Finite Group Databasebeta

← #15684894

Subgroups — #15684894

Order 2944.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093079C211yesmaximal, characteristic, complemented
4D4×D92C211yesmaximal, characteristic, complemented
5#13092806C211yesmaximal, characteristic, complemented
6#13092664C211yesmaximal, characteristic, complemented
7#13092654C211yesmaximal, characteristic, complemented
8#13092632C211yesmaximal, characteristic, complemented
9#13092617C211yesmaximal, characteristic, complemented
10#13092569C211yesmaximal, characteristic, complemented
11#13092565C211yesmaximal, characteristic, complemented
12#13092557C211yesmaximal, characteristic, complemented
13#13092552C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic, complemented
17C2×Q8×D23C2211yescharacteristic, complemented
18C2×D4×D23C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C22×D92—21no—
21C2×SD16×C23C2211yescharacteristic
22C4×Q8×C23C2211yescharacteristic, complemented
23C4×D4×C23C2211yescharacteristic
24C2×#67274C2211yescharacteristic, complemented
25C2×#67274C2211yescharacteristic, complemented
26C2×#67273C2211yescharacteristic
27C2×#67272C2211yescharacteristic
28#10625101—21no—
29#10625085—24no—
30SD16×D23—24no—
31C2×D184C2211yescharacteristic, complemented
32C2×D184C2211yescharacteristic, complemented
33C2×#67263C2211yescharacteristic, complemented
34C2×#67263C2211yescharacteristic, complemented
35C2×#67262C2211yescharacteristic, complemented
36C2×C8×D23C2211yescharacteristic, complemented
37#10625068—21no—
38#10625068C2211yescharacteristic, complemented
39#10625066—21no—
40#10625066C2211yescharacteristic
41#10625066C2211yescharacteristic
42#10625066C2211yescharacteristic, complemented
43#10625053—21no—
44#10625053—21no—
45#10625046—21no—
46#10625046C2211yescharacteristic, complemented
47#10625045C2211yescharacteristic
48C4×D92—21no—
49C4×D92C2211yescharacteristic
50C23×#107C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic
53C23×#97C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68#67292—22no—
69#67292—41no—
70Q8×D23—22no—
71Q8×D23—41no—
72D4×D23—22no—
73D4×D23—22no—
74D4×D23—41no—
75D4×D23—41no—
76C2×D92—21no—
77C2×D92—21no—
78C2×D92—21no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—44no—
83C2×D92D411yescharacteristic
84C2×D92C2311yescharacteristic
85C2×D92C2311yescharacteristic
86C2×D92C2311yescharacteristic
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23C2311yescharacteristic
90C2×C4×D23C2311yescharacteristic
91C2×Dic46—21no—
92C2×Dic46C2311yescharacteristic
93SD16×C23D414yescomplemented
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C4⋊C4×C23—21no—
97C4⋊C4×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C42×C23—21no—
101C42×C23C2311yescharacteristic
102#67274—22no—
103#67274—22no—
104#67273—22no—
105#67272—22no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4D411yescharacteristic
113(C2×D23)⋊C4D411yescharacteristic
114C4⋊Dic23—21no—
115C4⋊Dic23D411yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117C2×C23⋊C8C2311yescharacteristic
118D184—22no—
119D184—41no—
120#67263—22no—
121#67263—41no—
122#67262—22no—
123C8×D23—22no—
124C23×C23—21no—
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—81no—
133C22×D23—81no—
134C22×D23C2×D411yescharacteristic
135C22×D23C2×D411yescharacteristic
136Q8×C23—21no—
137Q8×C23C2×D412yescomplemented
138D4×C23—21no—
139D4×C23C2×D412yes—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—42no—
