Finite Group Databasebeta

← #15683597

Subgroups — #15683597

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#13093020C211yesmaximal, characteristic, complemented
2#13092900C211yesmaximal, characteristic, complemented
3#13092736C211yesmaximal, characteristic, complemented
4#13092728C211yesmaximal, characteristic, complemented
5#13092722C211yesmaximal, characteristic, complemented
6#13092719C211yesmaximal, characteristic, complemented
7#13092615C211yesmaximal, characteristic, complemented
8#13092610C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic, complemented
10#13092529C211yesmaximal, characteristic, complemented
11#13092520C211yesmaximal, characteristic, complemented
12SD16×Dic23C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#449C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C23×#121C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22C2×#67274C2211yescharacteristic
23#10625111C2211yescharacteristic
24#10625110—21no—
25#10625109—21no—
26D4×Dic23—21no—
27D4×Dic23—21no—
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic
30D4×Dic23C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32#10625101C2211yescharacteristic
33#10625097—21no—
34#10625097C2211yescharacteristic
35C2×C4⋊Dic23—21no—
36C2×C4⋊Dic23C2211yescharacteristic
37#10625064C2211yescharacteristic
38#10625061C2211yescharacteristic
39#10625057—21no—
40#10625054—21no—
41C23×#103C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624999C2211yescharacteristic
53#10624997C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56C8×Dic23C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624989C2211yescharacteristic
59#41×C23—22no—
60#41×C23—22no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73C22×Dic23—21no—
74C22×Dic23—21no—
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77SD16×C23—22no—
78D8×C23—22no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23C2311yescharacteristic
82C22⋊C4×C23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23D411yescharacteristic
87C22⋊Dic23D411yescharacteristic
88#67274—22no—
89#67272—22no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92C4⋊Dic23—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23D411yescharacteristic
97C4⋊Dic23D411yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C2×D411yescharacteristic
111C22×D23—21no—
112Q8×C23—21no—
113Q8×C23#4112yes—
114D4×C23—24no—
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—81no—
119D4×C23#4112yes—
120C2×C4×C23—24no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2411yescharacteristic
127C22⋊D23—81no—
128C22⋊D23—81no—
129C22⋊D23—81no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—81no—
134C2×Dic23—81no—
135C2×Dic23—81no—
136C2×Dic23—81no—
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141D92—21no—
142D92—21no—
143C4×D23—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3119—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—22no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23C22×D411yescharacteristic
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—21no—
163C4×C23—22no—
164C4×C23—41no—
165C4×C23C2×#4111yescharacteristic
166C4×C23C2×#4111yescharacteristic
167Dic23—21no—
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#460—231no—
181#459—231no—
182#449—231no—
183#449D2311yescharacteristic, complemented
184#442—231no—
185#440—231no—
186C4×SD16—231no—
187C4×D8—231no—
188#433—231no—
189C2×C23—41no—
190C2×C23—42no—
191C2×C23—81no—
192C2×C23#52511yescharacteristic
193C2×C23#57611yescharacteristic
194C2×C23#57711yescharacteristic
195D23—81no—
196C2×#41C2×D2311yescharacteristic
197C2×SD16—231no—
198C2×SD16C2×D2311yescharacteristic
199C2×D8—231no—
200C2×D8C2×D2311yescharacteristic
201#127—231no—
202#125—231no—
203#123—461no—
204#123—461no—
205#121—231no—
206#121—461no—
207#121—461no—
208#121C2×D2311yescharacteristic
209C4×Q8—231no—
210C4×Q8—231no—
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⋊C8—231no—
227#103—231no—
228#103C2×D2311yescharacteristic
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102C2×D2311yescharacteristic
235C22⋊C8—231no—
236C22⋊C8C2×D2311yescharacteristic
237#97—231no—
238C4×C8—231no—
239C23#311911yescharacteristic, complemented, Sylow
240#41—22no—
241#41—22no—
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—21no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4C22×D2311yescharacteristic
258SD16—22no—
259SD16—462no—
260D8—22no—
261D8—462no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8C22×D2311yescharacteristic
265C2×C8C22×D2311yescharacteristic
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—231no—
279C22⋊C4—231no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C42—231no—
286C42—231no—
287C42—461no—
288C42—461no—
289C23—21no—
290C23—21no—
291C23—461no—
292C23D4×D2311yescharacteristic
293Q8—21no—
294Q8#6729012yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—461no—
301D4—461no—
302D4—1841no—
303D4—1841no—
304D4—1841no—
305D4#6729012yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—231no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4—1841no—
321C2×C4—1841no—
322C2×C4—1841no—
323C2×C4D4×D2311yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—21no—
326C8—21no—
327C8—461no—
328C8—461no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22C2×D4×D2311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—461no—
346C4—461no—
347C4—461no—
348C4—461no—
349C4—921no—
350C4—921no—
351C4—921no—
352C4C2×#6729011yescharacteristic
353C4C2×#6729011yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—1841no—
358C2#1309292311yescharacteristic
359C2#1309322111yescharacteristic
360C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#449C2
socleC22×C23C22×D4
hypercenter#449D23
hypocenterC23#3119
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #13093020C2semidirect
2. #13092900C2semidirect
3. #13092736C2semidirect
4. #13092728C2semidirect
5. #13092722C2semidirect
6. #13092719C2semidirect
7. #13092615C2semidirect
8. #13092610C2semidirect
9. #13092562C2semidirect
10. #13092529C2semidirect
11. #13092520C2semidirect
12. SD16×Dic23C2semidirect
13. #13092497C2semidirect
14. #13092475C2semidirect
15. C23×#449C2semidirect
183. #449D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130930202
#130929002
#130927362
#130927282
#130927222
#130927192
#130926152
#130926102
#130925622
#130925292
#130925202
SD16×Dic232
#130924972
#130924752
C23×#4492
#311923