Finite Group Databasebeta

← #72252794

Subgroups — #72252794

Order 2592.

890 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 79 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×C3⋊D3×#157C211yesmaximal, characteristic
2#13049546C212yesmaximal
3#13049439C212yesmaximal, complemented
4C3×#88940C212yesmaximal, complemented
5D3×#3773—32nomaximal
6C2×C3⋊D32C2211yescharacteristic
7C2×C3⋊(C3⋊#157)C2211yescharacteristic
8C2×C32×#157C2211yescharacteristic
9C3⋊D3×#157C414yescomplemented
10#10620150—22no—
11C3×#6294—22no—
12C3×#6294C2214yes—
13C2×D3×#157—32no—
14C2×D3×#157—61no—
15D3×#624—34no—
16D3×#624—62no—
17#88940D312yescomplemented
18#88934—34no—
19C3×#3773—32no—
20C2×C3⋊(C3⋊(C3⋊D3))D411yescharacteristic
21C2×C32×C3⋊D3D411yescharacteristic
22C2×C32×C3⋊D3C2311yescharacteristic
23C3⋊D32C2×C412yes—
24C3⋊D32Q812yes—
25C3⋊(C3⋊#157)C2×C412yescomplemented
26C32×#157C2×C412yescomplemented
27C32×C3⋊Dic3—24no—
28C2×#3773—91no—
29#63900—91nomaximal
30C2×D3×C3⋊D3—32no—
31C2×D3×C3⋊D3—62no—
32C2×D3×C3⋊D3—61no—
33C2×C3⋊#157—32no—
34C2×C3⋊#157—61no—
35C2×C3×#157—21no—
36C2×C3×#157C2×D312yes—
37D3×#157—38no—
38D3×#157—64no—
39#6294—22no—
40#6294C2×D314yes—
41#6289—64no—
42#6289—64no—
43#6289—124no—
44C3×#624—34no—
45C3×#624—62no—
46C3×D3×Dic3—64no—
47C3×D3×Dic3—64no—
48C2×C34C2×D411yescharacteristic
49C3⋊(C3⋊(C3⋊D3))C4⋊C412yescomplemented
50C32×C3⋊D3C4⋊C412yescomplemented
51C32×C3⋊D3C22×C411yescharacteristic
52C32×C3⋊D3C2×Q811yescharacteristic
53C22×#157—91no—
54C2×C4×C3⋊D3—91no—
55C2×#624—92no—
56C2×#624—92no—
57C4×D32—184no—
58#3773—32no—
59#3773—92no—
60C3×C4⋊Dic3—92no—
61#3724—92no—
62C2×C3⋊(C3⋊D3)—32no—
63C2×C3⋊(C3⋊D3)—62no—
64C2×C3⋊(C3⋊D3)—61no—
65C2×C3⋊(C3⋊D3)—124no—
66C2×C3⋊(C3⋊D3)—242no—
67C2×C3×C3⋊D3—22no—
68C2×C3×C3⋊D3—21no—
69C2×C3×C3⋊D3C22×D312yes—
70C2×C32×D3—32no—
71C2×C32×D3—62no—
72C2×C32×D3—61no—
73D3×C3⋊D3—34no—
74D3×C3⋊D3—34no—
75D3×C3⋊D3—64no—
76D3×C3⋊D3—64no—
77D3×C3⋊D3—62no—
78D3×C3⋊D3—62no—
79C3⋊#157—34no—
80C3⋊#157—62no—
81C3×#157—22no—
82C3×#157C4×D314yescomplemented
83C3×C3⋊Dic3—24no—
84C3×C3⋊Dic3—24no—
85C3×C3⋊Dic3—44no—
86C32×Dic3—64no—
87C32×Dic3—64no—
88C32×Dic3—124no—
89D3×C4⋊C4—272no—
90C34C2×C4⋊C411yescharacteristic, complemented, Sylow
91C22×C3⋊D3—91no—
92C22×C3⋊D3—91no—
93C2×D32—184no—
94C2×D32—362no—
95C2×#157—91no—
96C2×#157—94no—
97C2×#157D3211yescharacteristic
98C2×C32×C4—91no—