144C2×C4×C23C2×D411yescharacteristic
145C2×C4×C23C2×D411yescharacteristic
146C2×C4×C23C2411yescharacteristic
147C22⋊D23—42no—
148C22⋊D23—42no—
149C2×Dic23—21no—
150C2×Dic23C2×D411yescharacteristic
151C2×Dic23C2×D411yescharacteristic
152D92—22no—
153D92—21no—
154D92—21no—
155D92—21no—
156D92—21no—
157D92—21no—
158D92—21no—
159D92—42no—
160D92—42no—
161D92—42no—
162D92—42no—
163D92—42no—
164D92—81no—
165C4×D23—21no—
166C4×D23—21no—
167C4×D23—21no—
168C4×D23—21no—
169C4×D23—42no—
170C4×D23—42no—
171Dic46—21no—
172Dic46—21no—
173Dic46—42no—
174C8×C23—21no—
175C8×C23C2×D412yescomplemented
176C23⋊C8—21no—
177C23⋊C8—21no—
178#3265—231nomaximal, Sylow
179C22×C23—22no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23C22×D411yescharacteristic
183C2×D23—21no—
184C2×D23—21no—
185C2×D23—21no—
186C2×D23—21no—
187C2×D23—21no—
188C2×D23—41no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—84no—
198C2×D23—84no—
199C2×D23AGL(1,ℤ/8)12yescomplemented
200C4×C23—22no—
201C4×C23—21no—
202C4×C23—21no—
203C4×C23—41no—
204C4×C23—41no—
205C4×C23C22×D411yescharacteristic
206C4×C23H(5,𝔽2)11yescharacteristic
207Dic23—21no—
208Dic23—21no—
209Dic23—41no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16—231no—
212#548—231no—
213D42—231no—
214#496—231no—
215#468—231no—
216#466—231no—
217#463—231no—
218#460—231no—
219#450—231no—
220#449—231no—
221#448—231no—
222#447—231no—
223#440D2311yescharacteristic, complemented
224#435—231no—
225C2×C23—42no—
226C2×C23D4211yescharacteristic
227C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
228C2×C23#57711yescharacteristic
229D23—22no—
230D23—41no—
231D23—81no—
232D23—81no—
233D23—81no—
234C2×#41—231no—
235C22×Q8—231no—
236C22×D4—231no—
237C22×D4—231no—
238C22×D4—461no—
239AGL(1,ℤ/8)—464no—
240C2×SD16—231no—
241C2×SD16—231no—
242C2×SD16—231no—
243C2×SD16—231no—
244C2×SD16—231no—
245C2×SD16—464no—
246C2×SD16C2×D2311yescharacteristic
247C2×D8—231no—
248C2×D8—231no—
249C2×D8—231no—
250C2×M16—231no—
251C22×C8—231no—
252#127—231no—
253#124—231no—
254#124—461no—
255C22⋊Q8—231no—
256C22⋊Q8—461no—
257#121—231no—
258#121—231no—
259#121—231no—
260#121—461no—
261#121—461no—
262#120—461no—
263#120—461no—
264C4×Q8C2×D2311yescharacteristic, complemented
265C4×D4—231no—
266C4×D4—461no—
267C4×D4C2×D2311yescharacteristic
268#107C2×D2311yescharacteristic, complemented
269C4⋊C8—231no—
270#103—231no—
271#103C2×D2311yescharacteristic, complemented
272#102—231no—
273#102—231no—
274#102—231no—
275#102C2×D2311yescharacteristic
276C22⋊C8—231no—
277C22⋊C8—231no—
278#97C2×D2311yescharacteristic, complemented
279C23#326511yescharacteristic, complemented, Sylow
280C24—461no—
281C24—461no—
282#41—462no—
283#41—921no—
284C2×Q8—231no—
285C2×Q8—461no—
286C2×Q8—462no—
287C2×Q8—921no—
288C2×Q8C22×D2311yescharacteristic
289C2×D4—231no—
290C2×D4—231no—
291C2×D4—231no—
292C2×D4—231no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—462no—
300C2×D4—462no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—924no—
304C2×D4—921no—
305C2×D4—921no—
306C2×D4C22×D2311yescharacteristic
307C22×C4—21no—
308C22×C4—231no—
309C22×C4—231no—
310C22×C4—461no—
311C22×C4—461no—
312SD16—462no—
313SD16—462no—
314SD16—462no—
315SD16—462no—
316SD16—921no—
317SD16D9214yescomplemented
318D8—462no—
319D8—462no—
320D8—921no—
321M16—462no—
322C2×C8—231no—
323C2×C8—231no—
324C2×C8—462no—
325C2×C8C22×D2311yescharacteristic
326C2×C8C22×D2311yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—231no—
