×C3⋊D3C4×Q812yes—
119C2×C3⋊D3C4×Q812yes—
120C2×C3⋊D3#12112yes—
121C2×C3⋊D3C22⋊Q812yes—
122C2×C3⋊D3C22⋊Q812yes—
123C2×C3⋊D3#12412yes—
124C2×C3⋊D3#12512yes—
125C2×C3⋊D3C4⋊Q811yescharacteristic
126C2×C3⋊D3C4⋊Q811yescharacteristic
127#157—24no—
128#157#9518yescomplemented
129C32×C4—22no—
130C3⋊Dic3—22no—
131C3×Dic3—48no—
132C23×C4—94no—
133C23×C4—91no—
134C23×C4—91no—
135C23×C4—91no—
136C2×C4⋊C4—98no—
137C2×C4⋊C4—184no—
138C2×C4⋊C4—184no—
139C2×C42—94no—
140C2×C42—184no—
141#95—62no—
142#95—182no—
143#95—184no—
144C23×C3—22no—
145C22×D3—64no—
146C22×D3—62no—
147C22×D3—62no—
148C22×D3—62no—
149C22×D3—64no—
150C22×D3—62no—
151C22×D3—62no—
152C22×D3—62no—
153C22×D3—64no—
154C22×D3—64no—
155C2×C3×C4—24no—
156C2×C3×C4—44no—
157C2×C3×C4—68no—
158C2×C3×C4—124no—
159C2×C3×C4—124no—
160C2×Dic3—28no—
161C2×Dic3—44no—
162C2×Dic3—44no—
163C2×Dic3—64no—
164C2×Dic3—124no—
165C4×D3—128no—
166C4×D3—128no—
167C4×D3—124no—
168C4×D3—124no—
169C4×D3—128no—
170C4×D3—128no—
171C4×D3—128no—
172C2×C32C4×C4⋊C411yescharacteristic
173C2×C32#38011yescharacteristic
174C2×C32#38411yescharacteristic
175C2×C32#38912yes—
176C2×C32#39012yes—
177C3⋊D3C2×#9511yescharacteristic
178C3⋊D3C4×C4⋊C411yescharacteristic
179C3⋊D3#38011yescharacteristic
180C3⋊D3#38211yescharacteristic
181C3⋊D3#38912yes—
182C3⋊D3#39112yes—
183C24—91no—
184C22×C4—64no—
185C22×C4—98no—
186C22×C4—92no—
187C22×C4—94no—
188C22×C4—94no—
189C22×C4—92no—
190C22×C4—92no—
191C22×C4—92no—
192C22×C4—92no—
193C22×C4—92no—
194C22×C4—91no—
195C22×C4—92no—
196C22×C4—92no—
197C22×C4—182no—
198C22×C4—182no—
199C22×C4—184no—
200C22×C4—184no—
201C22×C4—184no—
202C22×C4—184no—
203C22×C4—184no—
204C22×C4—182no—
205C22×C4—182no—
206C22×C4GO+(4,𝔽2)11yescharacteristic
207C4⋊C4—1816no—
208C42—188no—
209C22×C3—22no—
210C22×C3—24no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—24no—
214C2×D3—64no—
215C2×D3—62no—
216C2×D3—62no—
217C2×D3—64no—
218C2×D3—64no—
219C2×D3—64no—
220C2×D3—64no—
221C2×D3—62no—
222C2×D3—64no—
223C2×D3—62no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—64no—
227C2×D3—64no—
228C2×D3—64no—
229C2×D3—64no—
230C2×D3—62no—
231C2×D3—62no—
232C3×C4—44no—
233C3×C4—128no—
234Dic3—48no—
235Dic3—124no—
236C32C4⋊#9511yescharacteristic, complemented, Sylow
237C23—91no—
238C23—91no—
239C23—92no—
240C23—92no—
241C23—91no—
242C23—91no—
243C23—91no—
244C23—91no—
245C23—92no—
246C23—92no—
247C23C2×GO+(4,𝔽2)11yescharacteristic
248C2×C4—22no—
249C2×C4—68no—
250C2×C4—94no—
251C2×C4—98no—
252C2×C4—94no—
253C2×C4—98no—
254C2×C4—94no—
255C2×C4—94no—
256C2×C4—92no—
257C2×C4—124no—
258C2×C4—124no—
259C2×C4—182no—
260C2×C4—182no—
261C2×C4—184no—
262C2×C4—188no—
263C2×C4—188no—
264C2×C4—182no—
265C2×C4—182no—
266C2×C4—184no—
267C2×C4—184no—
268C2×C4—182no—
269C2×C4—364no—
270C2×C4—364no—
271C2×C4#377312yescomplemented
272C2×C3—22no—
273C2×C3—24no—
274C2×C3—22no—
275C2×C3—24no—
276C2×C3—22no—
277D3—62no—
278D3—62no—
279D3—62no—
280D3—62no—
281D3—64no—
282D3—64no—
283C22—91no—
284C22—91no—
285C22—92no—
286C22—92no—
287C22—92no—
288C22—92no—
289C22—92no—
290C22—91no—
291C22—91no—
292C22—91no—
293C22—91no—
294C22—92no—
295C22—92no—
296C22—92no—
297C22—92no—
298C22—91no—
299C22—91no—
300C22—92no—
301C22#6422211yescharacteristic
302C22C4×GO+(4,𝔽2)12yes—
303C22#6423111yescharacteristic
304C22C2×#377311yescharacteristic
305C22#6424212yes—
306C4—22no—
307C4—98no—
308C4—128no—
309C4—184no—
310C4—182no—
311C3—22no—
312C2—91no—
313C2—91no—
314C2—91no—
315C2—91no—
316C2—92no—
317C2—92no—
318C2C4×#377311yescharacteristic
319C2#1059341012yes—
320C2#1059341311yescharacteristic
321C2#1059345412yes—
322C2#1059351611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4⋊#95
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. C2×C4×#157C4semidirect
13. C2×#3773C4semidirect
70. C2×#157C4⋊C4semidirect
72. C2×C32×C4C4⋊C4semidirect
74. C2×C3⋊Dic3C4⋊C4semidirect
128. #157#95semidirect
236. C32C4⋊#95semidirect
271. C2×C4#3773semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C22×#37732
C2×#637372
#105913702
C4⋊#959