Finite Group Databasebeta

← #15683116

Subgroups — #15683116

Order 2944.

452 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093217C211yesmaximal, characteristic, complemented
2#13093215C211yesmaximal, characteristic, complemented
3C2×#10625121C211yesmaximal, characteristic, complemented
4C2×#10625078C211yesmaximal, characteristic, complemented
5#13092691C212yesmaximal, complemented
6#13092686C212yesmaximal, complemented
7#13092683C212yesmaximal, complemented
8#13092679C212yesmaximal, complemented
9C2×#10625004C211yesmaximal, characteristic, complemented
10#13092399C211yesmaximal, characteristic, complemented
11C23×#413C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C2×#67288C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic
16C2×M16×C23C2211yescharacteristic
17#10625122—21no—
18#10625121—22no—
19#10625121—21no—
20#10625121—21no—
21#10625121—21no—
22#10625121—21no—
23#10625120—21no—
24C2×#67275C2211yescharacteristic, complemented
25#10625113C2212yes—
26C2×#67274C2211yescharacteristic, complemented
27C2×#67273C2211yescharacteristic, complemented
28#10625103C2212yes—
29C2×#67272C2211yescharacteristic, complemented
30C2×#67267C2211yescharacteristic
31C22×C23⋊C8C2211yescharacteristic
32#10625080—21no—
33#10625080C2212yes—
34#10625079—21no—
35#10625079C2212yes—
36#10625078—21no—
37#10625078—21no—
38#10625078C2212yes—
39#10625078C2212yes—
40#10625075—22no—
41C2×#67262—21no—
42C2×C8×D23—21no—
43C23×#101C2212yescomplemented
44C23×#100C2212yescomplemented
45#10625006C2212yescomplemented
46#10625005C2212yescomplemented
47#10625004C2212yescomplemented
48#10625004C2212yescomplemented
49#41×C23—21no—
50#41×C23—21no—
51#41×C23—21no—
52#41×C23—21no—
53C2×Q8×C23C2311yescharacteristic
54C2×D4×C23—21no—
55C2×D4×C23C2311yescharacteristic
56C22×C4×C23—21no—
57C22×C4×C23C2311yescharacteristic
58C2×C22⋊D23—21no—
59C2×C22⋊D23—21no—
60#67288—21no—
61#67288—21no—
62#67288—21no—
63#67288—21no—
64#67288—21no—
65#67288—21no—
66#67288D412yes—
67#67288C2312yes—
68C2×D92D411yescharacteristic
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×Dic46D411yescharacteristic
73C2×Dic46C2311yescharacteristic
74M16×C23—21no—
75M16×C23—21no—
76M16×C23C2312yes—
77M16×C23C2312yes—
78C2×C8×C23—21no—
79C2×C8×C23—21no—
80#67275—22no—
81#67275—21no—
82#67275—21no—
83#67274—22no—
84#67274—21no—
85#67274—21no—
86#67273—22no—
87#67273—21no—
88#67273—21no—
89#67272—22no—
90#67272—21no—
91#67272—21no—
92#67267—21no—
93#67267C2312yes—
94C2×C23⋊C8—21no—
95C2×C23⋊C8D411yescharacteristic
96C2×C23⋊C8D411yescharacteristic
97C2×C23⋊C8D411yescharacteristic
98C2×C23⋊C8D411yescharacteristic
99C2×C23⋊C8C2311yescharacteristic
100C2×C23⋊C8C2311yescharacteristic
101Dic92—22no—
102D184—22no—
103#67263—22no—
104#67263—22no—
105#67262—22no—
106#67262—22no—
107C8×D23—22no—
108C8×D23—22no—
109C23×C23—21no—
110C23×C23#4111yescharacteristic
111C22×D23—21no—
112C22×D23—21no—
113Q8×C23—21no—
114Q8×C23—21no—
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—41no—
118D4×C23—41no—
119C2×C4×C23—21no—
120C2×C4×C23—41no—
121C2×C4×C23—41no—
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23#4111yescharacteristic
127C2×C4×C23C2411yescharacteristic
128C22⋊D23—22no—
129C22⋊D23—22no—
130C22⋊D23—41no—
131C22⋊D23—41no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134D92—21no—
135D92—21no—
136D92—21no—
137D92C2×D412yes—
138C4×D23—22no—
139C4×D23—22no—
140C4×D23—41no—
141C4×D23—41no—
142Dic46—21no—
143Dic46—21no—
144Dic46—21no—
145Dic46C2×D412yes—
146C8×C23—22no—
147C8×C23—22no—
148C23⋊C8—22no—
149C23⋊C8C2×D411yescharacteristic
150C23⋊C8C2×D411yescharacteristic
151C23⋊C8C2×D411yescharacteristic
152C23⋊C8C2×D411yescharacteristic
153#3067—231nomaximal, Sylow
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—81no—
157C22×C23#12111yescharacteristic
158C22×C23#12111yescharacteristic
159C22×C23C2×#4111yescharacteristic
160C2×D23—22no—
161C2×D23—42no—
162C2×D23—41no—
163C2×D23—81no—
164C4×C23—41no—
165C4×C23#12111yescharacteristic
166C4×C23#12111yescharacteristic
167C4×C23C22×D411yescharacteristic
168C4×C23C22×D411yescharacteristic
169Dic23—22no—
170Dic23—41no—
171#575—231no—
172#575—231no—
173C2×#135—231no—
174C2×#131—231no—
175#473—232no—
176#472—232no—
177#471—232no—
