Finite Group Databasebeta

← #15685305

Subgroups — #15685305

Order 2944.

398 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#13093119C211yesmaximal, characteristic, complemented
2#13093073C211yesmaximal, characteristic, complemented
3#13092770C211yesmaximal, characteristic, complemented
4#13092760C211yesmaximal, characteristic, complemented
5#13092733C211yesmaximal, characteristic, complemented
6#13092723C211yesmaximal, characteristic, complemented
7#13092645C211yesmaximal, characteristic, complemented
8#13092630C211yesmaximal, characteristic, complemented
9#13092559C211yesmaximal, characteristic, complemented
10#13092555C211yesmaximal, characteristic, complemented
11#13092508C211yesmaximal, characteristic, complemented
12C8×C22⋊D23C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14C2×#10624998C211yesmaximal, characteristic, complemented
15C23×#466C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic
20C23×#121C2211yescharacteristic
21C23×#121C2211yescharacteristic
22#10625110—21no—
23#10625110—21no—
24#10625109C2211yescharacteristic
25#10625107C2211yescharacteristic
26D4×Dic23—21no—
27D4×Dic23—21no—
28D4×Dic23C2211yescharacteristic
29C2×#67273C2211yescharacteristic
30C2×#67273C2211yescharacteristic
31C4×C22⋊D23C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33C2×C8×D23C2211yescharacteristic
34#10625068C2211yescharacteristic
35#10625063C2211yescharacteristic
36#10625061C2211yescharacteristic
37#10625058C2211yescharacteristic
38#10625057—21no—
39#10625056—21no—
40#10625050—21no—
41#10625049—21no—
42C23×#107C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×#102C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47C22⋊(C23⋊C8)C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10624998C2211yescharacteristic
50#10624998C2211yescharacteristic
51#10624998C2211yescharacteristic
52#10624998C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624990C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23D411yescharacteristic
67C22×Dic23—21no—
68C22×Dic23—21no—
69C22×Dic23—21no—
70C22×Dic23—21no—
71#67290—22no—
72#67290—41no—
73C2×C4×D23C2311yescharacteristic
74C2×Dic46—22no—
75C2×Dic46—21no—
76C2×Dic46—41no—
77C2×Dic46C2311yescharacteristic
78C2×Dic46C2311yescharacteristic
79D8×C23—41no—
80C2×C8×C23—41no—
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23D411yescharacteristic
92#67273—22no—
93#67273—41no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4D411yescharacteristic
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23C2×D411yescharacteristic
114C22×D23C2×D411yescharacteristic
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—42no—
120D4×C23—42no—
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—22no—
128C22⋊D23—42no—
129C22⋊D23—81no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—42no—
135C2×Dic23—42no—
136C2×Dic23—81no—
137C2×Dic23—81no—
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141C4×D23—21no—
142C4×D23—21no—
143Dic46—21no—
144Dic46—21no—
145Dic46—21no—
146Dic46—42no—
147Dic46#4112yes—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3301—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23#13512yes—
162C22×C23C22×D411yescharacteristic
163C2×D23—21no—
164C2×D23—21no—
165C2×D23—21no—
166C4×C23—21no—
167C4×C23—41no—
168C4×C23—41no—
169C4×C23C2×#4111yescharacteristic
170C4×C23H(5,𝔽2)11yescharacteristic
171Dic23—22no—
172Dic23—21no—
173Dic23—21no—
174Dic23—21no—
175Dic23—41no—
176Dic23—41no—
177Dic23—41no—
178#553—231no—
179#548—231no—
180#488—231no—
181#485—231no—
182#481—231no—
183#479—231no—
184#466D2311yescharacteristic, complemented
185#465—231no—
186#463—231no—
187#449—231no—
188#448—231no—
189C4×SD16—231no—
190C8×D4—231no—
191#416—231no—
192C2×#103—231no—
193C2×C23—22no—
194C2×C23—81no—
195C2×C23—81no—
196C2×C23#54611yescharacteristic
197C2×C23C2×#13511yescharacteristic
198C2×C23#57711yescharacteristic
199D23—41no—
200C2×#41—231no—
201C22×Q8—231no—
202C2×SD16—231no—
203C2×SD16—231no—
204C2×D8C2×D2311yescharacteristic
205C22×C8—231no—
206C22×C8C2×D2311yescharacteristic
207#126—461no—
208#125—231no—
209#124—231no—
210#124—461no—
211#123—461no—
212C22⋊Q8—231no—
213C22⋊Q8—461no—
214#121—231no—
215#121—461no—
216#121—461no—
217#121C2×D2311yescharacteristic
218#121C2×D2311yescharacteristic
219C4×Q8—231no—
220C4×D4—231no—
221C4×D4—231no—
222C4×D4—461no—
223C4×D4—461no—
224#117—231no—
225C2×C4⋊C4—231no—
226#107C2×D2311yescharacteristic
227#106—231no—
228#106—231no—
229C4⋊C8—231no—
230#103—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103—231no—
235#103—231no—
236#102—231no—
237#102—231no—
238#102C2×D2311yescharacteristic
239#102C2×D2311yescharacteristic
240C22⋊C8—231no—
241C22⋊C8—231no—
242C4×C8—231no—
243C23#330111yescharacteristic, complemented, Sylow
244#41—462no—
245#41—921no—
246C2×Q8—231no—
247C2×Q8—231no—
248C2×Q8—462no—
249C2×Q8—461no—
250C2×Q8—921no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—231no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4C22×D2311yescharacteristic
257C2×D4C22×D2311yescharacteristic
258C22×C4—231no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4C22×D2311yescharacteristic
264SD16—462no—
265SD16—921no—
266D8—41no—
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—21no—
285C22⋊C4—231no—
286C22⋊C4—231no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—231no—
294C42—461no—
295C42—461no—
296C23—21no—
297C23—21no—
298C23—231no—
299C23D4×D2311yescharacteristic
300Q8—232no—
301Q8—461no—
302Q8—461no—
303Q8—461no—
304Q8—922no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—42no—
311D4—462no—
312D4—922no—
313D4—1841no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—231no—
319C2×C4—231no—
320C2×C4—231no—
321C2×C4—461no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—922no—
328C2×C4—922no—
329C2×C4—1841no—
330C2×C4—1841no—
331C2×C4D4×D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—461no—
336C8—461no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—461no—
346C22—461no—
347C22—461no—
348C22#1062508312yes—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—461no—
354C4—461no—
355C4—461no—
356C4—462no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4#1062515511yescharacteristic
361C4#41×D2311yescharacteristic
362C2—22no—
363C2—81no—
364C2—81no—
365C2—921no—
366C2#1309305611yescharacteristic
367C2C2×#1062508311yescharacteristic
368C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#466C2
socleC22×C23C22×D4
hypercenter#466D23
hypocenterC23#3301
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #13093119C2semidirect
2. #13093073C2semidirect
3. #13092770C2semidirect
4. #13092760C2semidirect
5. #13092733C2semidirect
6. #13092723C2semidirect
7. #13092645C2semidirect
8. #13092630C2semidirect
9. #13092559C2semidirect
10. #13092555C2semidirect
11. #13092508C2semidirect
12. C8×C22⋊D23C2semidirect
13. #13092410C2semidirect
14. C2×#10624998C2semidirect
15. C23×#466C2semidirect
184. #466D23semidirect
243. C23#3301semidirect

Maximal subgroups

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

subgroupindex
#130931192
#130930732
#130927702
#130927602
#130927332
#130927232
#130926452
#130926302
#130925592
#130925552
#130925082
C8×C22⋊D232
#130924102
C2×#106249982
C23×#4662
#330123