Finite Group Databasebeta

← #15683595

Subgroups — #15683595

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093021C211yesmaximal, characteristic, complemented
2#13092899C211yesmaximal, characteristic, complemented
3#13092734C211yesmaximal, characteristic, complemented
4#13092729C211yesmaximal, characteristic, complemented
5#13092724C211yesmaximal, characteristic, complemented
6#13092718C211yesmaximal, characteristic, complemented
7#13092609C211yesmaximal, characteristic, complemented
8#13092561C211yesmaximal, characteristic, complemented
9#13092561C211yesmaximal, characteristic, complemented
10#13092526C211yesmaximal, characteristic, complemented
11#13092518C211yesmaximal, characteristic, complemented
12SD16×Dic23C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#460C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C23×#127C2211yescharacteristic
20C4×Q8×C23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22#10625110—21no—
23#10625110—21no—
24#10625109C2211yescharacteristic
25#10625109C2211yescharacteristic
26#10625106—21no—
27#10625106—21no—
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32#10625064—21no—
33#10625064C2211yescharacteristic
34C4⋊C4×D23—21no—
35C4⋊C4×D23C2211yescharacteristic
36C4×D92—21no—
37C4×D92C2211yescharacteristic
38#10625043—21no—
39#10625043C2211yescharacteristic
40#10625041C2211yescharacteristic
41C23×C4⋊C8C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10625000C2211yescharacteristic
53#10624999C2211yescharacteristic
54#10624997C2211yescharacteristic
55C8×Dic23C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23—21no—
61C2×D4×C23—21no—
62C2×D4×C23C2311yescharacteristic
63C2×D4×C23C2311yescharacteristic
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C22×Dic23—21no—
67C22×Dic23—21no—
68#67292—22no—
69#67292—22no—
70C2×D92—21no—
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×C4×D23C2311yescharacteristic
77SD16×C23—22no—
78SD16×C23—22no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C42×C23—21no—
84C42×C23C2311yescharacteristic
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89#67272—22no—
90#67272—22no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4D411yescharacteristic
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23—21no—
110C22×D23—21no—
111C22×D23C2×D411yescharacteristic
112Q8×C23—21no—
113Q8×C23#4112yes—
114D4×C23—21no—
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—81no—
119D4×C23—81no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—81no—
126C22⋊D23—81no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—81no—
131C2×Dic23—81no—
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—24no—
136D92—21no—
137D92#4112yes—
138C4×D23—24no—
139C4×D23—21no—
140C4×D23—21no—
141C4×D23—81no—
142C4×D23—81no—
143C4×D23—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3119—231nomaximal, Sylow
149C22×C23—41no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23C22×D411yescharacteristic
156C2×D23—21no—
157C2×D23—22no—
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—22no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23C2×#4111yescharacteristic
167C4×C23C2×#4111yescharacteristic
168Dic23—21no—
169Dic23—21no—
170Dic23—21no—
171Dic23—41no—
172Dic23—41no—
173Dic23—41no—
174#540—231no—
175#520—231no—
176#481—231no—
177#480—231no—
178#479—231no—
179#478—231no—
180#460D2311yescharacteristic, complemented
181#459—231no—
182#449—231no—
183#449—231no—
184#442—231no—
185#440—231no—
186C4×SD16—231no—
187C4×D8—231no—
188#433—231no—
189C2×C23—81no—
190C2×C23—81no—
191C2×C23#52511yescharacteristic
192C2×C23#57611yescharacteristic
193C2×C23#57711yescharacteristic
194D23—41no—
195D23—42no—
196C2×#41—231no—
197C2×SD16C2×D2311yescharacteristic
198C2×SD16C2×D2311yescharacteristic
199C2×D8—231no—
200C2×D8—231no—
201#127C2×D2311yescharacteristic
202#125—231no—
203#123—461no—
204#123—461no—
205#121—231no—
206#121—231no—
207#121—461no—
208#121—461no—
209C4×Q8—231no—
210C4×Q8C2×D2311yescharacteristic
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—461no—
216C4×D4—461no—
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—461no—
221#107—231no—
222#107—231no—
223#106—231no—
224#106—231no—
225C4⋊C8—231no—
226C4⋊C8C2×D2311yescharacteristic
227#103—231no—
228#103—231no—
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102C2×D2311yescharacteristic
234#102C2×D2311yescharacteristic
235C22⋊C8—231no—
236C22⋊C8—231no—
237#97—231no—
238C4×C8—231no—
239C23#311911yescharacteristic, complemented, Sylow
240#41—462no—
241#41—462no—
242C2×Q8C22×D2311yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—231no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C22×C4—231no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258SD16—22no—
259SD16—22no—
260D8—462no—
261D8—462no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8C22×D2311yescharacteristic
265C2×C8C22×D2311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—231no—
271C4⋊C4—231no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4—461no—
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—231no—
278C22⋊C4—231no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C42—21no—
286C42—231no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C23—21no—
290C23—21no—
291C23—231no—
292C23—461no—
293Q8—21no—
294Q8#6729012yes—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—232no—
302D4—464no—
303D4—461no—
304D4—1841no—
305D4—1841no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—231no—
309C2×C4—231no—
310C2×C4—231no—
311C2×C4—464no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—1841no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4—1841no—
321C2×C4—1841no—
322C2×C4D4×D2311yescharacteristic
323C2×C4D4×D2311yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—21no—
326C8—21no—
327C8—461no—
328C8—461no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—462no—
336C22—461no—
337C22—461no—
338C22—461no—
339C22—921no—
340C22—921no—
341C22C2×D4×D2311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—461no—
347C4—461no—
348C4—461no—
349C4—921no—
350C4—921no—
351C4—921no—
352C4C2×#6729011yescharacteristic
353C4#41×D2311yescharacteristic
354C2—81no—
355C2—81no—
356C2—921no—
357C2—922no—
358C2#1309292711yescharacteristic
359C2#1309322111yescharacteristic
360C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#460C2
socleC22×C23C22×D4
hypercenter#460D23
hypocenterC23#3119
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #13093021C2semidirect
2. #13092899C2semidirect
3. #13092734C2semidirect
4. #13092729C2semidirect
5. #13092724C2semidirect
6. #13092718C2semidirect
7. #13092609C2semidirect
8. #13092561C2semidirect
9. #13092561C2semidirect
10. #13092526C2semidirect
11. #13092518C2semidirect
12. SD16×Dic23C2semidirect
13. #13092497C2semidirect
14. #13092477C2semidirect
15. C23×#460C2semidirect
180. #460D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130930212
#130928992
#130927342
#130927292
#130927242
#130927182
#130926092
#130925612
#130925262
#130925182
SD16×Dic232
#130924972
#130924772
C23×#4602
#311923