99C2×C3⋊Dic3—91no—
100C4×C3⋊D3—94no—
101C4×C3⋊D3—184no—
102C2×C3×Dic3—94no—
103C2×C3×Dic3—182no—
104C3×C4×D3—184no—
105C3×C4×D3—184no—
106#624—34no—
107#624—62no—
108#624—182no—
109#624—182no—
110#624—184no—
111#624—364no—
112#624—364no—
113#624—364no—
114D3×Dic3—64no—
115D3×Dic3—64no—
116C2×C33—22no—
117C2×C33—21no—
118C2×C33—44no—
119C2×C33—82no—
120C2×C33D3×D412yes—
121C3⋊(C3⋊D3)—34no—
122C3⋊(C3⋊D3)—64no—
123C3⋊(C3⋊D3)—62no—
124C3⋊(C3⋊D3)—128no—
125C3⋊(C3⋊D3)—244no—
126C3×C3⋊D3—24no—
127C3×C3⋊D3—21no—
128C3×C3⋊D3—21no—
129C3×C3⋊D3C2×C4×D312yes—
130C3×C3⋊D3D3×Q812yes—
131C32×D3—34no—
132C32×D3—62no—
133C32×D3—62no—
134C32×D3—62no—
135C2×C4×D3—274no—
136C2×C4×D3—272no—
137C2×C4×D3—542no—
138C2×C4×D3—541no—
139C3×C4⋊C4—272no—
140C4⋊Dic3—92no—
141Dic3⋊C4—274no—
142C22×C32—91no—
143C22×C32—91no—
144C2×C3⋊D3—91no—
145C2×C3⋊D3—92no—
146C2×C3⋊D3—92no—
147C2×C3⋊D3—91no—
148C2×C3⋊D3—92no—
149C2×C3⋊D3—92no—
150C2×C3⋊D3—184no—
151C2×C3⋊D3—364no—
152C2×C3⋊D3—362no—
153C2×C3⋊D3—364no—
154C2×C3⋊D3—364no—
155C2×C3⋊D3—722no—
156C2×C3⋊D3—722no—
157C2×C3⋊D3—724no—
158C2×C3⋊D3GO+(4,𝔽2)11yescharacteristic
159C2×C3⋊D3C2×D3211yescharacteristic
160C2×C3×D3—64no—
161C2×C3×D3—64no—
162C2×C3×D3—122no—
163C2×C3×D3—122no—
164D32—188no—
165D32—188no—
166D32—364no—
167D32—364no—
168#157—92no—
169#157#62412yescomplemented
170C32×C4—92no—
171C32×C4—184no—
172C3⋊Dic3—24no—
173C3⋊Dic3—92no—
174C3×Dic3—64no—
175C3×Dic3—64no—
176C3×Dic3—64no—
177C3×Dic3—64no—
178C3×Dic3—124no—
179C3×Dic3—124no—
180C3×Dic3—124no—
181C3×Dic3—124no—
182C3×Dic3—128no—
183C2×C4⋊C4—811noSylow
184C33—22no—
185C33—21no—
186C33—44no—
187C33—82no—
188C33D3×C4⋊C412yescomplemented
189C22×D3—272no—
190C22×D3—542no—
191C22×D3—541no—
192C2×C3×C4—92no—
193C2×C3×C4—181no—
194C2×C3×C4—274no—
195C2×C3×C4—542no—
196C2×Dic3—94no—
197C2×Dic3—182no—
198C2×Dic3—272no—
199C2×Dic3—541no—
200C4×D3—184no—
201C4×D3—184no—
202C4×D3—278no—
203C4×D3—544no—
204C4×D3—544no—
205C4×D3—544no—
206C4×D3—1084no—
207C2×C32—24no—
208C2×C32—42no—
209C2×C32—44no—
210C2×C32—44no—
211C2×C32—44no—
212C2×C32—82no—
213C2×C32—82no—
214C2×C32—84no—
215C2×C32—91no—
216C2×C32—91no—
217C2×C32—92no—
218C2×C32#380211yescharacteristic
219C2×C32C2×GO+(4,𝔽2)11yescharacteristic
220C3⋊D3—92no—
221C3⋊D3—92no—
222C3⋊D3—188no—
223C3⋊D3—368no—
224C3⋊D3—364no—
225C3⋊D3—368no—
226C3⋊D3—368no—
227C3⋊D3—724no—
