Finite Group Databasebeta

← #15683072

Subgroups — #15683072

Order 2944.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic, complemented
2C2×#10625078C211yesmaximal, characteristic, complemented
3#13092997C211yesmaximal, characteristic, complemented
4#13092983C211yesmaximal, characteristic, complemented
5#13092670C211yesmaximal, characteristic, complemented
6#13092669C211yesmaximal, characteristic, complemented
7#13092666C211yesmaximal, characteristic, complemented
8#13092654C211yesmaximal, characteristic, complemented
9#13092651C211yesmaximal, characteristic, complemented
10#13092648C211yesmaximal, characteristic, complemented
11#13092643C211yesmaximal, characteristic, complemented
12#13092458C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#468C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic
20C2×M16×C23C2211yescharacteristic, complemented
21C23×C22⋊Q8C2211yescharacteristic, complemented
22C23×#121C2211yescharacteristic
23#10625117C2211yescharacteristic, complemented
24C2×#67274C2211yescharacteristic
25#10625111—21no—
26#10625109C2211yescharacteristic
27#10625108—21no—
28C2×#67272C2211yescharacteristic
29#10625101C2211yescharacteristic
30#10625101C2211yescharacteristic, complemented
31C22×C23⋊C8C2211yescharacteristic, complemented
32#10625085—24no—
33#10625078—24no—
34C2×D184C2211yescharacteristic
35C2×#67262C2211yescharacteristic
36C2×#67262C2211yescharacteristic, complemented
37C2×C8×D23C2211yescharacteristic
38C2×C8×D23C2211yescharacteristic, complemented
39#10625067—21no—
40#10625066—21no—
41#10625066C2211yescharacteristic
42#10625066C2211yescharacteristic, complemented
43#10625063C2211yescharacteristic
44C4⋊C4×D23C2211yescharacteristic
45#10625056—21no—
46#10625055—21no—
47#10625055—21no—
48#10625053—21no—
49C23×#107C2211yescharacteristic, complemented
50C23×#103C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic
52#10625017C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic
55#10625003C2211yescharacteristic, complemented
56#10624999C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic
58#10624991C2211yescharacteristic, complemented
59#10624990C2211yescharacteristic, complemented
60#10624989C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23D411yescharacteristic
71C2×C22⋊D23D411yescharacteristic
72#67292—22no—
73#67292—22no—
74D4×D23—22no—
75D4×D23—22no—
76#67288—22no—
77#67288—22no—
78C2×D92—21no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92D411yescharacteristic
82C2×D92C2311yescharacteristic
83C2×D92C2311yescharacteristic
84C2×C4×D23—21no—
85C2×C4×D23—21no—
86C2×C4×D23C2311yescharacteristic
87C2×C4×D23C2311yescharacteristic
88C2×Dic46D411yescharacteristic
89SD16×C23—22no—
90M16×C23—22no—
91C2×C8×C23C2311yescharacteristic
92C2×C8×C23C2311yescharacteristic
93C4⋊C4×C23—21no—
94C4⋊C4×C23C2311yescharacteristic
95C4⋊C4×C23C2311yescharacteristic
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C22⋊Dic23—21no—
99#67274—22no—
100#67272—22no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107C4⋊Dic23C2311yescharacteristic
108C4⋊Dic23C2311yescharacteristic
109Dic23⋊C4—21no—
110Dic23⋊C4—21no—
111C4×Dic23—21no—
112C2×C23⋊C8—22no—
113C2×C23⋊C8C2311yescharacteristic
114C2×C23⋊C8C2311yescharacteristic
115D184—22no—
116#67262—22no—
117#67262D414yescomplemented
