Finite Group Databasebeta

← #15676717

Subgroups — #15676717

Order 2944.

1056 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 159 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×#67292C211yesmaximal, characteristic, complemented
2C2×#10625053C212yesmaximal, complemented
3C2×C22⋊C4×D23C211yesmaximal, characteristic, complemented
4#13092328C211yesmaximal, characteristic, complemented
5#13092327C211yesmaximal, characteristic, complemented
6#13092326C211yesmaximal, characteristic, complemented
7#13092295C212yesmaximal, complemented
8#13092295C212yesmaximal, complemented
9#13092293C212yesmaximal, complemented
10#13092279C211yesmaximal, characteristic, complemented
11C23×#393C211yesmaximal, characteristic, complemented
12C24×D23C2211yescharacteristic
13C22×Q8×C23C2211yescharacteristic, complemented
14C22×C22⋊D23C2212yes—
15C2×#67292—28no—
16C2×#67292—24no—
17C22×D92C2212yes—
18C22×D92C2212yes—
19C22×D92C2211yescharacteristic, complemented
20C22×C4×D23C2211yescharacteristic
21C22×C4×D23C2211yescharacteristic
22C22×C4×D23C2212yescomplemented
23C2×C22⋊C4×C23C2212yes—
24C2×C22⋊C4×C23C2211yescharacteristic
25C2×C22⋊Dic23C2211yescharacteristic
26C2×(C2×D23)⋊C4C2212yes—
27C2×(C2×D23)⋊C4C2212yes—
28C2×(C2×D23)⋊C4C2211yescharacteristic
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2212yescomplemented
31C2×(C2×D23)⋊C4C2212yescomplemented
32#10625053—28no—
33C22⋊C4×D23—24no—
34C23×#95C2211yescharacteristic, complemented
35C23×#95C2212yescomplemented
36C23⋊#95C2212yescomplemented
37C23⋊#95C2211yescharacteristic, complemented
38C23⋊#95C2212yescomplemented
39C24×C23C2311yescharacteristic
40C23×D23—22no—
41C23×D23—22no—
42C23×D23—22no—
43C23×D23—24no—
44C23×D23—42no—
45C23×D23C2312yes—
46C23×D23C2311yescharacteristic
47C23×D23C2311yescharacteristic
48C2×Q8×C23—24no—
49C2×Q8×C23—22no—
50C22×C4×C23C2311yescharacteristic
51C22×C4×C23C2312yes—
52C22×C4×C23C2311yescharacteristic
53C22×C4×C23C2312yes—
54C2×C22⋊D23—24no—
55C2×C22⋊D23—24no—
56C2×C22⋊D23—42no—
57C22×Dic23C2312yes—
58C22×Dic23C2311yescharacteristic
59C22×Dic23C2311yescharacteristic
60#67292—232no—
61C2×D92—24no—
62C2×D92—24no—
63C2×D92—24no—
64C2×D92—22no—
65C2×D92—24no—
66C2×D92—24no—
67C2×D92—42no—
68C2×D92D418yescomplemented
69C2×C4×D23—24no—
70C2×C4×D23—24no—
71C2×C4×D23—24no—
72C2×C4×D23—24no—
73C2×C4×D23—22no—
74C2×C4×D23—42no—
75C2×C4×D23D414yescomplemented
76C22⋊C4×C23—22no—
77C22⋊C4×C23—24no—
78C22⋊Dic23—22no—
79(C2×D23)⋊C4—24no—
80(C2×D23)⋊C4—22no—
81(C2×D23)⋊C4—24no—
82(C2×D23)⋊C4—22no—
83(C2×D23)⋊C4—42no—
84(C2×D23)⋊C4—42no—
85C23×C23—21no—
86C23×C23—22no—
87C23×C23—21no—
88C23×C23—22no—
89C23×C23#4112yescomplemented
90C23×C23C2411yescharacteristic
91C22×D23—21no—
92C22×D23—21no—
93C22×D23—22no—
94C22×D23—28no—
95C22×D23—21no—
96C22×D23—22no—
97C22×D23—22no—
98C22×D23—22no—
99C22×D23—22no—
100C22×D23—22no—
101C22×D23—21no—
102C22×D23—22no—
103C22×D23—22no—
104C22×D23—22no—