228C3⋊D3—724no—
229C3⋊D3—728no—
230C3⋊D3#377312yescomplemented
231C3⋊D3#379711yescharacteristic
232C3⋊D3C2×#62411yescharacteristic
233C3×D3—68no—
234C3×D3—64no—
235C3×D3—64no—
236C3×D3—122no—
237C3×D3—122no—
238C3×D3—124no—
239C22×C4—811no—
240C22×C4—812no—
241C4⋊C4—272no—
242C4⋊C4—812no—
243C22×C3—92no—
244C22×C3—182no—
245C22×C3—181no—
246C2×D3—32no—
247C2×D3—62no—
248C2×D3—61no—
249C2×D3—274no—
250C2×D3—274no—
251C2×D3—272no—
252C2×D3—542no—
253C2×D3—544no—
254C2×D3—544no—
255C2×D3—542no—
256C2×D3—542no—
257C2×D3—541no—
258C2×D3—1084no—
259C2×D3—2162no—
260C3×C4—94no—
261C3×C4—182no—
262C3×C4—184no—
263C3×C4—184no—
264C3×C4—364no—
265Dic3—64no—
266Dic3—64no—
267Dic3—124no—
268Dic3—274no—
269Dic3—542no—
270C32—24no—
271C32—42no—
272C32—44no—
273C32—44no—
274C32—44no—
275C32—82no—
276C32—82no—
277C32—84no—
278C32#6390011yescharacteristic, complemented
279C32C2×#377311yescharacteristic, complemented
280C23—811no—
281C2×C4—91no—
282C2×C4—274no—
283C2×C4—542no—
284C2×C4—814no—
285C2×C4—811no—
286C2×C4—1622no—
287C2×C3—22no—
288C2×C3—21no—
289C2×C3—44no—
290C2×C3—82no—
291C2×C3—92no—
292C2×C3—92no—
293C2×C3—181no—
294C2×C3—184no—
295C2×C3—181no—
296C2×C3D3×GO+(4,𝔽2)12yes—
297D3—34no—
298D3—62no—
299D3—62no—
300D3—62no—
301D3—274no—
302D3—544no—
303D3—542no—
304D3—1088no—
305D3—2164no—
306C22—91no—
307C22—91no—
308C22—812no—
309C22—812no—
310C22—811no—
311C4—92no—
312C4—184no—
313C4—812no—
314C3—22no—
315C3—21no—
316C3—44no—
317C3—82no—
318C3D3×#377312yescomplemented
319C2—91no—
320C2—92no—
321C2—91no—
322C2—812no—
323C2(#157⋊D3)⋊D311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2(#157⋊D3)⋊D3
commutatorC32×C3⋊D3C22×C4
Fitting, socleC2×C34C2×D4
prime radicalC2×C3⋊D32C22
cosocleC2×C32×C3⋊D3C23
hypocenterC34C2×C4⋊C4
LCSG ▷ C32×C3⋊D3 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. #13049439C2semidirect
4. C3×#88940C2semidirect
9. C3⋊D3×#157C4semidirect
17. #88940D3semidirect
25. C3⋊(C3⋊#157)C2×C4semidirect
26. C32×#157C2×C4semidirect
49. C3⋊(C3⋊(C3⋊D3))C4⋊C4semidirect
50. C32×C3⋊D3C4⋊C4semidirect
82. C3×#157C4×D3semidirect
90. C34C2×C4⋊C4semidirect
169. #157#624semidirect
188. C33D3×C4⋊C4semidirect
230. C3⋊D3#3773semidirect
278. C32#63900semidirect
279. C32C2×#3773semidirect
318. C3D3×#3773semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#1572
#130495462
#130494392
C3×#889402
D3×#37733
#639009