118C8×D23—22no—
119C8×D23—22no—
120C23×C23—21no—
121C23×C23C2×D411yescharacteristic
122C22×D23—21no—
123C22×D23—21no—
124C22×D23—42no—
125C22×D23—81no—
126C22×D23—81no—
127C22×D23C2×D411yescharacteristic
128C22×D23C2×D411yescharacteristic
129Q8×C23—21no—
130Q8×C23—21no—
131D4×C23—21no—
132D4×C23—21no—
133D4×C23—81no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2411yescharacteristic
141C22⋊D23—22no—
142C22⋊D23—22no—
143C22⋊D23—42no—
144C22⋊D23—81no—
145C22⋊D23—81no—
146C22⋊D23—81no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23C2×D411yescharacteristic
150C2×Dic23C2×D411yescharacteristic
151D92—22no—
152D92—21no—
153D92—21no—
154D92—21no—
155D92—21no—
156D92—42no—
157D92—81no—
158D92—81no—
159C4×D23—21no—
160C4×D23—21no—
161C4×D23—42no—
162C4×D23—81no—
163C4×D23C2×D412yes—
164C4×D23#4112yes—
165Dic46—22no—
166C8×C23—21no—
167C8×C23C2×D412yes—
168C23⋊C8—21no—
169C23⋊C8C2×D412yes—
170#3062—231nomaximal, Sylow
171C22×C23—21no—
172C22×C23—21no—
173C22×C23—21no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23—41no—
177C22×C23C22×D411yescharacteristic
178C2×D23—21no—
179C2×D23—21no—
180C2×D23—21no—
181C2×D23—21no—
182C2×D23—21no—
183C2×D23—41no—
184C2×D23—41no—
185C2×D23—41no—
186C2×D23—41no—
187C2×D23—41no—
188C2×D23—41no—
189C2×D23—84no—
190C2×D23#12112yes—
191C4×C23—21no—
192C4×C23—41no—
193C4×C23—41no—
194C4×C23—41no—
195C4×C23C22×D411yescharacteristic
196C4×C23C2×#4111yescharacteristic
197Dic23—21no—
198Dic23—41no—
199Dic23—41no—
200Dic23#12112yes—
201C2×AGL(1,ℤ/8)—231no—
202C2×#131—231no—
203#537—231no—
204#535—231no—
205#469—231no—
206#469—231no—
207#468—231no—
208#468D2311yescharacteristic, complemented
209#466—231no—
210#466—231no—
211#465—231no—
212#465—231no—
213#428—231no—
214#416—231no—
215C2×#102—231no—
216C2×C23—41no—
217C2×C23—81no—
218C2×C23C2×#12111yescharacteristic
219C2×C23#57611yescharacteristic
220C2×C23#57711yescharacteristic
221D23—22no—
222D23—41no—
223D23—81no—
224D23—81no—
225C2×#41—231no—
226C2×#41—231no—
227C22×D4—231no—
228AGL(1,ℤ/8)—464no—
229C2×SD16—231no—
230C2×SD16C2×D2311yescharacteristic
231C2×D8—231no—
232C2×D8—231no—
233#131—464no—
234C2×M16—231no—
235C2×M16—231no—
236C2×M16C2×D2311yescharacteristic, complemented
237C22×C8—231no—
238C22×C8—231no—
239C22×C8—231no—
240#127—461no—
241#124—461no—
242C22⋊Q8—231no—
243C22⋊Q8—461no—
244C22⋊Q8C2×D2311yescharacteristic, complemented
245#121—231no—
246#121—231no—
247#121—231no—
248#121—231no—
249#121—231no—
250#121—461no—
251#121—461no—
252#121—461no—
253#121C2×D2311yescharacteristic
254#120—461no—
255#120—461no—
256#117—231no—
257C2×C4⋊C4—231no—
258#107—231no—
259#107C2×D2311yescharacteristic, complemented
260#106—231no—
261#106—231no—
262#103—231no—
263#103C2×D2311yescharacteristic, complemented
264#102—231no—
265#102—231no—
266#102—231no—
267#102—231no—
268#102—231no—
269#102C2×D2311yescharacteristic
270C23#306211yescharacteristic, complemented, Sylow
271C24—461no—
272#41—462no—
273#41—462no—
274#41—462no—
275#41—462no—
276C2×Q8—231no—
277C2×Q8C22×D2311yescharacteristic
278C2×D4—21no—
279C2×D4—231no—
280C2×D4—231no—
281C2×D4—231no—
282C2×D4—231no—
283C2×D4—231no—
284C2×D4—461no—
285C2×D4—461no—
286C2×D4—461no—
287C2×D4—462no—
288C2×D4—462no—
289C2×D4—461no—
290C2×D4—461no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4C22×D2311yescharacteristic
