Finite Group Databasebeta

← #15686099

Subgroups — #15686099

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093126C211yesmaximal, characteristic, complemented
2#13093087C211yesmaximal, characteristic, complemented
3#13092781C211yesmaximal, characteristic, complemented
4#13092780C211yesmaximal, characteristic, complemented
5#13092762C211yesmaximal, characteristic, complemented
6#13092718C211yesmaximal, characteristic, complemented
7#13092715C211yesmaximal, characteristic, complemented
8#13092705C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092610C211yesmaximal, characteristic, complemented
11#13092546C211yesmaximal, characteristic, complemented
12#13092529C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14D8×Dic23C211yesmaximal, characteristic, complemented
15C23×#459C211yesmaximal, characteristic, complemented
16C2×#67290—21no—
17C2×D8×C23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C23×#127C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic
21#10625111C2211yescharacteristic
22#10625111C2211yescharacteristic
23#10625110—21no—
24#10625110—21no—
25#10625109—21no—
26D4×Dic23C2211yescharacteristic
27D4×Dic23C2211yescharacteristic
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625095—21no—
32C2×Dic23⋊C4—21no—
33#10625061C2211yescharacteristic
34#10625059C2211yescharacteristic
35#10625049—21no—
36#10625049—21no—
37C4×D92C2211yescharacteristic
38#10625041C2211yescharacteristic
39C4×Dic46C2211yescharacteristic
40C23×C4⋊C8C2211yescharacteristic
41C23×#102C2211yescharacteristic
42C23×#102C2211yescharacteristic
43#10625014C2211yescharacteristic
44#10625014C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625000C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624997C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55C8×Dic23C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C22×Dic23—21no—
70C22×Dic23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73#67290—44no—
74C2×D92C2311yescharacteristic
75C2×C4×D23—21no—
76C2×Dic46—21no—
77C2×Dic46D411yescharacteristic
78D8×C23—22no—
79D8×C23—22no—
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C42×C23C2311yescharacteristic
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89#67272—22no—
90(C2×D23)⋊C4—21no—
91C4⋊Dic23—21no—
92C4⋊Dic23D411yescharacteristic
93C4⋊Dic23C2311yescharacteristic
94C4⋊Dic23C2311yescharacteristic
95C4⋊Dic23C2311yescharacteristic
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23C2311yescharacteristic
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C23×C23—21no—
107C23×C23—21no—
108C23×C23—21no—
109C22×D23—21no—
110D4×C23—21no—
111D4×C23—21no—
112D4×C23—21no—
113D4×C23—21no—
114D4×C23—21no—
115D4×C23—42no—
116D4×C23—81no—
117D4×C23#4112yescomplemented
118C2×C4×C23—21no—
119C2×C4×C23—81no—
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2411yescharacteristic
123C22⋊D23—42no—
124C22⋊D23—42no—
125C22⋊D23—81no—
126C22⋊D23—81no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—42no—
131C2×Dic23—42no—
132C2×Dic23—42no—
133C2×Dic23—81no—
134C2×Dic23C2×D411yescharacteristic
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138D92—21no—
139D92—21no—
140C4×D23—42no—
141Dic46—22no—
142Dic46—81no—
143C8×C23—21no—
144C8×C23—21no—
145C23⋊C8—21no—
146C23⋊C8—21no—
147#3366—231nomaximal, Sylow
148C22×C23—22no—
149C22×C23—41no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23C22×D411yescharacteristic
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C4×C23—21no—
162C4×C23—21no—
163C4×C23—41no—
164C4×C23C2×#4111yescharacteristic
165C4×C232−1+411yescharacteristic
166Dic23—21no—
167Dic23—21no—
168Dic23—21no—
169Dic23—41no—
170Dic23—41no—
171Dic23—41no—
172Dic23AGL(1,ℤ/8)12yes—
