Finite Group Databasebeta

← #15674525

Subgroups — #15674525

Order 2944.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#13092976C211yesmaximal, characteristic
2C2×#10625100C211yesmaximal, characteristic, complemented
3C2×#10625016C211yesmaximal, characteristic, complemented
4C2×#10624988C211yesmaximal, characteristic, complemented
5#13092280C211yesmaximal, characteristic, complemented
6#13092183C211yesmaximal, characteristic, complemented
7C2×C23×#123C211yesmaximal, characteristic, complemented
8C22×D4×C23C2211yescharacteristic
9C23×C4×C23C2211yescharacteristic
10C22×C22⋊D23C2211yescharacteristic
11C23×#123—22no—
12C23×#123—22no—
13C2×C4⋊C4×C23—21no—
14C2×C22⋊C4×C23—21no—
15C2×C22⋊C4×C23C2211yescharacteristic
16#10625124—21no—
17C2×C22⋊Dic23C2211yescharacteristic
18C2×C22⋊Dic23C2211yescharacteristic
19C2×C22⋊Dic23C2211yescharacteristic
20#10625110—22no—
21#10625108—21no—
22#10625106—21no—
23#10625100—21no—
24#10625100—22no—
25#10625100—22no—
26C2×(C2×D23)⋊C4—21no—
27C2×Dic23⋊C4—21no—
28#10625016—22no—
29C23⋊#95—22no—
30#10624988—22no—
31C24×C23D411yescharacteristic
32C24×C23C2311yescharacteristic
33C23×D23D411yescharacteristic
34C2×D4×C23—21no—
35C2×D4×C23—21no—
36C2×D4×C23—21no—
37C2×D4×C23—21no—
38C2×D4×C23—21no—
39C2×D4×C23—21no—
40C22×C4×C23—21no—
41C22×C4×C23—21no—
42C22×C4×C23—21no—
43C22×C4×C23—21no—
44C22×C4×C23—21no—
45C22×C4×C23—21no—
46C22×C4×C23—21no—
47C22×C4×C23D411yescharacteristic
48C22×C4×C23D412yescomplemented
49C2×C22⋊D23—21no—
50C2×C22⋊D23—21no—
51C2×C22⋊D23—21no—
52C2×C22⋊D23—21no—
53C2×C22⋊D23—21no—
54C2×C22⋊D23—21no—
55C2×C22⋊D23—22no—
56C22×Dic23—21no—
57C22×Dic23—21no—
58C22×Dic23D411yescharacteristic
59C22×Dic23D412yes—
60C4⋊C4×C23—24no—
61C22⋊C4×C23—24no—
62C22⋊C4×C23—21no—
63C22⋊C4×C23D412yescomplemented
64C22⋊Dic23—22no—
65C22⋊Dic23—21no—
66C22⋊Dic23—21no—
67C22⋊Dic23—21no—
68C22⋊Dic23—21no—
69C22⋊Dic23—21no—
70C22⋊Dic23D412yescomplemented
71(C2×D23)⋊C4—24no—
72(C2×D23)⋊C4—22no—
73Dic23⋊C4—24no—
74Dic23⋊C4—22no—
75C23×C23—21no—
76C23×C23—21no—
77C23×C23—21no—
78C23×C23—42no—
79C23×C23—42no—
80C23×C23C2×D411yescharacteristic
81C23×C23C2×D411yescharacteristic
82C23×C23C2×D411yescharacteristic
83C23×C23C2×D411yescharacteristic
84C23×C23C2×D411yescharacteristic
85C23×C23C2×D411yescharacteristic
86C23×C23#4111yescharacteristic
87C22×D23—21no—
88C22×D23—21no—
89C22×D23—21no—
90C22×D23—42no—
91D4×C23—41no—
92D4×C23—41no—
93D4×C23—41no—
94D4×C23—41no—
95C2×C4×C23—22no—
96C2×C4×C23—21no—
97C2×C4×C23—22no—
98C2×C4×C23—22no—
99C2×C4×C23—21no—
100C2×C4×C23—22no—
101C2×C4×C23—21no—
102C2×C4×C23—42no—
103C2×C4×C23—41no—
104C2×C4×C23—41no—
105C2×C4×C23—41no—
106C2×C4×C23—41no—
107C22⋊D23—41no—
108C22⋊D23—41no—
109C22⋊D23—41no—
110C22⋊D23—41no—
111C22⋊D23—82no—
112C2×Dic23—21no—
113C2×Dic23—22no—
114C2×Dic23—21no—
115C2×Dic23—22no—
116C2×Dic23—21no—
117C2×Dic23—42no—
118C2×Dic23—42no—
119C2×Dic23—42no—
120C2×Dic23—41no—
121#2022—231nomaximal, Sylow
122C22×C23—22no—
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—41no—
126C22×C23—41no—
127C22×C23—41no—
128C22×C23—41no—
129C22×C23—42no—
130C22×C23—41no—
131C22×C23—42no—
132C22×C23—81no—
133C22×C23#12011yescharacteristic
134C22×C23#12011yescharacteristic
135C22×C23#12011yescharacteristic
136C22×C23#12111yescharacteristic
137C22×C23#12111yescharacteristic
138C22×C23#12111yescharacteristic
139C22×C23#12711yescharacteristic
140C2×D23—42no—
141C2×D23—41no—
142C2×D23—42no—
143C2×D23—81no—
144C4×C23—42no—
145C4×C23—42no—
146C4×C23—41no—
147Dic23—42no—
148Dic23—41no—