105C22×D23—48no—
106C22×D23—48no—
107C22×D23—44no—
108C22×D23—44no—
109C22×D23C2×D414yes—
110C22×D23C2×D414yes—
111C22×D23C2×D412yes—
112C22×D23#4112yescomplemented
113Q8×C23—28no—
114C2×C4×C23—22no—
115C2×C4×C23—22no—
116C2×C4×C23—22no—
117C2×C4×C23—21no—
118C2×C4×C23—22no—
119C2×C4×C23—22no—
120C2×C4×C23—22no—
121C2×C4×C23—22no—
122C2×C4×C23C2×D414yes—
123C2×C4×C23C2×D412yes—
124C22⋊D23—48no—
125C2×Dic23—22no—
126C2×Dic23—22no—
127C2×Dic23—21no—
128C2×Dic23—22no—
129C2×Dic23—22no—
130C2×Dic23—22no—
131C2×Dic23C2×D412yes—
132D92—28no—
133D92—216no—
134D92—48no—
135C4×D23—216no—
136C4×D23—28no—
137C4×D23—44no—
138#2404—231nomaximal, Sylow
139C22×C23—22no—
140C22×C23—24no—
141C22×C23—41no—
142C22×C23—41no—
143C22×C23—42no—
144C22×C23C22×D411yescharacteristic
145C22×C23C22×D412yes—
146C22×C23C2×#4111yescharacteristic
147C22×C23C2×#4111yescharacteristic
148C22×C23H(5,𝔽2)12yes—
149C2×D23—22no—
150C2×D23—22no—
151C2×D23—24no—
152C2×D23—24no—
153C2×D23—24no—
154C2×D23—22no—
155C2×D23—24no—
156C2×D23—24no—
157C2×D23—24no—
158C2×D23—416no—
159C2×D23—41no—
160C2×D23—42no—
161C2×D23—42no—
162C2×D23—41no—
163C2×D23—42no—
164C2×D23—42no—
165C2×D23—42no—
166C2×D23#12014yes—
167C4×C23—24no—
168C4×C23—22no—
169C4×C23—41no—
170C4×C23—42no—
171Dic23—22no—
172Dic23—41no—
173Dic23—42no—
174C22×#41—231no—
175C2×#120—232no—
176C22×C22⋊C4—231no—
177#393—231no—
178#393D2311yescharacteristic, complemented
179#392—231no—
180#392—231no—
181#386—232no—
182#386—232no—
183#386—232no—
184#381—231no—
185C2×C23—42no—
186C2×C23C2×#12011yescharacteristic
187C2×C23#52511yescharacteristic
188C2×C23#53511yescharacteristic
189C2×C23#54612yes—
190C2×C23#54612yes—
191D23—24no—
192D23—44no—
193D23—42no—
194C25—231no—
195C2×#41—464no—
196C2×#41—468no—
197C22×Q8C2×D2311yescharacteristic, complemented
198C22×D4—232no—
199C22×D4—232no—
200C22×D4—231no—
201C22×D4—232no—
202C23×C4—231no—
203C23×C4—232no—
204C23×C4—231no—
205#120—468no—
206C2×C22⋊C4—231no—
207C2×C22⋊C4—231no—
208C2×C22⋊C4—231no—
209C2×C22⋊C4—232no—
210C2×C22⋊C4—232no—
211C2×C22⋊C4—232no—
212C2×C22⋊C4—232no—
213C2×C22⋊C4—464no—
214C2×C22⋊C4C2×D2311yescharacteristic
215C2×C22⋊C4C2×D2312yes—
216#95—232no—
217#95—231no—
218#95—232no—
219#95C2×D2311yescharacteristic, complemented
220#95C2×D2312yescomplemented
221C23#240411yescharacteristic, complemented, Sylow
222C24—231no—
223C24—231no—
224C24—232no—
225C24—462no—
226C24—462no—
227C24—464no—
228C24—462no—
229C24—922no—
230C24C22×D2311yescharacteristic
231#41—4632no—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×D4—238no—
235C2×D4—464no—
236C2×D4—464no—
237C2×D4—464no—
238C2×D4—464no—
239C2×D4—464no—
240C2×D4—464no—
241C2×D4—464no—
242C2×D4—462no—
243C2×D4—922no—
244C2×D4—922no—
245C22×C4—231no—
246C22×C4—234no—
247C22×C4—232no—
248C22×C4—231no—
249C22×C4—464no—
250C22×C4—464no—
251C22×C4—464no—
252C22×C4—462no—
253C22×C4—464no—
254C22×C4—922no—
255C22×C4C22×D2312yes—
