Finite Group Databasebeta

← #15673698

Subgroups — #15673698

Order 2944.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D23C211yesmaximal, characteristic, complemented
2#13092929C211yesmaximal, characteristic
3C2×#10624987C211yesmaximal, characteristic, complemented
4C2×#10625007C211yesmaximal, characteristic, complemented
5C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
6#13092176C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×C4×D23C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C23×#117C2211yescharacteristic
12C2×C42×C23C2211yescharacteristic
13C2×(C2×D23)⋊C4—21no—
14C2×C4×Dic23C2211yescharacteristic
15C2×#67267C2211yescharacteristic
16M16×D23—22no—
17M16×D23—22no—
18C2×#67262—21no—
19C2×C8×D23—21no—
20#10625068C411yescharacteristic, complemented
21#10625068C411yescharacteristic, complemented
22#10625066C411yescharacteristic, complemented
23#10625066C411yescharacteristic, complemented
24#10625057—21no—
25#10625053—21no—
26C4×D92—21no—
27C4×D92—21no—
28C23⋊#95—21no—
29#10625007—22no—
30#10624987—22no—
31C23×D23D411yescharacteristic
32C22×C4×C23—21no—
33C22×C4×C23C2311yescharacteristic
34C2×C22⋊D23—21no—
35C22×Dic23—21no—
36C22×Dic23D411yescharacteristic
37#67288—21no—
38#67288—21no—
39#67288—21no—
40#67288—21no—
41C2×D92—21no—
42C2×D92—21no—
43C2×D92C2×C411yescharacteristic
44C2×C4×D23—21no—
45C2×C4×D23—21no—
46C2×C4×D23—21no—
47C2×C4×D23—21no—
48C2×C4×D23—21no—
49C2×C4×D23C2×C411yescharacteristic
50C2×C4×D23C2×C411yescharacteristic
51C2×C4×D23D411yescharacteristic
52C2×C4×D23D411yescharacteristic
53C2×Dic46C2×C411yescharacteristic
54M16×C23—21no—
55M16×C23D412yescomplemented
56C2×C8×C23—21no—
57C4⋊C4×C23C2×C411yescharacteristic
58C4⋊C4×C23C2×C411yescharacteristic
59C22⋊C4×C23—21no—
60C42×C23—21no—
61C42×C23—21no—
62C42×C23—21no—
63(C2×D23)⋊C4—24no—
64(C2×D23)⋊C4—21no—
65(C2×D23)⋊C4—21no—
66(C2×D23)⋊C4—21no—
67(C2×D23)⋊C4—21no—
68C4⋊Dic23—21no—
69C4⋊Dic23—21no—
70C4×Dic23—21no—
71C4×Dic23—21no—
72#67267—21no—
73#67267D412yescomplemented
74C2×C23⋊C8—21no—
75#67262—24no—
76C8×D23—24no—
77C23×C23C2×D411yescharacteristic
78C22×D23—21no—
79C22×D23—21no—
80C22×D23—22no—
81C22×D23—21no—
82C22×D23—41no—
83C22×D23C22⋊C411yescharacteristic
84C22×D23C22⋊C411yescharacteristic
85C2×C4×C23—22no—
86C2×C4×C23—21no—
87C2×C4×C23—21no—
88C2×C4×C23—41no—
89C2×C4×C23—41no—
90C2×C4×C23C22×C411yescharacteristic
91C2×C4×C23C2×D411yescharacteristic
92C2×C4×C23C2×D411yescharacteristic
93C2×C4×C23C2×D411yescharacteristic
94C2×C4×C23#4111yescharacteristic
95C2×C4×C23#4111yescharacteristic
96C22⋊D23—41no—
97C22⋊D23—41no—
98C2×Dic23—21no—
99C2×Dic23—21no—
100C2×Dic23—22no—
101C2×Dic23—21no—
102C2×Dic23—41no—
103C2×Dic23—41no—
104C2×Dic23C22⋊C411yescharacteristic
105C2×Dic23C22⋊C411yescharacteristic
106D92—21no—
107D92—21no—
108D92—42no—
109D92—42no—
110C4×D23—21no—
111C4×D23—21no—
112C4×D23—21no—
113C4×D23—21no—
114C4×D23—21no—
115C4×D23—21no—
116C4×D23—21no—
117C4×D23—21no—
118C4×D23—41no—
119C4×D23—41no—
120Dic46—21no—
121Dic46—21no—
122C8×C23—22no—
123C23⋊C8—22no—
124#1871—231nomaximal, Sylow
125C22×C23—21no—
126C22×C23—21no—
127C22×C23C2×C22⋊C411yescharacteristic
128C22×C23#12111yescharacteristic
129C22×C23#12111yescharacteristic
130C2×D23—21no—
131C2×D23—21no—
132C2×D23—21no—
133C2×D23—21no—
134C2×D23—21no—
135C2×D23—42no—
136C2×D23—42no—
137C2×D23—41no—
138C2×D23—41no—
139C2×D23—41no—
140C2×D23#10412yescomplemented
141C4×C23—42no—
142C4×C23—41no—
143C4×C23—41no—
144C4×C23C4×D411yescharacteristic
145C4×C23C4×D411yescharacteristic
146C4×C23#12011yescharacteristic
147C4×C23#12311yescharacteristic
148Dic23—21no—
149Dic23—21no—
150Dic23—42no—
151Dic23—41no—
152C22×M16—231no—
153#525—231no—
154C2×#104—231no—
155C2×#104—231no—
