Finite Group Databasebeta

← #15685278

Subgroups — #15685278

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#13093076C211yesmaximal, characteristic
2#13092774C211yesmaximal, characteristic, complemented
3#13092758C211yesmaximal, characteristic, complemented
4#13092730C211yesmaximal, characteristic, complemented
5#13092721C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092639C211yesmaximal, characteristic, complemented
9#13092577C211yesmaximal, characteristic, complemented
10#13092572C211yesmaximal, characteristic, complemented
11C4×#67275C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092411C211yesmaximal, characteristic, complemented
14C2×#10624992C211yesmaximal, characteristic, complemented
15C23×#552C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C23×#126—21no—
19C23×#125—21no—
20C23×#125C2211yescharacteristic
21C23×#123—21no—
22C23×C22⋊Q8C2211yescharacteristic
23C23×C22⋊Q8C2211yescharacteristic
24C4×Q8×C23C2211yescharacteristic
25C4×D4×C23C2211yescharacteristic
26C23×#117—21no—
27C23×#117C2211yescharacteristic
28C2×C4⋊C4×C23C2211yescharacteristic
29C2×#67275C2211yescharacteristic
30C2×#67275C2211yescharacteristic
31C2×#67274C2211yescharacteristic
32#10625110—21no—
33#10625101C2211yescharacteristic
34#10625095C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37#10625067—21no—
38#10625056—21no—
39(C22⋊D23)⋊C4—21no—
40#10625046C2211yescharacteristic
41C4×Dic46C2211yescharacteristic
42#10625017C2211yescharacteristic
43C22⋊(C23⋊C8)C2211yescharacteristic
44C22⋊(C23⋊C8)C2211yescharacteristic
45#10624992C2211yescharacteristic
46#10624992C2211yescharacteristic
47#10624992C2211yescharacteristic
48#10624992C2211yescharacteristic
49#10624992C2211yescharacteristic
50#10624992C2211yescharacteristic
51#10624991C2211yescharacteristic
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic
55#10624989C2211yescharacteristic
56#10624989C2211yescharacteristic
57C4⋊(C23⋊C8)C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23D411yescharacteristic
61C22×C4×C23—21no—
62C22×C4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C22×Dic23—21no—
67#67288—22no—
68#67288—41no—
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×Dic46—22no—
72C2×Dic46—21no—
73C2×Dic46—41no—
74C2×Dic46C2311yescharacteristic
75C2×Dic46C2311yescharacteristic
76C4⋊C4×C23—21no—
77C4⋊C4×C23—21no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23D411yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊C4×C23—21no—
87C22⋊C4×C23—21no—
88C22⋊C4×C23—21no—
89C22⋊C4×C23D411yescharacteristic
90C22⋊C4×C23D411yescharacteristic
91C42×C23—21no—
92C42×C23—21no—
93C42×C23C2311yescharacteristic
94C22⋊Dic23—21no—
95#67275—22no—
96#67275—41no—
97#67274—41no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104C4×Dic23—21no—
105C2×C23⋊C8—41no—
106C2×C23⋊C8—41no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C23×C23C2×D411yescharacteristic
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114Q8×C23—21no—
115Q8×C23—21no—
116D4×C23—22no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
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×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—42no—
132C22⋊D23—42no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—42no—
137D92—21no—
138D92—21no—
139C4×D23—42no—
140Dic46—21no—
141Dic46—21no—
142Dic46—21no—
143Dic46—42no—
144Dic46#4112yes—
145C23⋊C8—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149#3300—231nomaximal, Sylow
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—21no—
154C22×C23—21no—
155C22×C23#13512yes—
156C22×C23C22×D411yescharacteristic
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—21no—
163C4×C23—21no—
164C4×C23—41no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23—41no—
168C4×C23C2×#4111yescharacteristic