178#471—232no—
179C2×#108—231no—
180#413—231no—
181#413D2311yescharacteristic, complemented
182C2×C23—21no—
183C2×C23—21no—
184C2×C23—21no—
185C2×C23—81no—
186C2×C23C2×#12111yescharacteristic
187D23—42no—
188D23—81no—
189C2×#41—231no—
190C2×#41—231no—
191C2×#41C2×D2311yescharacteristic
192#137—232no—
193#137—232no—
194#137—461no—
195#137—461no—
196AGL(1,ℤ/8)—232no—
197AGL(1,ℤ/8)—232no—
198AGL(1,ℤ/8)—461no—
199AGL(1,ℤ/8)—461no—
200#135—462no—
201#135—461no—
202#135—461no—
203#135—461no—
204#135—461no—
205#135—462no—
206C2×Q16—231no—
207C2×SD16—231no—
208C2×SD16—231no—
209C2×D8—231no—
210#131—232no—
211#131—232no—
212#131—461no—
213#131—461no—
214C2×M16—231no—
215C2×M16—461no—
216C2×M16C2×D2311yescharacteristic
217C2×M16C2×D2311yescharacteristic
218C22×C8—231no—
219C22×C8—461no—
220#108—232no—
221#108—232no—
222#101—232no—
223#101C2×D2312yescomplemented
224#100—232no—
225#100C2×D2312yescomplemented
226C23#306711yescharacteristic, complemented, Sylow
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—232no—
232#41—232no—
233#41—461no—
234#41—461no—
235#41—461no—
236#41—461no—
237#41—461no—
238#41—461no—
239C2×Q8—231no—
240C2×Q8—231no—
241C2×Q8C22×D2311yescharacteristic
242C2×D4—21no—
243C2×D4—231no—
244C2×D4—231no—
245C2×D4—461no—
246C2×D4—461no—
247C2×D4C22×D2311yescharacteristic
248C22×C4—21no—
249C22×C4—461no—
250C22×C4—461no—
251C22×C4C22×D2311yescharacteristic
252Q16—462no—
253Q16—461no—
254Q16—461no—
255Q16—462no—
256SD16—462no—
257SD16—462no—
258SD16—461no—
259SD16—461no—
260SD16—461no—
261SD16—461no—
262SD16—462no—
263SD16—462no—
264D8—462no—
265D8—461no—
266D8—461no—
267D8—462no—
268M16—21no—
269M16—21no—
270M16—232no—
271M16—462no—
272M16—462no—
273M16—461no—
274M16C22×D2312yes—
275M16C22×D2312yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—231no—
279C2×C8—231no—
280C2×C8—231no—
281C2×C8—231no—
282C2×C8—231no—
283C2×C8—231no—
284C2×C8—462no—
285C2×C8—462no—
286C2×C8—461no—
287C23—21no—
288C23—461no—
289C23—461no—
290C23#6728811yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—232no—
294Q8—461no—
295Q8—461no—
296Q8—461no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301D4—232no—
302D4—462no—
303D4—462no—
304D4—461no—
305D4—461no—
306D4—461no—
307D4—921no—
308D4—921no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—461no—
313C2×C4—462no—
314C2×C4—462no—
315C2×C4—461no—
316C2×C4—921no—
317C2×C4—921no—
318C2×C4#6728811yescharacteristic
319C2×C4D4×D2311yescharacteristic
320C2×C4D4×D2311yescharacteristic
321C2×C4D4×D2311yescharacteristic
322C2×C4D4×D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—22no—
325C8—22no—
326C8—231no—
327C8—231no—
328C8—231no—
329C8—231no—
330C8—462no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—462no—
335C22—922no—
336C22—921no—
337C22—1841no—
338C22#1062505511yescharacteristic
339C22#1062505511yescharacteristic
340C22C2×#6728811yescharacteristic
341C4—41no—
342C4—462no—
343C4—921no—
344C4#1062505511yescharacteristic
345C4#1062505511yescharacteristic
346C4C2×D4×D2311yescharacteristic
347C4C2×D4×D2311yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2—922no—
353C2—1841no—
354C2C2×#1062505511yescharacteristic
subgroupG/H
centerC4#10625055
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#413C2
socleC2×C23C2×#121
hypercenter#413D23
hypocenterC23#3067
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #13093217C2semidirect
2. #13093215C2semidirect
3. C2×#10625121C2semidirect
4. C2×#10625078C2semidirect
5. #13092691C2semidirect
6. #13092686C2semidirect
7. #13092683C2semidirect
8. #13092679C2semidirect
9. C2×#10625004C2semidirect
10. #13092399C2semidirect
11. C23×#413C2semidirect
24. C2×#67275C22semidirect
26. C2×#67274C22semidirect
27. C2×#67273C22semidirect
29. C2×#67272C22semidirect
43. C23×#101C22semidirect
44. C23×#100C22semidirect
45. #10625006C22semidirect
46. #10625005C22semidirect
47. #10625004C22semidirect
48. #10625004C22semidirect
181. #413D23semidirect
223. #101C2×D23semidirect
225. #100C2×D23semidirect
226. C23#3067semidirect

Maximal subgroups

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

subgroupindex
#130932172
#130932152
C2×#106251212
C2×#106250782
#130926912
#130926862
#130926832
#130926792
C2×#106250042
#130923992
C23×#4132
#306723