Finite Group Databasebeta

← #15683350

Subgroups — #15683350

Order 2944.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13092983C211yesmaximal, characteristic
2#13092897C211yesmaximal, characteristic, complemented
3#13092743C211yesmaximal, characteristic, complemented
4#13092741C211yesmaximal, characteristic, complemented
5#13092740C211yesmaximal, characteristic, complemented
6#13092736C211yesmaximal, characteristic, complemented
7#13092734C211yesmaximal, characteristic, complemented
8#13092732C211yesmaximal, characteristic, complemented
9#13092728C211yesmaximal, characteristic, complemented
10#13092458C211yesmaximal, characteristic, complemented
11#13092452C211yesmaximal, characteristic, complemented
12#13092420C211yesmaximal, characteristic, complemented
13#102×D23C211yesmaximal, characteristic, complemented
14#13092382C211yesmaximal, characteristic, complemented
15C23×#482C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C23×#121C2211yescharacteristic
19C23×#117C2211yescharacteristic, complemented
20#10625111—21no—
21#10625109C2211yescharacteristic
22#10625108—21no—
23#10625101C2211yescharacteristic
24C2×C4⋊Dic23C2211yescharacteristic, complemented
25C2×#67262C2211yescharacteristic
26C2×C8×D23C2211yescharacteristic
27#10625066C2211yescharacteristic
28#10625063C2211yescharacteristic
29#10625063C2211yescharacteristic
30#10625063C2211yescharacteristic, complemented
31C4⋊C4×D23C2211yescharacteristic
32C4⋊C4×D23C2211yescharacteristic, complemented
33#10625056—21no—
34#10625053—21no—
35(C22⋊D23)⋊C4—21no—
36(C22⋊D23)⋊C4—21no—
37C4×D92—21no—
38C4×Dic46—21no—
39C23×#107C2211yescharacteristic, complemented
40C23×#106C2211yescharacteristic, complemented
41C23×#102C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic, complemented
44#10625014C2211yescharacteristic
45#10625014C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic, complemented
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic, complemented
50(C2×D23)⋊C8C2211yescharacteristic, complemented
51#10624999C2211yescharacteristic, complemented
52#10624999C2211yescharacteristic, complemented
53#10624991C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624990C2211yescharacteristic, complemented
56#10624989C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23C2311yescharacteristic
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23D411yescharacteristic
67C2×C22⋊D23D411yescharacteristic
68C22×Dic23—21no—
69D4×D23—22no—
70D4×D23—22no—
71#67288—22no—
72#67288—22no—
73C2×D92—21no—
74C2×D92D411yescharacteristic
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23C2311yescharacteristic
79C2×C4×D23C2311yescharacteristic
80C2×Dic46D411yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊C4×C23—21no—
87C22⋊C4×C23—21no—
88C42×C23—21no—
89C22⋊Dic23—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106#67262—22no—
107C8×D23—22no—
108C23×C23—21no—
109C23×C23C2×D411yescharacteristic
110C22×D23—21no—
111C22×D23—42no—
112C22×D23—81no—
113C22×D23—81no—
114C22×D23C2×D411yescharacteristic
115C22×D23C2×D411yescharacteristic
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—81no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—22no—
127C22⋊D23—22no—
128C22⋊D23—42no—
129C22⋊D23—81no—
130C22⋊D23—81no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—81no—
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137D92—22no—
138D92—21no—
139D92—21no—
140D92—81no—
141C4×D23—21no—
142C4×D23—21no—
143C4×D23—81no—
144C4×D23—81no—
145C4×D23#4112yes—
146C4×D23#4112yes—
147Dic46—22no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3096—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—21no—
164C2×D23—21no—
165C2×D23—41no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—84no—
169C2×D23#12312yes—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23—41no—
174C4×C23C2×#4111yescharacteristic
175C4×C23C2×#4111yescharacteristic
176Dic23—21no—
177Dic23—41no—
178Dic23—41no—
179Dic23—41no—
180Dic23#12312yes—
181#535—231no—
182#520—231no—
183#482—231no—
184#482—231no—
185#482—231no—
186#482D2311yescharacteristic, complemented
187#481—231no—
188#481—231no—
189#480—231no—
190#480—231no—
191#428—231no—
192#427—231no—
193#418—231no—
194C2×#102—231no—
195#408—231no—
196C2×C23—41no—
197C2×C23—81no—
198C2×C23C2×#12311yescharacteristic
199C2×C23#57611yescharacteristic
200C2×C23#57711yescharacteristic