256C22×C4C22×D2311yescharacteristic
257C22×C4C22×D2311yescharacteristic
258C22×C4C22×D2312yes—
259C22⋊C4—22no—
260C22⋊C4—24no—
261C22⋊C4—462no—
262C22⋊C4—464no—
263C22⋊C4—462no—
264C22⋊C4—462no—
265C22⋊C4—464no—
266C22⋊C4—922no—
267C22⋊C4—922no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—234no—
273C23—232no—
274C23—234no—
275C23—232no—
276C23—468no—
277C23—461no—
278C23—461no—
279C23—462no—
280C23—461no—
281C23—462no—
282C23—462no—
283C23—462no—
284C23—462no—
285C23—461no—
286C23—462no—
287C23—462no—
288C23—462no—
289C23—462no—
290C23—928no—
291C23—924no—
292C23—928no—
293C23—924no—
294C23#6729212yescomplemented
295C23C23×D2311yescharacteristic
296Q8—28no—
297D4—4616no—
298D4—468no—
299D4—928no—
300D4—928no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—232no—
310C2×C4—468no—
311C2×C4—4616no—
312C2×C4—462no—
313C2×C4—461no—
314C2×C4—462no—
315C2×C4—462no—
316C2×C4—462no—
317C2×C4—462no—
318C2×C4—924no—
319C2×C4D4×D2312yes—
320C2×C4D4×D2314yes—
321C22—22no—
322C22—24no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—234no—
327C22—462no—
328C22—462no—
329C22—464no—
330C22—464no—
331C22—464no—
332C22—462no—
333C22—464no—
334C22—464no—
335C22—464no—
336C22—9216no—
337C22—921no—
338C22—922no—
339C22—921no—
340C22—922no—
341C22—922no—
342C22—922no—
343C22—922no—
344C22C2×D4×D2311yescharacteristic
345C22C2×D4×D2312yes—
346C22C2×#6729211yescharacteristic
347C22#41×D2311yescharacteristic
348C22#1062516012yes—
349C4—22no—
350C4—24no—
351C4—41no—
352C4—42no—
353C4—462no—
354C4—921no—
355C4—922no—
356C2—42no—
357C2—464no—
358C2—922no—
359C2—924no—
360C2#120×D2311yescharacteristic
361C2#1309293011yescharacteristic
362C2#1309298511yescharacteristic
363C2#1309305812yes—
364C2#1309306012yes—
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, cosocleC23×C23C24
FittingC23×#393C2
hypercenter#393D23
hypocenterC23#2404
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#67292C2semidirect
2. C2×#10625053C2semidirect
3. C2×C22⋊C4×D23C2semidirect
4. #13092328C2semidirect
5. #13092327C2semidirect
6. #13092326C2semidirect
7. #13092295C2semidirect
8. #13092295C2semidirect
9. #13092293C2semidirect
10. #13092279C2semidirect
11. C23×#393C2semidirect
13. C22×Q8×C23C22semidirect
19. C22×D92C22semidirect
22. C22×C4×D23C22semidirect
30. C2×(C2×D23)⋊C4C22semidirect
31. C2×(C2×D23)⋊C4C22semidirect
34. C23×#95C22semidirect
35. C23×#95C22semidirect
36. C23⋊#95C22semidirect
37. C23⋊#95C22semidirect
38. C23⋊#95C22semidirect
68. C2×D92D4semidirect
75. C2×C4×D23D4semidirect
89. C23×C23#41semidirect
112. C22×D23#41semidirect
178. #393D23semidirect
197. C22×Q8C2×D23semidirect
219. #95C2×D23semidirect
220. #95C2×D23semidirect
221. C23#2404semidirect
294. C23#67292semidirect

Maximal subgroups

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

subgroupindex
C22×#672922
C2×#106250532
C2×C22⋊C4×D232
#130923282
#130923272
#130923262
#130922952
#130922932
#130922792
C23×#3932
#240423