329C4⋊C4—461no—
330C4⋊C4C22×D2311yescharacteristic
331C4⋊C4C22×D2311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—231no—
334C22⋊C4—231no—
335C22⋊C4—461no—
336C22⋊C4—461no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4—461no—
340C22⋊C4—461no—
341C42—21no—
342C42C22×D2311yescharacteristic
343C23—21no—
344C23—231no—
345C23—231no—
346C23—461no—
347C23—461no—
348C23—461no—
349C23—922no—
350C23—922no—
351C23—922no—
352C23—922no—
353C23—1841no—
354C23—1841no—
355Q8—21no—
356Q8—461no—
357Q8—461no—
358Q8—922no—
359Q8C2×D9212yescomplemented
360D4—21no—
361D4—462no—
362D4—461no—
363D4—461no—
364D4—461no—
365D4—461no—
366D4—461no—
367D4—461no—
368D4—922no—
369D4—922no—
370D4—922no—
371D4—922no—
372D4—922no—
373D4—922no—
374D4—922no—
375D4—1841no—
376D4C2×D9212yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—231no—
382C2×C4—231no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—922no—
389C2×C4—922no—
390C2×C4D4×D2311yescharacteristic
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—461no—
395C8—461no—
396C8C2×D9212yescomplemented
397C22—22no—
398C22—41no—
399C22—41no—
400C22—232no—
401C22—461no—
402C22—461no—
403C22—461no—
404C22—461no—
405C22—461no—
406C22—921no—
407C22—921no—
408C22—921no—
409C22—921no—
410C22—921no—
411C22—921no—
412C22—921no—
413C22—921no—
414C22—921no—
415C22—1844no—
416C22—1844no—
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—21no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—461no—
424C4—461no—
425C4—921no—
426C4C22×D9211yescharacteristic
427C4#1062516011yescharacteristic
428C2—42no—
429C2—462no—
430C2—921no—
431C2—1841no—
432C2—1841no—
433C2—1841no—
434C2D4×D9211yescharacteristic
435C2AGL(1,ℤ/8)×D2311yescharacteristic
436C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
hypercenter#440D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×SD16×D23C2semidirect
3. #13093079C2semidirect
4. D4×D92C2semidirect
5. #13092806C2semidirect
6. #13092664C2semidirect
7. #13092654C2semidirect
8. #13092632C2semidirect
9. #13092617C2semidirect
10. #13092569C2semidirect
11. #13092565C2semidirect
12. #13092557C2semidirect
13. #13092552C2semidirect
14. #13092490C2semidirect
15. C23×#440C2semidirect
16. C2×#67292C22semidirect
17. C2×Q8×D23C22semidirect
22. C4×Q8×C23C22semidirect
24. C2×#67274C22semidirect
25. C2×#67274C22semidirect
31. C2×D184C22semidirect
32. C2×D184C22semidirect
33. C2×#67263C22semidirect
34. C2×#67263C22semidirect
35. C2×#67262C22semidirect
36. C2×C8×D23C22semidirect
38. #10625068C22semidirect
42. #10625066C22semidirect
46. #10625046C22semidirect
50. C23×#107C22semidirect
51. C23×#103C22semidirect
53. C23×#97C22semidirect
54. (C2×D23)⋊C8C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624992C22semidirect
57. #10624991C22semidirect
58. #10624991C22semidirect
59. #10624991C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
93. SD16×C23D4semidirect
137. Q8×C23C2×D4semidirect
175. C8×C23C2×D4semidirect
199. C2×D23AGL(1,ℤ/8)semidirect
223. #440D23semidirect
264. C4×Q8C2×D23semidirect
268. #107C2×D23semidirect
271. #103C2×D23semidirect
278. #97C2×D23semidirect
279. C23#3265semidirect
317. SD16D92semidirect
359. Q8C2×D92semidirect
396. C8C2×D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×SD16×D232
#130930792
D4×D922
#130928062
#130926642
#130926542
#130926322
#130926172
#130925692
#130925652
#130925572
#130925522
#130924902
C23×#4402
#326523