Finite Group Databasebeta

← #15673849

Subgroups — #15673849

Order 2944.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10625053C211yesmaximal, characteristic
2C2×C22⋊C4×D23C211yesmaximal, characteristic, complemented
3C2×#10624988C211yesmaximal, characteristic, complemented
4C2×#10624988C211yesmaximal, characteristic, complemented
5#13092272C211yesmaximal, characteristic, complemented
6#13092184C211yesmaximal, characteristic, complemented
7C23×#342C211yesmaximal, characteristic, complemented
8C24×D23C2211yescharacteristic
9C22×C22⋊D23C2211yescharacteristic
10C22×D92C412yescomplemented
11C22×C4×D23—21no—
12C2×C22⋊C4×C23C2211yescharacteristic
13C2×C22⋊C4×C23C2211yescharacteristic
14C2×C22⋊C4×C23C2211yescharacteristic
15C2×C22⋊Dic23C2211yescharacteristic
16C2×C22⋊Dic23C2211yescharacteristic
17C2×(C2×D23)⋊C4—21no—
18C2×(C2×D23)⋊C4—22no—
19C2×(C2×D23)⋊C4C412yescomplemented
20#10625053—21no—
21#10625053—22no—
22#10625053—21no—
23C22⋊C4×D23—22no—
24C22⋊C4×D23—22no—
25#10624988—22no—
26#10624988—22no—
27C24×C23C2311yescharacteristic
28C23×D23—21no—
29C23×D23—21no—
30C23×D23—21no—
31C23×D23—21no—
32C23×D23—44no—
33C23×D23C2×C412yes—
34C23×D23C2×C411yescharacteristic, complemented
35C23×D23D411yescharacteristic
36C23×D23D412yes—
37C23×D23D411yescharacteristic
38C22×C4×C23—21no—
39C22×C4×C23—21no—
40C22×C4×C23C2×C412yescomplemented
41C2×C22⋊D23—21no—
42C2×C22⋊D23—21no—
43C2×C22⋊D23—21no—
44C2×C22⋊D23—21no—
45C2×C22⋊D23—21no—
46C2×C22⋊D23—21no—
47C22×Dic23—21no—
48C22×Dic23—21no—
49C22×Dic23C2×C411yescharacteristic, complemented
50C2×D92—22no—
51C2×D92—22no—
52C2×D92—44no—
53C2×C4×D23—24no—
54C2×C4×D23—44no—
55C22⋊C4×C23—21no—
56C22⋊C4×C23—21no—
57C22⋊C4×C23—21no—
58C22⋊C4×C23—21no—
59C22⋊C4×C23—21no—
60C22⋊C4×C23D412yescomplemented
61C22⋊Dic23—21no—
62C22⋊Dic23—21no—
63C22⋊Dic23—21no—
64C22⋊Dic23D412yescomplemented
65(C2×D23)⋊C4—24no—
66(C2×D23)⋊C4—22no—
67(C2×D23)⋊C4—22no—
68(C2×D23)⋊C4—44no—
69C23×C23—42no—
70C23×C23C22×C411yescharacteristic
71C23×C23C2×D411yescharacteristic
72C23×C23C2×D411yescharacteristic
73C23×C23C2×D411yescharacteristic
74C23×C23C2×D411yescharacteristic
75C23×C23#4111yescharacteristic
76C23×C23#4111yescharacteristic
77C22×D23—21no—
78C22×D23—21no—
79C22×D23—24no—
80C22×D23—22no—
81C22×D23—22no—
82C22×D23—21no—
83C22×D23—22no—
84C22×D23—22no—
85C22×D23—21no—
86C22×D23—24no—
87C22×D23—24no—
88C22×D23—21no—
89C22×D23—21no—
90C22×D23—21no—
91C22×D23—42no—
92C22×D23—42no—
93C22×D23—42no—
94C22×D23—44no—
95C22×D23—44no—
96C22×D23—44no—
97C22×D23—44no—
98C22×D23—42no—
99C22×D23C22⋊C412yes—
100C22×D23C22⋊C412yes—
101C2×C4×C23—22no—
102C2×C4×C23—22no—
103C2×C4×C23—42no—
104C2×C4×C23—42no—
105C2×C4×C23—42no—
106C2×C4×C23—41no—
107C22⋊D23—41no—
108C22⋊D23—41no—
109C22⋊D23—41no—
110C22⋊D23—41no—
111C2×Dic23—21no—
112C2×Dic23—21no—
113C2×Dic23—21no—
114C2×Dic23—22no—
115C2×Dic23—42no—
116C2×Dic23—42no—
117C2×Dic23—41no—
118D92—44no—
119D92—44no—
120C4×D23—48no—
121#1898—231nomaximal, Sylow
122C22×C23—22no—
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—41no—
126C22×C23—41no—
127C22×C23—41no—
128C22×C23—41no—
129C22×C23C2×C22⋊C411yescharacteristic
130C22×C23C4×D411yescharacteristic
131C22×C23C4×D411yescharacteristic
132C22×C23#12011yescharacteristic
133C22×C23#12111yescharacteristic
134C22×C23#12111yescharacteristic
135C22×C23#12311yescharacteristic
136C2×D23—24no—
137C2×D23—24no—
138C2×D23—22no—
139C2×D23—22no—
140C2×D23—22no—
141C2×D23—22no—
142C2×D23—22no—
143C2×D23—44no—
144C2×D23—44no—
145C2×D23—44no—
146C2×D23—44no—
147C2×D23—42no—
148C2×D23—42no—
149C2×D23—41no—
150C2×D23—42no—
151C2×D23—81no—
152C2×D23—81no—
153C2×D23#9914yescomplemented
154C4×C23—42no—
155C4×C23—42no—
156C4×C23—81no—
157Dic23—42no—
158Dic23—41no—
159Dic23—81no—
160C2×#120—231no—
161C22×C22⋊C4—231no—
