Finite Group Databasebeta

← #15685321

Subgroups — #15685321

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#13093130C211yesmaximal, characteristic, complemented
2#13093066C211yesmaximal, characteristic, complemented
3#13092766C211yesmaximal, characteristic, complemented
4#13092758C211yesmaximal, characteristic, complemented
5#13092756C211yesmaximal, characteristic, complemented
6#13092705C211yesmaximal, characteristic, complemented
7#13092649C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092621C211yesmaximal, characteristic, complemented
10#13092563C211yesmaximal, characteristic, complemented
11#13092562C211yesmaximal, characteristic, complemented
12#13092497C211yesmaximal, characteristic, complemented
13C8×C22⋊D23C211yesmaximal, characteristic, complemented
14#13092410C211yesmaximal, characteristic, complemented
15C23×#416C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C23×#117C2211yescharacteristic
20#10625117C2211yescharacteristic
21#10625115C2211yescharacteristic
22C2×#67274C2211yescharacteristic
23#10625110—21no—
24#10625106—21no—
25D4×Dic23C2211yescharacteristic
26C2×#67272C2211yescharacteristic
27#10625101C2211yescharacteristic
28#10625100—21no—
29C4×C22⋊D23C2211yescharacteristic
30#10625095C2211yescharacteristic
31C2×Dic23⋊C4—21no—
32C2×#67263C2211yescharacteristic
33C2×C8×D23C2211yescharacteristic
34#10625066C2211yescharacteristic
35#10625064C2211yescharacteristic
36#10625063C2211yescharacteristic
37#10625059C2211yescharacteristic
38#10625056—21no—
39#10625055—21no—
40#10625046—21no—
41#10625043—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#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⋊D23—21no—
68C2×C22⋊D23D411yescharacteristic
69C22×Dic23—21no—
70C22×Dic23—21no—
71#67290—22no—
72#67290—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#67274—41no—
90#67272—22no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4D411yescharacteristic
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—21no—
117D4×C23—21no—
118D4×C23—42no—
119D4×C23#4112yes—
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—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—42no—
135C2×Dic23—42no—
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139D92—21no—
140D92—21no—
141D92—81no—
142C4×D23—21no—
143C4×D23—21no—
144C4×D23—42no—
145Dic46—21no—
146Dic46—21no—
147Dic46—81no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3303—231nomaximal, Sylow
153C22×C23—22no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—21no—
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—21no—
167C4×C23—41no—
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#555—231no—
179#547—231no—
180#487—231no—
181#485—231no—
182#485—231no—
183#476—231no—
184#465—231no—
185#465—231no—
186#461—231no—
187#449—231no—
188#449—231no—
189C4×D8—231no—
190C8×D4—231no—
191#416—231no—
192#416D2311yescharacteristic, complemented
193C2×C23—41no—
194C2×C23—42no—
195C2×C23#54611yescharacteristic
196C2×C23C2×#13511yescharacteristic
197C2×C23#57711yescharacteristic
198D23—41no—
199D23—81no—
200C2×#41—231no—
201C2×#41C2×D2311yescharacteristic
202C2×SD16—231no—
203C2×SD16—231no—
204C2×D8—231no—
205C22×C8—231no—
206C22×C8C2×D2311yescharacteristic
207C4⋊Q8—231no—
208C4⋊Q8—231no—
209#124—461no—
210#124—461no—
211#123—461no—
212#123—461no—
213C22⋊Q8—231no—
214C22⋊Q8—231no—
215#121—231no—
216#121—231no—
217#121—461no—
218#121—461no—
219C4×D4—231no—
220C4×D4—231no—
221C4×D4—231no—
222#117—231no—
223#117—461no—
224#117C2×D2311yescharacteristic
225C2×C4⋊C4—461no—
226#107—231no—
227#106—231no—
228#106—231no—
229C4⋊C8—231no—
230#103—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103C2×D2311yescharacteristic
235#103C2×D2311yescharacteristic
236#102—231no—
237#102—231no—
238#102C2×D2311yescharacteristic
239#102C2×D2311yescharacteristic
240C22⋊C8—231no—
241C22⋊C8—231no—
242C4×C8—231no—
243C23#330311yescharacteristic, 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×D4C22×D2311yescharacteristic
258C22×C4—21no—
259C22×C4—231no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4C22×D2311yescharacteristic
264SD16—921no—
265SD16—921no—
266D8—462no—
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—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—21no—
294C42—231no—
295C42—461no—
296C23—21no—
297C23—231no—
298C23—461no—
299C23D4×D2311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—461no—
303Q8—461no—
304Q8—1841no—
305D4—21no—
306D4—42no—
307D4—462no—
308D4—461no—
309D4—461no—
310D4—922no—
311D4—1841no—
312D4—1841no—
313D4#6728812yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—922no—
329C2×C4—922no—
330C2×C4—922no—
331C2×C4D4×D2311yescharacteristic
332C2×C4C23×D2311yescharacteristic
333C8—21no—
334C8—21no—
335C8—461no—
336C8—461no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—461no—
344C22—461no—
345C22—461no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22C2×D4×D2311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—232no—
355C4—461no—
356C4—461no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4C2×#6728811yescharacteristic
361C4#1062515511yescharacteristic
362C2—41no—
363C2—42no—
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
hypercenter#416D23
hypocenterC23#3303
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. #13093130C2semidirect
2. #13093066C2semidirect
3. #13092766C2semidirect
4. #13092758C2semidirect
5. #13092756C2semidirect
6. #13092705C2semidirect
7. #13092649C2semidirect
8. #13092646C2semidirect
9. #13092621C2semidirect
10. #13092563C2semidirect
11. #13092562C2semidirect
12. #13092497C2semidirect
13. C8×C22⋊D23C2semidirect
14. #13092410C2semidirect
15. C23×#416C2semidirect
192. #416D23semidirect
243. C23#3303semidirect

Maximal subgroups

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

subgroupindex
#130931302
#130930662
#130927662
#130927582
#130927562
#130927052
#130926492
#130926462
#130926212
#130925632
#130925622
#130924972
C8×C22⋊D232
#130924102
C23×#4162
#330323