173#554—231no—
174#550—231no—
175#490—231no—
176#490—231no—
177#486—231no—
178#478—231no—
179#478—231no—
180#476—231no—
181#459—231no—
182#459—231no—
183#459D2311yescharacteristic, complemented
184#446—231no—
185#442—231no—
186#442—231no—
187C4×D8—231no—
188C2×C23—42no—
189C2×C23—81no—
190C2×C23—81no—
191C2×C23#54811yescharacteristic
192C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C23#57611yescharacteristic
194D23—81no—
195C2×#41—461no—
196C2×D8—231no—
197C2×D8C2×D2311yescharacteristic
198C2×D8C2×D2311yescharacteristic
199C4⋊Q8—231no—
200#127—231no—
201#127—231no—
202#127C2×D2311yescharacteristic
203#125—231no—
204#125—231no—
205C22⋊Q8—461no—
206C22⋊Q8—461no—
207C22⋊Q8—461no—
208#121—461no—
209#121—461no—
210#121—461no—
211C4×Q8—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—231no—
216C4×D4—231no—
217C4×D4C2×D2311yescharacteristic
218C2×C4⋊C4—461no—
219#107—231no—
220#106—231no—
221#106—231no—
222C4⋊C8—231no—
223C4⋊C8—231no—
224C4⋊C8C2×D2311yescharacteristic
225#102—231no—
226#102—231no—
227#102—231no—
228#102—231no—
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102C2×D2311yescharacteristic
234#102C2×D2311yescharacteristic
235#97—231no—
236#97—231no—
237C4×C8—231no—
238C23#336611yescharacteristic, complemented, Sylow
239#41—924no—
240C2×Q8—231no—
241C2×Q8—461no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—231no—
245C2×D4—461no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C2×D4C22×D2311yescharacteristic
252C22×C4—21no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258D8—22no—
259D8—22no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—231no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4—461no—
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C42—231no—
284C42—231no—
285C42C22×D2311yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—461no—
290Q8—462no—
291Q8—1841no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—461no—
300D4—461no—
301D4—922no—
302D4—922no—
303D4—1841no—
304D4—1841no—
305D4#6729012yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—231no—
309C2×C4—231no—
310C2×C4—231no—
311C2×C4—231no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—922no—
316C2×C4—922no—
317C2×C4—922no—
318C2×C4—922no—
319C2×C4—1841no—
320C2×C4D4×D2311yescharacteristic
321C2×C4D4×D2311yescharacteristic
322C2×C4C23×D2311yescharacteristic
323C8—21no—
324C8—21no—
325C8—461no—
326C8—461no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22C2×D4×D2311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—232no—
344C4—461no—
345C4—461no—
346C4—461no—
347C4—921no—
348C4—921no—
349C4—921no—
350C4C2×#6729011yescharacteristic
351C4#1062516111yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—1841no—
356C2#1309307311yescharacteristic
357C2AGL(1,ℤ/8)×D2311yescharacteristic
358C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#459C2
socleC22×C23C22×D4
hypercenter#459D23
hypocenterC23#3366
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #13093126C2semidirect
2. #13093087C2semidirect
3. #13092781C2semidirect
4. #13092780C2semidirect
5. #13092762C2semidirect
6. #13092718C2semidirect
7. #13092715C2semidirect
8. #13092705C2semidirect
9. #13092610C2semidirect
10. #13092610C2semidirect
11. #13092546C2semidirect
12. #13092529C2semidirect
13. #13092527C2semidirect
14. D8×Dic23C2semidirect
15. C23×#459C2semidirect
117. D4×C23#41semidirect
183. #459D23semidirect
238. C23#3366semidirect
305. D4#67290semidirect

Maximal subgroups

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

subgroupindex
#130931262
#130930872
#130927812
#130927802
#130927622
#130927182
#130927152
#130927052
#130926102
#130925462
#130925292
#130925272
D8×Dic232
C23×#4592
#336623