162C2×#99—231no—
163C2×#99—231no—
164#379—231no—
165#342—231no—
166#342D2311yescharacteristic, complemented
167C2×C23—21no—
168C2×C23—21no—
169C2×C23—21no—
170C2×C23—21no—
171C2×C23—21no—
172C2×C23—21no—
173C2×C23#38611yescharacteristic
174C2×C23C2×#9912yes—
175D23—24no—
176D23—42no—
177D23—81no—
178C25—231no—
179C22×D4—231no—
180C22×D4—232no—
181C23×C4—461no—
182#120—461no—
183#120—462no—
184#120—461no—
185C2×C22⋊C4—231no—
186C2×C22⋊C4—232no—
187C2×C22⋊C4—231no—
188C2×C22⋊C4—462no—
189C2×C22⋊C4—461no—
190C2×C22⋊C4—462no—
191C2×C22⋊C4—462no—
192C2×C22⋊C4C2×D2311yescharacteristic
193C2×C22⋊C4C2×D2311yescharacteristic
194C2×C22⋊C4C2×D2311yescharacteristic
195#99—462no—
196#99—462no—
197C23#189811yescharacteristic, complemented, Sylow
198C24—231no—
199C24—232no—
200C24—232no—
201C24—231no—
202C24—231no—
203C24—461no—
204C24—461no—
205C24—461no—
206C24—461no—
207C24—924no—
208C24C22×D2311yescharacteristic
209C2×D4—462no—
210C2×D4—462no—
211C2×D4—461no—
212C2×D4—461no—
213C2×D4—461no—
214C2×D4—461no—
215C2×D4—461no—
216C2×D4—461no—
217C2×D4—924no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—231no—
221C22×C4—464no—
222C22×C4—461no—
223C22×C4—461no—
224C22×C4—924no—
225C22×C4C4×D2312yescomplemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—232no—
232C22⋊C4—462no—
233C22⋊C4—462no—
234C22⋊C4—464no—
235C22⋊C4—461no—
236C22⋊C4—461no—
237C22⋊C4—461no—
238C22⋊C4—924no—
239C22⋊C4D9212yescomplemented
240C23—42no—
241C23—232no—
242C23—232no—
243C23—464no—
244C23—464no—
245C23—464no—
246C23—461no—
247C23—461no—
248C23—462no—
249C23—461no—
250C23—462no—
251C23—462no—
252C23—461no—
253C23—462no—
254C23—461no—
255C23—461no—
256C23—461no—
257C23—922no—
258C23—922no—
259C23—922no—
260C23—922no—
261C23—924no—
262C23—924no—
263C23—924no—
264C23—924no—
265C23C2×C4×D2311yescharacteristic
266C23C2×D9211yescharacteristic
267C23#6728811yescharacteristic
268C23D4×D2311yescharacteristic
269C23D4×D2311yescharacteristic
270C23D4×D2311yescharacteristic
271C23#6729211yescharacteristic
272D4—924no—
273D4—924no—
274D4—921no—
275D4—921no—
276D4—921no—
277D4—921no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—461no—
285C2×C4—461no—
286C2×C4—462no—
287C2×C4—461no—
288C2×C4—928no—
289C2×C4—922no—
290C2×C4—922no—
291C2×C4—921no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—234no—
300C22—464no—
301C22—464no—
302C22—462no—
303C22—462no—
304C22—462no—
305C22—462no—
306C22—462no—
307C22—924no—
308C22—924no—
309C22—924no—
310C22—924no—
311C22—922no—
312C22—922no—
313C22—922no—
314C22—921no—
315C22—1841no—
316C22—1841no—
317C22C4×D9211yescharacteristic
318C22C22⋊C4×D2311yescharacteristic
319C22#1062505311yescharacteristic
320C22#1062505511yescharacteristic
321C22#1062506411yescharacteristic
322C22#1062506511yescharacteristic
323C22#1062506611yescharacteristic
324C4—42no—
325C4—42no—
326C4—81no—
327C4—922no—
328C4—921no—
329C4—1841no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—464no—
337C2—922no—
338C2—1841no—
339C2#1309229511yescharacteristic
340C2#99×D2312yes—
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#10625053C2
cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1898
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D23C2semidirect
3. C2×#10624988C2semidirect
4. C2×#10624988C2semidirect
5. #13092272C2semidirect
6. #13092184C2semidirect
7. C23×#342C2semidirect
10. C22×D92C4semidirect
19. C2×(C2×D23)⋊C4C4semidirect
34. C23×D23C2×C4semidirect
40. C22×C4×C23C2×C4semidirect
49. C22×Dic23C2×C4semidirect
60. C22⋊C4×C23D4semidirect
64. C22⋊Dic23D4semidirect
153. C2×D23#99semidirect
166. #342D23semidirect
197. C23#1898semidirect
225. C22×C4C4×D23semidirect
239. C22⋊C4D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250532
C2×C22⋊C4×D232
C2×#106249882
#130922722
#130921842
C23×#3422
#189823