201D23—22no—
202D23—41no—
203D23—81no—
204C2×#41—231no—
205C22×D4—231no—
206C2×M16—231no—
207C22×C8—231no—
208#127—461no—
209#124—461no—
210#121—231no—
211#121—231no—
212#121—231no—
213#121C2×D2311yescharacteristic
214#120—461no—
215#120—461no—
216C4×Q8—461no—
217C4×D4—461no—
218C4×D4—461no—
219C4×D4—461no—
220#117—231no—
221#117—231no—
222#117—231no—
223#117C2×D2311yescharacteristic, complemented
224C2×C4⋊C4—231no—
225C2×C4⋊C4—231no—
226C2×C4⋊C4—231no—
227#107—231no—
228#107—231no—
229#107—231no—
230#107C2×D2311yescharacteristic, complemented
231#106—231no—
232#106—231no—
233#106—231no—
234#106C2×D2311yescharacteristic, complemented
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240#102—231no—
241#102C2×D2311yescharacteristic
242#102C2×D2311yescharacteristic
243C22⋊C8—231no—
244C22⋊C8—231no—
245C22⋊C8—231no—
246C22⋊C8C2×D2311yescharacteristic, complemented
247C23#309611yescharacteristic, complemented, Sylow
248C24—461no—
249#41—462no—
250#41—462no—
251C2×Q8—231no—
252C2×D4—21no—
253C2×D4—231no—
254C2×D4—231no—
255C2×D4—231no—
256C2×D4—231no—
257C2×D4—461no—
258C2×D4—462no—
259C2×D4—462no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4C22×D2311yescharacteristic
264C22×C4—231no—
265C22×C4—231no—
266C22×C4—461no—
267C22×C4—461no—
268C22×C4—461no—
269C22×C4C22×D2311yescharacteristic
270M16—462no—
271C2×C8—231no—
272C2×C8—231no—
273C2×C8—462no—
274C2×C8C22×D2311yescharacteristic
275C2×C8C22×D2311yescharacteristic
276C4⋊C4—231no—
277C4⋊C4—231no—
278C4⋊C4—231no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4C22×D2311yescharacteristic
283C4⋊C4C22×D2311yescharacteristic
284C4⋊C4C22×D2311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—21no—
294C42—461no—
295C42—461no—
296C42—461no—
297C23—21no—
298C23—231no—
299C23—231no—
300C23—461no—
301C23—922no—
302C23—1841no—
303C23—1841no—
304C23D4×D2311yescharacteristic
305Q8—462no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—462no—
310D4—462no—
311D4—462no—
312D4—461no—
313D4—461no—
314D4—922no—
315D4—1841no—
316D4—1841no—
317D4—1841no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—231no—
324C2×C4—232no—
325C2×C4—232no—
326C2×C4—231no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—461no—
330C2×C4—461no—
331C2×C4—461no—
332C2×C4—1841no—
333C2×C4—1841no—
334C2×C4—1841no—
335C2×C4D4×D2311yescharacteristic
336C2×C4C23×D2311yescharacteristic
337C8—21no—
338C8—21no—
339C8—461no—
340C8—461no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—232no—
348C22—461no—
349C22—461no—
350C22—461no—
351C22—461no—
352C22—461no—
353C22—921no—
354C22—921no—
355C22—921no—
356C22—1844no—
357C22C2×D4×D2311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—232no—
363C4—461no—
364C4—921no—
365C4—921no—
366C4—921no—
367C4#41×D2311yescharacteristic
368C4#41×D2311yescharacteristic
369C2—41no—
370C2—81no—
371C2—462no—
372C2—921no—
373C2—1841no—
374C2#123×D2311yescharacteristic
375C2#1309322111yescharacteristic
376C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#482C2
socleC22×C23C22×D4
prime radical#13092983C2
hypercenter#482D23
hypocenterC23#3096
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #13092897C2semidirect
3. #13092743C2semidirect
4. #13092741C2semidirect
5. #13092740C2semidirect
6. #13092736C2semidirect
7. #13092734C2semidirect
8. #13092732C2semidirect
9. #13092728C2semidirect
10. #13092458C2semidirect
11. #13092452C2semidirect
12. #13092420C2semidirect
13. #102×D23C2semidirect
14. #13092382C2semidirect
15. C23×#482C2semidirect
19. C23×#117C22semidirect
24. C2×C4⋊Dic23C22semidirect
30. #10625063C22semidirect
32. C4⋊C4×D23C22semidirect
39. C23×#107C22semidirect
40. C23×#106C22semidirect
43. C23×C22⋊C8C22semidirect
46. C22⋊(C23⋊C8)C22semidirect
49. (C2×D23)⋊C8C22semidirect
50. (C2×D23)⋊C8C22semidirect
51. #10624999C22semidirect
52. #10624999C22semidirect
55. #10624990C22semidirect
56. #10624989C22semidirect
57. #10624989C22semidirect
58. #10624989C22semidirect
186. #482D23semidirect
223. #117C2×D23semidirect
230. #107C2×D23semidirect
234. #106C2×D23semidirect
246. C22⋊C8C2×D23semidirect
247. C23#3096semidirect

Maximal subgroups

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

subgroupindex
#130929832
#130928972
#130927432
#130927412
#130927402
#130927362
#130927342
#130927322
#130927282
#130924582
#130924522
#130924202
#102×D232
#130923822
C23×#4822
#309623