Finite Group Databasebeta

← #15685332

Subgroups — #15685332

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093135C211yesmaximal, characteristic, complemented
2#13093086C211yesmaximal, characteristic
3#13092762C211yesmaximal, characteristic, complemented
4#13092741C211yesmaximal, characteristic, complemented
5#13092740C211yesmaximal, characteristic, complemented
6#13092700C211yesmaximal, characteristic, complemented
7#13092646C211yesmaximal, characteristic, complemented
8#13092645C211yesmaximal, characteristic, complemented
9#13092616C211yesmaximal, characteristic, complemented
10#13092582C211yesmaximal, characteristic, complemented
11#13092579C211yesmaximal, characteristic, complemented
12#13092509C211yesmaximal, characteristic, complemented
13C8×C22⋊D23C211yesmaximal, characteristic, complemented
14#13092412C211yesmaximal, characteristic, complemented
15C23×#416C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C23×#117C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21C2×#67275C2211yescharacteristic
22#10625111—21no—
23#10625111C2211yescharacteristic
24#10625109—21no—
25#10625109C2211yescharacteristic
26C2×#67273C2211yescharacteristic
27#10625101—21no—
28#10625101C2211yescharacteristic
29C4×C22⋊D23—21no—
30C4×C22⋊D23C2211yescharacteristic
31#10625095C2211yescharacteristic
32C2×#67263C2211yescharacteristic
33C2×C8×D23C2211yescharacteristic
34#10625068C2211yescharacteristic
35#10625063C2211yescharacteristic
36#10625059C2211yescharacteristic
37#10625058C2211yescharacteristic
38#10625056—21no—
39#10625050—21no—
40#10625047—21no—
41C4×Dic46—21no—
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624998C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
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⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23D411yescharacteristic
71#67292—22no—
72#67292—41no—
73C2×D92—21no—
74C2×D92C2311yescharacteristic
75C2×C4×D23—21no—
76C2×C4×D23C2311yescharacteristic
77C2×Dic46—21no—
78C2×Dic46C2311yescharacteristic
79C2×C8×C23—41no—
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85C42×C23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23D411yescharacteristic
89#67275—22no—
90#67273—41no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109#67263—41no—
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23#4112yes—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—42no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—42no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2411yescharacteristic
128C22⋊D23—22no—
129C22⋊D23—42no—
130C22⋊D23—81no—
131C22⋊D23—81no—
132C22⋊D23—81no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139D92—21no—
140D92—21no—
141D92—42no—
142C4×D23—21no—
143C4×D23—21no—
144C4×D23—42no—
145Dic46—21no—
146Dic46—21no—
147Dic46—42no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3304—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23C22×D411yescharacteristic
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—21no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C4×C23—22no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23H(5,𝔽2)11yescharacteristic
172Dic23—21no—
173Dic23—21no—
174Dic23—41no—
175Dic23—41no—
176Dic23—41no—
177Dic23#13512yes—
178#556—231no—
179#550—231no—
180#486—231no—
181#482—231no—
182#482—231no—
183#475—231no—
184#465—231no—
185#465—231no—
186#460—231no—
187#452—231no—
188#452—231no—
189C4×Q16—231no—
190C8×D4—231no—
191#416—231no—
192#416D2311yescharacteristic, complemented
193C2×C23—41no—
194C2×C23—81no—
195C2×C23#54611yescharacteristic
196C2×C23C2×#13511yescharacteristic
197C2×C23#57711yescharacteristic
198D23—41no—
199D23—81no—
200C2×#41—231no—
201C2×#41C2×D2311yescharacteristic
202C2×Q16—231no—
203C2×SD16—231no—
204C2×SD16—231no—
205C22×C8—231no—
206C22×C8C2×D2311yescharacteristic
207C4⋊Q8—231no—
208#127—231no—
209#127—461no—
210#126—461no—
211#126—461no—
212#124—461no—
213C22⋊Q8—231no—
214C22⋊Q8—231no—
215#121—231no—
216#121—231no—
217#121—461no—
218#121—461no—
219C4×Q8—231no—
220C4×Q8—231no—
221C4×Q8—461no—
222C4×D4—231no—
223C4×D4—461no—
224#117—231no—
225#117C2×D2311yescharacteristic
226#107—231no—
227#106—231no—
228#106—231no—
229C4⋊C8—231no—
230#103—231no—
231#103—231no—
232#103C2×D2311yescharacteristic
233#103C2×D2311yescharacteristic
234#102—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102C2×D2311yescharacteristic
239#102C2×D2311yescharacteristic
240C22⋊C8—231no—
241C22⋊C8—231no—
242C4×C8—231no—
243C23#330411yescharacteristic, complemented, Sylow
244#41—22no—
245#41—41no—
246#41—462no—
247#41—921no—
248C2×Q8—231no—
249C2×Q8—461no—
250C2×Q8C22×D2311yescharacteristic
251C2×D4—21no—
252C2×D4—231no—
253C2×D4—231no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4—461no—
258C2×D4—461no—
259C2×D4C22×D2311yescharacteristic
260C22×C4—21no—
261C22×C4—231no—
262C22×C4—461no—
263C22×C4C22×D2311yescharacteristic
264Q16—462no—
265SD16—921no—
266SD16—921no—
267C2×C8—41no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—921no—
271C2×C8C22×D2311yescharacteristic
272C2×C8C22×D2311yescharacteristic
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4C22×D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—231no—
285C22⋊C4—231no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C42—21no—
292C42—231no—
293C42—461no—
294C42—461no—
295C42—461no—
296C23—21no—
297C23—231no—
298C23—461no—
299C23D4×D2311yescharacteristic
300Q8—21no—
301Q8—461no—
302Q8—461no—
303Q8—922no—
304Q8#6728812yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—462no—
309D4—461no—
310D4—461no—
311D4—922no—
312D4—922no—
313D4—1841no—
314D4—1841no—
315D4—1841no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—231no—
323C2×C4—231no—
324C2×C4—231no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—461no—
330C2×C4—922no—
331C2×C4D4×D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—461no—
336C8—461no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—461no—
344C22—461no—
345C22—461no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—232no—
355C4—461no—
356C4—461no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4C2×#6728811yescharacteristic
361C4#1062515511yescharacteristic
362C2—41no—
363C2—81no—
364C2—921no—
365C2—1841no—
366C2#1309305711yescharacteristic
367C2#135×D2311yescharacteristic
368C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#416C2
socleC22×C23C22×D4
prime radical#13093086C2
hypercenter#416D23
hypocenterC23#3304
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. #13093135C2semidirect
3. #13092762C2semidirect
4. #13092741C2semidirect
5. #13092740C2semidirect
6. #13092700C2semidirect
7. #13092646C2semidirect
8. #13092645C2semidirect
9. #13092616C2semidirect
10. #13092582C2semidirect
11. #13092579C2semidirect
12. #13092509C2semidirect
13. C8×C22⋊D23C2semidirect
14. #13092412C2semidirect
15. C23×#416C2semidirect
192. #416D23semidirect
243. C23#3304semidirect

Maximal subgroups

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

subgroupindex
#130931352
#130930862
#130927622
#130927412
#130927402
#130927002
#130926462
#130926452
#130926162
#130925822
#130925792
#130925092
C8×C22⋊D232
#130924122
C23×#4162
#330423