294C22×C4—231no—
295C22×C4—231no—
296C22×C4—461no—
297C22×C4—461no—
298C22×C4C22×D2311yescharacteristic
299SD16—22no—
300SD16—462no—
301D8—462no—
302D8—462no—
303M16—22no—
304M16—234no—
305M16—462no—
306C2×C8—231no—
307C2×C8—231no—
308C2×C8—462no—
309C2×C8—462no—
310C2×C8—462no—
311C2×C8C22×D2311yescharacteristic
312C2×C8C22×D2311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—231no—
315C4⋊C4—231no—
316C4⋊C4—461no—
317C4⋊C4—461no—
318C4⋊C4C22×D2311yescharacteristic
319C4⋊C4C22×D2311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C22⋊C4—461no—
327C22⋊C4—461no—
328C22⋊C4—461no—
329C42—461no—
330C23—21no—
331C23—231no—
332C23—231no—
333C23—461no—
334C23—461no—
335C23—922no—
336C23—1841no—
337C23—1841no—
338C23D4×D2311yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—462no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—462no—
346D4—462no—
347D4—462no—
348D4—461no—
349D4—461no—
350D4—461no—
351D4—461no—
352D4—922no—
353D4—922no—
354D4—1841no—
355D4—1841no—
356D4—1841no—
357D4—1841no—
358D4—1841no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—231no—
365C2×C4—232no—
366C2×C4—232no—
367C2×C4—231no—
368C2×C4—461no—
369C2×C4—461no—
370C2×C4—461no—
371C2×C4—461no—
372C2×C4—922no—
373C2×C4—1841no—
374C2×C4D4×D2311yescharacteristic
375C2×C4C23×D2311yescharacteristic
376C8—21no—
377C8—232no—
378C8—461no—
379C8D4×D2312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—232no—
387C22—461no—
388C22—461no—
389C22—461no—
390C22—461no—
391C22—461no—
392C22—921no—
393C22—921no—
394C22—921no—
395C22—921no—
396C22—921no—
397C22—921no—
398C22—1844no—
399C22C2×D4×D2311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—232no—
405C4—461no—
406C4—921no—
407C4—921no—
408C4C2×D4×D2311yescharacteristic
409C4#41×D2311yescharacteristic
410C2—41no—
411C2—81no—
412C2—462no—
413C2—921no—
414C2—1841no—
415C2—1841no—
416C2#121×D2311yescharacteristic
417C2#1309322111yescharacteristic
418C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#468C2
socleC22×C23C22×D4
hypercenter#468D23
hypocenterC23#3062
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×#10625078C2semidirect
3. #13092997C2semidirect
4. #13092983C2semidirect
5. #13092670C2semidirect
6. #13092669C2semidirect
7. #13092666C2semidirect
8. #13092654C2semidirect
9. #13092651C2semidirect
10. #13092648C2semidirect
11. #13092643C2semidirect
12. #13092458C2semidirect
13. #13092412C2semidirect
14. #102×D23C2semidirect
15. C23×#468C2semidirect
20. C2×M16×C23C22semidirect
21. C23×C22⋊Q8C22semidirect
23. #10625117C22semidirect
30. #10625101C22semidirect
31. C22×C23⋊C8C22semidirect
36. C2×#67262C22semidirect
38. C2×C8×D23C22semidirect
42. #10625066C22semidirect
49. C23×#107C22semidirect
50. C23×#103C22semidirect
52. #10625017C22semidirect
55. #10625003C22semidirect
56. #10624999C22semidirect
58. #10624991C22semidirect
59. #10624990C22semidirect
60. #10624989C22semidirect
117. #67262D4semidirect
208. #468D23semidirect
236. C2×M16C2×D23semidirect
244. C22⋊Q8C2×D23semidirect
259. #107C2×D23semidirect
263. #103C2×D23semidirect
270. C23#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×#106250782
#130929972
#130929832
#130926702
#130926692
#130926662
#130926542
#130926512
#130926482
#130926432
#130924582
#130924122
#102×D232
C23×#4682
#306223