156C4×C22⋊C4—231no—
157#339—231no—
158#339D2311yescharacteristic, complemented
159C2×C23—21no—
160C2×C23—21no—
161C2×C23#38611yescharacteristic
162C2×C23C2×#10411yescharacteristic
163C2×C23#42111yescharacteristic
164D23—22no—
165D23—41no—
166D23—81no—
167C2×#41—231no—
168C23×C4—231no—
169C2×M16—231no—
170C2×M16—461no—
171C2×M16—462no—
172C2×M16—462no—
173C2×M16C2×D2311yescharacteristic
174C22×C8—461no—
175#123—461no—
176C22⋊Q8—231no—
177C22⋊Q8—231no—
178#121—231no—
179#121—231no—
180#120—461no—
181C4×D4—461no—
182C4×D4—461no—
183#117C2×D2311yescharacteristic
184C2×C22⋊C4—461no—
185C2×C42—231no—
186C2×C42C2×D2311yescharacteristic
187#104—462no—
188#104—462no—
189#95—461no—
190C23#187111yescharacteristic, complemented, Sylow
191C24—231no—
192#41—461no—
193#41—461no—
194#41—461no—
195#41—461no—
196C2×Q8—231no—
197C2×D4—231no—
198C2×D4—461no—
199C2×D4—461no—
200C2×D4—461no—
201C22×C4—21no—
202C22×C4—231no—
203C22×C4—231no—
204C22×C4—231no—
205C22×C4—231no—
206C22×C4—231no—
207C22×C4—461no—
208C22×C4—461no—
209C22×C4—461no—
210C22×C4—461no—
211C22×C4—461no—
212C22×C4—461no—
213C22×C4C22×D2311yescharacteristic
214M16—21no—
215M16—232no—
216M16—464no—
217M16—461no—
218M16D9212yescomplemented
219C2×C8—21no—
220C2×C8—464no—
221C2×C8—461no—
222C4⋊C4—461no—
223C4⋊C4—461no—
224C4⋊C4C4×D2311yescharacteristic
225C4⋊C4C4×D2311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—461no—
228C22⋊C4—461no—
229C22⋊C4—461no—
230C22⋊C4—461no—
231C22⋊C4—464no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—461no—
236C42—461no—
237C23—231no—
238C23—231no—
239C23—462no—
240C23—461no—
241C23—461no—
242C23—461no—
243C23—921no—
244C23D4×D2311yescharacteristic
245Q8—461no—
246Q8—461no—
247D4—461no—
248D4—461no—
249D4—922no—
250D4—922no—
251D4—921no—
252D4—921no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—231no—
259C2×C4—231no—
260C2×C4—461no—
261C2×C4—461no—
262C2×C4—461no—
263C2×C4—461no—
264C2×C4—461no—
265C2×C4—461no—
266C2×C4—461no—
267C2×C4—461no—
268C2×C4—461no—
269C2×C4—461no—
270C2×C4—462no—
271C2×C4—461no—
272C2×C4—921no—
273C2×C4—921no—
274C2×C4—921no—
275C2×C4—921no—
276C2×C4C2×C4×D2311yescharacteristic
277C2×C4C2×D9211yescharacteristic
278C2×C4#6728811yescharacteristic
279C2×C4D4×D2311yescharacteristic
280C2×C4D4×D2311yescharacteristic
281C2×C4#6729211yescharacteristic
282C8—22no—
283C8—462no—
284C22—21no—
285C22—21no—
286C22—232no—
287C22—461no—
288C22—461no—
289C22—461no—
290C22—461no—
291C22—461no—
292C22—922no—
293C22—922no—
294C22—921no—
295C22—921no—
296C22—921no—
297C22C22⋊C4×D2311yescharacteristic
298C22#1062505511yescharacteristic
299C22#1062506611yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—461no—
304C4—461no—
305C4—922no—
306C4—921no—
307C4C4×D9211yescharacteristic
308C4#1062505311yescharacteristic
309C4#1062506411yescharacteristic
310C4#1062506511yescharacteristic
311C2—21no—
312C2—21no—
313C2—462no—
314C2—921no—
315C2—1841no—
316C2#1309229511yescharacteristic
317C2#104×D2311yescharacteristic
318C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23C2×C22⋊C4
prime radical#13092929C2
cosocleC22×C4×C23C23
hypercenter#339D23
hypocenterC23#1871
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D23C2semidirect
3. C2×#10624987C2semidirect
4. C2×#10625007C2semidirect
5. C4×(C2×D23)⋊C4C2semidirect
6. #13092176C2semidirect
7. C23×#339C2semidirect
20. #10625068C4semidirect
21. #10625068C4semidirect
22. #10625066C4semidirect
23. #10625066C4semidirect
55. M16×C23D4semidirect
73. #67267D4semidirect
140. C2×D23#104semidirect
158. #339D23semidirect
190. C23#1871semidirect
218. M16D92semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D232
#130929292
C2×#106249872
C2×#106250072
C4×(C2×D23)⋊C42
#130921762
C23×#3392
#187123