149Dic23—42no—
150Dic23—81no—
151#534—231no—
152C2×#123—231no—
153C2×#123D2311yescharacteristic, complemented
154C2×#99—231no—
155C2×#99—231no—
156#381—231no—
157#342—231no—
158C2×C23—21no—
159C2×C23—21no—
160C2×C23—21no—
161C2×C23—21no—
162C2×C23—21no—
163C2×C23—21no—
164C2×C23—81no—
165C2×C23#39211yescharacteristic
166C2×C23#45812yes—
167D23—81no—
168C22×D4—231no—
169C22×D4C2×D2311yescharacteristic
170C23×C4C2×D2311yescharacteristic
171#123—22no—
172#123—22no—
173#123—462no—
174#123—461no—
175#123—461no—
176#123—462no—
177#121—462no—
178#120—461no—
179#120—461no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—461no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—231no—
184C2×C22⋊C4—231no—
185C2×C22⋊C4—231no—
186C2×C22⋊C4—461no—
187C2×C22⋊C4C2×D2311yescharacteristic
188#99—462no—
189#99—462no—
190#95—462no—
191C23#202211yescharacteristic, complemented, Sylow
192C24—231no—
193C24C22⋊D2311yescharacteristic
194C24C22×D2311yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—461no—
202C2×D4—461no—
203C2×D4—461no—
204C2×D4—461no—
205C2×D4—461no—
206C2×D4—461no—
207C2×D4—462no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—231no—
216C22×C4—232no—
217C22×C4—461no—
218C22×C4—461no—
219C22×C4C22⋊D2311yescharacteristic
220C22×C4C22⋊D2312yescomplemented
221C4⋊C4—24no—
222C4⋊C4—464no—
223C4⋊C4—462no—
224C22⋊C4—24no—
225C22⋊C4—21no—
226C22⋊C4—232no—
227C22⋊C4—464no—
228C22⋊C4—462no—
229C22⋊C4—462no—
230C22⋊C4—461no—
231C22⋊C4—461no—
232C22⋊C4—461no—
233C22⋊C4—461no—
234C22⋊C4—461no—
235C22⋊C4C22⋊D2312yescomplemented
236C23—21no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—42no—
241C23—461no—
242C23—461no—
243C23—461no—
244C23—922no—
245C23D4×D2311yescharacteristic
246C23D4×D2311yescharacteristic
247C23D4×D2311yescharacteristic
248C23#6729011yescharacteristic
249C23C2×C22⋊D2311yescharacteristic
250C23C2×C22⋊D2311yescharacteristic
251C23C2×C22⋊D2311yescharacteristic
252D4—41no—
253D4—41no—
254D4—41no—
255D4—41no—
256D4—921no—
257D4—921no—
258D4—921no—
259D4—921no—
260D4—1842no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—462no—
274C2×C4—461no—
275C2×C4—462no—
276C2×C4—461no—
277C2×C4—461no—
278C2×C4—922no—
279C2×C4—922no—
280C2×C4—922no—
281C2×C4—921no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—41no—
291C22—42no—
292C22—81no—
293C22—922no—
294C22—921no—
295C22—922no—
296C22—1841no—
297C22#1062510811yescharacteristic
298C22#1062510811yescharacteristic
299C22#1062510911yescharacteristic
300C22#1062511011yescharacteristic
301C22#1062511011yescharacteristic
302C22#1062511111yescharacteristic
303C22#1062512411yescharacteristic
304C4—42no—
305C4—42no—
306C4—41no—
307C4—922no—
308C4—921no—
309C4—922no—
310C4—1841no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2—1841no—
319C2#1309232511yescharacteristic
320C2#1309260612yes—
subgroupG/H
centerC22#10625108
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC2×C23×#123C2
socleC22×C23#120
prime radical#13092976C2
hypercenterC2×#123D23
hypocenterC23#2022
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#10625100C2semidirect
3. C2×#10625016C2semidirect
4. C2×#10624988C2semidirect
5. #13092280C2semidirect
6. #13092183C2semidirect
7. C2×C23×#123C2semidirect
48. C22×C4×C23D4semidirect
63. C22⋊C4×C23D4semidirect
70. C22⋊Dic23D4semidirect
153. C2×#123D23semidirect
191. C23#2022semidirect
220. C22×C4C22⋊D23semidirect
235. C22⋊C4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130929762
C2×#106251002
C2×#106250162
C2×#106249882
#130922802
#130921832
C2×C23×#1232
#202223