169C4×C23H(5,𝔽2)11yescharacteristic
170Dic23—22no—
171Dic23—41no—
172Dic23—41no—
173#552D2311yescharacteristic, complemented
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#416—231no—
187C2×#103—231no—
188C2×C23—22no—
189C2×C23—41no—
190C2×C23#54611yescharacteristic
191C2×C23C2×#13511yescharacteristic
192C2×C23#57811yescharacteristic
193D23—81no—
194C2×#41—231no—
195C22×Q8—231no—
196C2×Q16—231no—
197C2×Q16—231no—
198C2×SD16—231no—
199C22×C8—231no—
200C22×C8—231no—
201#126—21no—
202#125—21no—
203#125C2×D2311yescharacteristic
204#124—231no—
205#124—461no—
206#123—21no—
207C22⋊Q8—231no—
208C22⋊Q8—461no—
209C22⋊Q8C2×D2311yescharacteristic
210C22⋊Q8C2×D2311yescharacteristic
211#121—231no—
212#121—461no—
213C4×Q8—231no—
214C4×Q8C2×D2311yescharacteristic
215C4×D4—461no—
216C4×D4C2×D2311yescharacteristic
217#117—21no—
218#117C2×D2311yescharacteristic
219C2×C4⋊C4C2×D2311yescharacteristic
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#103—231no—
230#103—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234C22⋊C8—231no—
235C22⋊C8—231no—
236C4×C8—231no—
237C23#330011yescharacteristic, complemented, Sylow
238#41—462no—
239#41—921no—
240C2×Q8—231no—
241C2×Q8—231no—
242C2×Q8—462no—
243C2×Q8—461no—
244C2×Q8—921no—
245C2×Q8C22×D2311yescharacteristic
246C2×D4—231no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4C22⋊D2311yescharacteristic
250C22×C4—21no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4C22×D2311yescharacteristic
254C22×C4C22×D2311yescharacteristic
255Q16—462no—
256Q16—921no—
257SD16—921no—
258C2×C8—231no—
259C2×C8—231no—
260C2×C8—231no—
261C2×C8—231no—
262C2×C8—921no—
263C2×C8—921no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—231no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4C22⋊D2311yescharacteristic
274C4⋊C4C22×D2311yescharacteristic
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4C22⋊D2311yescharacteristic
285C22⋊C4C22⋊D2311yescharacteristic
286C42—21no—
287C42—21no—
288C42—461no—
289C42C22×D2311yescharacteristic
290C23—461no—
291C23C2×C22⋊D2311yescharacteristic
292C23C2×C22⋊D2311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—232no—
296Q8—461no—
297Q8—461no—
298Q8—461no—
299Q8—922no—
300D4—22no—
301D4—461no—
302D4—461no—
303D4—922no—
304D4—922no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—922no—
318C2×C4—922no—
319C2×C4C2×C22⋊D2311yescharacteristic
320C2×C4C2×C22⋊D2311yescharacteristic
321C2×C4C2×C22⋊D2311yescharacteristic
322C2×C4C2×C22⋊D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—461no—
325C8—461no—
326C8—461no—
327C8—461no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—921no—
334C22—921no—
335C22—921no—
336C22#1062512112yes—
337C22C22×C22⋊D2311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—462no—
347C4—921no—
348C4—921no—
349C4#41×D2311yescharacteristic
350C4#1062516011yescharacteristic
351C2—22no—
352C2—41no—
353C2—1841no—
354C2#1309305511yescharacteristic
355C2C2×#1062512111yescharacteristic
356C2#1309323211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#552C2
socleC22×C23C22×D4
prime radical#13093076C2
hypercenter#552D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #13092774C2semidirect
3. #13092758C2semidirect
4. #13092730C2semidirect
5. #13092721C2semidirect
6. #13092656C2semidirect
7. #13092648C2semidirect
8. #13092639C2semidirect
9. #13092577C2semidirect
10. #13092572C2semidirect
11. C4×#67275C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092411C2semidirect
14. C2×#10624992C2semidirect
15. C23×#552C2semidirect
173. #552D23semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130930762
#130927742
#130927582
#130927302
#130927212
#130926562
#130926482
#130926392
#130925772
#130925722
C4×#672752
D4×C23⋊C82
#130924112
C2×#106249922
C23×#5522
#330023