Finite Group Databasebeta

← #15685285

Subgroups — #15685285

Order 2944.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093106C211yesmaximal, characteristic, complemented
2#13093074C211yesmaximal, characteristic
3#13092770C211yesmaximal, characteristic, complemented
4#13092758C211yesmaximal, characteristic, complemented
5#13092729C211yesmaximal, characteristic, complemented
6#13092726C211yesmaximal, characteristic, complemented
7#13092658C211yesmaximal, characteristic, complemented
8#13092645C211yesmaximal, characteristic, complemented
9#13092638C211yesmaximal, characteristic, complemented
10#13092579C211yesmaximal, characteristic, complemented
11#13092574C211yesmaximal, characteristic, complemented
12#13092509C211yesmaximal, characteristic, complemented
13C8×C22⋊D23C211yesmaximal, characteristic, complemented
14#103×D23C211yesmaximal, characteristic, complemented
15C23×#416C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C23×#117C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21C2×#67275C2211yescharacteristic
22#10625109—21no—
23#10625109C2211yescharacteristic
24#10625107—21no—
25#10625107C2211yescharacteristic
26C2×#67273C2211yescharacteristic
27C4×C22⋊D23—21no—
28C4×C22⋊D23C2211yescharacteristic
29#10625095—21no—
30#10625095C2211yescharacteristic
31#10625095C2211yescharacteristic
32C2×Dic92C2211yescharacteristic
33C2×C8×D23C2211yescharacteristic
34#10625068C2211yescharacteristic
35C4⋊C4×D23C2211yescharacteristic
36#10625061C2211yescharacteristic
37#10625058C2211yescharacteristic
38#10625054—21no—
39#10625050—21no—
40#10625043—21no—
41#10625041—21no—
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10625000C2211yescharacteristic
51#10624998C2211yescharacteristic
52#10624998C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59#41×C23—22no—
60#41×C23—41no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23D411yescharacteristic
68Q8×D23—22no—
69Q8×D23—41no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23C2311yescharacteristic
73C2×Dic46—21no—
74C2×Dic46C2311yescharacteristic
75C2×Dic46C2311yescharacteristic
76C2×C8×C23—41no—
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C22⋊C4×C23—21no—
82C42×C23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23D411yescharacteristic
89#67275—22no—
90#67273—41no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4D411yescharacteristic
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109Dic92—41no—
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23C2×D411yescharacteristic
114Q8×C23—21no—
115Q8×C23#4112yes—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—42no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—42no—
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2411yescharacteristic
127C22⋊D23—22no—
128C22⋊D23—42no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135C2×Dic23C2×D411yescharacteristic
136C4×D23—21no—
137C4×D23—21no—
138C4×D23—42no—
139C4×D23—42no—
140Dic46—21no—
141Dic46—21no—
142Dic46—21no—
143Dic46—21no—
144Dic46—42no—
145C8×C23—21no—
146C8×C23—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149#3300—231nomaximal, Sylow
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—21no—
159C2×D23#13512yes—
160C4×C23—22no—
161C4×C23—21no—
162C4×C23—41no—
163C4×C23—41no—
164C4×C23C2×#4111yescharacteristic
165C4×C23H(5,𝔽2)11yescharacteristic
166Dic23—21no—
167Dic23—21no—
168Dic23—21no—
169Dic23—41no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173#552—231no—
174#548—231no—
175#488—231no—
176#485—231no—
177#480—231no—
178#479—231no—
179#467—231no—
180#465—231no—
181#464—231no—
182#452—231no—
183#451—231no—
184C4×Q16—231no—
185C8×D4—231no—
186#416D2311yescharacteristic, complemented
187C2×#103—231no—
188C2×C23—41no—
189C2×C23—81no—
190C2×C23#54611yescharacteristic
191C2×C23C2×#13511yescharacteristic
192C2×C23#57811yescharacteristic
193D23—22no—
194C2×#41C2×D2311yescharacteristic
195C22×Q8—231no—
196C2×Q16—231no—
197C2×Q16—231no—
198C2×SD16—231no—
199C22×C8—231no—
200C22×C8C2×D2311yescharacteristic
201#126—461no—
202#125—231no—
203#125—461no—
204#124—231no—
205#124—461no—
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—231no—
209C22⋊Q8—231no—
210C22⋊Q8—461no—
211#121—231no—
212#121—461no—
213C4×Q8—231no—
214C4×Q8—231no—
215C4×D4—231no—
216C4×D4—461no—
217#117—461no—
218#117C2×D2311yescharacteristic
219C2×C4⋊C4—231no—
220#107—231no—
221#107—231no—
222#106—231no—
223C4⋊C8—231no—
224#103—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103—231no—
229#103C2×D2311yescharacteristic
230#103C2×D2311yescharacteristic
231#102—231no—
232#102C2×D2311yescharacteristic
233#102C2×D2311yescharacteristic
234C22⋊C8—231no—
235C22⋊C8—231no—
236C4×C8—231no—
237C23#330011yescharacteristic, complemented, Sylow
238#41—22no—
239#41—41no—
240C2×Q8—231no—
241C2×Q8—231no—
242C2×Q8—461no—
243C2×Q8—462no—
244C2×Q8—921no—
245C2×Q8C22×D2311yescharacteristic
246C2×D4—21no—
247C2×D4—231no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C22×C4—21no—
251C22×C4—231no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4C22×D2311yescharacteristic
255Q16—462no—
256Q16—921no—
257SD16—921no—
258C2×C8—41no—
259C2×C8—231no—
260C2×C8—231no—
261C2×C8—921no—
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C4⋊C4—231no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—461no—
268C4⋊C4—461no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4C22×D2311yescharacteristic
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—
285C22⋊C4—461no—
286C42—21no—
287C42—231no—
288C42—461no—
289C42—461no—
290C23—21no—
291C23—231no—
292C23D4×D2311yescharacteristic
293Q8—21no—
294Q8—461no—
295Q8—461no—
296Q8—461no—
297Q8—461no—
298Q8—922no—
299Q8#6728812yes—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—462no—
304D4—922no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—461no—
319C2×C4—461no—
320C2×C4—922no—
321C2×C4—922no—
322C2×C4D4×D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—21no—
325C8—21no—
326C8—461no—
327C8—461no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—232no—
335C22—461no—
336C22—461no—
337C22C2×D4×D2311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—461no—
343C4—461no—
344C4—461no—
345C4—921no—
346C4—921no—
347C4—921no—
348C4—921no—
349C4C2×#6728811yescharacteristic
350C4#1062515511yescharacteristic
351C2—41no—
352C2—81no—
353C2—462no—
354C2#1309305711yescharacteristic
355C2#135×D2311yescharacteristic
356C2#1309323111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#416C2
socleC22×C23C22×D4
prime radical#13093074C2
hypercenter#416D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #13093106C2semidirect
3. #13092770C2semidirect
4. #13092758C2semidirect
5. #13092729C2semidirect
6. #13092726C2semidirect
7. #13092658C2semidirect
8. #13092645C2semidirect
9. #13092638C2semidirect
10. #13092579C2semidirect
11. #13092574C2semidirect
12. #13092509C2semidirect
13. C8×C22⋊D23C2semidirect
14. #103×D23C2semidirect
15. C23×#416C2semidirect
186. #416D23semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130931062
#130930742
#130927702
#130927582
#130927292
#130927262
#130926582
#130926452
#130926382
#130925792
#130925742
#130925092
C8×C22⋊D232
#103×D232
C23×#4162
#330023